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A simple application of classical density functional theory is derived and applied to a system of polymers grafted to a plane. The system is assumed to have symmetry in directions parallel to the grafting plane hence it being a…
A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning…
The integral expression for gravitational potential of a homogeneous circular torus composed of infinitely thin rings is obtained. Approximate expressions for torus potential in the outer and inner regions are found. In the outer region a…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
Position-deformed Heisenberg algebra with maximal length uncertainty has recently been proven to induce strong quantum gravitational fields at the Planck scale (2022 J. Phys. A: Math. Theor.55 105303). In the present study, we use the…
We revisit the classical problem of a polymer confined in a slit in both of its static and dynamic aspects. We confirm a number of well known scaling predictions and analyse their range of validity by means of comprehensive Molecular…
p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.
In this article we study existence of pathwise stochastic integrals with respect to a general class of $n$-dimensional Gaussian processes and a wide class of adapted integrands. More precisely, we study integrands which are functions that…
A recently developed lattice field theory approach to the statistical mechanics of charged polymers in electrolyte solutions [S. Tsonchev, R. D. Coalson, and A. Duncan, Phys. Rev. E {\bf{60}}, 4257, (1999)] is generalized to the case where…
The increasing availability of high-dimensional, longitudinal measures of gene expression can facilitate understanding of biological mechanisms, as required for precision medicine. Biological knowledge suggests that it may be best to…
The electron motion along a chain is described by a continuum version of the Su-Schrieffer-Heeger Hamiltonian in which phonon fields and electronic coordinates are mapped onto the time scale. The path integral formalism allows us to derive…
Hamiltonian Monte Carlo (HMC) is an efficient and effective means of sampling posterior distributions on Euclidean space, which has been extended to manifolds with boundary. However, some applications require an extension to more general…
An integral representation is suggested for generalized parton distributions which automatically satisfies the polynomiality and positivity constraints. This representation has the form of an integral of perturbative triangle diagrams over…
The sequence of random probability measures $\nu_n$ that gives a path of length $n$, $\unsur{n}$ times the sum of the random weights collected along the paths, is shown to satisfy a large deviations principle with good rate function the…
We show that the formation of large-scale structures through gravitational instability in the expanding universe can be fully described through a path-integral formalism. We derive the action S[f] which gives the statistical weight…
We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show…
A new approach to study the response of portable gamma detector to terrestrial gamma ray is proposed. This approach is based on two-stage Monte Carlo simulation. First, the probability distributions of the phase space coordinates of the…
We investigate interfacial properties between two highly incompatible polymers of different stiffness. The extensive Monte Carlo simulations of the binary polymer melt yield detailed interfacial profiles and the interfacial tension via an…
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and…