arXiv subjects

David V. Svintradze

Publications and source records attributed to David V. Svintradze.

10 recordsLinked to original sources

arXiv2026

Electromagnetic Field Equivalence from Moving Manifolds

We apply a geometric formulation of electromagnetic fields on moving manifolds to the problem of field equivalence between dynamically separated domains. Starting from the tensorially invariant equations of motion for moving hypersurfaces, we introduce an electromagnetic specialization by constructing an energy density from the electromagnetic field tensor, yielding a geometric extension of Maxwell electrodynamics. The classical Maxwell equations then emerge as a constrained geometric sector of the broader evolution system. Hence, by comparing internal and external electromagnetic configurations, we show that under isolation conditions with no interfacial current exchange, the field difference satisfies the source-free Maxwell equation. Furthermore, the equilibrium Maxwell sector establishes a direct correspondence between the Lorentz-invariant electromagnetic structure and the geometry of constant-mean-curvature manifolds. The resulting field-difference equations admit equivalence solutions generated by specific velocity sectors of the moving-manifold dynamics. We further demonstrate that the resulting field-equivalence regime is intrinsically dynamical: static curved configurations generically retain nonvanishing electromagnetic contrast through curvatureinduced contributions to the geometric pressure balance, whereas dynamically evolving manifolds admit nontrivial admissible sectors satisfying the equivalence condition. Explicit nonvacuum realizations are obtained within the tangential-flow sector of the moving-manifold system, while bounded static Euclidean configurations are generically excluded.

cond-mat.stat-mech↗

arXiv2026

Geometric Foundations of Stochastic and Quantum Dynamics

We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally imposed randomness. Within the theory of moving manifolds, we establish a curvature-noise correspondence: fluctuations are governed by the inverse curvature tensor, while entropy production is controlled by curvature deformation. The invariant continuity law on a moving hypersurface yields a geometric Fokker-Planck equation, and curvature-velocity coupling generates a quadratic Onsager-Machlup functional determining path weights. The resulting entropy functional satisfies a curvature-driven monotonicity law, providing a geometric derivation of the Second Law. In two dimensions, the curvature invariant reduces to Gaussian curvature and encodes topology, so topological transitions produce discrete entropy jumps. When the ambient space carries a Minkowskian signature, the same curvature-kinetic quadratic form that generates dissipative thermal weights produces oscillatory phase weights, and the Laplace-Beltrami operator governing entropy evolution acquires a Schrödinger-type structure. This provides a geometric resolution of the apparent distinction between classical stochastic behaviour and quantum dynamics. These results show that stochastic behaviour, thermodynamic irreversibility, and quantum transition amplitudes are unified within the moving manifold framework. Geometry does not merely accommodate stochasticity; stochastic behaviour arises as a consequence of deterministic geometric evolution. The theory predicts curvature-controlled anisotropic diffusion, entropy jumps at topology-changing events, and a geometric thermal-quantum crossover in which classical stochastic weights and quantum amplitudes are generated by the same curvature-kinetic action.

cond-mat.stat-mech↗

arXiv2025

Moving Manifolds and the Poincare Conjecture

We present a differential geometric formulation of the Poincare problem using the calculus of moving surfaces (CMS). In this framework, an n dimensional compact hypersurface evolves under a velocity field that couples motion to the extrinsic curvature tensor while preserving topology through smooth diffeomorphic flow. A variational energy principle identifies constant mean curvature (CMC) manifolds as the unique stationary equilibria of CMS dynamics. Consequently, the evolution of any compact simply connected hypersurface relaxes to a CMC equilibrium and, in the isotropic case, to the round sphere. Unlike Ricci flow approaches, which are dimension restricted and require topological surgery, the CMS formulation holds for all dimensions and preserves manifold topology for all time. This provides a deterministic geometric mechanical route to the Poincare conclusion, unifying dynamics, topology, and equilibrium geometry within a single analytic framework.

math.DG↗

arXiv2024

Moving Manifolds and General Relativity

We revise general relativity (GR) from the perspective of calculus for moving surfaces (CMS). While GR is intrinsically constructed in pseudo-Riemannian geometry, a complete understanding of moving manifolds requires embedding in a higher dimension. It can only be defined by extrinsic Gaussian differential geometry and its extension to moving surfaces, known as CMS. Following the recent developments in CMS, we present a new derivation for the Einstein field equation and demonstrate the fundamental limitations of GR. Explicitly, we show that GR is an approximation of moving manifold equations and only stands for dominantly compressible space-time. While GR, with a cosmological constant, predicts an expanding universe, CMS shows fluctuation between inflation and collapse. We also show that the specific solution to GR with cosmological constant is constant mean curvature shapes. In the end, by presenting calculations for incompressible but deforming two-dimensional spheres, we indicate that material points moving with constant spherical velocities move like waves, strongly suggesting a resolution of the wave-corpuscular dualism problem.

gr-qc↗

arXiv2024

Manifold Solutions to Navier-Stokes Equations

We have developed dynamic manifold solutions for the Navier-Stokes equations using an extension of differential geometry called the calculus for moving surfaces. Specifically, we have shown that the geometric solutions to the Navier-Stokes equations can take the form of fluctuating spheres, constant mean curvature surfaces, generic wave equations for compressible systems, and arbitrarily curved shapes for incompressible systems in various scenarios. These solutions apply to predominantly incompressible and compressible systems for the equations in any dimension, while the remaining cases are yet to be solved. We have demonstrated that for incompressible Navier-Stokes equations, geometric solutions are always bound by the curvature tensor of the closed smooth manifold for every smooth velocity field. As a result, solutions always converge for systems with constant volumes.

math.AP↗

arXiv2019

Generalization of the Kelvin Equation for Arbitrarily Curved Surfaces

Capillary condensation, which takes place in confined geometries, is the first-order vapor-to-liquid phase transition and is explained by the Kelvin equation, but the equations applicability for arbitrarily curved surface has been long debated and is a sever problem. Recently, we have proposed generic dynamic equations for moving surfaces. Application of the equations to static shapes and modelling the pressure at the interface nearly trivially solves the generalization problem for the Kelvin equation. The equations are universally true for any surfaces: atomic, molecular, micro or macro scale, real or virtual, Riemannian or pseudo-Riemannian, active or passive.

physics.chem-ph↗

arXiv2018

Shape Dynamics of Freely Falling Droplets

Oscillating shape motion of a freely falling water droplet has long fascinated and inspired scientists. We propose dynamic non-linear equations for closed, two dimensional surfaces in gravity and apply it to analyze shape dynamics of freely falling water drops. The analytic solutions qualitatively well explain why drops oscillate among prolate/oblate morphologies and display a number of features consistent with experiments.

physics.flu-dyn↗

arXiv2018

Closed, Two Dimensional Surface Dynamics

We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in normal direction indicates that any closed, two dimensional, homogeneous surface with time invariable surface energy density adopts constant mean curvature shape when it comes in equilibrium with environment. As an example, we apply the formalism to analyze equilibrium shapes of micelles and explain why they adopt spherical, lamellar and cylindrical shapes. We show that theoretical calculation for micellar optimal radius is in good agreement with all atom simulations and experiments.

physics.bio-ph↗

arXiv2016

Moving Manifolds in Electromagnetic Fields

We propose dynamic non-linear equations for moving surfaces in electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary, can be written as an addition of four-potential times four-current to a contraction of electromagnetic tensor. Proper application of minimal action principle to the system Lagrangian yields dynamic non-linear equations for moving three dimensional manifolds in electromagnetic fields. The equations, in different conditions simplify to Maxwell equations for massless three surfaces, to Euler equations for dynamic fluid, to magneto-hydrodynamic equations and to Poisson-Boltzmann equation. To illustrate effectiveness of the equations of motion we apply the formalism to analyze dynamics of macro-molecules and membranes.

cond-mat.soft↗

arXiv2016

Micelles Hydrodynamics

A micelle consists of monolayer of lipid molecules containing hydrophilic head and hydrophobic tail. These amphiphilic molecules in aqueous environment aggregate spontaneously into monomolecular layer held together due to hydrophobic effect by weak non-covalent forces. Micelles are flexible surfaces that show variety of shapes of different topology, but remarkably in mechanical equilibrium conditions they are spherical in shape. The shape and size of a micelle are functions of many variables such as lipid concentration, temperature, ionic strength, etc. Addressing the question, why the shape of micelles is sphere in mechanical equilibrium conditions, analytically proved to be a difficult problem. In the following paper we offer the shortest and elegant analytical proof of micelles spheroidal nature when they are thermodynamically equilibrated with solvent. The formalism presented in this paper can be readily extended to any homogenous surfaces, such are vesicles and membranes.

physics.bio-ph↗