arXiv subjects

Sergii V. Siryk

Publications and source records attributed to Sergii V. Siryk.

6 recordsLinked to original sources

arXiv2026

Some Unexplored Topics in The Reconstruction of Scalar Parameters of Subdiffusion

In the paper, we discuss the reconstruction of scalar parameters in a linear diffusion equation with fractional in time differential operators and with additional nonlocal (convolution) terms, which incorporate memory effects in models. Although, under suitable assumptions on the data, inverse problems associated with recovery of these parameters are nowadays well understood, several important questions related with numerical reconstructions of these parameters via a nonlocal observation in a small time interval have not yet been analyzed. This paper aims to provide some answers.

math.AP↗

arXiv2025

Many interacting particles in solution. I. Screening-ranged expansions of electrostatic potential and energy

We present an analytical many-body formalism for systems of spherical particles carrying arbitrary free charge distributions and interacting in a polarizable electrolyte solution, that we model within the linearized Poisson--Boltzmann framework. Building on the detailed spectral analysis of the associated nonstandard Neumann--Poincaré-type operators developed in our companion study arXiv:2512.08684, we construct exact explicit expansions of the electrostatic potential and energy in ascending orders of Debye screening thereby obtaining systematic "screening-ranged" series for potentials and energies. These screening-ranged expansions provide a unified and tractable description of many-body electrostatics. We demonstrate the versatility of the approach by showing how it generalizes and improves upon both classical and modern methods, enabling rigorous treatment of heterogeneously charged systems (such as Janus particles) and accurate modeling of higher-order phenomena (such as asymmetric dielectric screening, opposite-charge repulsion, like-charge attraction) as well as yielding many-body generalizations to analytical explicit results previously known only in the two-body setting.

cond-mat.soft↗

arXiv2025

Many interacting particles in solution. II. Screening-ranged expansion of electrostatic forces

We present a fully analytical integration of the Maxwell stress tensor and derive exact relations for interparticle forces in systems of multiple dielectric spheres immersed in a polarizable ionic solvent, within the framework of the linearized Poisson--Boltzmann theory. Building upon the screening-ranged (in ascending orders of Debye screening) expansions of the potentials developed and rigorously analyzed in the accompanying works arXiv:2512.08407, arXiv:2512.08684, arXiv:2512.09421, we construct exact screening-ranged many-body expansions for electrostatic forces in explicit analytical form. These results establish a rigorous foundation for evaluating screened electrostatic interactions in complex particle systems and provide direct analytical connections to, and systematic improvements upon, various earlier approximate or limited-case formulations available in the literature, both at zero and finite ionic strength.

cond-mat.soft↗

arXiv2025

Many interacting particles in solution. III. Spectral analysis of the associated Neumann--Poincaré-type operators

The interaction of particles in an electrolytic medium can be calculated by solving the Poisson equation inside the solutes and the linearized Poisson--Boltzmann equation in the solvent, with suitable boundary conditions at the interfaces. Analytical approaches often expand the potentials in spherical harmonics, relating interior and exterior coefficients and eliminating some coefficients in favor of others, but a rigorous spectral analysis of the corresponding formulations is still lacking. Here, we introduce pertinent composite many-body Neumann--Poincaré-type operators and prove that they are compact with spectral radii strictly less than one. These results provide the foundation for systematic screening-ranged expansions, in powers of the Debye screening parameters, of electrostatic potentials, interaction energies, and forces, and establish the analytical framework for the accompanying works arXiv:2512.09421, arXiv:2512.08407, arXiv:2512.08682.

cond-mat.soft↗

arXiv2025

Exact Screening-Ranged Expansions for Many-Body Electrostatics

We present an exact many-body framework for electrostatic interactions among $N$ arbitrarily charged spheres in an electrolyte, modeled by the linearized Poisson--Boltzmann equation. Building on a spectral analysis of nonstandard Neumann--Poincaré-type operators introduced in a companion mathematical work arXiv:2512.08684, we construct convergent screening-ranged series for the potential, interaction energy, and forces, where each term is associated with a well-defined Debye--Hückel screening order and can be obtained evaluating an analytical expression rather than numerically solving an infinitely dimensional linear system. This formulation unifies and extends classical and recent approaches, providing a rigorous basis for electrostatic interactions among heterogeneously charged particles (including Janus colloids) and yielding many-body generalizations of analytical explicit-form results previously available only for two-body systems. The framework captures and clarifies complex effects such as asymmetric dielectric screening, opposite-charge repulsion, and like-charge attraction, which remain largely analytically elusive in existing treatments. Beyond its fundamental significance, the method leads to numerically efficient schemes, offering a versatile tool for modeling colloids and soft/biological matter in electrolytic solution.

cond-mat.soft↗

arXiv2025

NextGenPB: an analytically-enabled super resolution and local (de)refinement Poisson-Boltzmann Equation solver

The Poisson-Boltzmann equation (PBE) is a relevant partial differential equation commonly used in biophysical applications to estimate the electrostatic energy of biomolecular systems immersed in electrolytic solutions. A conventional mean to improve the accuracy of its solution, when grid-based numerical techniques are used, consists in increasing the resolution, locally or globally. This, however, usually entails higher complexity, memory demand and computational cost. Here, we introduce NextGenPB, a linear PBE, adaptive-grid, FEM solver that leverages analytical calculations to maximize the accuracy-to-computational-cost ratio. Indeed, in NextGenPB (aka NGPB), analytical corrections at the surface of the solute enhance the solution's accuracy without requiring grid adaptation. This leads to more precise estimates of the electrostatic potential, fields, and energy at no perceptible additional cost. Also, we apply computationally efficient yet accurate boundary conditions by taking advantage of local grid de-refinement. To assess the accuracy of our methods directly, we expand the traditionally available analytical case set to many non-overlapping dielectric spheres. Then, we use an existing benchmark set of real biomolecular systems to evaluate the energy convergence concerning grid resolution. Thanks to these advances, we have improved state-of-the-art results and shown that the approach is accurate and largely scalable for modern high-performance computing architectures. Lastly, we suggest that the presented core ideas could be instrumental in improving the solution of other partial differential equations with discontinuous coefficients.

physics.comp-ph↗