Inhomogeneous Density Profile Research Articles

Slow body magnetohydrodynamic waves in solar photospheric flux tubes with density inhomogeneity

ABSTRACT Pores and sunspots are ideal environments for the propagation of guided magnetohydrodynamic (MHD) waves. However, modelling such photospheric waveguides with varying background quantities such as plasma density and magnetic field has thus far been very limited. Such modelling is required to correctly interpret MHD waves observed in pores and sunspots with resolved inhomogeneities such as light bridges and umbral dots. This study will investigate the propagation characteristics and the spatial structure of slow body MHD modes in a magnetic flux tube with a circular cross-section with inhomogeneous equilibrium density distribution under solar photospheric conditions in the short wavelength limit. For simplicity, the equilibrium density profile is taken to have a circular density enhancement or depletion. The advantage of this is that the strength, size, and position of the density inhomogeneity can be easily changed. Calculating the eigenfrequencies and eigenfunctions of the slow body modes is addressed numerically with use of the Fourier–Chebyshev Spectral method. The radial and azimuthal variation of eigenfunctions is obtained by solving a Helmholtz-type partial differential equation with Dirichlet boundary conditions. The inhomogeneous equilibrium density profile results in modified eigenvalues and eigenvectors. It was found that a localized density inhomogeneity leads to a decrease in the eigenvalues and the spatial structure of modes ceases to be a global harmonic oscillation, as the modes migrate towards regions of lower density. Comparing the homogeneous case and the cases corresponding to depleted density enhancement, the dimensionless phase speed undergoes a significant drop in its value (at least 40 per cent).

Revisiting the density profile of the fuzzy sphere model for microgel colloids.

Common neutral polymer microgels exhibit an inhomogeneous density profile with a gradual decay that is commonly described using the fuzzy sphere model. The model is based on the idea of convolving the collapsed solid sphere profile with a Gaussian to describe inhomogeneous swelling of the microgel in a good solvent. Here we show that the corresponding density profile in real space used in several recent works - such as in super-resolution microscopy - is different from the fuzzy sphere model, and we explain how to correctly transition between reciprocal space modelling to real space. Our work aims to clarify the application of the model so that errors can be avoided in the future. Our discussion is also crucial when comparing alternative real-space models for the density profile with the established fuzzy sphere model.

Comparative study of force-based classical density functional theory.

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [S. M. Tschopp et al., Phys. Rev. E 106, 014115 (2022)2470-004510.1103/PhysRevE.106.014115]. We compare inhomogeneous density profiles for hard sphere fluids to results from both standard density functional theory and from computer simulations. Test situations include the equilibrium hard sphere fluid adsorbed against a planar hard wall and the dynamical relaxation of hard spheres in a switched harmonic potential. The comparison to grand canonical Monte Carlo simulation profiles shows that equilibrium force-DFT alone does not improve upon results obtained with the standard Rosenfeld functional. Similar behavior holds for the relaxation dynamics, where we use our event-driven Brownian dynamics data as benchmark. Based on an appropriate linear combination of standard and force-DFT results, we investigate a simple hybrid scheme which rectifies these deficiencies in both the equilibrium and the dynamical case. We explicitly demonstrate that although the hybrid method is based on the original Rosenfeld fundamental measure functional, its performance is comparable to that of the more advanced White Bear theory.

Structural properties of liquids in extreme confinement.

We simulate a hard-sphere liquid in confined geometry where the separation of the two parallel, hard walls is smaller than two particle diameters. By systematically reducing the wall separation we analyze the behavior of structural and thermodynamic properties, such as inhomogeneous density profiles, structure factors, and compressibilities when approaching the two-dimensional limit. In agreement with asymptotic predictions, we find for quasi-two-dimensional fluids that the density profile becomes parabolic and the structure factor converges toward its two-dimensional counterpart. To extract the compressibility in polydisperse samples a perturbative expression is used which qualitatively influences the observed nonmonotonic dependence of the compressibility with wall separation. We also present theoretical calculations based on fundamental-measure theory and integral-equationtheory, which are in very good agreement with the simulation results.

Permeability of Polymer Membranes beyond Linear Response

The permeability of a membrane to solute penetrants is well defined on the linear response level simply as the ratio of penetrants’ flux and concentration gradient at the membrane boundary layers. However, nonlinearities emerge in the flux–force relation j(f) for large driving forces f, in which the definition of permeability becomes ambiguous. Here, we study nonequilibrium membrane permeation orchestrated by a generic driving force using penetrant- and monomer-resolved computer simulations of transport in a polymer network, supported by exact solutions of the Smoluchowski (drift–diffusion) equation in the stationary state. In the simulations, we consider the transport across a finite polymer membrane immersed in a reservoir of penetrants, addressing one- and two-component penetrant systems. We calculate the f-dependent inhomogeneous steady-state density profiles, boundary layer concentrations, and fluxes of the penetrants. The Smoluchowski approach, using solely coarse-grained equilibrium partitioning and diffusion profiles as input, exhibits remarkable qualitative agreement with our nonequilibrium simulations, which serves for rationalization of the observations. We discuss possible definitions of nonequilibrium, f-dependent permeability, distinguishing between “system” and “membrane” permeabilities. In particular, we introduce the concept of differential permeability as a response to f. The latter turns out to be a highly nonmonotonic function of f for low-permeable systems, demonstrating how a differential permselectivity is substantially tunable by the driving force beyond linear response.

New Framework for Computing a General Local Self-Diffusion Coefficient Using Statistical Mechanics.

Widely applicable, modified Green-Kubo expressions for the local diffusion coefficient (Dl) are obtained using linear response theory. In contrast to past definitions in use, these expressions are statistical mechanical results. Molecular simulations of systems with anisotropic diffusion and an inhomogeneous density profile confirm the validity of the results. Diffusion coefficients determined from different expressions in terms of currents and velocity correlations agree in the limit of large systems. Furthermore, they apply to arbitrarily small local regions, making them readily applicable to nanoscale and inhomogeneous systems where knowledge of Dl is important.

Nonequilibrium free energy during polymer chain growth.

During fast diffusion-influenced polymerization, nonequilibrium behavior of the polymer chains and the surrounding reactive monomers has been reported recently. Based on the laws of thermodynamics, the emerging nonequilibrium structures should be characterizable by some "extra free energy" (excess over the equilibrium Helmholtz free energy). Here, we study the nonequilibrium thermodynamics of chain-growth polymerization of ideal chains in a dispersion of free reactive monomers, using off-lattice, reactive Brownian dynamics computer simulations in conjunction with approximative statistical mechanics and relative entropy (Gibbs-Shannon and Kullback-Leibler) concepts. In the case of fast growing polymers, we indeed report increased nonequilibrium free energies ΔFneq of several kBT compared to equilibrium and near-equilibrium, slowly growing chains. Interestingly, ΔFneq is a non-monotonic function of the degree of polymerization and thus also of time. Our decomposition of the thermodynamic contributions shows that the initial dominant extra free energy is stored in the nonequilibrium inhomogeneous density profiles of the free monomer gas (showing density depletion and wakes) in the vicinity of the active center at the propagating polymer end. At later stages of the polymerization process, we report significant extra contributions stored in the nonequilibrium polymer conformations. Finally, our study implies a nontrivial relaxation kinetics and "restoring" of the extra free energy during the equilibration process after polymerization.

Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling

Applying time-periodic modulations is routinely used to control and design synthetic matter in quantum-engineered settings. In lattice systems, this approach is explored to engineer band structures with non-trivial topological properties, but also to generate exotic interaction processes. A prime example is density-assisted tunneling, by which the hopping amplitude of a particle between neighboring sites explicitly depends on their respective occupations. Here, we show how density-assisted tunneling can be tailored in view of simulating the effects of strain in synthetic graphene-type systems. Specifically, we consider a mixture of two atomic species on a honeycomb optical lattice: one species forms a Bose-Einstein condensate in an anisotropic harmonic trap, whose inhomogeneous density profile induces an effective uniaxial strain for the second species through density-assisted tunneling processes. In direct analogy with strained graphene, the second species experiences a pseudo-magnetic field, hence exhibiting relativistic Landau levels and the valley Hall effect. Our proposed scheme introduces a unique platform for the investigation of strain-induced gauge fields, opening the door to future studies of their possible interplay with quantum fluctuations and collective excitations.

Layering and packing in confined colloidal suspensions.

Confinement modifies the properties of a fluid. The particle density is no longer uniform but depends on the distance from the walls; parallel to the walls, layers with different particle densities form. This affects the particle packing in the layers. We investigated colloidal fluids with volume fractions between 0.19 and 0.32 confined between rough walls. The particle–particle interactions were dominated by hard-sphere interactions but also contained some electrostatic interactions. The particle locations were determined using confocal microscopy and served to calculate the density profile, radial distribution function, anisotropic and generalized structure factors but also to characterize the arrangement of the wall particles leading to the roughness of the walls. The experiments are complemented by molecular dynamics simulations and fundamental-measure theory. While the particle arrangements are mainly controlled by hard-core interactions, electrostatic interactions become more important as the volume fraction decreases. Furthermore, the structure of the rough walls was varied and found to have a significant effect on the fluid structure. An appropriate representation of the rough walls in the simulations is thus crucial to successfully mimic the experiments.

Spatial Crossover Between Far-From-Equilibrium and Near-Equilibrium Dynamics in Locally Driven Suspensions

We examine the response of a quasi-two-dimensional colloidal suspension to a localized circular driving induced by optical tweezers. This approach allows us to resolve over 3 orders of magnitude in the Péclet number (Pe) and provide a direct observation of a sharp spatial crossover from far- to near-thermal-equilibrium regions of the suspension. In particular, particles migrate from high to low Pe regions and form strongly inhomogeneous steady-state density profiles with an emerging length scale that does not depend on the particle density and is set by Pe≈1. We show that the phenomenological two phase fluid constitutive model is in line with our results.

Sedimentation of a colloidal monolayer down an inclined plane

We study the driven collective dynamics of a colloidal monolayer sedimentating down an inclined plane. The action of the gravity force parallel to the bottom wall creates a flow around each colloid, and the hydrodynamic interactions among the colloids accelerate the sedimentation as the local density increases. This leads to the creation of a universal "triangular" inhomogeneous density profile, with a traveling density shock at the leading front moving in the downhill direction. Unlike density shocks in a colloidal monolayer driven by applied torques rather than forces [Phys. Rev. Fluids, 2(9):092301, 2017], the density front during sedimentation remains stable over long periods of time even though it develops a roughness on the order of tens of particle diameters. Through experimental measurements and particle-based computer simulations, we find that the Burgers equation can model the density profile along the sedimentation direction as a function of time remarkably well, with a modest improvement if the nonlinear conservation law accounts for the sub-linear dependence of the collective sedimentation velocity on density.

Optimal synchronization of laser pulses in THz generation scheme with colliding plasma wakes

This paper discusses optimal conditions for setting up a laboratory experiment on the generation of narrow-band THz radiation due to the head-on collision of two plasma wakes excited by a pair of femtosecond laser pulses in a supersonic helium jet. In this case, emission of electromagnetic waves at the second harmonic of the plasma frequency is caused by nonlinear interaction of counterpropagating plasma waves having different transverse potential profiles in the focus of the laser beams. Using particle-in-cell simulations, we study how strongly the efficiency of laser-to-terahertz energy conversion in this scheme is affected by the inhomogeneous electron density profile arising during field ionization of helium, as well as by the time-delay between arrivals of laser pulses to the focal point.

Active binary switching of soft colloids: stability and structural properties.

We employ reactive dynamical density functional theory (R-DDFT) and reactive Brownian dynamics (R-BD) simulations to study the non-equilibrium structure and phase behavior of an active dispersion of soft Gaussian colloids with binary interaction switching, i.e., we consider a one-component colloidal system in which every particle can individually switch stochastically between two interaction states (here, sizes 'big' and 'small') at predefined rates. We consider the influence of switching activity on the inhomogeneous density profiles of the colloids confined by various external potentials, as well as on their pair structure and phase behavior in bulk solutions. For the latter, we extend the R-DDFT method to incorporate the Percus test-particle route. Our results demonstrate that switching activity strongly modifies the steady-state density profiles and structural (pair) correlations. In particular, the switching rate interpolates from a near-equilibrium binary colloidal mixture of two states at very low rates to a non-equilibrium, 'one-state liquid' at very high rates characterized by one, average interaction size. The latter limit can be described by an equivalent effective one-component (EOC) equilibrium system, for which the exact analytical expression for the effective pair potential is a diffusion-weighted superposition of the active systems' pair potentials. This leads to the interesting fact that under certain conditions an interacting switching system can behave like a non-interacting (ideal) gas in the limit of high switching rates. Moreover, for colloids that are unstable (i.e., demix) near equilibrium, we demonstrate that phase separation and micro-clustering in both confinement and bulk can be dynamically controlled by the switching rate, and vanish for high rates. All R-DDFT results are in excellent agreement with our R-BD simulations.

Configuraional Entropy of a parabolic potential system: A density functional approach

We study the configurational entropy of many-particle system interacting with parabolic potential. The classical density functional theory(cDFT) is used here to study it. In this work, the parabolic potential system is mapped to a hard-sphere system (Mondal et al 2017 Phys. Rev. E 96, 012 124) with a properly chosen diameter and evaluate the free energy. The configurational entropy is obtained from this free energy. In cDFT the inhomogeneous density profile is described in terms of Gaussian density profile located at all the lattice points, which are characterized through Bernal pair correlation function. The extrapolated configurational entropy vanishes at Kauzmann packing fraction(η k ). The η k shows amorphous structure dependence. The dependence of η k with the strength of the parabolic potential is also studied here.

Effect of an inhomogeneous electron density profile on the transmission microwave frequency spectrum of the cutoff probe

The cutoff probe (CP), which precisely measures electron density from a microwave transmission (S 21) spectrum, has been successfully developed through physical models under the assumption of homogeneous plasma between the probe tips. In practice, however, the chamber and sheath structure, flow effects, and the probe insertion itself produce plasma inhomogeneity between the probe tips, which necessitates the study of any related effects on the CP measurement results. This paper investigated the effect of inhomogeneous plasma on the S 21 of the CP through a three-dimensional E/M wave simulation with various density gradient directions. The simulations found, notably, double cutoff peaks and a cutoff frequency shift in the S 21 that depend on the gradient direction. These results are analyzed via a simple circuit model of the CP, and their origins are elucidated at the end of this paper.

Measuring pressure in equilibrium and nonequilibrium lattice-gas models.

We develop an algorithm based on the method proposed by Dickman for directly measuring pressure in lattice-gas models. The algorithm gives the possibility to access the equation of state with a single run by adding multiple ghost sites to the original system. This feature considerably improves calculations and makes the algorithm particularly efficient for systems with inhomogeneous density profiles, both in equilibrium and nonequilibrium steady states. We illustrate its broad applicability by considering some paradigmatic systems of statistical mechanics such as the lattice gas under gravity, nearest-neighbor exclusion models in finite dimension and on regular random graphs, and the boundary-driven simple symmetric exclusion process.

Anisotropic transport induced by DC electrical current bias near the critical current

We investigated the transport characteristics of a square shape superconducting Ta thin film under DC electrical current bias along the diagonal direction. The resistance parallel (R∥) and perpendicular (R⊥) to the DC current, IDC, is measured with various magnetic fields. R∥ and R⊥ show contrasting dependence on IDC. First, the critical current of R∥ is smaller than that of R⊥. Second, R⊥ shows an unexpected reduction at current bias where R∥ shows a rapid increase near the transition from a flux flow state to a normal state. The intriguing anisotropic transport characteristics can be understood by the inhomogeneous current density profile over the square sample. Diagonal DC current induces an anisotropic current density profile where the current density is high near the biasing electrode and low at the center of the sample. Accordingly, the electrical transport in the perpendicular direction could remain less affected even near the critical current of R∥, which leads to the higher critical current in R⊥. Complicated conduction profile may also allow the anomalous reduction in the R⊥ before finally shifting to the normal state.

Effect of optical field ionisation on the generation of wake fields by femtosecond laser pulses in an inhomogeneous plasma

We consider the interaction of a high-intensity short laser pulse with an argon gas during optical field ionisation. Modelling in a three-dimensional cylindrical symmetric geometry is performed at various moderately relativistic intensities and positions of the focal plane of the laser beam in the case of both optical gas ionisation and a pre-ionised plasma. The influence of the processes occurring during optical field ionisation of the gas on the generation of wake waves is investigated, and the conditions are found under which intense wake fields are produced in a plasma formed from an inhomogeneous argon gas jet. The possibility of using a gas with a large number of electrons on the outer shell (argon) to excite intense wake waves and accelerate electrons is demonstrated. Despite significant ionisation refraction of the laser pulse on a radially inhomogeneous density profile of plasma electrons formed during optical field ionisation, the region of the parameters of the laser pulse and the gas target is determined at which ionisation refraction leads to the excitation of an intense wake wave. It is found that in a pre-ionised plasma a wake wave is not generated even at the same laser radiation intensity.

An acoustic invisible medium: A first-principles study

We design and build an acoustic invisible medium (AIM) based on first principles. Isotropic, inhomogeneous mass density and bulk modulus profiles of the AIM are derived from scattering-free conditions. Acoustic invisibility is illustrated by two types of examples: the AIM under plane-wave incidence and point sound sources. It is found that an AIM of arbitrary shape is invisible to plane waves of any incident angle. The invisibility of the AIM holds for any sound source sitting anywhere except for in the AIM region. Acoustic field distributions show that the acoustic wave enters the AIM from one side and recovers its initial shape at the other side. The designed AIMs are numerically verified by the finite element method, and are highly consistent with theoretical results. This work offers an alternative strategy to achieve a scattering-free AIM and could be extendable to the three-dimensional cases.

Glauber model for a small system using the anisotropic and inhomogeneous density profile of a proton

Recent studies reveal that at high energies, collisions of a small system such as $p+p$ gives signatures similar to that widely observed in heavy ion collisions hinting toward the possibility of forming a medium with collective behavior. With this motivation, we have used the Glauber model, which is traditionally applied to heavy ion collisions, in a small system using the anisotropic and inhomogeneous density profile of a proton and found that the proposed model reproduces the charged particle multiplicity distribution of $p+p$ collisions at LHC energies very well. Collision geometric properties such as the mean impact parameter, the mean number of binary collisions ($⟨{N}_{\mathrm{coll}}⟩$), and the mean number of participants ($⟨{N}_{\mathrm{part}}⟩$) at different multiplicities are determined. Having estimated $⟨{N}_{\mathrm{coll}}⟩$, we have calculated the nuclear modificationlike factor (${R}_{\mathrm{HL}}$) in $p+p$ collisions. We also estimated eccentricity and elliptic flow as a function of charged particle multiplicity using the linear response to the initial geometry.