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A wide class of microscopic car-following traffic models deals with a system of ODEs describing N cars driving on a circular highway. The symmetry of the road naturally leads to (quasi-)stationary solutions and to an analysis of their stability. Breaking this symmetry with small perturbations we show the existence of a branch of some special solutions that occur instead of the stationary points. Those solutions can be interpreted in reality, they describe the behavior of the cars on the road as expected. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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玻璃划分的数学模型 总被引:2,自引:0,他引:2
鲁习文 《应用数学与计算数学学报》1999,13(2):47-54
本文讨论了玻璃合理划分问题,建立了玻璃划分的数学模型.该模型既使得坯料用量最优,也考虑了余料尽可能少,同时划分得到的各种规格的成品玻璃尽可能刚好满足需要,数值计算结果表明该模型是有效和合理的. 相似文献
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In this paper, we study the evolution equation derived by Xu and Xiang (SIAM J Appl Math 69(5):1393–1414, 2009) to describe heteroepitaxial growth in \(2+1\) dimensions with elastic forces on vicinal surfaces is in the radial case and uniform mobility. This equation is strongly nonlinear and contains two elliptic integrals and defined via Cauchy principal value. We will first derive a formally equivalent parabolic evolution equation (i.e., full equivalence when sufficient regularity is assumed), and the main aim is to prove existence, uniqueness and regularity of strong solutions. We will extensively use techniques from the theory of evolution equations governed by maximal monotone operators in Banach spaces. 相似文献
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Ryzhov V. N. Tareyeva E. E. Schelkacheva T. I. Chtchelkatchev N. M. 《Theoretical and Mathematical Physics》2004,141(1):1443-1451
Using the classical distribution-function approach to simple liquids, we estimate the orientational interaction between clusters consisting of a particle and its nearest neighbors. We show that there are density and temperature ranges where the interaction changes sign as a function of the cluster radius. On this basis, the corresponding model of interacting cubic and icosahedral clusters (of the type of a spin glass model) is proposed and solved in the replica-symmetric approximation. We show that the glass order parameter grows continuously on cooling and the replica-symmetry-breaking temperature can be identified with the glass transition temperature. We also show that on cooling a system of particles with a Lennard-Jones interaction, cubic clusters freeze first. The transition temperature for icosahedral clusters is somewhat lower; therefore, the cubic structure of the short-range order is more likely in a Lennard-Jones glass near transition. 相似文献
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We provide an explicit necessary condition to have that no extremal for the best constant in the Caffarelli-Kohn-Nirenberg inequality is radially symmetric. 相似文献
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We consider the procedure for analytic continuation of the replica matrix. We formulate a particular form of this procedure
in which the analytic continuation is defined by a sequence of maps. Using this definition, we construct a solution that breaks
the Parisi replica symmetry and find the corresponding p-adic pseudodifferential operator.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 336–341, August, 2005 相似文献
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G. Sartori 《Acta Appl Math》2002,70(1-3):183-207
Functions which are covariant or invariant under the transformations of a reductive linear algebraic group can be advantageously expressed in terms of functions defined in the orbit space of the group, i.e. as functions of a finite set of basic invariant polynomials. This fact and the tools of geometric invariant theory can be exploited in many physical contexts where the study of covariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry and/or supersymmetry breaking in possibly supersymmetric quantum field theories of elementary particles, in the analysis of phase spaces and structural phase transitions in solid state physics (Landau's theory), in covariant bifurcation theory, in crystal field theory and in most areas of solid state theory where use is made of symmetry adapted functions. We shall present some elements of geometric invariant theory and illustrate some of the possible applications in the study of spontaneous symmetry and supersymmetry breaking. 相似文献
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E. E. Tareyeva T. I. Schelkacheva N. M. Chtchelkatchev 《Theoretical and Mathematical Physics》2008,155(2):812-823
We propose a model for describing the low-temperature transition to the orientational glass state in solid molecular C60 in the framework of a theory similar to spin glass theory. We find a replica symmetric solution and also break the replica
symmetry. The obtained results agree with experimental data on the partial retention of the orientational long-range order
in the glass phase and on the presence of a broad maximum on the curve corresponding to the temperature dependence of the
orientational part of the heat capacity.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 356–368, May, 2008. 相似文献
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A 1-D model of a slab of glass of a small thickness is considered. The governing equations are those of the classical 1-D linear viscoelasticity. A load due to the temperature gradients is assumed. The aim is to model the process called annealing. It is shown that an additional load due to structural strain is crucial for the success of the model. Algorithms of a numerical solution of the governing equations are proposed. Numerical results are presented and commented. 相似文献
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SymmetryReductionsoftheCombinedKdV-mKdVEquationZhangJiefang(张解放);XuXuejun(许学军);ChengDesheng(程德声)(DepartmentofPhysics,Zhejiang... 相似文献
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q-Symmetry in Condensed Matter Physics: an Effective Generalized Hubbard Model with Quantum Symmetry
Using the generalized LangFirsov transformation, we reduce the Hubbard model with phonons (which, under particular circumstances, has recently been shown to exhibit the quantum symmetry su(2)[su(2)]q into an effective electron Hamiltonian. The effective Hamiltonian is explicitly proved to maintain the quantum symmetry, which survives even when relaxing one of the constraints on the Hamiltonian parameters that must hold in the model with phonons. We investigate under which circumstances some superconducting eigenstates of the effective Hamiltonian, which can be built thanks to the quantum symmetry, could become metastable. Bibliography: 12 titles. 相似文献
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M. G. Vasin 《Theoretical and Mathematical Physics》2006,147(2):721-728
We show that the paramagnet-spin glass transition can be described in the Edwards-Anderson model using critical-dynamics methods
and taking the ultrametric topology of the temporal space into account. In the framework of the suggested approach, we derive
the Vogel-Fulcher relation for the system relaxation time. We prove that the fluctuation-dissipation theorem holds for the
given model if there is no relaxation-time hierarchy.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 328–336, May, 2006. 相似文献
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Daniele Castorina Filomena Pacella 《Calculus of Variations and Partial Differential Equations》2005,23(2):125-138
We consider the subcritical problem
& 0 & \qquad\textrm{in} \; A\\
u & = & 0 & \qquad\textrm{on} \; \delta A\\
\end{array}
\right.$$" align="middle" border="0">
where A is an annulus in
,
,
is the critical Sobolev exponent and
0$" align="middle" border="0">
is a small parameter. We prove that solutions of (I) which concentrate at one or two points are axially symmetric.Received: 7 July 2003, Accepted: 10 May 2004, Published online: 16 July 2004Filomena Pacella: Research supported by MIUR, project Variational Methods and Nonlinear Differential Equations. 相似文献
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Zongming Guo Linfeng Mei Fangshu Wan 《NoDEA : Nonlinear Differential Equations and Applications》2016,23(6):59
We obtain non-radial bifurcation from radial solutions of a semilinear elliptic equation in expanding annuli of \(\mathbb {R}^N\). To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equation The main results of this paper can be seen as applications of the properties of regular entire solutions of (0.1).
相似文献
$$\begin{aligned} -\Delta u=\lambda u^p \quad \text {in}\quad \mathbb {R}^N. \end{aligned}$$
(0.1)
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利用动态力学分析仪,详细研究了小应力作用下聚氯乙烯(PVC)接近玻璃化转变温度(63℃)时的短期蠕变性能.根据Struik-Kohlrausch (SK)方程及Struik移位方法,分析了物理老化对PVC瞬时蠕变柔量的影响,并提出了基于多松弛机制的新模型定量描述初始蠕变柔量、松弛时间和形状因子.结果表明:SK方程虽可表征不同老化时间下PVC的蠕变性能,但通过Struik移位方法却无法获得理想的主曲线,且初始蠕变柔量、松弛时间、形状因子和蠕变率均受物理老化显著影响,并在双对数坐标下随老化时间呈明显的非线性变化;新模型不仅揭示了物理老化控制参量的演化规律,而且极好地预测了PVC在物理老化进程中的高温蠕变行为. 相似文献