相关论文: Solutions of matrix models in the DIII generator e…
We calculate the free energy of the disordered urn model using the law of large numbers. It is revealed that the saddle point equation obtained by the usage of the law of large numbers is the same as that obtained by the replica method.…
In this paper a unifying energy-based approach is provided to the modeling and stability analysis of power systems coupled with market dynamics. We consider a standard model of the power network with a third-order model for the synchronous…
We propose an improved iterative scheme for calculating higher genus contributions to the multi-loop (or multi-point) correlators and the partition function of the hermitian one matrix model. We present explicit results up to genus two. We…
We write down and solve a closed set of Schwinger-Dyson equations for the two-matrix model in the large $N$ limit. Our elementary method yields exact solutions for correlation functions involving angular degrees of freedom whose calculation…
Diffusion models achieve state-of-the-art image quality. However, sampling is costly at inference time because it requires a large number of function evaluations (NFEs). To reduce NFEs, classical ODE numerical methods have been adopted.…
A unified classification framework for models of extended plasticity is presented. The models include well known micromorphic and strain gradient plasticity formulations. A unified treatment is possible due to the representation of strain…
The superintegrability, wavefunctions and overlap coefficients of the Dunkl oscillator model in the plane were considered in the first part. Here finite-dimensional representations of the symmetry algebra of the system, called the…
For the SU(N) invariant supersymmetric matrix model related to membranes in 4 space-time dimensions, the general solution to the equation(s) $Q^{\dagger}\Psi=0$ $(Q\chi =0)$ is determined for N odd. For any such (bosonic) solution of…
In this paper, we design and analyze second order positive and free energy satisfying schemes for solving diffusion equations with interaction potentials. The semi-discrete scheme is shown to conserve mass, preserve solution positivity, and…
We obtain a {\it complete set} of one-loop RGE's for a set of combinations of neutrino parameters for the case of two-fold degenerate hierarchical three-neutrino models. The requirement of consistency of exact solutions to these RGE's with…
In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer melts with a dominant phase. The model is simple enough to be amenable not only to numerics but also to analysis, yet sophisticated enough to…
We present examples and diagrams illustrating the proofs appearing in "Real second-order freeness and the asymptotic real second-order freeness of several real matrix models", to which this paper is meant to be an appendix. We show how…
Using matrix-model methods we study three different N=2 models: U(N) x U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find…
We summarize our recent results on the large N renormalization group (RG) approach to matrix models for discretized two-dimensional quantum gravity. We derive exact RG equations by solving the reparametrization identities, which reduce…
A hermitian one-matrix model with an even quartic potential exhibits a third-order phase transition when the cuts of the matrix model curve coalesce. We use the known solutions of this matrix model to compute effective superpotentials of an…
Random matrix models based on an integral over supermatrices are proposed as a natural extension of bosonic matrix models. The subtle nature of superspace integration allows these models to have very different properties from the analogous…
We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution…
An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large…
In the supersymmetric SO(10) models, the doublet-triplet splitting problem can be solved through the Dimopoulos-Wilczek mechanism. This mechanism is extended in the non-renormalizable version. Improvement on the realistic model is also…
Symmetry in differential equations reveals invariances and offers a powerful means to reduce model complexity. Lie group analysis characterizes these symmetries through infinitesimal generators, which provide a local, linear criterion for…