Search Results (585)

:Solvents represent the quiet majority in biomolecular systems, yet modeling their influence with both speed and ri:gor remains a central challenge. This study maps the state of the art in implicit solvent theory and practice, spanning classical continuum electrostatics (PB/GB; DelPhi, APBS), modern nonpolar and cavity/dispersion treatments, and quantum–continuum models (PCM, COSMO/COSMO-RS, SMx/SMD). We highlight where these methods excel and where they falter, namely, around ion specificity, heterogeneous interfaces, entropic effects, and parameter sensitivity. We then spotlight two fast-moving frontiers that raise both accuracy and throughput: machine learning-augmented approaches that serve as PB-accurate surrogates, learn solvent-averaged potentials for MD, or supply residual corrections to GB/PB baselines, and quantum-centric workflows that couple continuum solvation methods, such as IEF-PCM, to sampling on real quantum hardware, pointing toward realistic solution-phase electronic structures at emerging scales. Applications across protein–ligand binding, nucleic acids, and intrinsically disordered proteins illustrate how implicit models enable rapid hypothesis testing, large design sweeps, and long-time sampling. Our perspective argues for hybridization as a best practice, meaning continuum cores refined by improved physics, such as multipolar water, ML correctors with uncertainty quantification and active learning, and quantum–continuum modules for chemically demanding steps. Full article

In this work, we present the procedure to obtain exact spherical shape functions for finite element modeling applications, without resorting to any kind of approximation, for generic prismatic spherical elements and for the case of spherical six-node tri-rectangular and eight-node quadrangular spherical prisms. The proposed spherical shape functions, given in explicit analytical form, are expressed in geographic coordinates, namely colatitude, longitude and distance from the center of the sphere. We demonstrate that our analytical shape functions satisfy all the properties required by this class of functions, deriving at the same time the analytical expression of the Jacobian, which allows us changes in coordinate systems. Within the perspective of volume integration on Earth, entering a variety of geophysical and geodetic problems, as for mass change contribution to gravity, we consider our analytical expression of the shape functions and Jacobian for the six-node tri-rectangular and eight-node quadrangular right spherical prisms as reference volumes to evaluate the volume of generic spherical triangular and quadrangular prisms over the sphere; volume integration is carried out via Gauss–Legendre quadrature points. We show that for spherical quadrangular prisms, the percentage volume difference between the exact and the numerically evaluated volumes is independent from both the geographical position and the depth and ranges from 10⁻³ to lower than 10⁻⁴ for angular dimensions ranging from 1° × 1° to 0.25° × 0.25°. A satisfactory accuracy is attained for eight Gauss–Legendre quadrature points. We also solve the Poisson equation and compare the numerical solution with the analytical solution, obtained in the case of steady-state heat conduction with internal heat production. We show that, even with a relatively coarse grid, our elements are capable of providing a satisfactory fit between numerical and analytical solutions, with a maximum difference in the order of 0.2% of the exact value. Full article

This paper investigates a slow–fast stochastic reaction–diffusion–advection equation with Hölder-continuous coefficients, where the irregularity of the coefficients presents significant analytical challenges. Our approach fundamentally relies on techniques from Poisson equations in Hilbert spaces, through which we establish optimal strong convergence rates for the approximation of the averaged solution by the slow component. The key advantage that this paper presents is that the coefficients are merely Hölder continuous yet the optimal rate can still be obtained, which is crucial for subsequent central limit theorems and numerical approximations. Full article

The present work analyzes the combined viscoelectric and steric effects on electroosmotic flow in a soft channel with polyelectrolyte coating. The structured channel surface, which controls the electric potential, creates two different flow regions: the electrolyte flow within the permeable polyelectrolyte layer (PEL) and the bulk electrolyte. Thus, this study discusses the interaction of various electrostatic effects to predict the electroosmotic flow field. The nonlinear governing equations describing the fluid flow are the modified Poisson–Boltzmann equation for the electric potential distribution, the mass conservation equation, and the modified Navier–Stokes equations for the flow field, which are solved numerically using a one-dimensional (1D) scheme. The results indicate that the flow enhances when increasing the electric potential magnitude across the channel cross-section via the rise in different dimensionless parameters, such as the PEL thickness, the steric factor, and the ratio of the electrokinetic parameter of the PEL to that of the electrolyte layer. This research demonstrates that the PEL significantly enhances control over electroosmotic flow. However, it is crucial to consider that viscoelectric effects at high electric fields and the friction generated by the grafted polymer brushes of the PEL can reduce these benefits. Full article

Efficient autonomous exploration in unknown obstacle cluttered environments with interior obstacles remains a challenging task for mobile robots. In this work, we present a novel exploration process for a non-holonomic agent exploring 2D spaces using onboard LiDAR sensing. The proposed method generates velocity commands based on the calculation of the solution of an elliptic Partial Differential Equation with Dirichlet boundary conditions. While solving Laplace’s equation yields collision-free motion towards the free space boundary, the agent may become trapped in regions distant from free frontiers, where the potential field becomes almost flat, and consequently the agent’s velocity nullifies as the gradient vanishes. To address this, we solve a Poisson equation, introducing a source point on the free explored boundary which is located at the closest point from the agent and attracts it towards unexplored regions. The source values are determined by an exponential function based on the shortest path of a Hybrid Visibility Graph, a graph that models the explored space and connects obstacle regions via minimum-length edges. The computational process we apply is based on the Walking on Sphere algorithm, a method that employs Brownian motion and Monte Carlo Integration and ensures efficient calculation. We validate the approach using a real-world platform; an AmigoBot equipped with a LiDAR sensor, controlled via a ROS-MATLAB interface. Experimental results demonstrate that the proposed method provides smooth and deadlock-free navigation in complex, cluttered environments, highlighting its potential for robust autonomous exploration in unknown indoor spaces. Full article

Piping systems can be analogized to the “vascular systems” of vessels, but their transmission characteristics often result in loud noises and large vibrations. The integration of flexible inserts within these piping systems has been shown to isolate and/or mitigate such vibrations and noise. In this work, a novel sandwich flexible insert (NSFI) was presented specifically to reduce the vibrations and noise associated with piping systems on vessels. In contrast to conventional flexible inserts, the NSFI features a distinctive three-layer configuration, comprising elastic inner and outer layers, along with a honeycomb core exhibiting a zero Poisson’s ratio. The dynamic characteristics, specifically axial impedance, of the fluid-filled NSFI are examined utilizing a fluid–structure interaction (FSI) four-equation model. The validity of the theoretical predictions is corroborated through finite element analysis, experimental results, and comparisons with existing literature. Furthermore, the study provides a comprehensive evaluation of the effects of geometric and structural parameters on the dynamic characteristics of the NSFI. It is worth noting that axial impedance is significantly affected by these parameters, which suggests that the dynamic characteristics of the NSFI can be customized by parameter adjustments. Full article

In this paper, we propose a fuzzy formulation of the classic Frankot–Chellappa algorithm by which surfaces can be reconstructed using normal vectors. In the fuzzy formulation, the surface normal vectors may be uncertain or ambiguous, yielding a fuzzy Poisson partial differential equation that requires appropriate definitions of fuzzy derivatives. The solution of the resulting fuzzy model is approached by adopting a fuzzy variant of the discrete sine transform, which results in a fast and robust algorithm for surface reconstruction. An adaptive defuzzification strategy is also introduced to improve noise handling in highly uncertain regions. In experiments, we demonstrate that our fuzzy Frankot–Chellappa algorithm achieves accuracy on par with the classic approach for smooth surfaces and offers improved robustness in the presence of noisy normal data. We also show that it can naturally handle missing data (such as gaps) in the normal field by filling them using neighboring information. Full article

We propose the zero-inflated Polynomially Adjusted Poisson (zPAP) model. It extends the usual zero-inflated Poisson by multiplying the Poisson kernel with a nonnegative polynomial, enabling the model to handle extra zeros, overdispersion, skewness, and even multimodal counts. We derive the maximum-likelihood framework—including the log-likelihood and score equations under both general and regression settings—and fit zPAP to the zero-inflated, highly dispersed Fish Catch data as well as a synthetic bimodal mixture. In both cases, zPAP not only outperforms the standard zero-inflated Poisson model but also yields reliable inference via parametric bootstrap confidence intervals. Overall, zPAP is a clear and tractable tool for real-world count data with complex features. Full article

This work investigates fractional stochastic Schrödinger evolution equations in a Hilbert space, incorporating complex potential symmetry and Poisson jumps. We establish the existence of mild solutions via stochastic analysis, semigroup theory, and the Mönch fixed-point theorem. Sufficient conditions for exponential stability are derived, ensuring asymptotic decay. We further explore trajectory controllability, identifying conditions for guiding the system along prescribed paths. A numerical example is provided to validate the theoretical results. Full article

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using classical Legendre polynomials is a special case of interpolation with the proposed Legendre Delta-Shaped Basis Functions (LDSBFs). To illustrate the potential of LDSBFs, we apply the corresponding series to approximate a rectangular pulse. The results reveal that Gibbs oscillations decay rapidly, resulting in significantly improved accuracy across smooth regions. This example underscores the effectiveness and novelty of our approach. Furthermore, LDSBFs are employed within the collocation framework to solve Poisson-type equations and systems of nonlinear differential equations arising in energy transfer problems. We also derive new error bounds for interpolation polynomials in a special case, expressed in both the discrete ${(L}_2)$ norm and the Sobolev $\left(H_p\right)$ norm. To validate the proposed method, we compare our results with those obtained using the Legendre pseudospectral method. Numerical experiments confirm that our approach is accurate, efficient, and highly competitive with existing techniques. Full article

This study addresses computational challenges in the immersed boundary method (IBM) with the pressure implicit with split operator (PISO) algorithm for simulating incompressible flows. We introduce a novel time-step splitting method to implement communication overlapping optimization, aiming to reduce costs dominated by the pressure Poisson solver. Using a fast Fourier transform (FFT)-based approach, the Poisson equation is solved efficiently with $O(NlogN)$ complexity. Our method interleaves IBM force calculations with Poisson phases, employing asynchronous communication to overlap computation with global data exchanges. This reduces communication overhead, enhancing scalability. Validation through benchmark simulations, including flow around a cylinder and particle-laden flows, shows improved efficiency and accuracy comparable with traditional methods. Implemented in a custom C++ solver using the FFTW library, tests indicate substantial acceleration, with results showing a 40% speed-up and less than 3% deviation in drag and lift coefficients. This research provides an efficient and promising simulation tool for complex flow. Full article

This article proposes a 3D mathematical model of the influence of electrical heterogeneity of the ion exchange membrane surface on the processes of salt ion transfer in membrane systems with axial symmetry; in particular, we investigate an annular membrane disk in the form of a coupled system of Nernst–Planck–Poisson and Navier–Stokes equations in a cylindrical coordinate system. A hybrid numerical–analytical method for solving the boundary value problem is proposed, and a comparison of the results for the annular disk model obtained by the hybrid method and the independent finite element method is carried out. The areas of applicability of each of these methods are determined. The proposed model of an annular disk takes into account electroconvection, which is understood as the movement of an electrolyte solution under the action of an external electric field on an extended region of space charge formed at the solution–membrane boundary under the action of the same electric field. The main regularities and features of the occurrence and development of electroconvection associated with the electrical heterogeneity of the surface of the membrane disk of the annular membrane disk are determined; namely, it is shown that electroconvective vortices arise at the junction of the conductivity and non-conductivity regions at a certain ratio of the potential jump and angular velocity and flow down in the radial direction to the edge of the annular membrane. At a fixed potential jump greater than the limiting one, the formed electroconvective vortices gradually decrease with an increase in the angular velocity of rotation until they disappear. Conversely, at a fixed value of the angular velocity of rotation, electroconvective vortices arise at a certain potential jump, and with its subsequent increase gradually increase in size. Full article

We explore a modified, including some relativistic effects, Newtonian formalism in cosmology, using a system of constituent equations that includes a modified first Friedmann equation—incorporating its homogeneous counterpart—alongside the classical Poisson equation. Furthermore, we include the dynamical equations arising from stress-energy tensor conservation. Within this framework, we examine stellar equilibrium under spherical symmetry. By specifying the equation of state, we derive the corresponding equilibrium configurations. Finally, we investigate gravitational collapse in this context. Full article

In the classical problem of the motion of a rigid body around a fixed point, which is described by the Euler–Poisson equations, we propose a new method for computing cases of integrability: first, we provide algorithms for computing values of parameters ensuring potential integrability, and then we select cases of global integrability. By this method we have obtained all the known cases of global integrability and six new cases of potential integrability for which the absence of their global integrability is proven. Full article