Hard Wall Research Articles

Enhanced viscous dissipation of sound in phononic supercrystal

Sound wave propagating in a homogeneous viscous medium decays due viscous losses with decay coefficient γ;0∼ηω2, where η is shear viscosity. Presence of a hard wall strongly increases viscous losses which now occurs mainly within a narrow boundary layer δ. Viscous losses in a 2D phononic crystal are analytically calculated in the low-frequency limit for arbitrary Bravais lattice. The decay coefficient is expressed through series over reciprocal lattice vectors. If the phononic crystal possesses less than 3-fold rotational symmetry it behaves as anisotropic viscous medium. Otherwise, the decay coefficient is isotropic. Depending on the crystal structure and the filling fraction of solid cylinders the decay coefficient γ;ph may exceed γ;0 by two-four orders of magnitude. The decay coefficient may be further enhanced in a supercrystal – a structure with doubly periodicity. The supercrystal is a 2D structure of two sets of aluminum cylinders in air. A periodic set of larger cylinders is imbedded in another set of smaller cylinders arranged in a lattice with smaller period. We present analytical, numerical, and experimental results for decay of sound in a hexagonal supercrystal of aluminum cylinders in air. [This work is supported by the NSF under EFRI Grant No. 1741677.]

Electron density analysis of two-electron systems confined by prolate spheroids with hard walls

The electron density of two-electron systems, He and H2, was analyzed when prolate spheroids with hard walls confine these systems. For this purpose, Hartree–Fock equations were solved using Roothaan's approach with a basis set defined in prolate spheroidal coordinates imposing Dirichlet boundary conditions. Total energy, its components, and orbital energies were analyzed for several confinements, and some of these results were compared with those reported by other authors to test the performance of the proposed approach. For both systems, the electron density exhibits a maximum value out of the nuclear region for extreme confinements. The chemical bond for H2 was analyzed through the concepts of the quantum theory of atoms in molecules, concluding that the chemical bond of this molecule disappears under extreme conditions. For this system, estimations of the correlation energy indicate that this is a small contribution to the total energy, and the Hartree–Fock method contains the necessary elements to describe the chemical bond for strong confinements.

Machine Learning of a Density Functional for Anisotropic Patchy Particles.

Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here, we formulate an approach to the Kern-Frenkel model via the classical density functional theory to describe the positionally and orientationally resolved equilibrium density distributions in flat wall geometries. The density functional is split into a reference part for the orientationally averaged density and an orientational part in mean-field approximation. To bring the orientational part into a kernel form suitable for machine learning (ML) techniques, an expansion into orientational invariants and the proper incorporation of single-particle symmetries are formulated. The mean-field kernel is constructed via ML on the basis of hard wall simulation data. The results are compared to the well-known random-phase approximation, which strongly underestimates the orientational correlations close to the wall. Successes and shortcomings of the mean-field treatment of the orientational part are highlighted and perspectives are given for attaining a full-density functional via ML.

External field-driven property localization in liquids of responsive macromolecules.

We explore theoretically the effects of external potentials on the spatial distribution of particle properties in a liquid of explicitly responsive macromolecules. In particular, we focus on the bistable particle size as a coarse-grained internal degree of freedom (DoF, or "property"), σ, that moves in a bimodal energy landscape, in order to model the response of a state-switching (big-to-small) macromolecular liquid to external stimuli. We employ a mean-field density functional theory (DFT) that provides the full inhomogeneous equilibrium distributions of a one-component model system of responsive colloids (RCs) interacting with a Gaussian pair potential. For systems confined between two parallel hard walls, we observe and rationalize a significant localization of the big particle state close to the walls, with pressures described by an exact RC wall theorem. Application of more complex external potentials, such as linear (gravitational), osmotic, and Hamaker potentials, promotes even stronger particle size segregation, in which macromolecules of different size are localized in different spatial regions. Importantly, we demonstrate how the degree of responsiveness of the particle size and its coupling to the external potential tune the position-dependent size distribution. The DFT predictions are corroborated by Brownian dynamics simulations. Our study highlights the fact that particle responsiveness can be used to localize liquid properties and therefore helps to control the property- and position-dependent function of macromolecules, e.g., in biomedical applications.

Core-shell particle formation via Co-assembly of AB diblock copolymers and nanoparticles in 3D soft confinement.

Core-shell particle formation via co-assembly of AB diblock copolymers and nanoparticles in 3D soft confinement was studied using a simulated annealing method. Several sequences of soft confinement-induced core-shell particles were predicted as functions of the volume fraction of the nanoparticle to core-shell particles, the incompatibility between blocks, the volume fractions of A-blocks, the chain length of AB diblocks, the eccentricity of the nanoparticle, and the initial concentration of copolymers. Simulation results demonstrate that those factors are able to tune the morphology of the core-shell particles precisely. Calculated data indicate that the copolymer chain was located between a hard confinement wall composed of the nanoparticle and a soft confinement wall composed of solvents, and the arrangement direction of the copolymer chains was in a competitive equilibrium between the two. We anticipate that this work will be helpful and instructive for the preparation of polymer shells with different structures and shapes, as well as the study of self-assembly morphology of copolymers in a complex confinement systems.

Outdoor engine test using acoustic liners combined with Fine-Perforated-Film

Resonant-type liner panels are one the primary countermeasures for the fan noise of aircraft engines, though the noise reduction performances of the liners are known to be tolerated by the flow streaming on the liner surface. Therefore, suppressing the effect of the flow on the liners is greatly important for larger noise reduction. In this study, a liner panel with a special surface structure was manufactured and applied to an outdoor test using a small turbofan engine, DGEN 380. The surface structure consisted of a special thin film, Fine-Perforated-Film (FPF), and a gap. The gap was fixed between the FPF and liner surface. In addition, a typical resonant-type liner and a hard wall were used for comparison, to investigate the effect of the structure. During the test, the samples were installed to the exhaust bypass duct of the DGEN 380 engine. The acoustic pressure was measured with a far field microphone array. Analysis and comparison of the results showed that the new structure suppressed the effect of the grazing flow and caused a larger amount of noise reduction, compared to the typical liner sample.

Trajectories of square lattice staircase polygons

The distribution of monomers in a coating of grafted and adsorbing polymers is modelled using a grafted staircase polygon in the square lattice. The adsorbing staircase polygon consists of a bottom and a top lattice path (branches) and the asymptotic probability density that vertices in the lattice are occupied by these paths is determined. This is a model consisting of two linear polymers grafted to a hard wall in a coating. The probability that either the bottom path, or the top path, of a staircase polygon passes through a lattice site with coordinates , for 0 < ϵ < 1 and δ ≥ 0, is determined asymptotically as n → ∞ . This gives the probability density of vertices in the staircase polygon in the scaling limit (as n → ∞ ): = The densities of other cases, grafted and adsorbed, and at the adsorption critical point (or special point), are also determined. In these cases the most likely and mean trajectories of the paths are determined. The results show that low density regions in the distribution induce entropic forces on test particles which confine them next to the hard wall, or between branches of the staircase polygon. These results give qualitative mechanisms for the stabilisation of a drug particle confined to a polymer coating in a drug delivery system such as a drug-eluding stent covered by a grafted polymer.

Exponential moments for disk counting statistics at the hard edge of random normal matrices

We consider the multivariate moment generating function of the disk counting statistics of a model Mittag-Leffler ensemble in the presence of a hard wall. Let n be the number of points. We focus on two regimes: (a) the “hard edge regime” where all disk boundaries are at a distance of order \frac{1}{n} from the hard wall, and (b) the “semi-hard edge regime” where all disk boundaries are at a distance of order \frac{1}{\sqrt{n}} from the hard wall. As n \to + \infty , we prove that the moment generating function enjoys asymptotics of the form \exp (C_{1}n + C_{2}\ln n + C_{3} + \frac{C_{4}}{\sqrt{n}} + \mathcal{O}(n^{-\frac{3}{5}})) for the hard edge, \exp (C_{1}n + C_{2}\sqrt{n} + C_{3} + \frac{C_{4}}{\sqrt{n}} + \mathcal{O}(\frac{(\ln n)^{4}}{n})) for the semi-hard edge. In both cases, we determine the constants C_{1},\dots,C_{4} explicitly. We also derive precise asymptotic formulas for all joint cumulants of the disk counting function, and establish several central limit theorems. Surprisingly, and in contrast to the “bulk”, “soft edge”, and “semi-hard edge” regimes, the second and higher order cumulants of the disk counting function in the “hard edge” regime are proportional to n and not to \sqrt{n} .

Application of a Navigated Drill for Cervical Pedicle Screw Insertion at C3-6.

Background Perforation of the cervical pedicle screw, especially lateral perforation, may lead to critical complications, such as vertebral artery injury. Sub-axial cervical spines (C3-6) are at risk of complications because these levels have limited area and angle. This study aimed to compare a navigated drill and a navigated probe for the insertion of cervical pedicle screws at C3-6. Methodology This retrospective study included 106 patients treated with cervical pedicle screws at C3-6. In total, 52 patients with 200 cervical pedicle screws using a navigated drill (group D) and 54 patients with 170 cervical pedicle screws using a navigated probe (group P) were compared. The perforation rate, anatomical medial angle of the pedicle, and actual angle of the screw were investigated using computed tomography. The planning error was defined as when the pedicle screw was applied for a small pedicle width of <3.5 mm. All perforations except for planning errors were defined as technical perforations. Results Grade 1 screw perforations were identified in 16 and 17 screws in groups D and P, respectively. Overall, 88% of the perforations were medial in group D, and 82% of perforations were lateral in group P. Technical perforations were found in 7/191 (3.7%, group D) and 15/168 (8.9%, group P) screws. There were no significant differences in the anatomical angle of the pedicle between the groups. The mean medial angle of the pedicle screws was 24.7° (group D) and 30.9° (group P) (p < 0.05). Conclusions The perforation rate of group D was less than half of that of group P. This was because a navigated drill was able to create a bony pilot hole at the hard medial cortical wall of the pedicle with a small medial angle, which was difficult to do with a navigated probe. A navigated drill can be useful for cervical pedicle screw insertion at C3-6 because of its easiness and safety.

Generalized geometric criteria for the absence of effective many-body interactions in the Asakura–Oosawa model

We investigate variants of the Asakura–Oosawa (AO) model for colloid-polymer mixtures, represented by hard classical particles interacting via their excluded volume. The interaction between the polymers is neglected but the colloid-polymer and colloid-colloid interactions are present and can be condensed into an effective depletion interaction among the colloids alone. The original AO model involves hard spherical particles in three spatial dimensions with colloidal radii R and the so-called depletion radius δ of the polymers, such that the minimum possible center-to-center distance between polymers and colloids allowed by the excluded-volume constraints is R + δ. It is common knowledge among physicists that there are only pairwise effective depletion interactions between the colloids if the geometric condition δ/R&amp;lt;2/3−1 is fulfilled. In this case, triplet and higher-order many body interactions are vanishing and the equilibrium statistics of the binary mixture can exactly be mapped onto that of an effective one-component system with the effective depletion pair-potential. Here we rigorously prove that the criterion δ/R&amp;lt;2/3−1 is both sufficient and necessary to guarantee the absence of triplet and higher-order many body interactions among the colloids. For an external hard wall confining the system, we also include a criterion which guarantees that the system can be exactly mapped onto one with effective external one-body interactions. Our general formulation also accounts for polydisperse mixtures and anisotropic shapes of colloids in any spatial dimension. In those cases where the resulting condition is only sufficient, we further demonstrate how to specify improved bounds.

Nambu-goldstone Modes in Two Segregated Bose-einstein Condensates Limited by Two Hard Walls

The Nambu-Goldstone (NG) modes in the system of two segregated Bose-Einstein condensates (BECs) limited by two hard walls are studied by means of the Gross-Pitaevskii (GP) theory. Based on the double-parabola approximation (DPA) combining with the Bogoliubov-de Gennes (BdG) equations we found four NG modes that proves the failure of the Watanabe-Brauner counting rule and, furthermore, their dispersion relations depend explicitly on the geometrical structure.&#x0D; &#x0D; &#x0D;

Lane formation of colloidal particles driven in parallel by gravity.

We investigate the lane formation in nonequilibrium systems of colloidal particles moving in parallel that are driven by the force of gravity. For this setup, an experimental implementation of a channel on a slope can be conceptualized. We employ the Brownian dynamics algorithm and confine the repulsive particles with hard walls based on the solution of the Smoluchowski equationin the half space. A difference of the driving force acting on the colloids could be achieved by using two spherical particle types with differing diameters but equal mass density. First, we investigate how a difference in the channel slope affects the lane formation of the systems, after which we analyze the lanes that formed. We find that the large particles push the small particles to the walls, resulting in exclusively small particle lanes at the walls. This contrasts the equilibrium state, where depletion forces push the larger particles to the walls. Additionally, we have a closer look at the mechanisms by which the lanes form. Finally, we find system parameter values that foster lane formation to lay the foundation for an experimental realization of our proposed setup. To round this off, we give an exemplary calculation of the slope angle needed to get the experimental system into a state of lane order. With the examination of lane order in systems that are driven in parallel, we hope to deepen our understanding of nonequilibrium order phenomena.

Elliptic billiard with harmonic potential: Classical description.

The classical dynamics of the isotropic two-dimensional harmonic oscillator confined by an elliptic hard wall is discussed. The interplay between the harmonic potential with circular symmetry and the boundary with elliptical symmetry does not spoil the separability in elliptic coordinates; however, it generates nontrivial energy and momentum dependencies in the billiard. We analyze the equimomentum surfaces in the parameter space and classify the kinds of motion the particle can have in the billiard. The winding numbers and periods of the rotational and librational trajectories are analytically calculated and numerically verified. A remarkable finding is the possibility of having degenerate rotational trajectories with the same energy but different second constant of motion and different caustics and periods. The conditions to get these degenerate trajectories are analyzed. Similarly, we show that obtaining two different rotational trajectories with the same period and second constant of motion but different energy is possible.

Layer-by-Layer Nanofluidic Membranes for Promoting Blue Energy Conversion.

Access to and use of energy resources are now crucial components of modern human existence thanks to the exponential growth of technology. Traditional energy sources provide significant challenges, such as pollution, scarcity, and excessive prices. As a result, there is more need than ever before to replace depleting resources with brand-new, reliable, and environmentally friendly ones. With the aid of reverse electrodialysis, the salinity gradient between rivers and seawater as a clean supply with easy and infinite availability is a viable choice for energy generation. The development of nanofluidic-based reverse electrodialysis (NRED) as a novel high-efficiency technology is attributable to the progress of nanoscience. However, understanding the predominant mechanisms of this process at the nanoscale is necessary to develop and disseminate this technology. One viable option to gain insight into these systems while saving expenses is to employ simulation tools. In this study, we looked at how a layer-by-layer (LBL) soft layer influences ion transport and energy production in charged nanochannels. We solved the steady-state Poisson-Nernst-Planck (PNP) and Navier-Stokes (NS) equations for three different types of nanochannels with a trumpet geometry, where the narrow part is covered with a built-up LbL soft layer and the rest is a hard wall with a surface charge density of σ = -10, 0, or +10 mC/m2. The findings show that in type (I) nanochannels, at NPEL/NA = 100 mol/m3 and pH = 7, the maximum power output rises 675-fold as the concentration ratio rises from 10 to 1000. The results of this study can aid in a better understanding of energy harvesting processes using nanofluidic-based reverse electrodialysis in order to identify optimal conditions for the design of an intelligent route with great controllability and minimal pollution.

Diffusion in inhomogeneous fluids: Hard spheres to polymer coatings.

We investigate diffusion in fluids near surfaces that may be coated with polymer films. We first consider diffusion in hard sphere fluids near a planar hard wall. We specifically consider color diffusion, where hard spheres are labeled A or B but are otherwise identical in all respects. In this inhomogeneous fluid, we consider a surface reaction-diffusion problem. At the left wall, a particle of species A is converted to one of species B upon a wall collision. At the opposing wall, the reverse reaction takes place: B → A. Using molecular dynamics simulation, we study the steady state of this system. We demonstrate that in the homogeneous region, a diffusing particle is subject to an equilibrium oscillatory force, the solvation force, that arises from the interfacial structuring of the fluid at the wall. For the hard sphere/hard wall system, the solvation force can be determined in various ways. We use the solvation force [the potential of mean force (PMF)] to solve the continuum diffusion equation. This provides an adequate and accurate description of the reaction-diffusion problem. The analysis is then extended to consider both color diffusion in the presence of a slowly varying one-body field such as gravity and a more applied problem of diffusion of free species through a surface film consisting of tethered chains. In both cases, the PMF experienced by the free particles is affected, but the diffusion problem can be treated in the same way as for the simpler hard sphere color diffusion case.

The escape transition in a self-avoiding walk model of linear polymers

A linear polymer grafted to a hard wall and underneath an atomic force microscopy tip can be modeled in a lattice as a grafted lattice polymer (self-avoiding walk) compressed underneath a piston near the wall. As the piston approaches the wall the increasingly confined polymer escapes from the confined region to explore conformations beside the piston. This conformational change is believed to be a phase transition in the thermodynamic limit, and has been argued to be first order, based on numerical results in the literature. In this paper a lattice self-avoiding walk model of the escape transition is constructed. It is proven that this model has a critical point in the thermodynamic limit corresponding to the escape transition of compressed grafted linear polymers. This result relies on the analysis of self-avoiding walks in slits and slabs in the square and cubic lattices. Additionally, numerical estimates of the location of the escape transition critical point is reported based on Monte Carlo simulations of self-avoiding walks in slits and in slabs.

Local measures of fluctuations in inhomogeneous liquids: statistical mechanics and illustrative applications

We show in detail how three one-body fluctuation profiles, namely the local compressibility, the local thermal susceptibility, and the reduced density, can be obtained from a statistical mechanical many-body description of classical particle-based systems. We present several different and equivalent routes to the definition of each fluctuation profile, facilitating their explicit numerical calculation in inhomogeneous equilibrium systems. This underlying framework is used for the derivation of further properties such as hard wall contact theorems and novel types of inhomogeneous one-body Ornstein–Zernike equations. The practical accessibility of all three fluctuation profiles is exemplified by grand canonical Monte Carlo simulations that we present for hard sphere, Gaussian core and Lennard–Jones fluids in confinement.

Bandwidths of vocal tract resonances in physical models compared to transmission-line simulations.

This study investigated how the bandwidths of resonances simulated by transmission-line models of the vocal tract compare to bandwidths measured from physical three-dimensional printed vowel resonators. Three types of physical resonators were examined: models with realistic vocal tract shapes based on Magnetic Resonance Imaging (MRI) data, straight axisymmetric tubes with varying cross-sectional areas, and two-tube approximations of the vocal tract with notched lips. All physical models had hard walls and closed glottis so the main loss mechanisms contributing to the bandwidths were sound radiation, viscosity, and heat conduction. These losses were accordingly included in the simulations, in two variants: A coarse approximation of the losses with frequency-independent lumped elements, and a detailed, theoretically more precise loss model. Across the examined frequency range from 0 to 5 kHz, the resonance bandwidths increased systematically from the simulations with the coarse loss model to the simulations with the detailed loss model, to the tube-shaped physical resonators, and to the MRI-based resonators. This indicates that the simulated losses, especially the commonly used approximations, underestimate the real losses in physical resonators. Hence, more realistic acoustic simulations of the vocal tract require improved models for viscous and radiation losses.

Evaluation of metal foam liners for broadband noise reduction of turbofan engines

Previous research shows that open-celled metal foam liners have the potential to provide substantial aircraft noise reduction benefits. Our recent results show that their normal incidence sound absorption performance can be further improved by compressing them uniformly; this compression reduces their effective pore size and increases the thermoviscous losses. Further, their performance may be optimized by stacking foams with varying degrees of compression and creating a step-wise effective relative density gradient. Here, we present the results from our recent experiments, evaluating the attenuation performance of such a step-wise gradient metal foam liner using the Advanced Noise Control Fan (ANCF). Liner spools with two different step-wise configurations were fabricated and tested using the ANCF test rig at the Notre Dame Turbomachinery Laboratory. Farfield data was gathered with the liner spool mounted at the inlet and aft locations. In this paper, we present our results comparing the attenuation performance under both test conditions as compared to measurements obtained using a hard wall baseline configuration. Our results show that step-wise metal foam configurations can provide robust acoustical performance for aircraft noise reduction applications.

A branching random walk in the presence of a hard wall

AbstractWe consider a branching random walk on a d-ary tree of height n ( $n \in \mathbb{N}$ ), in the presence of a hard wall which restricts each value to be positive, where d is a natural number satisfying $d\geqslant2$ . We consider the behaviour of Gaussian processes with long-range interactions, for example the discrete Gaussian free field, under the condition that it is positive on a large subset of vertices. We observe a relation with the expected maximum of the processes. We find the probability of the event that the branching random walk is positive at every vertex in the nth generation, and show that the conditional expectation of the Gaussian variable at a typical vertex, under positivity, is less than the expected maximum by order of $\log n$ .