Related papers: Geometric-algebraic approach to aqueous solutions …
Closed-form expressions for the pH of ideal weak acid and weak acid buffer solutions (and their titration with a strong base) were obtained and analyzed with the aid of computer algebra systems. These expressions are used to evaluate,…
We propose a simple algebraic method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid. The problem reduces to consecutively solving three linear partial differential equations for a…
The dielectric constant ($\varepsilon^{\prime}$) of interfacial water is an important parameter, but its measurement has posed challenges, and no consensus has been reached on a generalized expression. We derived a formula for…
[ This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in The Journal of Chemical Physics, 157, 024504 (2022) and may be found at:…
A recently developed method has been extended to a nonlocal equation arising in steady water wave propagation in two dimensions. We obtain analyic approximation of steady water wave solution in two dimensions with rigorous error bounds for…
Because it is sensitive to fluctuations occurring over femtoseconds to picoseconds, gigahertz-to-terahertz dielectric relaxation spectroscopy can provide a valuable window into water's most rapid intermolecular motions. In response, we have…
An analytical linear solution of the fully compressible Euler equations is found, in the particular case of a stationary two dimensional flow that passes over an orographic feature with small height-width ratio. A method based on the…
Diffusion processes with boundaries are models of transport phenomena with wide applicability across many fields. These processes are described by their probability density functions (PDFs), which often obey Fokker-Planck equations (FPEs).…
We have developed a method to calculate the hydration of hydrophobic solutes by the fundamental measure theory. This method allows us to carry out calculations of the density profile and the hydration energy for hydrophobic molecules. An…
For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
We introduce a notion of approximate viscosity solution for a class of nonlinear path-dependent PDEs (PPDEs), including the Hamilton-Jacobi-Bellman type equations. Existence, comparaison and stability results are established under fairly…
We study a geometric flow on curves, immersed in $\mathbb{R}^3$, that have strictly positive torsion. The evolution equation is given by $$X_{t}=\frac{1}{\sqrt{\tau}} \textbf{B}$$ where $\tau$ is the torsion and $\textbf{B}$ is the unit…
In this paper, we study the higher-order regularity of solutions to the large scale moist atmosphere system through the way of $p$-strong solutions. On the basis of the well-posedness results of strong solutions, we first improve the…
The work presents the detailed analysis of the water dimer properties. Their parameters are investigated on the basis of a multipole interaction potential extended up to the quadrupole--quadrupole and dipole--octupole terms. All main…
We study the variation of the dielectric response of ionic aqueous solutions as function of their ionic strength. The effect of salt on the dielectric constant appears through the coupling between ions and dipolar water molecules. On a…
An analytic solution is presented to the three-dimensional problem of steady axisymmetric fluid flow through an accretion disk. The solution has been obtained through a systematic expansion in the small parameter epsilon =H/R (the ratio of…
Acid solutions exhibit a variety of complex structural and dynamical features arising from the presence of multiple interacting reactive proton defects and counterions. However, disentangling the transient structural motifs of proton…
In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…
A continuous solution of an algebraic equation with holomorphic almost periodic coefficients is also almost periodic.
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…