The NonCovalent Interaction index (NCI) enables identification of attractive and repulsive noncovalent interactions from promolecular densities in a fast manner. However, the approach remained up to now qualitative, only providing visual information. We present new version NCIPLOT, NCIPLOT4, which allows quantifying properties NCI regions (volume, charge) small big systems Examples are provided how this twist characterization retrieval local information supramolecular chemistry biosystems at...

Abstract Noncovalent interactions are of utmost importance. However, their accurate treatment is still difficult. This partially induced by the coexistence many types and physical phenomena, which hampers generality in simple treatments. The NCI index has been successfully used for nearly over 10 years order to identify, analyze, understand noncovalent a wide variety systems, ranging from proteins molecular crystals. In this work, development implications method will be reviewed, modern...

In this article, we study the energy dissipation property of time-fractional Allen-Cahn equation. We propose a decreasing upper bound that decreases with respect to time and coincides original at $t = 0$ as $t$ tends $\infty$. This can also be viewed nonlocal-in-time modified energy, summation an accumulation term due memory effect fractional derivative. particular, indicates indeed decays w.r.t. in small neighborhood $t=0$. illustrate theory mainly equation, but it could applied other...

.This work establishes \(H^1\) -norm stability and convergence for an L2 method on general nonuniform meshes when applied to the subdiffusion equation. Under mild constraints time step ratio \(\rho_k\) , such as \(0.4573328\leq \rho_k\leq 3.5615528\) \(k\geq 2\) positive semidefiniteness of a crucial bilinear form associated with fractional-derivative operator is proved. This result enables us derive long -stability schemes. These properties hold standard graded grading parameter \(1\lt...

The Linearized Poisson-Boltzmann (LPB) equation is a popular and widely accepted model for accounting solvent effects in computational (bio-) chemistry. In the present article, we derive analytical forces using domain-decomposition-based LPB-method with van-der Waals or solvent-accessible surface. We an efficient strategy to compute its implementation, allowing linear scaling of method respect number atoms fast multipole method. Numerical tests illustrate accuracy computation compare...

Implicit-explicit methods have been successfully used for the efficient numerical simulation of phase field problems such as Cahn-Hilliard equation or thin film type equations. Due to lack maximum principle and stiffness caused by effect small dissipation coefficient, most existing theoretical analysis relies on adding additional stabilization terms, mollifying nonlinearity introducing auxiliary variables which implicitly either changes structure problem trades accuracy stability in a subtle...

In this paper, a domain decomposition method for the Poisson--Boltzmann solvation model that is widely used in computational chemistry proposed. This method, called ddLPB short, solves linear equation defined $\mathbb R^3$ using van der Waals cavity as solute cavity. The Schwarz to formulate local problems by decomposing into overlapping balls and only solving set of coupled subequations balls. A series numerical experiments presented test robustness efficiency including comparisons with...

This paper builds on two previous works, Lindgren et al. J. Comp. Phys. 371, 712-731 (2018) and Quan arXiv:1807.05384 (2018), to devise a new method solve the problem of calculating electrostatic interactions in system composed by many dielectric particles, embedded homogeneous medium, which turn can also be permeated charge carriers. The is defined charge, size, position constant each particle, as well Debye length medium. effects taking into account nature particles explored selected...

In this paper, an efficient solver for the polarizable continuum model in quantum chemistry is developed which takes solvent excluded surface (the smooth molecular surface) as solute–solvent boundary. This requires to solve a generalized Poisson (GP) equation defined [Formula: see text] with space-dependent dielectric permittivity function. First, original GP-equation transformed into system of two coupled equations bounded domain. Then, domain decomposed overlapping balls and Schwarz...

The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties solution such as energy dissipation and maximum principle.Although theory for classical phase field models well established, corresponding time-fractional still incomplete.In this article, we study certain nonlocal-in-time energies using first-order stabilized semi-implicit L1 scheme.In particular, will establish fractional law weighted law.The extension (2...

Abstract This work delves into the exponential time differencing (ETD) schemes for matrix-valued Allen–Cahn equation. In fact, maximum bound principle (MBP) first- and second-order ETD is presented in a prior publication [SIAM Review, 63(2), 2021], assuming symmetric initial matrix field. Noteworthy our novel contribution, demonstrating that equation—both being linear schemes—unconditionally preserve MBP, even instances of nonsymmetric conditions. Furthermore, we prove these two energy...

The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties solution such as energy dissipation and maximum principle. Although theory for classical phase field models well established, corresponding time-fractional still incomplete. In this article, we study certain nonlocal-in-time energies using first-order stabilized semi-implicit L1 scheme. particular, will establish fractional law weighted law. extension...

<p style='text-indent:20px;'>We consider a class of time-fractional phase field models including the Allen-Cahn and Cahn-Hilliard equations. We establish several weighted positivity results for functionals driven by Caputo derivative. Several novel criterions are examined showing positive-definiteness associated kernel functions. deduce strict energy-dissipation number non-local energy functionals, thereby proving fractional dissipation laws.</p>