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We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a…
We construct some extension ({\it Stable Field Theory}) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some vector spaces generated by spheres and disks with punctures. It is described by a formal…
Hitchin's twistor treatment of Schlesinger's equations is extended to the general isomonodromic deformation problem. It is shown that a generic linear system of ordinary differential equations with gauge group SL(n,C) on a Riemann surface X…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
In this note we consider general formulation of Euler's equations for an inviscid incompressible homogeneous fluid with an oscillating body force. Our aim is to derive the averaged equations for these flows with the help of two-timing…
In this paper we study some aspects of thermodynamic formalism, more specifically topological pressure and, as a consequence, topological entropy for piecewise smooth vector fields, using topological conjugation with shift maps and the…
We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…
We use Hodge theory and functional analysis to develop a clean approach to heat flows and Onsager's conjecture on Riemannian manifolds with boundary, where the weak solution lies in the trace-critical Besov space $B_{3,1}^{\frac{1}{3}}$. We…
We consider the problem of density estimation on Riemannian manifolds. Density estimation on manifolds has many applications in fluid-mechanics, optics and plasma physics and it appears often when dealing with angular variables (such as…
In this letter, we present the general form of equations that generate a volume-preserving flow on a symplectic manifold (M, \omega). It is shown that every volume-preserving flow has some 2-forms acting the role of the Hamiltonian…
A supersymmetric extension of the two-phase fluid flow system is formulated. A superalgebra of Lie symmetries of the supersymmetric extension of this system is computed. The classification of the one-dimensional subalgebras of this…
Hexagon relations are combinatorial or algebraic realizations of four-dimensional Pachner moves. We introduce some simple set-theoretic hexagon relations and then `quantize' them using what we call `polynomial hexagon cohomologies'. Based…
A brief introduction to Topological Quantum Field Theory as well as a description of recent progress made in the field is presented. I concentrate mainly on the connection between Chern-Simons gauge theory and Vassiliev invariants, and…
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive and absorbing dielectric medium is developed. The classical Maxwell equations with spatially…
The present paper deals with the interior solid-fluid interaction problem in harmonic regime with randomly perturbed boundaries. Analysis of the shape derivative and shape Hessian of vector- and tensor-valued functions is provided. Moments…
We interpret tensors on a smooth manifold M as differential forms over a graded commutative algebra called the algebra of iterated differential forms over M. This allows us to put standard tensor calculus in a new differentially closed…
We use covariant phase space methods to study the metric and tetrad formulations of General Relativity in a manifold with boundary and compare the results obtained in both approaches. Proving their equivalence has been a long-lasting…
In this paper, multi-component generalizations to the Camassa-Holm equation, the modified Camassa-Holm equation with cubic nonlinearity are introduced. Geometric formulations to the dual version of the Schr\"odinger equation, the complex…
A class of trigonometric integrator is proposed for the constrained ring polymer Hamiltonian dynamics, arising from the path integral molecular dynamics. The integrator is formulated by the composition of flows, thereby integrating the…