Inhomogeneous Density Profile Research Articles

Instationary compaction wave propagation in highly porous cohesive granular media

We study the collision of a highly porous granular aggregate of adhesive $$\upmu $$ m-sized silica grains with a hard wall using a granular discrete element method. A compaction wave runs through the granular sample building up an inhomogeneous density profile. The compaction is independent of the length of the aggregate, within the regime of lengths studied here. Also short pulses, as they might be exerted by a piston pushing the granular material, excite a compaction wave that runs through the entire material. The speed of the compaction wave is larger than the impact velocity but considerably smaller than the sound speed. The wave speed is related to the compaction rate at the colliding surface and the average slope of the linear density profile.

An EQT-cDFT approach to determine thermodynamic properties of confined fluids

We present a continuum-based approach to predict the structure and thermodynamic properties of confined fluids at multiple length-scales, ranging from a few angstroms to macro-meters. The continuum approach is based on the empirical potential-based quasi-continuum theory (EQT) and classical density functional theory (cDFT). EQT is a simple and fast approach to predict inhomogeneous density and potential profiles of confined fluids. We use EQT potentials to construct a grand potential functional for cDFT. The EQT-cDFT-based grand potential can be used to predict various thermodynamic properties of confined fluids. In this work, we demonstrate the EQT-cDFT approach by simulating Lennard-Jones fluids, namely, methane and argon, confined inside slit-like channels of graphene. We show that the EQT-cDFT can accurately predict the structure and thermodynamic properties, such as density profiles, adsorption, local pressure tensor, surface tension, and solvation force, of confined fluids as compared to the molecular dynamics simulation results.

Orbital-Free Density Functional Theory of Out-of-Plane Charge Screening in Graphene

We propose a density functional theory of Thomas-Fermi-Dirac-von Weizs\"acker type to describe the response of a single layer of graphene resting on a dielectric substrate to a point charge or a collection of charges some distance away from the layer. We formulate a variational setting in which the proposed energy functional admits minimizers, both in the case of free graphene layers and under back-gating. We further provide conditions under which those minimizers are unique and correspond to configurations consisting of inhomogeneous density profiles of charge carrier of only one type. The associated Euler-Lagrange equation for the charge density is also obtained, and uniqueness, regularity and decay of the minimizers are proved under general conditions. In addition, a bifurcation from zero to non-zero response at a finite threshold value of the external charge is proved.

Communication: Intraparticle segregation of structurally homogeneous polyelectrolyte microgels caused by long-range Coulomb repulsion.

Structurally homogeneous polyelectrolyte microgels in dilute aqueous solutions are shown to exhibit inhomogeneous density profile including intraparticle "phase" coexistence of hollow core and dense "skin." This effect is a consequence of long-range Coulomb repulsion of charged groups which appear because of entropy-driven escape of monovalent counterions into the outer solvent. Excess of the charged groups at the periphery of the microgel particle reduces electrostatic energy and overall free energy of the system despite a penalty in the elastic free energy of strongly stretched subchains in the hole. This finding can serve as additional tool controlling encapsulation, transport, and release of high- and low-molecular-weight species in processes where the microgels are used as delivery systems.

An ab initio molecular dynamics study of the liquid-vapor interface of an aqueous NaCl solution: inhomogeneous density, polarity, hydrogen bonds, and frequency fluctuations of interfacial molecules.

We have presented a first principles simulation study of the structural and dynamical properties of a liquid-vapor interfacial system of a concentrated (5.3 M) aqueous NaCl solution. We have used ab initio molecular dynamics to examine the structural and dynamical properties of the bulk and interfacial regions. The structural aspects of the system that have been considered here include the inhomogeneous density profiles of ions and water molecules, hydrogen bond distributions, orientational profiles, and also vibrational frequency distributions in the bulk and interfacial regions. It is found that the sodium ions are mostly located in the interior, while the chloride anions occupy a significant portion of the interface of the slab. The water dipoles at the interface prefer to orient parallel to the surface. The dynamical aspects of the interfaces are investigated in terms of diffusion, orientational relaxation, hydrogen bond dynamics, and vibrational spectral diffusion. The results of the interfacial dynamics are compared with those of the corresponding bulk region. It is observed that the interfacial molecules exhibit faster diffusion and orientational relaxation with respect to the bulk. However, the interfacial molecules are found to have longer hydrogen bond lifetimes than those of the bulk. We have also investigated the correlations of hydrogen bond relaxation with the vibrational frequency fluctuations of interfacial water molecules.

Hydrogen bonded structure, polarity, molecular motion and frequency fluctuations at liquid-vapor interface of a water-methanol mixture: an ab initio molecular dynamics study.

We have performed ab initio molecular dynamics simulations of a liquid-vapor interfacial system consisting of a mixture of water and methanol molecules. Detailed results are obtained for the structural and dynamical properties of the bulk and interfacial regions of the mixture. Among structural properties, we have looked at the inhomogeneous density profiles of water and methanol molecules, hydrogen bond distributions and also the orientational profiles of bulk and interfacial molecules. The methanol molecules are found to have a higher propensity to be at the interface than water molecules. It is found that the interfacial molecules show preference for specific orientations so as to form water-methanol hydrogen bonds at the interface with the hydrophobic methyl group pointing towards the vapor side. It is also found that for both types of molecules, the dipole moment decreases at the interface. It is also found that the local electric field of water influences the dipole moment of methanol molecules. Among the dynamical properties, we have calculated the diffusion, orientational relaxation, hydrogen bond dynamics, and vibrational frequency fluctuations in bulk and interfacial regions. It is found that the diffusion and orientation relaxation of the interfacial molecules are faster than those of the bulk. However, the hydrogen bond lifetimes are longer at the interface which can be correlated with the time scales found from the decay of frequency time correlations. The slower hydrogen bond dynamics for the interfacial molecules with respect to bulk can be attributed to diminished cooperative effects at the interface due to reduced density and number of hydrogen bonds.

Structure and Dynamics of the Liquid–Liquid Interface of an Aqueous NaCl Solution with Liquid Carbon Tetrachloride from First-Principles Simulations

The present work deals with a first-principles theoretical study of the liquid–liquid interfacial system of an aqueous NaCl solution with the hydrophobic liquid of carbon tetrachloride (CCl4). Various structural and electronic properties of the system such as the inhomogeneous density profiles of ions and water molecules, hydrogen bond distributions, orientational profiles, vibrational frequency distributions, and also dipole moments of water at the bulk and interface are investigated. It is found that the chloride ions have a higher propensity for the interface and the sodium ions have a tendency to reside in the inner side of the aqueous medium. The dynamical aspects of the interfaces are analyzed in terms of the diffusion, orientational relaxation, hydrogen bond dynamics, and vibrational spectral diffusion and are compared with those of the bulk regions. It is found that the interfacial molecules have a faster diffusion and orientation relaxation with respect to the bulk molecules. The interfacial wate...

Surface plasmon dependence on the electron density profile at metal surfaces.

We use an extension of the hydrodynamic model to study nonlocal effects in the collective plasmon excitations at metal surfaces and narrow gaps between metals, including the surface spill-out of conduction band electrons. In particular, we simulate metal surfaces consisting of a smooth conduction-electron density profile and an abrupt jellium edge. We focus on aluminum and gold as prototypical examples of simple and noble metals, respectively. Our calculations agree with the dispersion relations measured from planar surfaces for these materials. Systems involving small gaps display a regime of tunnelling electrons, which is partially captured by the overlap of electron densities. This extension of the hydrodynamic model to cope with inhomogeneous density profiles provides a relatively fast and accurate way of describing the optical response of metal surfaces at subnanometer distances.

Structure, thermodynamics, and position-dependent diffusivity in fluids with sinusoidal density variations.

Molecular dynamics simulations and a stochastic method based on the Fokker-Planck equation are used to explore the consequences of inhomogeneous density profiles on the thermodynamic and dynamic properties of the hard-sphere fluid and supercooled liquid water. Effects of the inhomogeneity length scale are systematically considered via the imposition of sinusoidal density profiles of various wavelengths. For long-wavelength density profiles, bulk-like relationships between local structure, thermodynamics, and diffusivity are observed as expected. However, for both systems, a crossover in behavior occurs as a function of wavelength, with qualitatively different correlations between the local static and dynamic quantities emerging as density variations approach the scale of a particle diameter. Irrespective of the density variation wavelength, average diffusivities of hard-sphere fluids in the inhomogeneous and homogeneous directions are coupled and approximately correlate with the volume available for insertion of another particle. Unfortunately, a quantitatively reliable static predictor of position-dependent dynamics has yet to be identified for even the simplest of inhomogeneous fluids.

The effect of plasma radius and profile on the development of self-modulation instability of electron bunches

Plasmas available for plasma wakefield accelerator experiments may have longitudinal and transverse density profiles that could affect the outcome of an experiment. This paper investigates the effect of plasmas with finite radius and inhomogeneous transverse density profiles on the wakefield excitation and the self-modulation instability (SMI) development in overdense plasmas. We focus here on the case of an electron bunch. Simulation results show that such plasmas generate larger focusing force for the propagating electron beam and therefore higher growth rate for the SMI. Although the initial accelerating field (Ez) amplitude is lower in such plasmas, the increased focusing force can dominate the development trend of the SMI, i.e., larger saturated Ez amplitude can be reached over similar plasma lengths.

Effects of nanoscale density inhomogeneities on shearing fluids

It is well known that density inhomogeneities at the solid-liquid interface can have a strong effect on the velocity profile of a nanoconfined fluid in planar Poiseuille flow. However, it is difficult to control the density inhomogeneities induced by solid walls, making this type of system unsuitable for a comprehensive study of the effect on density inhomogeneity on nanofluidic flow. In this paper, we employ an external force compatible with periodic boundary conditions to induce the density variation, which greatly simplifies the problem when compared to flow in nonperiodic nanoconfined systems. Using the sinusoidal transverse force method to produce shearing velocity profiles and the sinusoidal longitudinal force method to produce inhomogeneous density profiles, we are able to observe the interactions between the two property inhomogeneities at the level of individual Fourier components. This gives us a method for direct measurement of the coupling between the density and velocity fields and allows us to introduce various feedback control mechanisms which customize fluid behavior in individual Fourier components. We briefly discuss the role of temperature inhomogeneity and consider whether local thermal expansion due to nonuniform viscous heating is sufficient to account for shear-induced density inhomogeneities. We also consider the local Newtonian constitutive relation relating the shear stress to the velocity gradient and show that the local model breaks down for sufficiently large density inhomogeneities over atomic length scales.

2D and 3D modeling of wave propagation in cold magnetized plasma near the Tore Supra ICRH antenna relying on the perfecly matched layer technique

A novel method to simulate ion cyclotron wave coupling in the edge of a tokamak plasma with the finite element technique is presented. It is applied in the commercial software COMSOL Multiphysics. Its main features include the perfectly matched layer (PML) technique to emulate radiating boundary conditions beyond a critical cutoff layer for the fast wave (FW), full-wave propagation across the inhomogeneous cold peripheral plasma and a detailed description of the wave launcher geometry. The PML technique, while widely used in numerical simulations of wave propagation, has scarcely been used for magnetized plasmas, due to specificities of this gyrotropic material. A versatile PML formulation, valid for full dielectric tensors, is summarized and interpreted as wave propagation in an artificial medium. The behavior of this technique has been checked for plane waves on homogeneous plasmas. Wave reflection has been quantified and compared to analytical predictions. An incompatibility issue for adapting the PML for forward (FW) and backward (slow wave (SW)) propagating waves simultaneously has been evidenced. In a tokamak plasma, this critical issue is overcome by taking advantage of the inhomogeneous density profile to reflect the SW before it reaches the PML. The simulated coupling properties of a Tore Supra ion cyclotron resonance heating (ICRH) antenna have been compared to experimental values in a situation of good single-pass absorption. The necessary antenna elements to include in the geometry to recover the coupling properties obtained experimentally are also discussed.

Experimental determination ofp-wave scattering parameters in ultracold6Li atoms

We report the experimental determination of the scattering parameters for a p-wave Feshbach resonance in a single component Fermi gas of 6Li atoms in the lowest spin state. The time scale of the cross-dimensional relaxation reflects the elastic scattering rate of the atoms, and scattering parameters are determined from the scattering rate as a function of magnetic field by taking into account the momentum distribution and inhomogeneous density profile of the atoms in a trap. Precise determination of the scattering parameters for a p-wave Feshbach resonance is an important step toward the realization of a p-wave superfluid in an ultracold atomic gas.

Ponderomotive force on solitary structures created during radiation pressure acceleration of thin foils

We estimate the ponderomotive force on an expanded inhomogeneous electron density profile, created in the later phase of laser irradiated diamond like ultrathin foil. When ions are uniformly distributed along the plasma slab and electron density obeys the Poisson's equation with space charge potential equal to negative of ponderomotive potential, ϕ=−ϕp=−(mc2/e)(γ−1), where γ=(1+|a|2)1/2, and |a| is the normalized local laser amplitude inside the slab; the net ponderomotive force on the slab per unit area is demonstrated analytically to be equal to radiation pressure force for both overdense and underdense plasmas. In case electron density is taken to be frozen as a Gaussian profile with peak density close to relativistic critical density, the ponderomotive force has non-monotonic spatial variation and sums up on all electrons per unit area to equal radiation pressure force at all laser intensities. The same result is obtained for the case of Gaussian ion density profile and self consistent electron density profile, obeying Poisson's equation with ϕ=−ϕp.

Pauli paramagnetism of an ideal Fermi gas

We show how to use trapped ultracold atoms to measure the magnetic susceptibility of a two-component Fermi gas. The method is illustrated for a noninteracting gas of ${}^{6}$Li, using the tunability of interactions around a wide Feshbach resonance. The susceptibility versus effective magnetic field is directly obtained from the inhomogeneous density profile of the trapped atomic cloud. The wings of the cloud realize the high-field limit where the polarization approaches 100$%$, which is not accessible for an electron gas.

Double ionization effect in electron accelerations by high-intensity laser pulse interaction with a neutral gas

We study the effect of laser-induced double-ionization of a helium gas (with inhomogeneous density profile) on vacuum electron acceleration. For enough laser intensity, helium gas can be found doubly ionized and it strengthens the divergence of the pulse. The double ionization of helium gas can defocus the laser pulse significantly, and electrons are accelerated by the front of the laser pulse in vacuum and then decelerated by the defocused trail part of the laser pulse. It is observed that the electrons experience a very low laser-intensity at the trailing part of the laser pulse. Hence, there is not much electron deceleration at the trailing part of the pulse. We found that the inhomogeneity of the neutral gas reduced the rate of tunnel ionization causing less defocusing of the laser pulse and thus the electron energy gain is reduced.

Validity of Calibrated Photoluminescence Lifetime Measurements of Crystalline Silicon Wafers for Arbitrary Lifetime and Injection Ranges

We investigate the validity of calibrated photoluminescence lifetime measurements of crystalline silicon wafers for arbitrary lifetime and injection ranges. Absolute lifetime images are obtained from steady-state photoluminescence measurements by relating the photoluminescence signal to the excess carrier density. Since the luminescence signal is expected to be related to the integral of the depth distribution of the excess carrier density, an adequate calibration of the luminescence signal requires a secondary method which yields the integral of the depth distribution of the excess carrier density in absolute units. In this paper, we investigate the applicability of steady-state photoconductance measurements for the calibration of the photoluminescence signal. We derive a generalized relation linking the photoluminescence signal with the excess carrier density, considering the impact of an inhomogeneous carrier concentration profile. We experimentally verify the impact of the carrier distribution on the photoluminescence calibration by investigating two silicon wafers with different electronic bulk properties. Finally, we propose an iterative correction procedure reducing the deviations due to an inhomogeneous carrier density profile of calibrated photoluminescence-based lifetime measurements significantly.

Microwave propagation in a magnetized inhomogeneous plasma slab using the Appleton–Hartree magnetoionic theory

Electromagnetic wave propagation in a nonuniform, collisional, magnetized plasma slab is investigated within magnetoionic theory. We allow for the presence of an ideal conductor at a distance d from the right transmissive plasma boundary, and derive the reflection, absorption, and transmission coefficients analytically for an arbitrary inhomogeneous plasma density profile. Dividing the inhomogeneous plasma slab into n thin layers allows for treating each layer as a homogeneous plasma and, therefore, the complex index of refraction of the magnetoionic theory is used to express the complex propagation vector of the waves in each layer. Upon matching the fields at all interfaces, a global matrix is formed that allows for the determination of the reflection, absorption, and transmission coefficients analytically. Results show that in the absence of the metallic wall, the reflected signal is a weak peak near ωce, while in the presence of the metallic wall this weak signal is overwhelmed by a strong transmitted...

A first principles simulation study of fluctuations of hydrogen bonds and vibrational frequencies of water at liquid–vapor interface

We present a theoretical study of the structure and dynamics of water–vapor interface by means of ab initio molecular dynamics simulations. The inhomogeneous density, hydrogen bond and orientational profiles, voids and vibrational frequency distributions are investigated. We have also studied various dynamical properties of the interface such as diffusion, orientational relaxation, hydrogen bond dynamics and vibrational frequency fluctuations. The diffusion and orientational relaxation of water molecules are found to be faster at the interface which can be correlated with the voids present in the system. The hydrogen bond dynamics, however, is found to be slightly slower at the interface than that in bulk water. The correlations of hydrogen bond relaxation with the dynamics of vibrational frequency fluctuations are also discussed.

Theory of spatially inhomogeneous Bloch oscillations in semiconductor superlattices

In a semiconductor superlattice with long scattering times, damping of Bloch oscillations due to scattering is so small that nonlinearities may compensate it and Bloch oscillations persist even in the hydrodynamic regime. To demonstrate this, a Boltzmann-Poisson transport model of miniband superlattices with inelastic collisions is proposed and hydrodynamic equations for electron density, electric field and the complex amplitude of the Bloch oscillations are derived by singular perturbation methods. For appropriate parameter ranges, numerical solutions of these equations show stable Bloch oscillations with spatially inhomogeneous field, charge, current density and energy density profiles. These Bloch oscillations disappear as scattering times become sufficiently short. For sufficiently low lattice temperatures, Bloch and Gunn type oscillations mediated by electric field, current and energy domains coexist for a range of voltages. For larger lattice temperatures (300 K), there are only Bloch oscillations with stationary amplitude and electric field profiles.