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Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann's "molecular chaos" hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.

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A shock wave is a flow phenomenon that needs to be considered in the development of high-speed aircraft and engines. The traditional computational fluid dynamics (CFD) method describes it from the perspective of macroscopic variables, such as the Mach number, pressure, density, and temperature. The thickness of the shock wave is close to the level of the molecular free path, and molecular motion has a strong influence on the shock wave. According to the analysis of the Chapman-Enskog approach, the nonequilibrium effect is the source term that causes the fluid system to deviate from the equilibrium state. The nonequilibrium effect can be used to obtain a description of the physical characteristics of shock waves that are different from the macroscopic variables. The basic idea of the nonequilibrium effect approach is to obtain the nonequilibrium moment of the molecular velocity distribution function by solving the Boltzmann-Bhatnagar-Gross-Krook (Boltzmann BGK) equations or multiple relaxation times Boltzmann (MRT-Boltzmann) equations and to explore the nonequilibrium effect near the shock wave from the molecular motion level. This article introduces the theory and understanding of the nonequilibrium effect approach and reviews the research progress of nonequilibrium behavior in shock-related flow phenomena. The role of nonequilibrium moments played on the macroscopic governing equations of fluids is discussed, the physical meaning of nonequilibrium moments is given from the perspective of molecular motion, and the relationship between nonequilibrium moments and equilibrium moments is analyzed. Studies on the nonequilibrium effects of shock problems, such as the Riemann problem, shock reflection, shock wave/boundary layer interaction, and detonation wave, are introduced. It reveals the nonequilibrium behavior of the shock wave from the mesoscopic level, which is different from the traditional macro perspective and shows the application potential of the mesoscopic kinetic approach of the nonequilibrium effect in the shock problem.

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Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy-momentum tensor calculated from a post-Newtonian Maxwell-Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory.

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A semi-analytical solution to the unified Boltzmann equation is constructed to exactly describe the scatter distribution on a flat-panel detector for high-quality conebeam CT (CBCT) imaging. The solver consists of three parts, including the phase space distribution estimator, the effective source constructor and the detector signal extractor. Instead of the tedious Monte Carlo solution, the derived Boltzmann equation solver achieves ultrafast computational capability for scatter signal estimation by combining direct analytical derivation and time-efficient one-dimensional numerical integration over the trajectory along each momentum of the photon phase space distribution. The execution of scatter estimation using the proposed ultrafast Boltzmann equation solver (UBES) for a single projection is finalized in around 0.4 seconds. We compare the performance of the proposed method with the state-of-the-art schemes, including a time-expensive Monte Carlo (MC) method and a conventional kernel-based algorithm using the same dataset, which is acquired from the CBCT scans of a head phantom and an abdominal patient. The evaluation results demonstrate that the proposed UBES method achieves comparable correction accuracy compared with the MC method, while exhibits significant improvements in image quality over learning and kernel-based methods. With the advantages of MC equivalent quality and superfast computational efficiency, the UBES method has the potential to become a standard solution to scatter correction in high-quality CBCT reconstruction.

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Levy et al. [1] reported the breakdown of electroneutrality in confined nanopores embedded in a dielectric medium. A Robin boundary condition was derived which eliminates the need to include the dielectric medium explicitly when solving for the electric field within the nanopore. In this comment, we point out issues related to the approximations made during the derivation of the boundary condition. The errors caused by the use of this boundary condition can be significant even for nanochannels of large aspect (length to radius) ratio, a condition on which the approximations in Levy et al. [1] are based.

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Almost all biological reactions are pH dependent and understanding the origin of pH dependence requires knowledge of the pKa's of ionizable groups. Here we report a new edition of PKAD, the PKAD-2, which is a database of experimentally measured pKa's of proteins, both wild type and mutant proteins. The new additions include 117 wild type and 54 mutant pKa values, resulting in total 1742 experimentally measured pKa's. The new edition of PKAD-2 includes 8 new wild type and 12 new mutant proteins, resulting in total of 220 proteins. This new edition incorporates a visual 3D image of the highlighted residue of interest within the corresponding protein or protein complex. Hydrogen bonds were identified, counted, and implemented as a search feature. Other new search features include the number of neighboring residues <4A from the heaviest atom of the side chain of a given amino acid. Here, we present PKAD-2 with the intention to continuously incorporate novel features and current data with the goal to be used as benchmark for computational methods.

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The one-dimensional confinement of quasiparticles in individual carbon nanotubes (CNTs) leads to extremely anisotropic electronic and optical properties. In a macroscopic ensemble of randomly oriented CNTs, this anisotropy disappears together with other properties that make them attractive for certain device applications. The question however remains if not only anisotropy but also other types of behaviors are suppressed by disorder. Here, we compare the dynamics of quasiparticles under strong electric fields in aligned and random CNT networks using a combination of terahertz emission and photocurrent experiments and out-of-equilibrium numerical simulations. We find that the degree of alignment strongly influences the excited quasiparticles' dynamics, rerouting the thermalization pathways. This is, in particular, evidenced in the high-energy, high-momentum electronic population (probed through the formation of low energy excitons via exciton impact ionization) and the transport regime evolving from diffusive to superdiffusive.

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This study calculated the magnetoresistance (MR) in the Dirac electron system, Dresselhaus-Kip-Kittel (DKK) model, and nodal-line semimetals based on the semiclassical Boltzmann theory, with particular focus on the detailed energy dispersion structure. The negative off-diagonal effective-mass was found to induce negative transverse MR owing to the energy dispersion effect. The impact of the off-diagonal mass was more prominent in case of a linear energy dispersion. Further, Dirac electron systems could realize negative MR even if the Fermi surface was perfectly spherical. The obtained negative MR in the DKK model may explain the long-standing mystery in p-type Si.

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The Boltzmann equation for d-dimensional inelastic Maxwell models is considered to determine the collisional moments of the second, third and fourth degree in a granular binary mixture. These collisional moments are exactly evaluated in terms of the velocity moments of the distribution function of each species when diffusion is absent (mass flux of each species vanishes). The corresponding associated eigenvalues as well as cross coefficients are obtained as functions of the coefficients of normal restitution and the parameters of the mixture (masses, diameters and composition). The results are applied to the analysis of the time evolution of the moments (scaled with a thermal speed) in two different nonequilibrium situations: the homogeneous cooling state (HCS) and the uniform (or simple) shear flow (USF) state. In the case of the HCS, in contrast to what happens for simple granular gases, it is demonstrated that the third and fourth degree moments could diverge in time for given values of the parameters of the system. An exhaustive study on the influence of the parameter space of the mixture on the time behavior of these moments is carried out. Then, the time evolution of the second- and third-degree velocity moments in the USF is studied in the tracer limit (namely, when the concentration of one of the species is negligible). As expected, while the second-degree moments are always convergent, the third-degree moments of the tracer species can be also divergent in the long time limit.

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In applications of bio-inspired nanoparticles (NPs), their composition is often optimised by including ionizable lipids. I use a generic statistical model to describe the charge and potential distributions in lipid nanoparticles (LNPs) containing such lipids. The LNP structure is considered to contain the biophase regions separated by narrow interphase boundaries with water. Ionizable lipids are uniformly distributed at the biophase-water boundaries. The potential is there described at the mean-filed level combining the Langmuir-Stern equation for ionizable lipids and the Poisson-Boltzmann equation for other charges in water. The latter equation is used outside a LNP as well. With physiologically reasonable parameters, the model predicts the scale of the potential in a LNP to be rather low, smaller or about [Formula: see text], and to change primarily near the LNP-solution interface or, more precisely, inside an NP near this interface because the charge of ionizable lipids becomes rapidly neutralized along the coordinate towards the center of a LNP. The extent of dissociation-mediated neutralization of ionizable lipids along this coordinate increases but only slightly. Thus, the neutralization is primarily due to the negative and positive ions related to the ionic strength in solution and located inside a LNP.

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The existence of an exclusion zone in which particles of a colloidal suspension in water are repelled from hydrophilic surfaces has been experimentally demonstrated in numerous studies, especially in the case of Nafion surfaces. Various explanations have been proposed for the origin of this phenomenon, which is not completely understood yet. In particular, the existence of a fourth phase of water has been proposed by G. Pollack and if this theory is proven correct, its implications on our understanding of the properties of water, especially in biological systems, would be profound and could give rise to new medical therapies. Here, a simple approach based on the linearized Poisson-Boltzmann equation is developed in order to study the repulsive forces mediated by ordered water and involving the following interacting biomolecules: 1) microtubule and a tubulin dimer, 2) two tubulin dimers and 3) a tubulin sheet and a tubulin dimer. The choice of microtubules in this study is motivated because they could be a good candidate for the generation of an exclusion zone in the cell and these models could be a starting point for detailed experimental investigations of this phenomenon.

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HYPOTHESIS: The origin of the negative charge at water/air interface was proved to be not only specific adsorption of OH- ions but that of HCO3- and/or CO32- ions in the previous study [1]. To determine which anionic species is primarily responsible for the surface charge, the surface density of ions in the Stern layer is numerically evaluated from foam-film thickness of aqueous solutions of NaHCO3 and Na2CO3. EXPERIMENTS: Equilibrium thickness (equivalent thickness at equilibrium) of the foam films formed from aqueous solutions of NaHCO3 and Na2CO3 was measured as a function of electrolyte concentration at 298.15 K. FINDINGS: Applying a modified Poisson-Boltzmann (PB) equation developed for various kinds of electrolytes to the equilibrium thickness gave the surface density of ions in the Stern layer for NaHCO3 and Na2CO3 systems. From the concentration dependence of the surface density together with that for NaCl and NaOH in the previous study [1], the negative surface charges for water and very dilute solutions were found to be due to specific adsorption of HCO3- ions. The surface charge at high electrolyte concentration is determined by the specific adsorption of electrolyte anions. The specific-adsorption ability of anion increases in the order CO32-≫ HCO3-> OH-≫ Cl-.

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Electrically injected and detected nonlocal magnon transport has emerged as a versatile method for transporting spin as well as probing the spin excitations in a magnetic insulator. We examine the role of drift currents in this phenomenon as a method for controlling the magnon propagation length. Formulating a phenomenological description, we identify the essential requirements for existence of magnon drift. Guided by this insight, we examine magnetic field gradient, asymmetric contribution to dispersion, and temperature gradient as three representative mechanisms underlying a finite magnon drift velocity, finding temperature gradient to be particularly effective.

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Motivated by recent successes in model-based pre-election polling, we propose a kinetic model for opinion formation which includes voter demographics and socio-economic factors like age, sex, ethnicity, education level, income and other measurable factors like behaviour in previous elections or referenda as a key driver in the opinion formation dynamics. The model is based on Toscani's kinetic opinion formation model (Toscani G. 2006 Kinetic models of opinion formation. Commun. Math. Sci. 4, 481-496.) and the leader-follower model of Düring et al. (Düring B. et al. 2009 Boltzmann and Fokker-Planck equations modelling opinion formation in the presence of strong leaders. Proc. R. Soc. A 465, 3687-3708.), and leads to a system of coupled Boltzmann-type equations and associated, approximate Fokker-Planck-type systems. Numerical examples using data from general elections in the UK show the effect different demographics have on the opinion formation process and the outcome of elections. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

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The Elo rating system, which was originally proposed by Arpad Elo for chess, has become one of the most important rating systems in sports, economics and gaming. Its original formulation is based on two-player zero-sum games, but it has been adapted for team sports and other settings. In 2015, Junca and Jabin proposed a kinetic version of the Elo model, and showed that under certain assumptions the ratings do converge towards the players' strength. In this paper, we generalize their model to account for variable performance of individual players or teams. We discuss the underlying modelling assumptions, derive the respective formal mean-field model and illustrate the dynamics with computational results. This article is part of the theme issue 'Kinetic exchange models of societies and economies'.

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The structure near polyelectrolyte-coated gold nanoparticles (AuNPs) is of significant interest because of the increased use of AuNPs in technological applications and the possibility that the acquisition of polyelectrolytes can lead to novel chemistry in downstream environments. We use all-atom molecular dynamics (MD) simulations to reveal the electric potential around citrate-capped gold nanoparticles (cit-AuNPs) and poly(allylamine hydrochloride) (PAH)-wrapped cit-AuNP (PAH-AuNP). We focus on the effects of the overall ionic strength and the shape of the electric potential. The ionic number distributions for both cit-AuNP and PAH-AuNP are calculated using MD simulations at varying salt concentrations (0, 0.001, 0.005, 0.01, 0.05, 0.1, and 0.2 M NaCl). The net charge distribution (Z(r)) around the nanoparticle is determined from the ionic number distribution observed in the simulations and allows for the calculation of the electric potential (ϕ(r)). We find that the magnitude of ϕ(r) decreases with increasing salt concentration and upon wrapping by PAH. Using a hydrodynamic radius (RH) estimated from the literature and fits to the Debye-Hü̈ckel expression, we found and report the ζ potential for both cit-AuNP and PAH-AuNP at varying salt concentrations. For example, at 0.001 M NaCl, MD simulations suggest that ζ = -25.5 mV for cit-AuNP. Upon wrapping of cit-AuNP by one PAH chain, the resulting PAH-AuNP exhibits a reduced ζ potential (ζ = -8.6 mV). We also compare our MD simulation results for ϕ(r) to the classic Poisson-Boltzmann equation (PBE) approximation and the well-known Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. We find agreement with the limiting regimes─with respect to surface charge, salt concentration and particle size─in which the assumptions of the PBE and DLVO theory are known to be satisfied.

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We present a theory of the Seebeck effect in nanomagnets with dimensions smaller than the spin diffusion length, showing that the spin accumulation generated by a temperature gradient strongly affects the thermopower. We also identify a correction arising from the transverse temperature gradient induced by the anomalous Ettingshausen effect and an induced spin-heat accumulation gradient. The relevance of these effects for nanoscale magnets is illustrated byab initiocalculations on dilute magnetic alloys.

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A statistical theory is presented of the magnesium ion interacting with lysozyme under conditions where the latter is positively charged. Temporarily assuming magnesium is not noncovalently bound to the protein, I solve the nonlinear Poisson-Boltzmann equation accurately and uniformly in a perturbative fashion. The resulting expression for the effective charge, which is larger than nominal owing to overshooting, is subtle and cannot be asymptotically expanded at high ionic strengths that are practical. An adhesive potential taken from earlier work together with the assumption of possibly bound magnesium is then fitted to be in accord with measurements of the second virial coefficient by Tessier et al. The resulting numbers of bound magnesium ions as a function of MgBr[Formula: see text] concentration are entirely reasonable compared with densitometry measurements.

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The Bhatnagar-Gross-Krook (BGK) single-relaxation-time collision model for the Boltzmann equation serves as the foundation of the lattice BGK (LBGK) method developed in recent years. The description of the collision as a uniform relaxation process of the distribution function towards its equilibrium is, in many scenarios, simplistic. Based on a previous series of papers, we present a collision model formulated as independent relaxations of the irreducible components of the Hermite coefficients in the reference frame moving with the fluid. These components, corresponding to the irreducible representation of the rotation group, are the minimum tensor components that can be separately relaxed without violating rotation symmetry. For the 2nd, 3rd and 4th moments, respectively, two, two and three independent relaxation rates can exist, giving rise to the shear and bulk viscosity, thermal diffusivity and some high-order relaxation process not explicitly manifested in the Navier-Stokes-Fourier equations. Using the binomial transform, the Hermite coefficients are evaluated in the absolute frame to avoid the numerical dissipation introduced by interpolation. Extensive numerical verification is also provided. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.

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An adaptive finite element solver for the numerical calculation of the electrostatic coupling between molecules in a solvent environment is developed and tested. At the heart of the solver is a goal-oriented a posteriori error estimate for the electrostatic coupling, derived and implemented in the present work, that gives rise to an orders of magnitude improved precision and a shorter computational time as compared to standard finite difference solvers. The accuracy of the new solver ARGOS is evaluated by numerical experiments on a series of problems with analytically known solutions. In addition, the solver is used to calculate electrostatic couplings between two chromophores, linked to polyproline helices of different lengths and between the spike protein of SARS-CoV-2 and the ACE2 receptor. All the calculations are repeated by using the well-known finite difference solvers MEAD and APBS, revealing the advantages of the present finite element solver.

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