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Theoretical and Mathematical Physics - We study bound states in an s-wave superconducting strip on the surface of a topological superconductor with the perpendicular Zeeman field. We prove...  相似文献   

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Theoretical and Mathematical Physics - Using the Bogoliubov–de Gennes Hamiltonian, we analytically study two models with superconducting order, the p-wave model with an impurity potential and...  相似文献   

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By introducing a curled fifth dimension, Kaluza–Klein theory predicted for the first time a connection between gravity and electromagnetism. An exacting look at this result shows that for a radius R of the fifth dimension equal to the Planck length, the coupling is exactly unity. The result is utilized to show that by introducing correction terms to the one loop renormalization equation of unification it can be made exact and subsequently quark confinement can be proven non-perturbatively as a property of the topology of quantum spacetime at the classical-quantum interface and the Planck phase transition.  相似文献   

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In this article we study the existence and profile of high-energy solutions for the phase transition model
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Phase field methods are a widely accepted tool for the approximation of moving free interfaces in sharp interface problems. Topological changes in the solution, such as nucleation or vanishing of particles or merging or pinching of interfaces, lead to singularities in the free boundary. In the sharp interface model, these singularities cause both numerical and theoretical problems, whereas they are handled “automatically” in phase field simulations. Phase field models contain a length scale ε > 0 that vanishes in the sharp interface limit. Therefore, when ε → 0, practical numerical methods have to be robust in the sense that error estimates may only depend polynomially on ε-1, not exponentially. We show that robust error control is possible past the occurrence of topological changes and without restrictive assumptions on the initial data. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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The mountain-pass theorem guarantees the existence of a critical point on a path that connects two points separated by a sufficiently high barrier. We propose the elastic string algorithm for computing mountain passes in finite-dimensional problems and analyze the convergence properties and numerical performance of this algorithm for benchmark problems in chemistry and discretizations of infinite-dimensional variational problems. We show that any limit point of the elastic string algorithm is a path that crosses a critical point at which the Hessian matrix is not positive definite.This work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng-38.  相似文献   

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In this article, we study the dynamics of transition layers for a system of 1D non-linear thermoviscoelasticity with non-monotone stress–strain relation.  相似文献   

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Let c be a constant and (e1,f1),(e2,f2),…,(ecn,fcn) be a sequence of ordered pairs of edges from the complete graph Kn chosen uniformly and independently at random. We prove that there exists a constant c2 such that if c > c2, then whp every graph which contains at least one edge from each ordered pair (ei,fi) has a component of size Ω(n), and, if c < c2, then whp there is a graph containing at least one edge from each pair that has no component with more than O(n1?? vertices, where ? is a constant that depends on c2 ? c. The constant c2 is roughly 0.97677. © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2006  相似文献   

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Summary We consider a particular Markov process t u on S ,S= n . The random variable t u (x) is interpreted as the number of particles atx at timet. The initial distribution of this process is a translation invariant measure withf(x)d<. The evolution is as follows: At rateb(x) a particle is born atx but moves instantaneously toy chosen with probabilityq(x, y). All particles at a site die at ratepd withp[0, 1],d, + and individual particles die independently from each other at rate (1–p)d. Every particle moves independently of everything else according to a continuous time random walk.We are mainly interested in the caseb=d andn3. The process exhibits a phase transition with respect to the parameterp: Forp<p * all weak limit points of ( t µ ) ast still have particle density (x)d. Forp>p *, t µ ) converges ast to the measure concentrated on the configuration identically 0. We calculatep * as well asp (n) , the points with the property that the extremal invariant measures have forp>p (n) infiniten-th moment of (x) and forp<p (n) finiten-th moment. We show the case 1>p *>p(2)>p(3)...p (n) >0, p(n)0 occurs for suitable values of the other parameters. Forp<p (2) we prove the system has a one parameter set of extremal invariant measures and we determine their domain of attraction. Part I contains statements of all results but only the proofs of the results about the process for values ofp withp<p (2) and the behaviour of then-th moments andp (n) .  相似文献   

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We prove that in various natural models of a random quotient of a group, depending on a density parameter, for each hyperbolic group there is some critical density under which a random quotient is still hyperbolic with high probability, whereas above this critical value a random quotient is very probably trivial. We give explicit characterizations of these critical densities for the various models.  相似文献   

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An Allen–Cahn phase transition model with a periodic nonautonomous term is presented for which an infinite number of transition states is shown to exist. A constrained minimization argument and the analysis of a limit problem are employed to get states having a finite number of transitions. A priori bounds and an approximation procedure give the general case. Decay properties are also studied and a sharp transition result with an arbitrary interface is proved.  相似文献   

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Suppose thatL is a second order elliptic differential operator on a manifoldM, B is a vector field, andV is a continuous function. The paper studies by probabilistic and dynamical systems means the behavior asɛ → 0 of the principal eigenvalueλ ε (V) for the operatorL ε = ɛL + (B, ∇) +V considered on a compact manifold or in a bounded domain with zero boundary conditions. Under certain hyperbolicity conditions on invariant sets of the dynamical system generated by the vector fieldB the limit asɛ → 0 of this principal eigenvalue turns out to be the topological pressure for some function. This gives a natural transition asɛ → 0 from Donsker-Varadhan’s variational formula for principal eigenvalues to the variational principle for the topological pressure and unifies previously separate results on random perturbations of dynamical systems. This work was supported by US-Israel Binational Science Foundation.  相似文献   

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We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behavior of the shattering times, defined as the first instants when all the blocks of the partition process have cardinality less than a fixed integer. Our results may be applied to the study of certain random split trees. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 247‐274, 2011  相似文献   

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A simple method based on generalized coherent states is proposed for calculation of Berry's phase. In this paper we calculate Berry's phase for a translated oscillator in standard coherent states as well as Berry's phase in squeezed states and spin coherent states, i.e., coherent states for the SU(1, 1) and SU(2) groups, respectively.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 51–59, 1988.  相似文献   

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