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Computer-based simulations of non-invasive cardiac electrical outputs, such as electrocardiograms and body surface potential maps, usually entail severe computational costs due to the need of capturing fine-scale processes and to the…
An exact calculation of the retarded electric field in the source region of a system of individual charges, expanded to third order in velocity, shows that all nonrelativistic accelerated charges in a system emit dipole electromagnetic…
Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…
Theory is presented to simulate both chronoamperometry and cyclic voltammetry at porous electrodes fabricated by means of electro-deposition around spherical templates. A theoretical method to extract heterogeneous rate constants for…
This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…
We consider a strongly damped wave equation on compact manifolds, both with and without boundaries, and formulate the corresponding inverse problems. For closed manifolds, we prove that the metric can be uniquely determined, up to an…
This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shr\"odinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and…
We consider the electromagnetic field in the presence of polarizable point dipoles. In the corresponding effective Maxwell equation these dipoles are described by three dimensional delta function potentials. We review the approaches…
Electrostatic interactions between point charges embedded into interfaces separating dielectric media are omnipresent in soft matter systems and often control their stability. Such interactions are typically complicated and do not resemble…
In this paper, we study the relation between geodesic and harmonic mappings. Harmonic mappings are defined between Riemannian manifolds as critical points of the energy functional, on the other hand, geodesic mappings are defined in a more…
In the framework of the grand-canonical ensemble of statistical mechanics, we give an exact diagrammatic representation of the density profiles in a classical multicomponent plasma near a dielectric wall. By a reorganization of Mayer…
Cardiac arrhythmias are a major cause of morbidity and mortality increasing the risk of stroke, heart failure, and sudden cardiac death. Imageless electrocardiographic imaging (ECGI) provides a non invasive alternative to electrical mapping…
We consider the N-body problem in a layered geometry containing cold polar molecules with dipole moments that are polarized perpendicular to the layers. A harmonic approximation is used to simplify the hamiltonian and bound state properties…
A hypothesis on the physical mechanism generating the heartbeat instability in complex (dusty) plasmas is presented. It is suggested that the instability occurs due to the periodically repeated critical transformation on the boundary…
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…
Recent progress in studying the physics of amorphous solids has revealed that mechanical strains can be strongly screened by the formation of plastic events that are typically quadrupolar in nature. The theory stipulated that gradients in…
The interaction potential of a two-dimensional system of excitons with spatially separated electron-hole layers is considered in the strong magnetic field limit. The excitons are assumed to have free dynamics in the $x$-$y$ plane, while…
The clinical application of patient-specific modelling of the heart can provide valuable insights in supplementing and advancing methods of diagnosis as well as helping to devise the best possible therapeutic approach for each individual…
We study quadrupole and monopole core polarization using harmonic oscillator wave functions but with different length parameters for the valence particle as compared to the core. We use perturbation theory with a delta interaction. The…
An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal…