Related papers: Approximation of potential function in the problem…
A dynamical generalisation of the nonlocal coherent-potential approximation is derived based upon the functional integral approach to the interacting electron problem. The free energy is proven to be variational with respect to the…
Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple…
We project the Wilson/Polchinski renormalization group equation onto its uniform external field dependent effective free energy and connected Green's functions. The result is a hierarchy of equations which admits a choice of "natural"…
By means of an effective potential associated to a constrained equilibrium measure and apt to study frozen systems, we investigate glassy freezing in simple liquids in the hypernetted chain (HNC) approximation. Differently from other…
We investigate a novel stochastic technique for the global optimization of complex potential energy surfaces (PES) that avoids the freezing problem of simulated annealing by allowing the dynamical process to tunnel energetically…
We consider the one-dimensional diffusion of a particle on a semi-infinite line and in a piecewise linear random potential. We first present a new formalism which yields an analytical expression for the Green function of the Fokker-Planck…
This paper proposes a robust approximation method for solving chance constrained optimization (CCO) of polynomials. Assume the CCO is defined with an individual chance constraint that is affine in the decision variables. We construct a…
We study the escape rate for the Farey map, an infinite measure preserving system, with a hole including the indifferent fixed point. Due to the ergodic properties of the map, the standard theoretical approaches to this problem cannot be…
Cold-atom experiments which measure Fermi-gas properties near unitarity confine fermionic atoms to a region of space using trapping potentials of various shapes. The presence of a trapping potential introduces a new characteristic physical…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
We show that efficient norm-conserving pseudopotentials for electronic structure calculations can be obtained from a polynomial Ansatz for the potential. Our pseudopotential is a polynomial of degree ten in the radial variable and fulfills…
We study periodic solutions of a one-degree of freedom micro-electro-mechanical system (MEMS) with a parallel-plate capacitor under $T$--periodic electrostatic forcing. We obtain analytical results concerning the existence of $T-$ periodic…
We demonstrate how an iterative method for potential inversion from distribution functions developed for simple liquid systems can be generalized to polymer systems. It uses the differences in the potentials of mean force between the…
Approximating the partition function of the ferromagnetic Ising model with general external fields is known to be #BIS-hard in the worst case, even for bounded-degree graphs, and it is widely believed that no polynomial-time approximation…
In undergraduate classes, the potential flow that goes around a circular cylinder is designed for complemental understanding of mathematical technique to handle the Laplace equation with Neumann boundary conditions and the physical concept…
Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…
The ideal Penning trap consists of a uniform magnetic field and an electrostatic quadrupole potential. In the classical low-energy limit, the three characteristic eigenfrequencies of a charged particle trapped in this configuration do not…
A test on the numerical accuracy of the semiclassical approximation as a function of the principal quantum number has been performed for the Pullen--Edmonds model, a two--dimensional, non--integrable, scaling invariant perturbation of the…
The AAA algorithm has become a popular tool for data-driven rational approximation of single variable functions, such as transfer functions of a linear dynamical system. In the setting of parametric dynamical systems appearing in many…
This work considers the infinite-time discounted optimal control problem for continuous time input-affine polynomial dynamical systems subject to polynomial state and box input constraints. We propose a sequence of sum-of-squares (SOS)…