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We give a short survey on plurisubharmonic interpolation, with focus on possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesic.
Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling…
A method for particle orientation tracking is developed and demonstrated specifically for anisotropic particles. Using (high-speed) multi-camera recordings of anisotropic particles from different viewpoints, we reconstruct the 3D location…
The theory of Chebyshev approximation has been extensively studied. In most cases, the optimality conditions are based on the notion of alternance or alternating sequence (that is, maximal deviation points with alternating deviation signs).…
Complete control of electromagnetic fields requires particles that exhibit bianisotropic constituent parameters (i.e. permittivity, permeability, and chirality). Here, methods to analyze and synthesize two-dimensional, bianisotropic…
Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase…
The effective quasistatic conductivity of composite polymeric electrolytes is studied in terms of a hard-core--penetrable-layer model. Used to incorporate the interface phenomena (such as amorphization of the polymer matrix around filler…
Mesoscopic samples of polarized dipolar atoms confined in three spatially separated traps conform an extended Bose-Hubbard Hamiltonian in which different quantum phases appear depending on the competition between tunneling, on-site and long…
We study a large family of axisymmetric Riesz-type singular interaction potentials with anisotropy in three dimensions. We generalize some of the results of our recent work in two dimensions to the present setting. For potentials with…
We apply the modern technique of approximation of multivariate functions - tensor train cross approximation - to the problem of the description of physical interactions between complex-shaped bodies in a context of computational…
A previously developed approach for the numerical treatment of two particles that are confined in a finite optical-lattice potential and interact via an arbitrary isotropic interaction potential has been extended to incorporate an…
The multipole expansion is a key tool in the study of light-matter interactions. All the information about the radiation of and coupling to electromagnetic fields of a given charge-density distribution is condensed into few numbers: The…
Besides the chemical constituents, it is the lattice geometry that controls the most important material properties. In many interesting compounds, the arrangement of elements leads to pronounced anisotropies, which reflect into a varying…
The dipolar interaction is known to substantially affect the properties of magnetic nanoparticles. This is particularly important when the particles are kept in a fluid suspension or packed inside nano-carriers. In addition to its usual…
The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are studied using sixteen different combinations of coordinate system for fitting and weight functions. For the application we use…
Driven by novel approaches and computational techniques, second-principles atomic potentials are nowadays at the forefront of computational materials science, enabling large-scale simulations of material properties with…
The mechanical, optical, and chemical properties of a wide variety of soft materials are enabled and constrained by their bulk structure. How this structure emerges at small system sizes during self-assembly has been the subject of decades…
We consider the Manev Potential in an anisotropic space, i.e., such that the force acts differently in each direction. Using a generalization of the Poincare' continuation method we study the existence of periodic solutions for weak…
Mixup is a powerful data augmentation method that interpolates between two or more examples in the input or feature space and between the corresponding target labels. Many recent mixup methods focus on cutting and pasting two or more…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…