a r X i v :n l i n /0511026v 1 [n l i n .S I ] 14 N o v 2005METASTABILITY AND DISPERSIVE SHOCK W A VES
IN FERMI-PASTA-ULAM SYSTEM
PAOLO LORENZONI AND SIMONE PALEARI
Abstract.We show the relevance of the dispersive analogue of the shock waves in the FPU dynamics.In particular we give strict numerical evidences that metastable states emerging from low frequency initial excitations,are indeed constituted by dispersive shock waves travelling through the chain.Relevant characteristics of the metastable states,such as their frequency extension and their time scale of formation,are correctly obtained within this framework,using the underlying continuum model,the KdV equation.1.Introduction The Fermi–Pasta–Ulam (FPU)model was introduced in [9]in order to study the rate of re-laxation to the equipartition in a chain of nonlinearly interacting particles,starting with initial conditions far away from equilibrium.Both the original and the subsequent numerical experiments show that this transition,if present,takes much longer times than expected,raising the so called FPU problem,or FPU paradox.Recently there has been a growing interest in the ?eld of continuum limits and modulation equations for lattice models (see e.g.,[5,6,10,11,25],just to cite a few without any claim of completeness).Actually,it is possible to say that one of the starting points of this activity goes back to a paper by Zabusky and Kruskal [27],where the recurrence phenomena observed in the FPU system are related to the soliton behaviour exhibited by the KdV equation,which emerges as a continuum limit of the FPU.Surprisingly,these two viewpoints evolved for several years somewhat independently,with some people working essentially on integrable systems,and other people interested mainly in the nearly integrable aspects of the FPU type models.In the ?rst community the work [27]was a milestone.A crucial remark in that paper is that the time evolution of a class of initial data for the KdV equation are approximately described by three phases:one dominated by the nonlinear term,one characterized by a balance between the nonlinear term and the dispersive term where some oscillations,approximately described by a train of solitons with increasing amplitude,start to develop,and the last where the oscillations prevail.Since the soliton velocities are related to their amplitude,at a certain time they start to interact.By observing the trajectories of the solitons in the space-time,Kruskal and Zabusky
realized that,periodically,they almost overlap and nearly reproduce the initial state.Clearly,such an overlapping is not exact,due to the phase shift given by the nonlinear interaction between solitons.They conjectured that this behaviour gives an explanation of the FPU phenomenology.As discovered later by Gurevich and Pitaevskii [15]in a di?erent context,the oscillations observed by Zabusky and Kruskal are more properly described in terms of modulated one-phase solutions of KdV equations,and the slow evolution of their wave parameters is governed by the so called Whitham’s equations [26].
The analytic treatment of the dispersive analogue of shock waves is less developed in the non integrable case even if some steps in this direction have been made (see for instance [8]);moreover,recently it has been conjectured that such phenomenon,in its early development,is governed by a universal equation [7].
From the FPU side,due to the original motivations arising from Statistical Mechanics,the core question become the possible persistence of the FPU problem in the thermodynamic limit,i.e.
2P.LORENZONI AND S.PALEARI
when the number of particles N goes to in?nity at a?xed speci?c energy(energy per particle). Izrailev and Chirikov[16]suggested the existence of an energy threshold below which the phe-nomenon is present;but such a threshold should vanish for growing N due to the overlapping of resonances;the recurrence in the FPU system is thus explained in terms of KAM theorem(see also[23]).According to Bocchieri et al.[4]instead,the threshold should be in speci?c energy and independent of N.
Along the lines of the second conjecture,Galgani,Giorgilli and coworkers[2,3,13,18]have recently put into evidence a metastability scenario(see also the previous paper by Fucito et al.[12]): for di?erent classes of initial data,among which those with low frequency initial conditions,the dynamics reaches in a relatively short time a metastable state.Such situation can be characterized in terms of energy spectrum by the presence of a natural packet of modes sharing most of the energy:and the corresponding shape in the spectrum does not evolve for times which appear to grow exponentially with an inverse power of the speci?c energy.The possible theoretical framework for such experimental results could be a suitably weakened form of Nekhoroshev theory.
As one of the?rst attempts to join again in an original way the two di?erent aspects of the FPU paradox and of its integrable aspects,we recall the paper[20];in that work,the approaching of the FPU chain to the shock is observed,but unfortunately the range of speci?c energy considered is too high to have the metastability(see the higher part of the Fig.1,left panel).
Some recent papers(see e.g.,[21])recovered the spirit of the work by Zabuskii and Kruskal: exploiting the typical time scales of the KdV equation,it is possible to recover those of the FPU system,in particular the time scale of creation of the metastable states;the length of the natural packet is also obtained and its spectrum is expected to be connected to that of solitons of the underlying KdV.
Given all the elements we have put into evidence from the literature,it is natural to make a further step.Our claim is that,concerning the metastability scenario,among the several aspects of the KdV equation,precisely the dispersive analogue of the shock wave is the relevant one.
Thus the aim of this paper is to show,at least numerically,that the metastable state is com-pletely characterized by the formation and persistence of the modulated solutions of KdV equation and by their self interactions.We are indeed able to put into evidence exactly such phenomena directly in the FPU dynamics.
In fact,we observe the formation of dispersive shock waves in the FPU chain:correspondingly the metastable state sets in.Exploiting the scaling properties of the KdV equation one obtains for the spatial frequency(wave number)of the dispersive waves,which can be naturally thought as an upper bound for the natural packet,the dependence on the speci?c energy?,as observed in the numerical experiments:ω～?1/4.
Similarly we can also explain the dependence of the formation time of the metastable state on the number N of particles and on the speci?c energy?:t～N??1/2+??3/4when energy is initially placed on a low frequency mode.
Although this is a kind of preliminary and qualitative investigation,we think in this way to give a uni?ed and synthetic picture of the metastability scenario in the FPU system,providing the precise dynamical mechanism leading to its creation.
In what follows,after a short description of the FPU model,we recall the main facts about the metastability scenario in the FPU(see Sect.2),and some elements of the Gurevich–Pitaevskii phenomenon for KdV equation(see Sect.3);we then show in Sect.4the deep relations between the two aspects.
1.1.The model.In the original paper[9],Fermi,Pasta and Ulam considered the system given by the following Hamiltonian
H(x,y)=
N
j=1 12s2+α4s4,
METASTABILITY AND DISPERSIVE SHOCK WA VES IN FERMI-PASTA-ULAM SYSTEM3 describing the one–dimensional chain of N+2particles with?xed ends,which are represented by x0=x N+1=0.For the free particles,x1,...,x N are the displacements with respect to the equilibrium positions.This is the FPUα,β–model.
The normal modes are given by
x j= N+1N k=1q k sin jkπ2N+1,
(q k,p k)being the new coordinates and momenta.The quadratic part of the Hamiltonian in the normal coordinates is given the form
(1)H2=
N
j=1E j,E j=12(N+1),
E j being the harmonic energies andωj the harmonic frequencies.
Given the following limit,representing the equipartition,
T T0E j(t)dt?→?:=E
4P.LORENZONI AND S.PALEARI
Figure1.Metastability.Left panel:natural packet phenomenon.β–model,
withβ=1/10,N=255,initial energy on mode1;the thresholdγis?xed to0.1.
Abscissa:critical time t s for every packet1;ordinate:speci?c energy(from[18]).
Right panel:exponentially long relaxation times.β–model,withβ=1/10.Time
needed by n e?to overcome the threshold0.5vs.the speci?c energy power to
?1/4,for?xed N=255and?in the range[0.0089,7.7],in semi-log scale;every
point is obtained averaging over25orbits with di?erent phases.The straight line
is the best?t using all the points with?≤1(from[3,18]).
seem to be stable structures.The lower is the energy,the longer the FPU takes to manifest its non integrability and to behave di?erently from the Toda system.
A quantitative estimate of the second time scale related to the equipartition is given in[3](but see also[19]).Using,as usual in this type of investigation,the spectral entropy indicator n e?:=e S
N j=1E j,it is possible to estimate the e?ective number of normal modes involved in the dynamics.Plotting the time necessary for n e?to overcome a?xed threshold close to its saturating value,as a function of the speci?c energy,one obtains a reasonable estimate of the relaxation times to equipartition,that is an estimate for the metastability times. The corresponding results are shown in Fig.1:the numerical evidence supports the exponential scaling,with a possible law of the type T～exp(??1/4),for theβ–model.
The previous descriptions are concerned with a kind of more global picture:concentrating on a single evolution at a?xed speci?c energy,it is possible to have a better insight to the approach to equipartition looking at the time evolution of the distribution of energy among the modes.We plot in Fig.2some frames to give an idea:the thick symbols represent the average over all the times,while the thin ones are the averages over a short time window.In the upper left panel, in the?rst stage of the evolution,one observes the small but regular transfer of energy towards the higher frequencies.In the subsequent panel,as this process goes on,some modulations on the shape of the spectrum appear.At longer times the spread to the higher part slows down,i.e.the slope of the straight line converges to a certain value(see the lower left panel),and the amplitude of the modulating bumps increases and their position slowly moves leftward.In the last frame we see quite well the spectral structure of the metastable state:in the low frequency region the slow motion of the bumps produces a plateau once one look at the average over all times;and in the rest of the spectrum essentially nothing happens a part from an extremely slow emergence of narrow peaks.Such a situation remain practically frozen for times growing exponentially with a suitable power of the inverse of the speci?c energy.
METASTABILITY AND DISPERSIVE SHOCK WA VES IN FERMI-PASTA-ULAM SYSTEM5
a.t=2.5×103
b.t=6×103
c.t=1.15×104
d.t=6×104
Figure2.Time averaged distribution of energy among the harmonic modes at
di?erent times.α–model,withα=1/4,N=127,speci?c energy?=0.001,
initially on mode1.Absciss?:k/N,k being the mode number.Ordinates:the
energy of the modes averaged up to time t reported in the label(thick points:
average from the beginning;thin points:average over a time window given by the
last100time units).
3.The dispersive analogue of the shock waves
This section is a brief summary of some well-known facts about dispersive shock waves.For our purposes it is su?cient to discuss the case of the KdV equation
(2)u t+uu x+μ2u xxx=0
which is known to give a good approximation the continuum limit of the FPU model for long-wave initial conditions.
If the parameterμis equal to zero it is well-known that,if the initial data is decreasing somewhere,after a?nite time t0,the gradient u x(x,t)of the solution becomes in?nite in a point x0(point of gradient catastrophe).For monotone initial data,the solution is given in implicit form by the formula x=tu+f(u),(where f(u)is the inverse function of the initial datum u(x,0)); consequently,u x=1/(f′(u)+t)and the time of gradient catastrophe is
f′(u).
(3)t0=max
u∈R
Forμ=0,far from the point of gradient catastrophe,due to the small in?uence of the dispersive term,the solution has a behaviour similar to the previous case,while,in a neighbourhood of the singular point,where the in?uence of the dispersion cannot be neglected anymore,modulated oscillations of wave number of order1/μdevelop(see Fig.3).
According to the theory of Gurevich and Pitaevskii,these oscillations can be approximately described in terms of one-phase solutions of the KdV equation
(4)u(x,t)=u2+a cn2 3(x?ct);m ,
6P.LORENZONI AND S.PALEARI
Figure3.Formation of dispersive shock waves in the KdV equation u t+uu x+
μ2u xxx=0,withμ=0.022(?gures reproducing the original Zabusky-Kruskal
numerical experiments,obtained using a Matlab code from[24]).The initial
datum,shown in the left panel,is u(x,0)=cos(πx);in the central panel the early
stage of formation of the dispersive shock is visible;in the right panel one clearly
observes the train of dispersive waves.
that slowly vary in the time.
The wave parameters of the solution(4)depend on the functions u j which evolve according to an hyperbolic system of quasi-linear PDEs:the Whitham’s equations[26].Moreover,for generic initial data,the region?lled by the oscillations grows as t3/2[1,15,22].Outside this region the evolution of the solution is governed by the dispersionless KdV equation.
Inside the oscillation region,two limiting situations arise when the values of two of the three parameters u j coincide:
?m?0,a?0:in this case we have an harmonic wave with small amplitude which corresponds to the small oscillations that one can observe near the trailing edge of the oscillation zone;
?m=1:in this case we have a soliton which one can observe near the leading edge of the oscillation zone.
Since the Whitham’s equations are hyperbolic,further points of gradient catastrophe could appear in their solutions.As a consequence also multiphase solutions of KdV equation could enter into the picture.
It turns out that,forμ→0,the plane(x,t)can be divided in domains D g where the principal term of the asymptotics of the solution is given by modulated g-phase solutions[17].For monoton-ically decreasing initial data there exists rigorous theorems which provide an upper bound to the number g[14].Unfortunately for more general initial data,such as those we need,the analytical description is less developed.
4.Dispersive shock waves in the FPU
The connection between the FPU dynamics,when initial conditions involve only low frequency modes,and KdV equation has been already pointed out in the sixties by Zabusky and Kruskal[27]. And in many other subsequent papers it is heuristically deduced that the KdV(respectively mKdV)may be viewed as continuum limit for FPUα–model(respectivelyβ–model).
In this section we will?rst show in qualitative way how,in this framework,the metastability is deeply related with the presence of the dispersive shock waves;we will then give some more detail on the continuum model involved.
4.1.Metastability and dispersive shock waves.As we described in Sec.2,the metastability in the FPU model is a property well visible in the energy spectrum(see Fig.2).We show now that it can be also detected on the dynamics of the particles.
In order to clarify this point we show in Fig.4some frames of the time evolution of positions and velocities of the chain.We choose the orbit whose spectrum is depicted in Fig.2.
METASTABILITY AND DISPERSIVE SHOCK WA VES IN FERMI-PASTA-ULAM SYSTEM7
a.t=6×103
b.t=1.15×104
Figure4.Time evolution of the chain at di?erent times,for the same orbit as in
?g.2.Absciss?:k/N,k being the mode number.Ordinates:as written on each
subpanel.The picture clearly shows the correspondence between the appearance
of the dispersive wave and the emergence of bumps in the energy spectrum.
In the panel referring to time t=6×103,it is possible to see that the emergence of the bump in the energy spectrum corresponds the formation of the dispersive shock waves in the pro?le of the velocity.When the wave train has completely?lled the chain,the evolution of the energy spectrum stops:the system has reached the metastable state(second panel).
It is worth to point out that the wave number of the modulated waves is exactly of the same order of the bump;this fact suggests that their slow motion,described in Sec.2,could be explained in terms of the evolution of the wave parameters(see Eq.4)given by the Whitham’s equations.
Thus the central point is that in the?rst stage of the dynamics,the evolution may be divided in three regimes:
dispersionless regime:
the corresponding continuum model is dominated by the non dispersive term,with the string approaching the shock and the almost regular energy transfer towards higher fre-quency modes,as shown in Fig.2,panel a.
mixed regime:
in the corresponding PDE is visible the e?ect of the dispersive term,which prevents the shock and creates the typical spatial oscillations in the chain;correspondingly the energy spectrum exhibits the formation of the bumps located at the correct frequency and at its higher harmonics.The part of the string non occupied by the growing dispersive wave is still governed by the dispersionless part and for this reason the?ow of energy slows down and eventually stops when the train involves the whole chain(see Fig.2,panel b,and Fig.4,panel a).
dispersive regime:
the dispersive shock wave?lls the lattice and travels through it:the metastable state is formed(see Fig.2,panel c,and Fig.4,panel b).In the underlying integrable continuum limit one has the elastic interactions of the solitons in the head of the train,together with the recurrence phenomena already observed in[27]:this motivates the long time persistence of the natural packet(see Fig.2,panel d).
Such a correspondence between the evolution of the energy spectrum and the appearance of dispersive waves and their growth up to the occupation of the whole chain,has been observed in all our numerical experiments:it appears to be independent of the number of particles N,of the speci?c energy(in the range for which one has metastability)and of the particular choice of the initial low frequency mode excited.We are working on a more systematic and quantitative comparison.
8P.LORENZONI AND S.PALEARI
a.t=5.98×103
b.t=6.03×103
c.t=6.08×103
Figure5.Apparent elastic interaction of dispersive wave trains,explained in
terms of the two decoupled KdV equations forξandη.α–model,withα=1/4,
N=255,?=0.001,initial energy on mode2.Absciss?:k/N,k being the
mode number.In the velocity subpanel one observes two wave trains travelling in
opposite directions without interaction.The same two trains appear respectively
in theξandηsubpanels.
In the remaining part of this section we will show more precisely that the above mentioned dispersive and non dispersive regimes admit a clear understanding in terms of the underlying continuum model.
4.2.The continuum model.As observed by Bambusi and Ponno[21],the FPU,with periodic boundary conditions is well approximated,for low frequency initial data,by a pair of evolutionary PDEs whose resonant normal form,in the sense of canonical perturbation theory,is given by two uncoupled KdV:
ξt=?ξx?1?
24N2ηxxx+ 2ηηx,
(6)
using the rescaling with respect to the original FPU variables(x FPU=Nx KdV,t FPU=Nt KdV);ξandηcan be written in terms of two functions q x and p that,a part from a constant factorα, respectively interpolates the discrete spatial derivative q j?q j?1and the momenta p j:
ξ(x,t)?α(q x+p)
η(x,t)?α(q x?p)
Taking into account that,in our case,we deal with?xed boundary conditions,we must add to the equations(5,6)the following boundary conditions:
ξ(0,t)=η(0,t)
ξ(L,t)=η(L,t).
In other words the variablesξandηexchange their role at the boundary.Moreover,ifη(x,t) satis?es(5)thenη(?x,t)satis?es(6)and vice-versa.
As a consequence,we can substitute the evolution of(ξ(x,t),η(x,t))with the evolution of a single function u(x,t)de?ned in terms ofξandηin the following way
u(x,t)=ξ(x,t)x∈[0,L]
u(x,t)=η(2L?x,t)x∈[L,2L],
governed by the KdV equation
(7)u t=?u x?μ21?
METASTABILITY AND DISPERSIVE SHOCK WA VES IN FERMI-PASTA-ULAM SYSTEM9
a.t=1.576×104
b.t=1.596×104
c.t=1.616×104
Figure6.Evolution of the chain.α–model,withα=1/4,N=511,?=0.001,
initial energy in equipartition on modes2and3.Absciss?:the index particle
j.Ordinates:ξ(j)in each left sub-panel(full circles),η?(j)=η(N?j)in each
right sub-panel(empty circles).The dynamics develop three wave trains;in these
frames one observes the bigger one?owing in the left direction and passing from
theη?subpanel to theξone,while the smaller ones go out theξsubpanel and
reenter in the other one:the two variables satisfy indeed a common KdV equation
on a circle.
and satisfying periodic boundary conditions.
These facts are clearly visible in Fig.5and Fig.6.In the?rst one,in order to show the role of the variables(ξ,η),we give three almost consecutive frames of the evolution of a chain,with energy initially placed on the second normal mode.As expected,one has the generation of two trains of dispersive waves(the number of trains generated is exactly k,when the initially excited normal mode is the k th one).Looking at the velocity sub-panel(the lower left one)of each frame,a sort of elastic interaction appears between the trains:they approach each other in frame(a),they interact in frame(b)and they come out unmodi?ed in frame(c).But looking at the sub-panels ofξandηone realizes that such“elastic interaction”is the superposition of two independent,in the normal form approximation,dynamics.
Moreover,the relation between(q,p)and(ξ,η)explains why the dispersive shock is well visible in the velocities,which are directly a linear combination of the variablesξandη;the con?gurations instead are approximately obtained by means of an integration which has a smoothing e?ect.
Fig.6illustrates the role of?xed boundary conditions,with the two KdV equations of the normal form for the periodic case,degenerating into a single KdV.In the three consecutive frames it is perfectly clear that the big wave train supported by theηvariable?ows into the equation for ξ,and the two smaller trains,initially present in theξsubpanel,go out through the left border and re-enter from the right side of theηpart.The true equation is the periodic KdV7for the variable u.
The recurrence appearing in the dispersive regime,and well visible in our numerical experi-ments(?gures not shown),may be seen as the e?ect of the quasi-periodic motion on a torus of the underlying integrable system.On the other hand,following Kruskal and Zabusky,it also has a natural explanation in terms of the elastic scattering of solitons.Clearly,a more re?ned descrip-tion of this phenomenon should also take into account the e?ect of the interactions of the small oscillations near the trailing edge.Indeed it could be interesting to study the analytical aspects of the interaction of dispersive wave trains,where the higher genus modulated solutions of KdV equation could play a role.
4.3.The relevant scalings.In the previous section we showed that the continuum limit for the FPU model with?xed ends,N particles,speci?c energy?and an initial datum of low frequency,
10P.LORENZONI AND S.PALEARI
is given by the single KdV equation7,which in the moving frame is
1?
(8)u t=?
√24u xxx.
We have seen that the metastable state is characterized by its size in the modal energy spectrum,
and by its time of creation and destruction.
Let us start with the?rst aspect.Following the numerical evidence we claim that the initial wave number of the dispersive wave provides a good estimate,or at least an upper bound,for the width of the packet of modes involved in the metastability.Denoting byω?the relevant wave number for equation11,the corresponding wave numberωKdV for equation8is
ωKdV=N?1/4ω?,
due to the spatial rescaling9.
Recalling the spatial scaling in the continuum limit process(x FPU=Nx KdV),one remains with the experimentally observed law
ωFPU～?1/4,
without any dependence on N.
Let us now consider the second point:the time scales.As pointed out in the previous discussion, the time of formation of metastable state is characterized by two di?erent regimes:one governed by dispersionless KdV,where the e?ect of the nonlinearity prevails and drive the dynamics towards a shock,and one governed by the full KdV equation,where the dispersion prevents the shock and generates the dispersive train.Therefore we can approximately estimate the time of formation of the metastable state as the sum of the two contribution
t FPU?N(t1+t2);
t1is the time of validity of the?rst regime,that we estimate from above with the time t s of formation of the shock in the dispersionless KdV,while t2is the time needed by the dispersive wave to occupy the whole chain in equation8(t?2in equation11),and the factor N is again due
to the rescaling in the continuum limit process(t FPU=Nt KdV).
√
For the equation u t=
METASTABILITY AND DISPERSIVE SHOCK WA VES IN FERMI-PASTA-ULAM SYSTEM11
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[25]G.Schneider and C.E.W ayne,Counter-propagating waves on?uid surfaces and the continuum limit of
the Fermi-Pasta-Ulam model,in International Conference on Di?erential Equations,Vol.1,2(Berlin,1999), World Sci.Publishing,River Edge,NJ,2000,pp.390–404.
[26]G.B.Whitham,Non-linear dispersive waves,Proc.Roy.Soc.Ser.A,283(1965),pp.238–261.
[27]N.J.Zabusky and M.D.Kruskal,Interaction of“solitons”in a collisionless plasma and the recurrence of
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Universit`a degli Studi di Milano Bicocca,Dipartimento di Matematica e Applicazioni,Via R.Cozzi, 53,20125—Milano,Italy
E-mail address:paolo.lorenzoni@unimib.it
E-mail address:simone.paleari@unimib.it
放假说说心情短语 导读：1、哎，放完假后又该开学了。 2、再忍两个月，又是一个可爱的寒假。 3、三个人的友情，总有一个是被冷落的。 4、现在担心的不应该是你的寒假作业吗？ 5、五一假期，鲜花献给辛勤的劳动人民。 6、老师我不想写作业，那样一点都不酷。 7、元旦过去啦，是该收收心准备过寒假了。 8、我和寒假分手了，都是因为开学那贱人。 9、其实我也不想跟作业相亲，都是老师逼的！ 10、中国的放假原则——欠了的终归是要还的！ 11、老师，毕业那天的试卷您还没有给我们讲。 12、查个分比表白还紧张查完了比失恋还难过！ 13、暑假真的很短，在两次大姨妈中就没有了。 14、对我们来说，放假就是换了个地方写作业。 15、放假了，逃脱了老师严厉眼神的扫射范围。 16、祖国尚未统一，我却放假无聊，惭愧惭愧！ 17、放假就像做无痛人流开始了吗？已经结束了。 18、我和暑假手拉手中间却夹着一条叫作业的狗！ 19、所谓放假就是在家挨骂，出门没钱，一天特闲。 20、我对暑假的概念就是：我的充电器从来没闲过。
21、放假开学前一天晚上，我国用电量将直线上升。 22、我真是个花心的人，暑假刚走了我就想着寒假。 23、都在改变只能沉默只能向前前往成熟大人世界。 24、你若军训，便是晴天，你若放假，便是作业连连。 25、我的灵魂和身体已不在一起去，灵魂早已到了家！ 26、所谓放假就是，家里遭嫌，出门没钱，每天特闲。 27、要是明天就放假，我就回去吧我家的猪痛亲一顿。 28、放假了才发现，只有爱你的人才会和你保持联系。 29、中国的放假告诉了我一个道理，欠了的总是要还的！ 30、“你的作业怎么样”“活得挺好的，养的白白的。” 31、男生见过女生放假在家的样子还喜欢那一定是真爱。 32、上学的时候总想玩电脑，放假了只能对着电脑发呆。 33、放个寒假才20几天，这年头，连失个恋都得33天呢。 34、与暑假先森约会的时候，总会出现一个叫作业的**。 35、“哇，下雪了！”“不，是上帝在撕他的寒假作业。” 36、这年头，放假真不容易，清明节放假还是沾老祖宗的光。 37、告诉你比鬼片还**的事：你们的暑假已经过了一半啦。 38、老师一点也不酷，一点儿也不给力，还布置那么多作业。 39、老师，作业在手里攒一寒假了，有感情了，咱不交了成吗？ 40、放假以后，学神在刷难题，学霸在刷作业，学渣在刷动态。 41、暑假作业写完请按写了一半请按写了一点请按一点没写请按
放假了心情说说短语 【篇一：放假了心情说说短语】 关于放假说说心情短语 说说心情：放假就像摘除了孙悟空的紧箍咒，又可以无法无天的玩 耍了！关于放假说说心情短语,放假就像卸去了心中的千金的重担，终于可以享清闲了！ 1、一年之中最喜欢两个假期，一个叫寒假，一个叫暑假!关于放假说说心情短语 2、这次放假最想去夏威夷，太远;所以，我去了三亚，好好放松! 3、所谓放假就是在家挨骂，出门没钱，一天特闲。 4、讨厌放假、作业多那是借口、只是因为不能再每天看见你。这你都不懂吗。 5、所谓放假，家里遭嫌，出门没钱，每天特闲~哎，放完假后又该 开学了，徘徊在兴奋与失落中。 6、在接下来的一个月里，你将听到七大姑八大姨各种亲戚各种家长的深情问候：考试考多少分啊?班里多少名啊? 7、放假了，是否激动? 恩，可作业会让你更激动! 8、放假的意义就在于，一个说不起就不起的早晨，一个说不睡就不睡的深夜和一个说不出门就不出门的白天。 9、躺在床上玩手机，一想到放假了好久了还没有碰过书，我就啪的抽了自己一耳光，tm的玩个手机还分心。 10、关闭放假模式，正式开启学霸模式! 对不起，您的配置太低， 无法启动该功能关于放假说说心情短语 11、现在的放假，暑假放得和寒假一样，寒假放得和国庆一样，国 庆放得和五一一样，五一放得和周末一样，周末放得和没放一样， 总结，放假就跟放屁一样。 12、放假了才发现，只有爱你的人才会和你保持联系。 13、感觉自己和放假之前一样轻盈啊说人话作业没写 14、放假在家每天必做三件事 [ 吃饭睡觉挨骂 ] 15、暑假到了快乐到，乘着夏风乐逍遥，休闲娱乐安排好，外出旅 游注安全，起居科学要规律，锻炼学习莫忘记。祝暑假快乐无忧、 平安健康。 16、暑假来临，不怕高温：空调吹吹，燥热逃掉，感觉美妙;冰糕吃吃，凉度增加，惬意留下;短信阅读，清凉假期，心情冰舞!假期快乐!
23、都在改变只能沉默只能向前前往成熟大人世界。 24、你若军训，便是晴天，你若放假，便是作业连连。 25、我的灵魂和身体已不在一起去，灵魂早已到了家！ 26、所谓放假就是，家里遭嫌，出门没钱，每天特闲。 27、要是明天就放假，我就回去吧我家的猪痛亲一顿。 28、放假了才发现，只有爱你的人才会和你保持联系。 29、中国的放假告诉了我一个道理，欠了的总是要还的！ 30、“你的作业怎么样”“活得挺好的，养的白白的。” 31、男生见过女生放假在家的样子还喜欢那一定是真爱。 32、上学的时候总想玩电脑，放假了只能对着电脑发呆。 33、放个寒假才20几天，这年头，连失个恋都得33天呢。 34、与暑假先森约会的时候，总会出现一个叫作业的**。 35、“哇，下雪了！”“不，是上帝在撕他的寒假作业。” 36、这年头，放假真不容易，清明节放假还是沾老祖宗的光。 37、告诉你比鬼片还**的事：你们的暑假已经过了一半啦。 38、老师一点也不酷，一点儿也不给力，还布置那么多作业。 39、老师，作业在手里攒一寒假了，有感情了，咱不交了成吗？ 40、放假以后，学神在刷难题，学霸在刷作业，学渣在刷动态。 41、暑假作业写完请按写了一半请按写了一点请按一点没写请按 42、与寒假先森约会的时候，总会出现一个叫寒假作业的
**。 43、放假就是，早上起不来，晚上睡不着，夜猫子模式已启 动。 44、一个完整的夏天=西瓜+空调+可乐+满格WIFI+没有暑假作业！ 45、本来有种要把寒假作业一口气写完的冲动，还好我自制力强。 46、放假再无聊，我也不愿上学；就像爱你再无助，我也不愿 放手。 47、“你觉得作业是个什么样的人？”“是个破坏别人寒假的人！” 48、对不起，作业先森。我们不合适、我爱的只有他——寒假 先森。 49、放假有什么好的，还不是一个人过，而且还见不到最想见 到的人。 50、上课时只知道星期几不知道日期，放假时只知道日期不知 道星期几。 51、我最爱的寒假和我最恨的学校生了个娃，叫作业，还要我 来养它，唉。 52、每个人身边都需要一个，出去玩当借口的人，家长听了肯 定放心的人。 53、最鄙视那些一放假就出去玩的人，我只想送给他们四个字：请带上我。 54、上学和放假的区别：上学，我起床了却没醒；放假，我醒 了却没起床。
放假的心情说说_一句话的简单心情说说 放假的心情说说_一句话的简单心情说说 1.这年头，放假真不容易，清明节放假还是沾老祖宗的光。 2.上课是为了下课，上学是为了放假。没有这么伟大的心念支持着，都不敢想象我是怎么有勇气来学校。 3.放假时，我醒了，不代表我起床了;上学时，我起床了，不代表我醒了。 4.中国的放假原则，欠了的终归是要还的! 5.放假的时候发烧都会坚持上网，上课的时候打个喷嚏都会觉得是癌症晚期。 6.世界上最近的距离，放假到开学;世界上最远的距离，开学到放假。 7.“上学你带了什么”?“一颗随时准备放假的心” 8.大家都在研究开学怎样进门最帅，我已经在研究什么时候
放假了。 9.五四运动为什么爆发?因为五一放假只有三天。 10.放假的意义就在于，一个说不起就不起的早晨，一个说不睡就不睡的深夜和一个说不出门就不出门的白天。 11.从前有群人一起放假，现在这群人放假的时间都不一样了。 12.放假靠祖宗，停课靠台风。 13.最鄙视那些一放假就出去玩的人，我只想送给他们四个字：请带上我。 14.你若军训，便是晴天，你若放假，便是作业连连。 15.躺在床上玩手机，一想到放假了好久了还没有碰过书，我就啪的抽了自己一耳光，TM的玩个手机还分心。 16.我对放假的概念就是：我的充电器从来没闲过。 17.读书的时候觉得不怎么擅长学习，放假以后发现原来玩也不太在行。
18.“放假你快乐吗?”“只有快，没有乐。” 19.留几年的长发五分钟就剪完，学几年的知识一放假就忘光。 20.“关闭放假模式，正式开启学霸模式!”“对不起，您的配置太低，无法启动该功能” 21.放假以后，学神在刷难题，学霸在刷作业，学渣在刷动态。 22.作业加载失败，请学校重新放假。 23.放假再无聊，我也不愿上学;就像爱你再无助，我也不愿放手。 24.“放假了，是否激动?”“恩，可作业会让你更激动!” 25.现在的放假，暑假放得和寒假一样，寒假放得和国庆一样，国庆放得和五一一样，五一放得和周末一样，周末放得和没放一样，总结，放假就跟放屁一样。 26.放假了才发现，只有爱你的人才会和你保持联系。
关于寒假作业的说说心情短语句子 一、有些老师真是过瘾,我抄作业,她说我抄别人作业干什么?还不如空着.我空着作业交上去,她说我空着还交上来 二、老师一点也不酷，一点儿也不给力，还布置那么多作业。 三、在与寒假先森约会的时候总会出现一个叫寒假作业的小三 四、对不起，作业先森。我们不合适、我爱的只有他——寒假先森。 五、抄作业，偶尔需要偷工减料 六、当我埋着头苦苦写着作业的时候，我真想捏死班主任。 七、今天我们的挑战是一边嚼着炫迈口香糖一边写作业，过一段时间再看作业很多根本停不下来。 八、现在担心的不应该是你的寒假作业吗？！！！ 九、作业我们分手吧，我感觉我们不适合。 十、作业烧不尽，老师吹又生。
十一、我学会了说脏话，学会了早恋，学会了攀比，学会了叛逆，学会了抄作业，知道是在哪儿吗？是在学校。 十二、老师我不想写作业，那样一点都不酷。 十三、每次我做作业的时候看到不会的题就自动跳过，可是这一跳就像嚼了炫迈一样，根本停不下来。 十四、作业小三，请你自重，我是个有寒假的人 十五、“为什么寒假比暑假短？”“热胀冷缩啊。”“那为什么作业一样多？”“因为质量不变嘛。” 十六、祖宗啊我烧点作业给你多帮我做做题有不会的把我们老师叫过去问问 十七、与寒假先森约会的时候，总会出现一个叫寒假作业的小三、 十八、本来有种要把寒假作业一口气写完的冲动还好我自制力强 十九、“你觉得作业是个什么样的人？”“是个破坏别人寒假的人！”
二十、扔硬币：正面就去上网、反面就去睡觉，立起来就去写作业。 二十一、待寒假来临，只等作业成山。https://www.doczj.com/doc/0a9512726.html, 二十二、其实我也不想跟作业相亲，都是老师逼的！ 二十三、这年头，不早恋，不犯贱，不作弊，不叛逆，不抄作业，不玩手机，都没人相信你是学生。 二十四、作业快到火里来，你才到火里去，就不能找个大一点的火吗，作业这么多怎么烧的完。
关于生活感悟的心情说说短语 1)总有那么一天，有一个人，会走进你的生活，让你明白，为什么你和其他人都没有结果. 2)一直都不想说其实孙浣琪孙慧芳孙淇琦孙锦纯孙悦容刘玉鑫彭超你们一直在我生活圈里 3)我们没有资格去逃避生活. 4)带着你的为我好滚出我的生活 5)爱是与生活勾结一起的幻术!直到最后才会发现我们相信自己胜过相信爱情!爱自己，胜过爱对方。 6)暑假君，你别走啊别走，我不要和上学先生生活在一起，不要啊你别走呜呜呜 7)生活比电影难过多了。 8)也许我只是你生活中的一个很平常的过客，你或许不知道，你曾是我的全部。 9)再难受又怎样,生活还要继续,现实就是这样,没有半点留情,你不争就得输, 10)生活、像一把无情刻刀，改变了我们模样，未曾绽放就要枯萎吗，我有过梦想。 1)我愿和你齐飞，远走天涯，过属于我们自己的幸福生活 2)不知你是我敌友已没法望透被推着走跟着生活流来年陌生的是昨日最亲的某某。 3)-如今从容面对生活的人，却多是受过伤的人。 4)生活如此多娇
5)生活有进有退，输什么也不能输了心情. 6)其实我很想像爱情公寓那样和几个最要好的朋友生活在一栋房子里，有说有笑。 7)上天安排某个人进入你的生活是有原因的，让他消失是有理由的。? 8)好的生活就是不瞎想，做得多，要得少，常微笑，懂知足。 9)每天吃一颗糖然后告诉自己今天的生活又是甜的 10)对生命最佳的回应，是生活得很快乐 1)听说你在我背后乱嚼舌根是吧挑拨离间是吧你很讨厌我是吧亲爱的你好可怜生活没我精彩嫉妒了是吧 2)总有一个人一直住在我心里，却告别在生活里。 3)-凡事看得开，生活才能嗨。 4)自从放假后我的生活里就没有了上午 5)生活就是,,生下来活下去， 6)演出一場壹個人的童話，不必一直一路等候他，没戀愛出現不用生活嗎?無緣騎上白馬我自行回家。 7)我从没被谁知道，所以也没被谁忘记。在别人的回忆中生活，并不是我的目的 8)幸福是什么?幸福就是我和我爱的人快快乐乐的生活。 9)从此以后，各自天涯，彼此不再纠缠，生活于是归于平淡。 10)我不爱生活我没有那么假; 11)既然无法挽回，那就付诸一笑，生活就是要乐观一点! 12)现在的生活并不是我想要的,但确实是我自找的,所以活该,我认了
回家的空间说说心情短语 离家的路有千万条，回家的路只有一条。想知道更多关于回家的空间说说吗?今天在这里分享一些回家的空间说说心情短语，希望大家喜欢。 回家的空间说说心情短语【精选篇】1.回老家的，每年最痛苦了，今年又大着肚子，尤其要困难。 2.回家的感觉真好!但在路途中真累! 3.在车上想着母亲现在可都会忙些什么农活，想着一回去就可以吃好多的东西。其实，我在城里随便可以买到，只是偏爱家里的好吃。现在想想那些游子思家之心，在异乡的思家情缘了。家，想你了。 4.想家多了。特别是周末，想着想着就有股冲动要回家看看。果不其然，化冲动为行动。上完课后就马上搭车回家。 5.每每想家心切之时，便大有舍弃人生一切的勇气。那种想家的心情就宛如街头遇雨时，偶得雨伞，雨过天晴，则随手一放，跟天边的彩虹一般，转眼便消失得无影无踪。 6.家是什么，家，是一间房一盏灯一张柔软的床。有了房，不再担心风吹和雨打，有了灯，不再害怕夜晚没有星星和月亮，有了床，累了困了可以睡上甜甜的觉做个美美的梦。家是什么，家是一轮太阳，爸爸妈妈欢乐的笑容，合成一缕温暖的阳光。 7.让我时时魂牵梦绕的家乡，其实是一个风景秀美的小山村，山
村四周连绵起伏的山峦手挽手呵护着这里的人们，如同一个慈祥的母亲深情的凝视着怀中的孩子。多少次趟过记忆的长河，多少回穿越时空的邃道，跋山涉水，梦回这山清水秀的故乡。 8.真想有个随意门，开门就到家了。 9.有钱没钱(有分没分)回家过年~ 10.欣喜，激动，还是有点无措。。 回家的空间说说心情短语【经典篇】1.想回又不想回... 2.我傻傻的望着车窗，脑中却是家的投影! 3.离家的距离一点点近了，心也一点点活了过来。 4.来两斤幸福，拿回家 5.君自故乡来。应知故乡事。 6.家是身后的山牵着思念的线。家里有爱让我永远享不完。 7.家就在眼前，而家人在哪里? 8.家，是每一个人脚步最终的落脚点。 9.回家是固执的守候。 10.回家的路很远、很累，但是很踏实。 11.回家的感觉，真好! 12.回家啊，你的名字叫做执着! 13.回家、回家，过年回家! 14.好开心、放假回家过年咯 15.归心似箭。 16.该如何回家，这幅模样。。。。
放假搞笑说说经典句子,幽默放假说说心情短语 导读：1、“放假你快乐吗？”“只有快，没有乐。” 2、留几年的长发五分钟就剪完，学几年的知识一放假就忘光。 3、所谓放假就是，家里遭嫌，出门没钱，每天特闲。 4、“关闭放假模式，正式开启学霸模式！”“对不起，您的配置太低，无法启动该功能” 5、讨厌放假、作业多那是借口、只是因为不能再每天看见你。这你都不懂吗。 6、放假靠祖宗，停课靠台风。 7、所谓放假就是在家挨骂，出门没钱，一天特闲。 8、“放假了，是否激动？”“恩，可作业会让你更激动！” 9、对我们来说，放假就是换了个地方写作业。 10、放假了才发现，只有爱你的人才会和你保持联系。 11、“感觉自己和放假之前一样轻盈啊”“说人话”“作业没写” 12、放假以后，学神在刷难题，学霸在刷作业，学渣在刷动态。 13、放假了，又想上学；开学了，又想放假；有木有？ 14、我对放假的概念就是，我的充电器从来没闲过。 15、中国的放假原则，欠了的终归是要还的！ 16、放假没意思想上学,上学太痛苦想放假，尼玛太纠结。 17、中国的放假告诉了我一个道理，欠了的总是要还的！ 18、这年头，手上没有几十张试卷都不好意思跟别人说学校放假。
19、哎，放完假后又该开学了 20、放假在家每天必做三件事 21、放假再无聊，我也不愿上学；就像爱你再无助，我也不愿放手。 22、作业加载失败，请学校重新放假。 23、放假有什么好的，还不是一个人过，而且还见不到最想见到的人。 24、从前有群人一起放假，现在这群人放假的时间都不一样了。 25、这年头，放假真不容易，清明节放假还是沾老祖宗的光。 26、读书的时候觉得不怎么擅长学习，放假以后发现原来玩也不太在行。 27、上课是为了下课，上学是为了放假。没有这么伟大的心念支持着，都不敢想象我是怎么有勇气来学校。 28、放假的意义就在于，一个说不起就不起的早晨，一个说不睡就不睡的深夜和一个说不出门就不出门的白天。 29、现在的放假，暑假放得和寒假一样，寒假放得和国庆一样，国庆放得和五一一样，五一放得和周末一样，周末放得和没放一样，总结，放假就跟放屁一样。 30、你若军训，便是晴天；你若放假，便是雨天；你若发奋写作业，便是开学前一天。 31、放假时，我醒了，不代表我起床了；上学时，我起床了，不
放假说说心情短语 1、我真是个花心的人，暑假刚走了我就想着寒假。 2、一个完整的夏天=西瓜+空调+可乐+满格WIFI+没有暑假作业！ 3、暑期新玩法：带着空调遥控器上街，看哪家店铺不爽就给他改成制热，反正遥控器都一样。 4、最鄙视那些一放假就出去玩的人，我只想送给他们四个字：请带上我。 5、查个分比表白还紧张查完了比失恋还难过！ 6、三年前，我们谁都不懂谁，走进了同一教室。三年后，谁都了解谁，各奔东西。 7、暑假作业写完请按写了一半请按写了一点请按一点没写请按 8、“我的诺基亚碎了。”“怎么可能？”“我不小心把它放寒假作业下面了。” 9、你若军训，便是晴天，你若放假，便是作业连连。 10、“寒假为什么比暑假短？”“热胀冷缩啊！”“那为什么寒假作业和暑假作业一样多？”“质量不变嘛！” 11、暑假来了，唐僧师徒四人不禁吐槽到：艾玛，暑假又到了，又要去西天取一次经。 12、他们问我烟盒上的“吸烟有害健康”是真的吗？我果断回答了他们，这好比我们的寒假作业上的“快乐寒假”。 13、中国的放假告诉了我一个道理，欠了的总是要还的！ 14、放假有什么好的，还不是一个人过，而且还见不到最想见到的人。 15、对不起，作业先森。我们不合适、我爱的只有他——寒假先森。 16、“暑假过完了，说明了什么？”“要开学了啊”“错，说明寒假要来了啊”。 17、上课时只知道星期几不知道日期，放假时只知道日期不知道星期几。 18、哎，放完假后又该开学了。 19、你存在，我昨天的熬夜里，我的夜里，我的梦里，我的通宵里。再见，我的暑假。 20、老师我不想写作业，那样一点都不酷。 21、放假开学前一天晚上，我国用电量将直线上升。 22、放假就是，早上起不来，晚上睡不着（next88），夜猫子模式已启动。 23、我最爱的寒假和我最恨的学校生了个娃，叫作业，还要我来养它，唉。 24、与暑假先森约会的时候，总会出现一个叫作业的小三。 25、中国的放假原则——欠了的终归是要还的！ 26、有些老师真是过瘾，我抄作业，她说我抄别人作业干什么？还不如空着.我空着作业交上去，她说我空着还交上来。 27、这年头，放假真不容易，清明节放假还是沾老祖宗的光。 28、上学和放假的区别：上学，我起床了却没醒；放假，我醒了却没起床。 29、告诉你比鬼片还恐怖的事：你们的暑假已经过了一半啦。 30、这年头，手里没几张卷子、七八本作业，都不好意思跟人说学校放假。 31、放假再无聊，我也不愿上学；就像爱你再无助，我也不愿放手。 32、放假了，逃脱了老师严厉眼神的扫射范围。
放假回家的空间说说心情短语 本文是关于放假回家的空间说说心情短语，仅供参考，希望对您有所帮助，感谢阅读。 放假回家的说说最新 1. 你在外闯荡的一年，却是父母在家牵挂的一年;你在外拼搏的一年，却是妻儿倚门守望的一年;你在外孤独的一年，却是亲人日夜期盼团圆的一年!朋友，春节到了，别忘了回家看看! 2. 努力奔波为生活，辛苦努力来工作，收获不大成功少，期盼回家有寄托，爱在心底和心窝，旅途焦急难按捺，父母亲情家温暖，春节幸福有团圆，愿你旅途多顺利，万事开心如意。 3. 收拾一下幸福的鞋带，整理一下开心的装备，盘点一下年度的收入，高兴一下回家的喜悦，现在你美了吧，赶快踏上如意的列车，唱起平安的歌谣，躺在温柔的靠椅，看看这可爱的祝福吧!祝你旅途进入温柔的梦乡，梦见我哦! 4. 此时此刻，所有念想都流向故乡，路口上等候着亲人藏了一年的盼望，火炉边积蓄了荒了一年的家常。春节将至，这些思念在无节制疯长，恨不得插上翅膀早点飞翔，归乡与家人欢聚一堂，让我的祝福伴随你一路平平安安，欢快返乡! 5. 抖一抖，奋斗的疲劳，拍一拍，奔波的尘埃，整一整，漂泊的行李，笑一笑，丰收的劳作，微笑的登上幸福的列车，希望在招手，亲人在招手，爱人在期盼，我在想念你，祝你旅途平安顺利! 6. 故乡的月-分外明，归家的心-急似箭，旅途的车-极速跑，家中的人-格外亲。家中的一切最诱人，合家团圆最兴奋。春节归家心切，愿你一路顺风，事事顺心。 7. 本想送你个“鸭梨”，怕你遭罪;还想送你个“杯具”，怕你太脆;又想送你片“浮云”，怕你崩溃;别妄想我送你个“苹果”啊，我嫌太贵。呵呵，只能送你一条短信，祝你旅途愉快，不要太累。不要嫌我小气哦! 8. 小蒋过年坐回家，买不到火车票，于是偷偷的溜进了火车站，被一巡警拦下：“鬼鬼祟祟的干什么?叫什么名字?”“讲英语。”小蒋答。“什么名字?”巡
放假说说心情短语 [标签:栏目] ，放假说说心情短语 1、我有一个技能，可以在两天内写完暑假作业，可这TM居然是个被动技能，要到最后两天才会触发。 2、作业快到火里来，你才到火里去，就不能找个大一点的火吗，作业这么多怎么烧的完。 3、查个分比表白还紧张查完了比失恋还难过！ 4、我的灵魂和身体已不在一起去，灵魂早已到了家！ 5、放假开学前一天晚上，我国用电量将直线上升。 6、“你觉得作业是个什么样的人？”“是个破坏别人寒假的人！” 7、老师一点也不酷，一点儿也不给力，还布置那么多作业。 8、这年头，放假真不容易，清明节放假还是沾老祖宗的光。 9、与寒假先森约会的时候，总会出现一个叫寒假作业的**。 10、放假了才发现，只有爱你的人才会和你保持联系。 11、我最爱的寒假和我最恨的学校生了个娃，叫作业，还要我来养它，唉。 12、三个人的友情，总有一个是被冷落的。 13、我和寒假分手了，都是因为开学那贱人。 14、暑假作业写完请按写了一半请按写了一点请按一点没写请按 15、现在担心的不应该是你的寒假作业吗？ 16、放假时，我醒了，不代表我起床了；上学时，我起床了，不代表我醒了。 17、放假以后，学神在刷难题，学霸在刷作业，学渣在刷动态。 18、五一假期，鲜花献给辛勤的劳动人民。 19、放假就像谈恋爱：憧憬它的到来令人兴奋不已，拥有它时觉得不过如此，等它结束了又会勾起无限怀念。 20、暑假真的很短，在两次大姨妈中就没有了。 21、中国的放假原则——欠了的终归是要还的！ 22、暑期新玩法：带着空调遥控器上街，看哪家店铺不爽就给他改成制热，反正遥控器都一样。
23、“我的诺基亚碎了。”“怎么可能？”“我不小心把它放寒假作业下面了。” 24、所谓放假就是在家挨骂，出门没钱，一天特闲。 25、与暑假先森约会的时候，总会出现一个叫作业的**。 26、从上学到放假，从校服到睡衣，从课本到漫画，从马尾到披头散发，这才是学生。 27、要是明天就放假，我就回去吧我家的猪痛亲一顿。 28、我和暑假相爱了，可我的情敌暑假作业一直困扰着我，我的岳母开学也不喜欢我，暑假也想和我分手，我好伤心。 29、都在改变只能沉默只能向前前往成熟大人世界。 30、“假期是超越对手最好的时机”“尼玛，我从不做这种偷偷摸摸的事……” 31、男生见过女生放假在家的样子还喜欢那一定是真爱。 32、每个人身边都需要一个，出去玩当借口的人，家长听了肯定放心的人。 33、放假了，逃脱了老师严厉眼神的扫射范围。 34、他们问我烟盒上的“吸烟有害健康”是真的吗？我果断回答了他们，这好比我们的寒假作业上的“快乐寒假”。 35、本来有种要把寒假作业一口气写完的冲动，还好我自制力强。 36、暑假到，快乐绕，学习缓，压力抛，烦恼弃，心开朗，阳光照，欢乐笑，祝福你，好运来，幸福罩，健康随，乐逍遥！ 37、上课时只知道星期几不知道日期，放假时只知道日期不知道星期几。 38、“寒假为什么比暑假短？”“热胀冷缩啊！”“那为什么寒假作业和暑假作业一样多？”“质量不变嘛！” 39、放假再无聊，我也不愿上学；就像爱你再无助，我也不愿放手。 40、最鄙视那些一放假就出去玩的人，我只想送给他们四个字：请带上我。 41、你若军训，便是晴天，你若放假，便是作业连连。 42、我真是个花心的人，暑假刚走了我就想着寒假。 43、这年头，手里没几张卷子、七八本作业，都不好意思跟人说学校放假。 44、放假就是，早上起不来，晚上睡不着，夜猫子模式已启动。 45、躺在床上玩手机，一想到放假了好久了还没有碰过书，我就啪的抽了自