Quantum Fluctuations for Gravitational Impulsive Waves

量子科学英语量子科学的英语是：Quantum Science。

例句：1.The field of quantum science is revolutionizing computing as researchers develop quantum algorithms capable of solving complex problems exponentially faster than classical methods.翻译：量子科学领域正在经历一场革命，随着研究人员开发出能够以比经典方法指数级更快的速度解决复杂问题的量子算法，它正在彻底改变计算机科学。

2.In quantum science, entanglement is a phenomenon where two particles become correlated in such a way that the state of one instantly influences the state of the other, regardless of the distance between them.翻译：在量子科学中，纠缠是一种现象，两个粒子以某种方式相互关联，以至于一个粒子的状态会立即影响到另一个粒子的状态，无论它们之间相隔多远。

3.Quantum cryptography harnesses the principles of quantum mechanics to develop unbreakable encryption methods, providing unprecedented levels of security for data transmission in the realm of quantum science."翻译：量子密码学利用量子力学原理开发出不可破解的加密方法，在量子科学领域为数据传输提供了前所未有的安全级别。

●A black hole exerts a strong gravitational pull and it has no matter.黑洞产生很强的吸引力，可是它没有物质。

● A calorie is defined as the quantity of heat required at one atmosphere to raise thetemperature of one gram of water through 1℃，usually from 14.5℃to 15.5℃.一卡路里定义为在一个大气压力条件下，使一克水温度增加1℃所需要的热量，通常是指从14.5℃t提高到15.5℃。

● A chicken is a suitable specimen for the study of the general external features of abird.鸡是研究禽类外部特征的合适范例。

● A collection of data is called a data set, and a single observation a data point.一批数据叫数据集，（而）单个观测结果叫数据点。

● A computer is a device which takes in a series of electrical impulses representinginformation, combines them, sorts them, analyses and compares the information with that stored in the computer.计算机是一种装置，该装置接受一系列含有信息的电脉冲，对这些电脉冲进行合并，整理，分析，并将它们与储存在机内的信息进行比较。

● A computer work many times more rapidly than nerve cells in the human brain.计算机工作起来比人类大脑中的神经细胞要快很多倍。

中考英语经典科学实验与科学理论深度剖析阅读理解20题1<背景文章>Isaac Newton is one of the most famous scientists in history. He is known for his discovery of the law of universal gravitation. Newton was sitting under an apple tree when an apple fell on his head. This event led him to think about why objects fall to the ground. He began to wonder if there was a force that acted on all objects.Newton spent many years studying and thinking about this problem. He realized that the force that causes apples to fall to the ground is the same force that keeps the moon in orbit around the earth. He called this force gravity.The discovery of the law of universal gravitation had a huge impact on science. It helped explain many phenomena that had previously been mysteries. For example, it explained why planets orbit the sun and why objects fall to the ground.1. Newton was sitting under a(n) ___ tree when he had the idea of gravity.A. orangeB. appleC. pearD. banana答案：B。

SCI论文摘要中常用的表达方法要写好摘要，需要建立一个适合自己需要的句型库（选择的词汇来源于SCI高被引用论文）引言部分（1）回顾研究背景，常用词汇有review, summarize, present, outline, describe等（2）说明写作目的，常用词汇有purpose, attempt, aim等，另外还可以用动词不定式充当目的壮语老表达（3）介绍论文的重点内容或研究范围，常用词汇有study, present, include, focus, emphasize, emphasis, attention等方法部分（1）介绍研究或试验过程，常用词汇有test study, investigate, examine,experiment, discuss, consider, analyze, analysis等（2）说明研究或试验方法，常用词汇有measure, estimate, calculate等（3）介绍应用、用途，常用词汇有use, apply, application等结果部分（1）展示研究结果，常用词汇有show, result, present等（2）介绍结论，常用词汇有summary, introduce,conclude等讨论部分（1）陈述论文的论点和作者的观点，常用词汇有suggest, repot, present, expect, describe 等（2）说明论证，常用词汇有support, provide, indicate, identify, find, demonstrate, confirm, clarify等（3）推荐和建议，常用词汇有suggest,suggestion, recommend, recommendation, propose,necessity,necessary,expect等。

摘要引言部分案例词汇review•Author(s): ROBINSON, TE; BERRIDGE, KC•Title:THE NEURAL BASIS OF DRUG CRA VING - AN INCENTIVE-SENSITIZATION THEORY OF ADDICTION•Source: BRAIN RESEARCH REVIEWS, 18 (3): 247-291 SEP-DEC 1993 《脑研究评论》荷兰SCI被引用1774We review evidence for this view of addiction and discuss its implications for understanding the psychology and neurobiology of addiction.回顾研究背景SCI高被引摘要引言部分案例词汇summarizeAuthor(s): Barnett, RM; Carone, CD; 被引用1571Title: Particles and field .1. Review of particle physicsSource: PHYSICAL REVIEW D, 54 (1): 1-+ Part 1 JUL 1 1996:《物理学评论，D辑》美国引言部分回顾研究背景常用词汇summarizeAbstract: This biennial review summarizes much of Particle Physics. Using data from previous editions, plus 1900 new measurements from 700 papers, we list, evaluate, and average measuredproperties of gauge bosons, leptons, quarks, mesons, and baryons. We also summarize searches for hypothetical particles such as Higgs bosons, heavy neutrinos, and supersymmetric particles. All the particle properties and search limits are listed in Summary Tables. We also give numerous tables, figures, formulae, and reviews of topics such as the Standard Model, particle detectors, probability, and statistics. A booklet is available containing the Summary Tables and abbreviated versions of some of the other sections of this full Review.SCI摘要引言部分案例attentionSCI摘要方法部分案例considerSCI高被引摘要引言部分案例词汇outline•Author(s): TIERNEY, L SCI引用728次•Title:MARKOV-CHAINS FOR EXPLORING POSTERIOR DISTRIBUTIONS 引言部分回顾研究背景，常用词汇outline•Source: ANNALS OF STATISTICS, 22 (4): 1701-1728 DEC 1994•《统计学纪事》美国•Abstract: Several Markov chain methods are available for sampling from a posterior distribution. Two important examples are the Gibbs sampler and the Metropolis algorithm.In addition, several strategies are available for constructing hybrid algorithms. This paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues. On the theoretical side, results from the theory of general state space Markov chains can be used to obtain convergence rates, laws of large numbers and central limit theorems for estimates obtained from Markov chain methods. These theoretical results can be used to guide the construction of more efficient algorithms. For the practical use of Markov chain methods, standard simulation methodology provides several Variance reduction techniques and also gives guidance on the choice of sample size and allocation.SCI高被引摘要引言部分案例回顾研究背景presentAuthor(s): L YNCH, M; MILLIGAN, BG SC I被引用661Title: ANAL YSIS OF POPULATION GENETIC-STRUCTURE WITH RAPD MARKERS Source: MOLECULAR ECOLOGY, 3 (2): 91-99 APR 1994《分子生态学》英国Abstract: Recent advances in the application of the polymerase chain reaction make it possible to score individuals at a large number of loci. The RAPD (random amplified polymorphic DNA) method is one such technique that has attracted widespread interest.The analysis of population structure with RAPD data is hampered by the lack of complete genotypic information resulting from dominance, since this enhances the sampling variance associated with single loci as well as induces bias in parameter estimation. We present estimators for several population-genetic parameters (gene and genotype frequencies, within- and between-population heterozygosities, degree of inbreeding and population subdivision, and degree of individual relatedness) along with expressions for their sampling variances. Although completely unbiased estimators do not appear to be possible with RAPDs, several steps are suggested that will insure that the bias in parameter estimates is negligible. To achieve the same degree of statistical power, on the order of 2 to 10 times more individuals need to be sampled per locus when dominant markers are relied upon, as compared to codominant (RFLP, isozyme) markers. Moreover, to avoid bias in parameter estimation, the marker alleles for most of these loci should be in relatively low frequency. Due to the need for pruning loci with low-frequency null alleles, more loci also need to be sampled with RAPDs than with more conventional markers, and sole problems of bias cannot be completely eliminated.SCI高被引摘要引言部分案例词汇describe•Author(s): CLONINGER, CR; SVRAKIC, DM; PRZYBECK, TR•Title: A PSYCHOBIOLOGICAL MODEL OF TEMPERAMENT AND CHARACTER•Source: ARCHIVES OF GENERAL PSYCHIATRY, 50 (12): 975-990 DEC 1993《普通精神病学纪要》美国•引言部分回顾研究背景，常用词汇describe 被引用926•Abstract: In this study, we describe a psychobiological model of the structure and development of personality that accounts for dimensions of both temperament and character. Previous research has confirmed four dimensions of temperament: novelty seeking, harm avoidance, reward dependence, and persistence, which are independently heritable, manifest early in life, and involve preconceptual biases in perceptual memory and habit formation. For the first time, we describe three dimensions of character that mature in adulthood and influence personal and social effectiveness by insight learning about self-concepts.Self-concepts vary according to the extent to which a person identifies the self as (1) an autonomous individual, (2) an integral part of humanity, and (3) an integral part of the universe as a whole. Each aspect of self-concept corresponds to one of three character dimensions called self-directedness, cooperativeness, and self-transcendence, respectively. We also describe the conceptual background and development of a self-report measure of these dimensions, the Temperament and Character Inventory. Data on 300 individuals from the general population support the reliability and structure of these seven personality dimensions. We discuss the implications for studies of information processing, inheritance, development, diagnosis, and treatment.摘要引言部分案例•（2）说明写作目的，常用词汇有purpose, attempt, aimSCI高被引摘要引言部分案例attempt说明写作目的•Author(s): Donoho, DL; Johnstone, IM•Title: Adapting to unknown smoothness via wavelet shrinkage•Source: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 90 (432): 1200-1224 DEC 1995 《美国统计学会志》被引用429次•Abstract: We attempt to recover a function of unknown smoothness from noisy sampled data. We introduce a procedure, SureShrink, that suppresses noise by thresholding the empirical wavelet coefficients. The thresholding is adaptive: A threshold level is assigned to each dyadic resolution level by the principle of minimizing the Stein unbiased estimate of risk (Sure) for threshold estimates. The computational effort of the overall procedure is order N.log(N) as a function of the sample size N. SureShrink is smoothness adaptive: If the unknown function contains jumps, then the reconstruction (essentially) does also; if the unknown function has a smooth piece, then the reconstruction is (essentially) as smooth as the mother wavelet will allow. The procedure is in a sense optimally smoothness adaptive: It is near minimax simultaneously over a whole interval of the Besov scale; the size of this interval depends on the choice of mother wavelet. We know from a previous paper by the authors that traditional smoothing methods-kernels, splines, and orthogonal series estimates-even with optimal choices of the smoothing parameter, would be unable to perform in a near-minimax way over many spaces in the Besov scale.Examples of SureShrink are given. The advantages of the method are particularly evident when the underlying function has jump discontinuities on a smooth backgroundSCI高被引摘要引言部分案例To investigate说明写作目的•Author(s): OLTV AI, ZN; MILLIMAN, CL; KORSMEYER, SJ•Title: BCL-2 HETERODIMERIZES IN-VIVO WITH A CONSERVED HOMOLOG, BAX, THAT ACCELERATES PROGRAMMED CELL-DEATH•Source: CELL, 74 (4): 609-619 AUG 27 1993 被引用3233•Abstract: Bcl-2 protein is able to repress a number of apoptotic death programs. To investigate the mechanism of Bcl-2's effect, we examined whether Bcl-2 interacted with other proteins. We identified an associated 21 kd protein partner, Bax, that has extensive amino acid homology with Bcl-2, focused within highly conserved domains I and II. Bax is encoded by six exons and demonstrates a complex pattern of alternative RNA splicing that predicts a 21 kd membrane (alpha) and two forms of cytosolic protein (beta and gamma). Bax homodimerizes and forms heterodimers with Bcl-2 in vivo. Overexpressed Bax accelerates apoptotic death induced by cytokine deprivation in an IL-3-dependent cell line. Overexpressed Bax also counters the death repressor activity of Bcl-2. These data suggest a model in which the ratio of Bcl-2 to Bax determines survival or death following an apoptotic stimulus.SCI高被引摘要引言部分案例purposes说明写作目的•Author(s): ROGERS, FJ; IGLESIAS, CA•Title: RADIATIVE ATOMIC ROSSELAND MEAN OPACITY TABLES•Source: ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES, 79 (2): 507-568 APR 1992 《天体物理学杂志增刊》美国SCI被引用512•Abstract: For more than two decades the astrophysics community has depended on opacity tables produced at Los Alamos. In the present work we offer new radiative Rosseland mean opacity tables calculated with the OPAL code developed independently at LLNL. We give extensive results for the recent Anders-Grevesse mixture which allow accurate interpolation in temperature, density, hydrogen mass fraction, as well as metal mass fraction. The tables are organized differently from previous work. Instead of rows and columns of constant temperature and density, we use temperature and follow tracks of constant R, where R = density/(temperature)3. The range of R and temperature are such as to cover typical stellar conditions from the interior through the envelope and the hotter atmospheres. Cool atmospheres are not considered since photoabsorption by molecules is neglected. Only radiative processes are taken into account so that electron conduction is not included. For comparison purposes we present some opacity tables for the Ross-Aller and Cox-Tabor metal abundances. Although in many regions the OPAL opacities are similar to previous work, large differences are reported.For example, factors of 2-3 opacity enhancements are found in stellar envelop conditions.SCI高被引摘要引言部分案例aim说明写作目的•Author(s):EDV ARDSSON, B; ANDERSEN, J; GUSTAFSSON, B; LAMBERT, DL;NISSEN, PE; TOMKIN, J•Title:THE CHEMICAL EVOLUTION OF THE GALACTIC DISK .1. ANALYSISAND RESULTS•Source: ASTRONOMY AND ASTROPHYSICS, 275 (1): 101-152 AUG 1993 《天文学与天体物理学》被引用934•Abstract:With the aim to provide observational constraints on the evolution of the galactic disk, we have derived abundances of 0, Na, Mg, Al, Si, Ca, Ti, Fe, Ni, Y, Zr, Ba and Nd, as well as individual photometric ages, for 189 nearby field F and G disk dwarfs.The galactic orbital properties of all stars have been derived from accurate kinematic data, enabling estimates to be made of the distances from the galactic center of the stars‘ birthplaces. 结构式摘要•Our extensive high resolution, high S/N, spectroscopic observations of carefully selected northern and southern stars provide accurate equivalent widths of up to 86 unblended absorption lines per star between 5000 and 9000 angstrom. The abundance analysis was made with greatly improved theoretical LTE model atmospheres. Through the inclusion of a great number of iron-peak element absorption lines the model fluxes reproduce the observed UV and visual fluxes with good accuracy. A new theoretical calibration of T(eff) as a function of Stromgren b - y for solar-type dwarfs has been established. The new models and T(eff) scale are shown to yield good agreement between photometric and spectroscopic measurements of effective temperatures and surface gravities, but the photometrically derived very high overall metallicities for the most metal rich stars are not supported by the spectroscopic analysis of weak spectral lines.•Author(s): PAYNE, MC; TETER, MP; ALLAN, DC; ARIAS, TA; JOANNOPOULOS, JD•Title:ITERA TIVE MINIMIZATION TECHNIQUES FOR ABINITIO TOTAL-ENERGY CALCULATIONS - MOLECULAR-DYNAMICS AND CONJUGA TE GRADIENTS•Source: REVIEWS OF MODERN PHYSICS, 64 (4): 1045-1097 OCT 1992 《现代物理学评论》美国American Physical Society SCI被引用2654 •Abstract: This article describes recent technical developments that have made the total-energy pseudopotential the most powerful ab initio quantum-mechanical modeling method presently available. In addition to presenting technical details of the pseudopotential method, the article aims to heighten awareness of the capabilities of the method in order to stimulate its application to as wide a range of problems in as many scientific disciplines as possible.SCI高被引摘要引言部分案例includes介绍论文的重点内容或研究范围•Author(s):MARCHESINI, G; WEBBER, BR; ABBIENDI, G; KNOWLES, IG;SEYMOUR, MH; STANCO, L•Title: HERWIG 5.1 - A MONTE-CARLO EVENT GENERA TOR FOR SIMULATING HADRON EMISSION REACTIONS WITH INTERFERING GLUONS SCI被引用955次•Source: COMPUTER PHYSICS COMMUNICATIONS, 67 (3): 465-508 JAN 1992:《计算机物理学通讯》荷兰Elsevier•Abstract: HERWIG is a general-purpose particle-physics event generator, which includes the simulation of hard lepton-lepton, lepton-hadron and hadron-hadron scattering and soft hadron-hadron collisions in one package. It uses the parton-shower approach for initial-state and final-state QCD radiation, including colour coherence effects and azimuthal correlations both within and between jets. This article includes a brief review of the physics underlying HERWIG, followed by a description of the program itself. This includes details of the input and control parameters used by the program, and the output data provided by it. Sample output from a typical simulation is given and annotated.SCI高被引摘要引言部分案例presents介绍论文的重点内容或研究范围•Author(s): IDSO, KE; IDSO, SB•Title: PLANT-RESPONSES TO ATMOSPHERIC CO2 ENRICHMENT IN THE FACE OF ENVIRONMENTAL CONSTRAINTS - A REVIEW OF THE PAST 10 YEARS RESEARCH•Source: AGRICULTURAL AND FOREST METEOROLOGY, 69 (3-4): 153-203 JUL 1994 《农业和林业气象学》荷兰Elsevier 被引用225•Abstract:This paper presents a detailed analysis of several hundred plant carbon exchange rate (CER) and dry weight (DW) responses to atmospheric CO2 enrichment determined over the past 10 years. It demonstrates that the percentage increase in plant growth produced by raising the air's CO2 content is generally not reduced by less than optimal levels of light, water or soil nutrients, nor by high temperatures, salinity or gaseous air pollution. More often than not, in fact, the data show the relative growth-enhancing effects of atmospheric CO2 enrichment to be greatest when resource limitations and environmental stresses are most severe.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围emphasizing •Author(s): BESAG, J; GREEN, P; HIGDON, D; MENGERSEN, K•Title: BAYESIAN COMPUTATION AND STOCHASTIC-SYSTEMS•Source: STATISTICAL SCIENCE, 10 (1): 3-41 FEB 1995《统计科学》美国•SCI被引用296次•Abstract: Markov chain Monte Carlo (MCMC) methods have been used extensively in statistical physics over the last 40 years, in spatial statistics for the past 20 and in Bayesian image analysis over the last decade. In the last five years, MCMC has been introduced into significance testing, general Bayesian inference and maximum likelihood estimation. This paper presents basic methodology of MCMC, emphasizing the Bayesian paradigm, conditional probability and the intimate relationship with Markov random fields in spatial statistics.Hastings algorithms are discussed, including Gibbs, Metropolis and some other variations. Pairwise difference priors are described and are used subsequently in three Bayesian applications, in each of which there is a pronounced spatial or temporal aspect to the modeling. The examples involve logistic regression in the presence of unobserved covariates and ordinal factors; the analysis of agricultural field experiments, with adjustment for fertility gradients; and processing oflow-resolution medical images obtained by a gamma camera. Additional methodological issues arise in each of these applications and in the Appendices. The paper lays particular emphasis on the calculation of posterior probabilities and concurs with others in its view that MCMC facilitates a fundamental breakthrough in applied Bayesian modeling.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围focuses •Author(s): HUNT, KJ; SBARBARO, D; ZBIKOWSKI, R; GAWTHROP, PJ•Title: NEURAL NETWORKS FOR CONTROL-SYSTEMS - A SURVEY•Source: AUTOMA TICA, 28 (6): 1083-1112 NOV 1992《自动学》荷兰Elsevier•SCI被引用427次•Abstract:This paper focuses on the promise of artificial neural networks in the realm of modelling, identification and control of nonlinear systems. The basic ideas and techniques of artificial neural networks are presented in language and notation familiar to control engineers. Applications of a variety of neural network architectures in control are surveyed. We explore the links between the fields of control science and neural networks in a unified presentation and identify key areas for future research.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围focus•Author(s): Stuiver, M; Reimer, PJ; Bard, E; Beck, JW;•Title: INTCAL98 radiocarbon age calibration, 24,000-0 cal BP•Source: RADIOCARBON, 40 (3): 1041-1083 1998《放射性碳》美国SCI被引用2131次•Abstract: The focus of this paper is the conversion of radiocarbon ages to calibrated (cal) ages for the interval 24,000-0 cal BP (Before Present, 0 cal BP = AD 1950), based upon a sample set of dendrochronologically dated tree rings, uranium-thorium dated corals, and varve-counted marine sediment. The C-14 age-cal age information, produced by many laboratories, is converted to Delta(14)C profiles and calibration curves, for the atmosphere as well as the oceans. We discuss offsets in measured C-14 ages and the errors therein, regional C-14 age differences, tree-coral C-14 age comparisons and the time dependence of marine reservoir ages, and evaluate decadal vs. single-year C-14 results. Changes in oceanic deepwater circulation, especially for the 16,000-11,000 cal sp interval, are reflected in the Delta(14)C values of INTCAL98.SCI高被引摘要引言部分案例介绍论文的重点内容或研究范围emphasis •Author(s): LEBRETON, JD; BURNHAM, KP; CLOBERT, J; ANDERSON, DR•Title: MODELING SURVIV AL AND TESTING BIOLOGICAL HYPOTHESES USING MARKED ANIMALS - A UNIFIED APPROACH WITH CASE-STUDIES •Source: ECOLOGICAL MONOGRAPHS, 62 (1): 67-118 MAR 1992•《生态学论丛》美国•Abstract: The understanding of the dynamics of animal populations and of related ecological and evolutionary issues frequently depends on a direct analysis of life history parameters. For instance, examination of trade-offs between reproduction and survival usually rely on individually marked animals, for which the exact time of death is most often unknown, because marked individuals cannot be followed closely through time.Thus, the quantitative analysis of survival studies and experiments must be based oncapture-recapture (or resighting) models which consider, besides the parameters of primary interest, recapture or resighting rates that are nuisance parameters. 结构式摘要•T his paper synthesizes, using a common framework, these recent developments together with new ones, with an emphasis on flexibility in modeling, model selection, and the analysis of multiple data sets. The effects on survival and capture rates of time, age, and categorical variables characterizing the individuals (e.g., sex) can be considered, as well as interactions between such effects. This "analysis of variance" philosophy emphasizes the structure of the survival and capture process rather than the technical characteristics of any particular model. The flexible array of models encompassed in this synthesis uses a common notation. As a result of the great level of flexibility and relevance achieved, the focus is changed from fitting a particular model to model building and model selection.SCI摘要方法部分案例•方法部分•（1）介绍研究或试验过程，常用词汇有test，study, investigate, examine,experiment, discuss, consider, analyze, analysis等•（2）说明研究或试验方法，常用词汇有measure, estimate, calculate等•（3）介绍应用、用途，常用词汇有use, apply, application等SCI高被引摘要方法部分案例discusses介绍研究或试验过程•Author(s): LIANG, KY; ZEGER, SL; QAQISH, B•Title: MULTIV ARIATE REGRESSION-ANAL YSES FOR CATEGORICAL-DATA •Source:JOURNAL OF THE ROY AL STA TISTICAL SOCIETY SERIES B-METHODOLOGICAL, 54 (1): 3-40 1992《皇家统计学会志，B辑：统计方法论》•SCI被引用298•Abstract: It is common to observe a vector of discrete and/or continuous responses in scientific problems where the objective is to characterize the dependence of each response on explanatory variables and to account for the association between the outcomes. The response vector can comprise repeated observations on one variable, as in longitudinal studies or genetic studies of families, or can include observations for different variables.This paper discusses a class of models for the marginal expectations of each response and for pairwise associations. The marginal models are contrasted with log-linear models.Two generalized estimating equation approaches are compared for parameter estimation.The first focuses on the regression parameters; the second simultaneously estimates the regression and association parameters. The robustness and efficiency of each is discussed.The methods are illustrated with analyses of two data sets from public health research SCI高被引摘要方法部分案例介绍研究或试验过程examines•Author(s): Huo, QS; Margolese, DI; Stucky, GD•Title: Surfactant control of phases in the synthesis of mesoporous silica-based materials •Source: CHEMISTRY OF MATERIALS, 8 (5): 1147-1160 MAY 1996•SCI被引用643次《材料的化学性质》美国•Abstract: The low-temperature formation of liquid-crystal-like arrays made up of molecular complexes formed between molecular inorganic species and amphiphilic organic molecules is a convenient approach for the synthesis of mesostructure materials.This paper examines how the molecular shapes of covalent organosilanes, quaternary ammonium surfactants, and mixed surfactants in various reaction conditions can be used to synthesize silica-based mesophase configurations, MCM-41 (2d hexagonal, p6m), MCM-48 (cubic Ia3d), MCM-50 (lamellar), SBA-1 (cubic Pm3n), SBA-2 (3d hexagonal P6(3)/mmc), and SBA-3(hexagonal p6m from acidic synthesis media). The structural function of surfactants in mesophase formation can to a first approximation be related to that of classical surfactants in water or other solvents with parallel roles for organic additives. The effective surfactant ion pair packing parameter, g = V/alpha(0)l, remains a useful molecular structure-directing index to characterize the geometry of the mesophase products, and phase transitions may be viewed as a variation of g in the liquid-crystal-Like solid phase. Solvent and cosolvent structure direction can be effectively used by varying polarity, hydrophobic/hydrophilic properties and functionalizing the surfactant molecule, for example with hydroxy group or variable charge. Surfactants and synthesis conditions can be chosen and controlled to obtain predicted silica-based mesophase products. A room-temperature synthesis of the bicontinuous cubic phase, MCM-48, is presented. A low-temperature (100 degrees C) and low-pH (7-10) treatment approach that can be used to give MCM-41 with high-quality, large pores (up to 60 Angstrom), and pore volumes as large as 1.6 cm(3)/g is described.Estimates 介绍研究或试验过程SCI高被引摘要方法部分案例•Author(s): KESSLER, RC; MCGONAGLE, KA; ZHAO, SY; NELSON, CB; HUGHES, M; ESHLEMAN, S; WITTCHEN, HU; KENDLER, KS•Title:LIFETIME AND 12-MONTH PREV ALENCE OF DSM-III-R PSYCHIATRIC-DISORDERS IN THE UNITED-STA TES - RESULTS FROM THE NATIONAL-COMORBIDITY-SURVEY•Source: ARCHIVES OF GENERAL PSYCHIATRY, 51 (1): 8-19 JAN 1994•《普通精神病学纪要》美国SCI被引用4350次•Abstract: Background: This study presents estimates of lifetime and 12-month prevalence of 14 DSM-III-R psychiatric disorders from the National Comorbidity Survey, the first survey to administer a structured psychiatric interview to a national probability sample in the United States.Methods: The DSM-III-R psychiatric disorders among persons aged 15 to 54 years in the noninstitutionalized civilian population of the United States were assessed with data collected by lay interviewers using a revised version of the Composite International Diagnostic Interview. Results: Nearly 50% of respondents reported at least one lifetime disorder, and close to 30% reported at least one 12-month disorder. The most common disorders were major depressive episode, alcohol dependence, social phobia, and simple phobia. More than half of all lifetime disorders occurred in the 14% of the population who had a history of three or more comorbid disorders. These highly comorbid people also included the vast majority of people with severe disorders.Less than 40% of those with a lifetime disorder had ever received professional treatment,and less than 20% of those with a recent disorder had been in treatment during the past 12 months. Consistent with previous risk factor research, it was found that women had elevated rates of affective disorders and anxiety disorders, that men had elevated rates of substance use disorders and antisocial personality disorder, and that most disorders declined with age and with higher socioeconomic status. Conclusions: The prevalence of psychiatric disorders is greater than previously thought to be the case. Furthermore, this morbidity is more highly concentrated than previously recognized in roughly one sixth of the population who have a history of three or more comorbid disorders. This suggests that the causes and consequences of high comorbidity should be the focus of research attention. The majority of people with psychiatric disorders fail to obtain professional treatment. Even among people with a lifetime history of three or more comorbid disorders, the proportion who ever obtain specialty sector mental health treatment is less than 50%.These results argue for the importance of more outreach and more research on barriers to professional help-seekingSCI高被引摘要方法部分案例说明研究或试验方法measure•Author(s): Schlegel, DJ; Finkbeiner, DP; Davis, M•Title:Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds•Source: ASTROPHYSICAL JOURNAL, 500 (2): 525-553 Part 1 JUN 20 1998 SCI 被引用2972 次《天体物理学杂志》美国•The primary use of these maps is likely to be as a new estimator of Galactic extinction. To calibrate our maps, we assume a standard reddening law and use the colors of elliptical galaxies to measure the reddening per unit flux density of 100 mu m emission. We find consistent calibration using the B-R color distribution of a sample of the 106 brightest cluster ellipticals, as well as a sample of 384 ellipticals with B-V and Mg line strength measurements. For the latter sample, we use the correlation of intrinsic B-V versus Mg, index to tighten the power of the test greatly. We demonstrate that the new maps are twice as accurate as the older Burstein-Heiles reddening estimates in regions of low and moderate reddening. The maps are expected to be significantly more accurate in regions of high reddening. These dust maps will also be useful for estimating millimeter emission that contaminates cosmic microwave background radiation experiments and for estimating soft X-ray absorption. We describe how to access our maps readily for general use.SCI高被引摘要结果部分案例application介绍应用、用途•Author(s): MALLAT, S; ZHONG, S•Title: CHARACTERIZATION OF SIGNALS FROM MULTISCALE EDGES•Source: IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 14 (7): 710-732 JUL 1992•SCI被引用508次《IEEE模式分析与机器智能汇刊》美国•Abstract: A multiscale Canny edge detection is equivalent to finding the local maxima ofa wavelet transform. We study the properties of multiscale edges through the wavelet。

宇宙的由来介绍英语作文Title: The Origin of the Universe。

Introduction:The universe, an unfathomable expanse of space, has captivated human curiosity for millennia. In our quest to comprehend its origins, we embark on a journey through time and space, exploring the theories that seek to explain the cosmic genesis.The Big Bang Theory:At the heart of modern cosmology lies the Big Bang theory, a paradigm-shifting concept that traces the universe's birth to a singular, cataclysmic event. According to this model, around 13.8 billion years ago, all matter, energy, space, and time were compressed into an infinitely dense point known as a singularity. In an incomprehensibly rapid expansion, this singularity erupted,giving rise to the universe as we know it.In the aftermath of the Big Bang, the universe was a seething, hot cauldron of energy. As it expanded and cooled, elementary particles formed, eventually coalescing into atoms. Over eons, these atoms condensed into stars, galaxies, and the myriad celestial structures that adornthe cosmos.Cosmic Inflation:Inflation theory expands upon the Big Bang model, positing a brief but exponentially rapid expansion of the universe in its earliest moments. Proposed by physicistAlan Guth in the 1980s, inflationary cosmology reconciles observed cosmic uniformity with the apparent isotropy ofthe universe. It explains why the universe appears homogeneous on large scales despite originating from a tiny, highly non-uniform state.Inflation suggests that a repulsive gravitational force drove the universe to expand exponentially, smoothing outirregularities and setting the stage for the subsequent evolution of cosmic structures. While still a subject of ongoing research and debate, inflationary cosmology offers profound insights into the early universe's dynamics.Multiverse Hypothesis:Beyond our observable universe lies the tantalizing possibility of a multiverse—a vast ensemble of parallel universes with their own distinct properties and laws of physics. The concept of a multiverse emerges from various theoretical frameworks, including string theory and quantum mechanics.In some multiverse models, each universe spawns from a parent universe through processes like cosmic inflation or quantum fluctuations. Each universe may exhibit different physical constants, dimensions, or even fundamental forces, leading to a staggering diversity of cosmic landscapes.While speculative, the multiverse hypothesis offers a compelling explanation for the fine-tuning of ouruniverse's parameters, raising profound questions about the nature of existence and our place within the cosmic tapestry.Conclusion:The quest to unravel the mysteries of the universe's origin continues to inspire awe and wonder in humanity. From the fiery crucible of the Big Bang to the speculative realms of cosmic inflation and the multiverse, our understanding of the cosmos undergoes constant evolution.As we peer ever deeper into the cosmic abyss, we are reminded of the profound interconnectedness of all things and the enduring quest for knowledge that drives us to explore the vast reaches of space and time. In the grand tapestry of existence, the origin of the universe stands as a testament to the boundless curiosity and ingenuity of the human spirit.。

Quasi-Normal Modes of Stars and Black HolesKostas D.KokkotasDepartment of Physics,Aristotle University of Thessaloniki,Thessaloniki54006,Greece.kokkotas@astro.auth.grhttp://www.astro.auth.gr/˜kokkotasandBernd G.SchmidtMax Planck Institute for Gravitational Physics,Albert Einstein Institute,D-14476Golm,Germany.bernd@aei-potsdam.mpg.dePublished16September1999/Articles/Volume2/1999-2kokkotasLiving Reviews in RelativityPublished by the Max Planck Institute for Gravitational PhysicsAlbert Einstein Institute,GermanyAbstractPerturbations of stars and black holes have been one of the main topics of relativistic astrophysics for the last few decades.They are of partic-ular importance today,because of their relevance to gravitational waveastronomy.In this review we present the theory of quasi-normal modes ofcompact objects from both the mathematical and astrophysical points ofview.The discussion includes perturbations of black holes(Schwarzschild,Reissner-Nordstr¨o m,Kerr and Kerr-Newman)and relativistic stars(non-rotating and slowly-rotating).The properties of the various families ofquasi-normal modes are described,and numerical techniques for calculat-ing quasi-normal modes reviewed.The successes,as well as the limits,of perturbation theory are presented,and its role in the emerging era ofnumerical relativity and supercomputers is discussed.c 1999Max-Planck-Gesellschaft and the authors.Further information on copyright is given at /Info/Copyright/.For permission to reproduce the article please contact livrev@aei-potsdam.mpg.de.Article AmendmentsOn author request a Living Reviews article can be amended to include errata and small additions to ensure that the most accurate and up-to-date infor-mation possible is provided.For detailed documentation of amendments, please go to the article’s online version at/Articles/Volume2/1999-2kokkotas/. Owing to the fact that a Living Reviews article can evolve over time,we recommend to cite the article as follows:Kokkotas,K.D.,and Schmidt,B.G.,“Quasi-Normal Modes of Stars and Black Holes”,Living Rev.Relativity,2,(1999),2.[Online Article]:cited on<date>, /Articles/Volume2/1999-2kokkotas/. The date in’cited on<date>’then uniquely identifies the version of the article you are referring to.3Quasi-Normal Modes of Stars and Black HolesContents1Introduction4 2Normal Modes–Quasi-Normal Modes–Resonances7 3Quasi-Normal Modes of Black Holes123.1Schwarzschild Black Holes (12)3.2Kerr Black Holes (17)3.3Stability and Completeness of Quasi-Normal Modes (20)4Quasi-Normal Modes of Relativistic Stars234.1Stellar Pulsations:The Theoretical Minimum (23)4.2Mode Analysis (26)4.2.1Families of Fluid Modes (26)4.2.2Families of Spacetime or w-Modes (30)4.3Stability (31)5Excitation and Detection of QNMs325.1Studies of Black Hole QNM Excitation (33)5.2Studies of Stellar QNM Excitation (34)5.3Detection of the QNM Ringing (37)5.4Parameter Estimation (39)6Numerical Techniques426.1Black Holes (42)6.1.1Evolving the Time Dependent Wave Equation (42)6.1.2Integration of the Time Independent Wave Equation (43)6.1.3WKB Methods (44)6.1.4The Method of Continued Fractions (44)6.2Relativistic Stars (45)7Where Are We Going?487.1Synergism Between Perturbation Theory and Numerical Relativity487.2Second Order Perturbations (48)7.3Mode Calculations (49)7.4The Detectors (49)8Acknowledgments50 9Appendix:Schr¨o dinger Equation Versus Wave Equation51Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt41IntroductionHelioseismology and asteroseismology are well known terms in classical astro-physics.From the beginning of the century the variability of Cepheids has been used for the accurate measurement of cosmic distances,while the variability of a number of stellar objects(RR Lyrae,Mira)has been associated with stel-lar oscillations.Observations of solar oscillations(with thousands of nonradial modes)have also revealed a wealth of information about the internal structure of the Sun[204].Practically every stellar object oscillates radially or nonradi-ally,and although there is great difficulty in observing such oscillations there are already results for various types of stars(O,B,...).All these types of pulsations of normal main sequence stars can be studied via Newtonian theory and they are of no importance for the forthcoming era of gravitational wave astronomy.The gravitational waves emitted by these stars are extremely weak and have very low frequencies(cf.for a discussion of the sun[70],and an im-portant new measurement of the sun’s quadrupole moment and its application in the measurement of the anomalous precession of Mercury’s perihelion[163]). This is not the case when we consider very compact stellar objects i.e.neutron stars and black holes.Their oscillations,produced mainly during the formation phase,can be strong enough to be detected by the gravitational wave detectors (LIGO,VIRGO,GEO600,SPHERE)which are under construction.In the framework of general relativity(GR)quasi-normal modes(QNM) arise,as perturbations(electromagnetic or gravitational)of stellar or black hole spacetimes.Due to the emission of gravitational waves there are no normal mode oscillations but instead the frequencies become“quasi-normal”(complex), with the real part representing the actual frequency of the oscillation and the imaginary part representing the damping.In this review we shall discuss the oscillations of neutron stars and black holes.The natural way to study these oscillations is by considering the linearized Einstein equations.Nevertheless,there has been recent work on nonlinear black hole perturbations[101,102,103,104,100]while,as yet nothing is known for nonlinear stellar oscillations in general relativity.The study of black hole perturbations was initiated by the pioneering work of Regge and Wheeler[173]in the late50s and was continued by Zerilli[212]. The perturbations of relativistic stars in GR werefirst studied in the late60s by Kip Thorne and his collaborators[202,198,199,200].The initial aim of Regge and Wheeler was to study the stability of a black hole to small perturbations and they did not try to connect these perturbations to astrophysics.In con-trast,for the case of relativistic stars,Thorne’s aim was to extend the known properties of Newtonian oscillation theory to general relativity,and to estimate the frequencies and the energy radiated as gravitational waves.QNMs werefirst pointed out by Vishveshwara[207]in calculations of the scattering of gravitational waves by a Schwarzschild black hole,while Press[164] coined the term quasi-normal frequencies.QNM oscillations have been found in perturbation calculations of particles falling into Schwarzschild[73]and Kerr black holes[76,80]and in the collapse of a star to form a black hole[66,67,68]. Living Reviews in Relativity(1999-2)5Quasi-Normal Modes of Stars and Black Holes Numerical investigations of the fully nonlinear equations of general relativity have provided results which agree with the results of perturbation calculations;in particular numerical studies of the head-on collision of two black holes [30,29](cf.Figure 1)and gravitational collapse to a Kerr hole [191].Recently,Price,Pullin and collaborators [170,31,101,28]have pushed forward the agreement between full nonlinear numerical results and results from perturbation theory for the collision of two black holes.This proves the power of the perturbation approach even in highly nonlinear problems while at the same time indicating its limits.In the concluding remarks of their pioneering paper on nonradial oscillations of neutron stars Thorne and Campollataro [202]described it as “just a modest introduction to a story which promises to be long,complicated and fascinating ”.The story has undoubtedly proved to be intriguing,and many authors have contributed to our present understanding of the pulsations of both black holes and neutron stars.Thirty years after these prophetic words by Thorne and Campollataro hundreds of papers have been written in an attempt to understand the stability,the characteristic frequencies and the mechanisms of excitation of these oscillations.Their relevance to the emission of gravitational waves was always the basic underlying reason of each study.An account of all this work will be attempted in the next sections hoping that the interested reader will find this review useful both as a guide to the literature and as an inspiration for future work on the open problems of the field.020406080100Time (M ADM )-0.3-0.2-0.10.00.10.20.3(l =2) Z e r i l l i F u n c t i o n Numerical solutionQNM fit Figure 1:QNM ringing after the head-on collision of two unequal mass black holes [29].The continuous line corresponds to the full nonlinear numerical calculation while the dotted line is a fit to the fundamental and first overtone QNM.In the next section we attempt to give a mathematical definition of QNMs.Living Reviews in Relativity (1999-2)K.D.Kokkotas and B.G.Schmidt6 The third and fourth section will be devoted to the study of the black hole and stellar QNMs.In thefifth section we discuss the excitation and observation of QNMs andfinally in the sixth section we will mention the more significant numerical techniques used in the study of QNMs.Living Reviews in Relativity(1999-2)7Quasi-Normal Modes of Stars and Black Holes 2Normal Modes–Quasi-Normal Modes–Res-onancesBefore discussing quasi-normal modes it is useful to remember what normal modes are!Compact classical linear oscillating systems such asfinite strings,mem-branes,or cavitiesfilled with electromagnetic radiation have preferred time harmonic states of motion(ωis real):χn(t,x)=e iωn tχn(x),n=1,2,3...,(1) if dissipation is neglected.(We assumeχto be some complex valuedfield.) There is generally an infinite collection of such periodic solutions,and the“gen-eral solution”can be expressed as a superposition,χ(t,x)=∞n=1a n e iωn tχn(x),(2)of such normal modes.The simplest example is a string of length L which isfixed at its ends.All such systems can be described by systems of partial differential equations of the type(χmay be a vector)∂χ∂t=Aχ,(3)where A is a linear operator acting only on the spatial variables.Because of thefiniteness of the system the time evolution is only determined if some boundary conditions are prescribed.The search for solutions periodic in time leads to a boundary value problem in the spatial variables.In simple cases it is of the Sturm-Liouville type.The treatment of such boundary value problems for differential equations played an important role in the development of Hilbert space techniques.A Hilbert space is chosen such that the differential operator becomes sym-metric.Due to the boundary conditions dictated by the physical problem,A becomes a self-adjoint operator on the appropriate Hilbert space and has a pure point spectrum.The eigenfunctions and eigenvalues determine the periodic solutions(1).The definition of self-adjointness is rather subtle from a physicist’s point of view since fairly complicated“domain issues”play an essential role.(See[43] where a mathematical exposition for physicists is given.)The wave equation modeling thefinite string has solutions of various degrees of differentiability. To describe all“realistic situations”,clearly C∞functions should be sufficient. Sometimes it may,however,also be convenient to consider more general solu-tions.From the mathematical point of view the collection of all smooth functions is not a natural setting to study the wave equation because sequences of solutionsLiving Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt8 exist which converge to non-smooth solutions.To establish such powerful state-ments like(2)one has to study the equation on certain subsets of the Hilbert space of square integrable functions.For“nice”equations it usually happens that the eigenfunctions are in fact analytic.They can then be used to gen-erate,for example,all smooth solutions by a pointwise converging series(2). The key point is that we need some mathematical sophistication to obtain the “completeness property”of the eigenfunctions.This picture of“normal modes”changes when we consider“open systems”which can lose energy to infinity.The simplest case are waves on an infinite string.The general solution of this problem isχ(t,x)=A(t−x)+B(t+x)(4) with“arbitrary”functions A and B.Which solutions should we study?Since we have all solutions,this is not a serious question.In more general cases, however,in which the general solution is not known,we have to select a certain class of solutions which we consider as relevant for the physical problem.Let us consider for the following discussion,as an example,a wave equation with a potential on the real line,∂2∂t2χ+ −∂2∂x2+V(x)χ=0.(5)Cauchy dataχ(0,x),∂tχ(0,x)which have two derivatives determine a unique twice differentiable solution.No boundary condition is needed at infinity to determine the time evolution of the data!This can be established by fairly simple PDE theory[116].There exist solutions for which the support of thefields are spatially compact, or–the other extreme–solutions with infinite total energy for which thefields grow at spatial infinity in a quite arbitrary way!From the point of view of physics smooth solutions with spatially compact support should be the relevant class–who cares what happens near infinity! Again it turns out that mathematically it is more convenient to study all solu-tions offinite total energy.Then the relevant operator is again self-adjoint,but now its spectrum is purely“continuous”.There are no eigenfunctions which are square integrable.Only“improper eigenfunctions”like plane waves exist.This expresses the fact that wefind a solution of the form(1)for any realωand by forming appropriate superpositions one can construct solutions which are “almost eigenfunctions”.(In the case V(x)≡0these are wave packets formed from plane waves.)These solutions are the analogs of normal modes for infinite systems.Let us now turn to the discussion of“quasi-normal modes”which are concep-tually different to normal modes.To define quasi-normal modes let us consider the wave equation(5)for potentials with V≥0which vanish for|x|>x0.Then in this case all solutions determined by data of compact support are bounded: |χ(t,x)|<C.We can use Laplace transformation techniques to represent such Living Reviews in Relativity(1999-2)9Quasi-Normal Modes of Stars and Black Holes solutions.The Laplace transformˆχ(s,x)(s>0real)of a solutionχ(t,x)isˆχ(s,x)= ∞0e−stχ(t,x)dt,(6) and satisfies the ordinary differential equations2ˆχ−ˆχ +Vˆχ=+sχ(0,x)+∂tχ(0,x),(7) wheres2ˆχ−ˆχ +Vˆχ=0(8) is the homogeneous equation.The boundedness ofχimplies thatˆχis analytic for positive,real s,and has an analytic continuation onto the complex half plane Re(s)>0.Which solutionˆχof this inhomogeneous equation gives the unique solution in spacetime determined by the data?There is no arbitrariness;only one of the Green functions for the inhomogeneous equation is correct!All Green functions can be constructed by the following well known method. Choose any two linearly independent solutions of the homogeneous equation f−(s,x)and f+(s,x),and defineG(s,x,x )=1W(s)f−(s,x )f+(s,x)(x <x),f−(s,x)f+(s,x )(x >x),(9)where W(s)is the Wronskian of f−and f+.If we denote the inhomogeneity of(7)by j,a solution of(7)isˆχ(s,x)= ∞−∞G(s,x,x )j(s,x )dx .(10) We still have to select a unique pair of solutions f−,f+.Here the information that the solution in spacetime is bounded can be used.The definition of the Laplace transform implies thatˆχis bounded as a function of x.Because the potential V vanishes for|x|>x0,the solutions of the homogeneous equation(8) for|x|>x0aref=e±sx.(11) The following pair of solutionsf+=e−sx for x>x0,f−=e+sx for x<−x0,(12) which is linearly independent for Re(s)>0,gives the unique Green function which defines a bounded solution for j of compact support.Note that for Re(s)>0the solution f+is exponentially decaying for large x and f−is expo-nentially decaying for small x.For small x however,f+will be a linear com-bination a(s)e−sx+b(s)e sx which will in general grow exponentially.Similar behavior is found for f−.Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt 10Quasi-Normal mode frequencies s n can be defined as those complex numbers for whichf +(s n ,x )=c (s n )f −(s n ,x ),(13)that is the two functions become linearly dependent,the Wronskian vanishes and the Green function is singular!The corresponding solutions f +(s n ,x )are called quasi eigenfunctions.Are there such numbers s n ?From the boundedness of the solution in space-time we know that the unique Green function must exist for Re (s )>0.Hence f +,f −are linearly independent for those values of s .However,as solutions f +,f −of the homogeneous equation (8)they have a unique continuation to the complex s plane.In [35]it is shown that for positive potentials with compact support there is always a countable number of zeros of the Wronskian with Re (s )<0.What is the mathematical and physical significance of the quasi-normal fre-quencies s n and the corresponding quasi-normal functions f +?First of all we should note that because of Re (s )<0the function f +grows exponentially for small and large x !The corresponding spacetime solution e s n t f +(s n ,x )is therefore not a physically relevant solution,unlike the normal modes.If one studies the inverse Laplace transformation and expresses χas a com-plex line integral (a >0),χ(t,x )=12πi +∞−∞e (a +is )t ˆχ(a +is,x )ds,(14)one can deform the path of the complex integration and show that the late time behavior of solutions can be approximated in finite parts of the space by a finite sum of the form χ(t,x )∼N n =1a n e (αn +iβn )t f +(s n ,x ).(15)Here we assume that Re (s n +1)<Re (s n )<0,s n =αn +iβn .The approxi-mation ∼means that if we choose x 0,x 1, and t 0then there exists a constant C (t 0,x 0,x 1, )such that χ(t,x )−N n =1a n e (αn +iβn )t f +(s n ,x ) ≤Ce (−|αN +1|+ )t (16)holds for t >t 0,x 0<x <x 1, >0with C (t 0,x 0,x 1, )independent of t .The constants a n depend only on the data [35]!This implies in particular that all solutions defined by data of compact support decay exponentially in time on spatially bounded regions.The generic leading order decay is determined by the quasi-normal mode frequency with the largest real part s 1,i.e.slowest damping.On finite intervals and for late times the solution is approximated by a finite sum of quasi eigenfunctions (15).It is presently unclear whether one can strengthen (16)to a statement like (2),a pointwise expansion of the late time solution in terms of quasi-normal Living Reviews in Relativity (1999-2)11Quasi-Normal Modes of Stars and Black Holes modes.For one particular potential(P¨o schl-Teller)this has been shown by Beyer[42].Let us now consider the case where the potential is positive for all x,but decays near infinity as happens for example for the wave equation on the static Schwarzschild spacetime.Data of compact support determine again solutions which are bounded[117].Hence we can proceed as before.Thefirst new point concerns the definitions of f±.It can be shown that the homogeneous equation(8)has for each real positive s a unique solution f+(s,x)such that lim x→∞(e sx f+(s,x))=1holds and correspondingly for f−.These functions are uniquely determined,define the correct Green function and have analytic continuations onto the complex half plane Re(s)>0.It is however quite complicated to get a good representation of these func-tions.If the point at infinity is not a regular singular point,we do not even get converging series expansions for f±.(This is particularly serious for values of s with negative real part because we expect exponential growth in x).The next new feature is that the analyticity properties of f±in the complex s plane depend on the decay of the potential.To obtain information about analytic continuation,even use of analyticity properties of the potential in x is made!Branch cuts may occur.Nevertheless in a lot of cases an infinite number of quasi-normal mode frequencies exists.The fact that the potential never vanishes may,however,destroy the expo-nential decay in time of the solutions and therefore the essential properties of the quasi-normal modes.This probably happens if the potential decays slower than exponentially.There is,however,the following way out:Suppose you want to study a solution determined by data of compact support from t=0to some largefinite time t=T.Up to this time the solution is–because of domain of dependence properties–completely independent of the potential for sufficiently large x.Hence we may see an exponential decay of the form(15)in a time range t1<t<T.This is the behavior seen in numerical calculations.The situation is similar in the case ofα-decay in quantum mechanics.A comparison of quasi-normal modes of wave equations and resonances in quantum theory can be found in the appendix,see section9.Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt123Quasi-Normal Modes of Black HolesOne of the most interesting aspects of gravitational wave detection will be the connection with the existence of black holes[201].Although there are presently several indirect ways of identifying black holes in the universe,gravitational waves emitted by an oscillating black hole will carry a uniquefingerprint which would lead to the direct identification of their existence.As we mentioned earlier,gravitational radiation from black hole oscillations exhibits certain characteristic frequencies which are independent of the pro-cesses giving rise to these oscillations.These“quasi-normal”frequencies are directly connected to the parameters of the black hole(mass,charge and angu-lar momentum)and for stellar mass black holes are expected to be inside the bandwidth of the constructed gravitational wave detectors.The perturbations of a Schwarzschild black hole reduce to a simple wave equation which has been studied extensively.The wave equation for the case of a Reissner-Nordstr¨o m black hole is more or less similar to the Schwarzschild case,but for Kerr one has to solve a system of coupled wave equations(one for the radial part and one for the angular part).For this reason the Kerr case has been studied less thoroughly.Finally,in the case of Kerr-Newman black holes we face the problem that the perturbations cannot be separated in their angular and radial parts and thus apart from special cases[124]the problem has not been studied at all.3.1Schwarzschild Black HolesThe study of perturbations of Schwarzschild black holes assumes a small per-turbation hµνon a static spherically symmetric background metricds2=g0µνdxµdxν=−e v(r)dt2+eλ(r)dr2+r2 dθ2+sin2θdφ2 ,(17) with the perturbed metric having the formgµν=g0µν+hµν,(18) which leads to a variation of the Einstein equations i.e.δGµν=4πδTµν.(19) By assuming a decomposition into tensor spherical harmonics for each hµνof the formχ(t,r,θ,φ)= mχ m(r,t)r Y m(θ,φ),(20)the perturbation problem is reduced to a single wave equation,for the func-tionχ m(r,t)(which is a combination of the various components of hµν).It should be pointed out that equation(20)is an expansion for scalar quantities only.From the10independent components of the hµνonly h tt,h tr,and h rr transform as scalars under rotations.The h tθ,h tφ,h rθ,and h rφtransform asLiving Reviews in Relativity(1999-2)13Quasi-Normal Modes of Stars and Black Holes components of two-vectors under rotations and can be expanded in a series of vector spherical harmonics while the components hθθ,hθφ,and hφφtransform as components of a2×2tensor and can be expanded in a series of tensor spher-ical harmonics(see[202,212,152]for details).There are two classes of vector spherical harmonics(polar and axial)which are build out of combinations of the Levi-Civita volume form and the gradient operator acting on the scalar spherical harmonics.The difference between the two families is their parity. Under the parity operatorπa spherical harmonic with index transforms as (−1) ,the polar class of perturbations transform under parity in the same way, as(−1) ,and the axial perturbations as(−1) +11.Finally,since we are dealing with spherically symmetric spacetimes the solution will be independent of m, thus this subscript can be omitted.The radial component of a perturbation outside the event horizon satisfies the following wave equation,∂2∂t χ + −∂2∂r∗+V (r)χ =0,(21)where r∗is the“tortoise”radial coordinate defined byr∗=r+2M log(r/2M−1),(22) and M is the mass of the black hole.For“axial”perturbationsV (r)= 1−2M r ( +1)r+2σMr(23)is the effective potential or(as it is known in the literature)Regge-Wheeler potential[173],which is a single potential barrier with a peak around r=3M, which is the location of the unstable photon orbit.The form(23)is true even if we consider scalar or electromagnetic testfields as perturbations.The parameter σtakes the values1for scalar perturbations,0for electromagnetic perturbations, and−3for gravitational perturbations and can be expressed asσ=1−s2,where s=0,1,2is the spin of the perturbingfield.For“polar”perturbations the effective potential was derived by Zerilli[212]and has the form V (r)= 1−2M r 2n2(n+1)r3+6n2Mr2+18nM2r+18M3r3(nr+3M)2,(24)1In the literature the polar perturbations are also called even-parity because they are characterized by their behavior under parity operations as discussed earlier,and in the same way the axial perturbations are called odd-parity.We will stick to the polar/axial terminology since there is a confusion with the definition of the parity operation,the reason is that to most people,the words“even”and“odd”imply that a mode transforms underπas(−1)2n or(−1)2n+1respectively(for n some integer).However only the polar modes with even have even parity and only axial modes with even have odd parity.If is odd,then polar modes have odd parity and axial modes have even parity.Another terminology is to call the polar perturbations spheroidal and the axial ones toroidal.This definition is coming from the study of stellar pulsations in Newtonian theory and represents the type offluid motions that each type of perturbation induces.Since we are dealing both with stars and black holes we will stick to the polar/axial terminology.Living Reviews in Relativity(1999-2)K.D.Kokkotas and B.G.Schmidt14where2n=( −1)( +2).(25) Chandrasekhar[54]has shown that one can transform the equation(21)for “axial”modes to the corresponding one for“polar”modes via a transforma-tion involving differential operations.It can also be shown that both forms are connected to the Bardeen-Press[38]perturbation equation derived via the Newman-Penrose formalism.The potential V (r∗)decays exponentially near the horizon,r∗→−∞,and as r−2∗for r∗→+∞.From the form of equation(21)it is evident that the study of black hole perturbations will follow the footsteps of the theory outlined in section2.Kay and Wald[117]have shown that solutions with data of compact sup-port are bounded.Hence we know that the time independent Green function G(s,r∗,r ∗)is analytic for Re(s)>0.The essential difficulty is now to obtain the solutions f±(cf.equation(10))of the equations2ˆχ−ˆχ +Vˆχ=0,(26) (prime denotes differentiation with respect to r∗)which satisfy for real,positives:f+∼e−sr∗for r∗→∞,f−∼e+r∗x for r∗→−∞.(27) To determine the quasi-normal modes we need the analytic continuations of these functions.As the horizon(r∗→∞)is a regular singular point of(26),a representation of f−(r∗,s)as a converging series exists.For M=12it reads:f−(r,s)=(r−1)s∞n=0a n(s)(r−1)n.(28)The series converges for all complex s and|r−1|<1[162].(The analytic extension of f−is investigated in[115].)The result is that f−has an extension to the complex s plane with poles only at negative real integers.The representation of f+is more complicated:Because infinity is a singular point no power series expansion like(28)exists.A representation coming from the iteration of the defining integral equation is given by Jensen and Candelas[115],see also[159]. It turns out that the continuation of f+has a branch cut Re(s)≤0due to the decay r−2for large r[115].The most extensive mathematical investigation of quasi-normal modes of the Schwarzschild solution is contained in the paper by Bachelot and Motet-Bachelot[35].Here the existence of an infinite number of quasi-normal modes is demonstrated.Truncating the potential(23)to make it of compact support leads to the estimate(16).The decay of solutions in time is not exponential because of the weak decay of the potential for large r.At late times,the quasi-normal oscillations are swamped by the radiative tail[166,167].This tail radiation is of interest in its Living Reviews in Relativity(1999-2)。

真空衰变（Vacuum decay）abstractPlease describe the entry in a few words and add a summary right away. Vacuum decay - the basic principle of introducing quantum theory is Werner Haisenberg (Werner, Heisenberg)Uncertainty principle. According to this principle, all attributes of a quantum object are not fully determined. For example, a photon or an electron cannot have definite positions and definite momenta at the same time. For a certain moment, it is impossible to have definite energy. What we are concerned about here is energy uncertainty. Although the energy in the macrocosm is conserved (it neither creates nor disappears), the law fails in the Ahara Koko domain. Energy can spontaneously occur unpredictable changes. The shorter the time interval considered, the greater the quantum random fluctuations. In fact, particles can borrow energy from somewhere we don't know, as soon as the energy is returned. Heisenberg uncertainty principle requires accurate mathematical form the bulk of the energy lending must be quickly returned, and a small amount of borrowing can be kept for a long time.Vacuum decay - more detailsEnergy uncertainty leads to some strange effects, like particles such as photons can suddenly be created out of nothing, but later it immediately disappear again, the probability of occurrence of this phenomenon is a strange effect in the. The particles depend on borrowed energy and therefore survive on borrowed time. We do not see them because they are justlightning flashes, but they do leave traces of their existence in the characteristics of the atomic system, which can be measured. In fact, the usual vacuum is indeed filled with streams of such instantaneous particles, not only photons but also electrons, protons, and other particles. In order to distinguish the instantaneous particles from the permanent particles which we know more, the former is called the imaginary particle, while the latter is called the real particle.Except for the instantaneous, the imaginary particles are exactly the same as the real particles. In fact, if in some way from the outside enough energy to repay the Heisenberg energy borrowing, so it is possible to upgrade the virtual particle real particles, and there is no difference with other species of real particles. For example, a virtual electron can only exist in a typical case10-21 seconds. In its short lifetime, the virtual electron is not stationary; it can pass 10-11 centimeters before it disappears (compared to an atomic diameter of about 10-8)Cm). If the virtual electron gets energy in such a short time (say, from the electromagnetic field), it does not necessarily disappear, but can continue to exist as a completely ordinary electron.Although they can not see these imaginary particles, they are really in the vacuum. This is not only because the vacuum contains a potentially permanent library, but also because although they occur in half true half empty form, the quantum entity of the phantom would still leave traces of theiractivities, but also can detect. One of the effects of virtual photons, for example, is a very small deviation of the energy levels of an atom. They also make minute changes in the electron magnetic moment. These minor but important changes have been accurately measured by spectroscopic techniques.Given that subatomic particles are generally free to move, but that they are subject to various forces associated with the particle type, the above simple quantum vacuum image is to be modified. This force also acts on the corresponding virtual particles. As a result, there may be more than one vacuum. The existence of many possible quantum states is a universal feature of quantum physics. The atomic energy levels are best known. Here, an electron orbiting an atom can have some very definite states of energy, and these states correspond to definite energies. The lowest level is called the ground state, and it is stable. Higher energy levels are called excited states, and they are unstable. If an electron breaks into a higher energy state,It will go down and return to the ground state, and there are more than one way to transition. This excited state has a definite half-life of decay.The same principle applies to vacuum. It can have one or more excited states. These excited states have different energies, but their actual appearances are exactly the same, that is, vacuum. The lowest energy state, that is, the ground state, sometimes called the real vacuum, reflects the fact that it is stable, and corresponds roughly to the vacuum region of today's universe. The excitation vacuum is called the pseudo vacuumstate.It should be said that pseudo vacuum is still a purely theoretical idea, and its nature depends to a great extent on the specific theory used. But the pseudo Vacuum States naturally appear in all the theories that attempt to unify the forces of nature at present. The basic forces now recognized appear to be4: familiar with the daily life of the gravitation and electromagnetic force, and two kinds of short-range nuclear forces, weak and strong. The list used to be longer. For example, electricity and magnetism have been regarded as very different things,The unified process of electricity and magnetism began in the early nineteenth Century. At that time, Hans Christian Oster (Hans, Christian, Oersted) found that the current produced a magnetic field, and Michael FaradMichel Faraday found that the moving magnet produced electricity. It is clear that electricity and magnetism are intrinsically related. But, until 1850s, James Clark MaxwellJames Clerk MaxwellOnly the details of the connection were indicated. Maxwell described these electromagnetic phenomena accurately through a set of mathematical equations, and predicted the existence of electromagnetic waves. It was not long before people realized that light was also an example of such waves, and thatother forms of waves, such as radio waves andX ray. Therefore, two different natural forces on the surface - power and magnetism - are the two manifestations of a single electromagnetic force, which have some of their own unique phenomena.In recent decades, this process of unification has been further developed. According to the current understanding of the electromagnetic force and the weak nuclear force is linked, is part of a single "weak force". Many physicists believe that, as part of the so-called "grand unification" theory, it will prove to be associated with electrical forces in the future. Not only that, allThe 4 forces may be synthesized at a sufficiently deep level into a single force.In an attempt to unify electroweak force and force some grand unified theory predicts a promising inflationary force. A key feature of these theories is that the pseudo vacuum energy is surprisingly large: typically, 1 cubic centimeter spaces contain10^87 Joule energy! Even the size of an atom will have the energy of 10^62 joules. A stimulated atom has only 10^-18The energy of about joules, compared to the latter, is negligible. Therefore, to stimulate the vacuum, requires a lot of energy, but in today's universe in which we hope will not find this state. On the other hand, once there are extremeconditions for the big bang, these figures are more telling.The enormous energy associated with a pseudo vacuum has a strong gravitational effect. This is because energy has mass, and Einstein has pointed it out for us, so it can be attracted by gravity like normal matter. The enormous power of quantum vacuum has great appeal: 1Cubic centimeter pseudo vacuum mass weighs 10^64 tons, which is about the mass of today's observable universe (about 10^48)) still big! Have no use for this abnormal gravity on inflation, which requires some kind of anti gravity process. But the enormous pseudo vacuum energy is associated with the same enormous pseudo vacuum pressure, and this pressure is wonderful. Normally, we don't see pressure as a source of gravity, but this pressure is a source of gravity. In a general object, the gravitational effect of an object's pressure is negligible compared to the gravitational effect of the mass of the body. Such as,The body weight of less than 1/1000000000 is produced by the pressure of the earth's interior, however, this effect does exist, and the system is in a huge pressure, the pressure can be compared with the quality of quasi gravity gravity.In the case of pseudo vacuum, there is tremendous energy, but also a huge pressure similar to it, and its mutual struggle for control over gravity, but the key nature is that the pressure is negative. The pseudo vacuum acts not as repulsion, but as attraction. Now negative pressure has a negative gravitationaleffect, which is called anti gravity. Thus, the gravitational attraction of pseudo vacuum comes down to the competition between the enormous attraction of its energy and the repulsive effects of its negative pressure. The final pressure won, the net effect is to produce a very large repulsive force, it can in an instant the universe burst. This is a huge thrust of inflation, so that the scale of the universe to speed the pace of eachDoubles in 10^-34 seconds.In its intrinsic nature, the pseudo vacuum is unstable. Like all excited quantum states, it decays to return to the ground state - the real vacuum. After dozens of ticks, it decays. As a kind of quantum process, it is bound to show discussed above can not avoid the unpredictability and random fluctuations, these properties are related with the Heisenberg uncertainty principle. This means that the decay is not homogeneous in the whole space, but there is fluctuation. Some theorists believe that these fluctuations may be the reason for the intensity fluctuations observed by cosmic background radiation detection satellites.In the pseudo vacuum decay after the universe regained its normal expansion speed, into the explosion by inflation. The energy enclosed in the pseudo vacuum is released and appears in the form of heat. The inflation produced the huge expansion of the universe cooled until the temperature is close to absolute zero, then inflation ended suddenly again heated to the universeOne thousand and twenty-eightExtreme high temperature. Today, the vast reservoir of heat has almost completely disappeared, leaving behind the cosmic background heat radiation. As a by-product of vacuum energy release, many imaginary particles in quantum vacuum acquire part of their energy and change into solid particles. The remains of these particles have survived until now, becoming 10^48 tons of materials that form you, me, the galaxy, and the entire observable universe.。

寻找太空奥秘英语作文Title: Unraveling the Mysteries of Space。

Space, the final frontier, has always intrigued humanity with its vastness and mysteries. From the enigmatic depths of black holes to the breathtaking beauty of distant galaxies, the universe holds countless secrets waiting to be uncovered. In this essay, we embark on a journey to explore some of the most intriguing mysteries of space and the ongoing quest to unravel them.One of the most captivating enigmas of space is the phenomenon of black holes. These cosmic entities possess such immense gravitational pull that not even light can escape their grasp, rendering them invisible to direct observation. Yet, their presence is inferred through the effects they exert on surrounding matter and light. Scientists have been tirelessly studying black holes, seeking to understand their formation, behavior, and ultimately, their role in shaping the cosmos.Another perplexing mystery lies in the nature of dark matter and dark energy. Despite comprising the majority of the universe's mass-energy content, these elusive substances remain largely undetectable through conventional means. Dark matter's gravitational influence is observed in the movement of galaxies and galaxy clusters, yet its composition eludes direct detection. Similarly, dark energy, thought to be responsible for the accelerating expansion of the universe, presents a profound challenge to our understanding of fundamental physics.The search for extraterrestrial life is a quest that continues to captivate the imagination of scientists and enthusiasts alike. While we have yet to find conclusive evidence of life beyond Earth, the discovery of exoplanets—planets orbiting stars outside our solar system—has fueled optimism. Each new exoplanet brings us closer to the tantalizing possibility of encountering life forms vastly different from those on our own planet, prompting us to explore the conditions necessary for lifeto emerge and thrive elsewhere in the universe.The cosmic microwave background radiation (CMB) serves as a relic of the early universe, offering invaluable insights into its infancy. Studying the fluctuations in the CMB provides a window into the conditions that prevailed shortly after the Big Bang, shedding light on the processes that led to the formation of galaxies, stars, and ultimately, life as we know it. By analyzing thisprimordial radiation, scientists endeavor to unlock the secrets of the universe's origin and evolution.Gravitational waves, predicted by Albert Einstein's theory of general relativity a century ago, were only recently detected for the first time. These ripples in the fabric of spacetime are produced by cataclysmic events such as the merging of black holes or neutron stars. Gravitational wave astronomy promises to revolutionize our understanding of the cosmos, offering a new way to observe the universe and probe its most extreme phenomena.In the pursuit of unraveling the mysteries of space, technological advancements play a pivotal role. Spacetelescopes like the Hubble Space Telescope and the James Webb Space Telescope enable us to peer deeper into the cosmos than ever before, capturing images of distant galaxies, nebulae, and other celestial objects. Robotic probes and landers explore the surfaces of planets and moons within our solar system, unveiling their geological features and atmospheric compositions.Furthermore, collaborations among international space agencies and research institutions foster a spirit of cooperation in the quest for cosmic knowledge. Projects such as the European Space Agency's Gaia mission, which aims to create the most detailed 3D map of the Milky Way galaxy, exemplify the global effort to unlock the secrets of the universe and expand the boundaries of human understanding.In conclusion, the mysteries of space continue to beckon us with their allure, inspiring curiosity anddriving scientific inquiry. From the depths of black holes to the expanse of cosmic horizons, the universe presents an endless array of puzzles waiting to be solved. Throughcollaboration, innovation, and unwavering curiosity, humanity stands poised to unlock the secrets of the cosmos and embark on a journey of discovery that transcends the boundaries of our own planet.。