Penetrable Walls Research Articles

Ultraconfined oblate hard particles between hybrid penetrable walls.

We have investigated, by Monte Carlo simulation, the orientational structure of very thin films of a discotic liquid crystal (DLC) confined between hybrid walls of controllable penetrability, as a function of wall separation L_{z}. Our purpose was to clarify whether, as predicted by continuum theory, the preferred orientation of the DLC is uniform, changes linearly, or changes discontinuously, when L_{z} and the anchoring strengths at either wall are changed. The model consists of oblate hard Gaussian overlap (HGO) particles: each wall sees a particle as a disk of zero thickness and diameter D less than or equal to that of the actual particle σ_{0}, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This provides a particle-level mechanism to control the anchoring properties of the walls, from planar (edge-on) for D∼0 to homeotropic (face-on) for D∼σ_{0}, which can be done independently at either wall. As in our earlier work [C. Anquetil-Deck et al., J. Phys. Chem. B 124, 7709 (2020)1520-610610.1021/acs.jpcb.0c05027], which was restricted to L_{z}=6σ_{0}, depending on the values of D_{s}≡D/σ_{0} at the top (D_{s}^{t}) and bottom (D_{s}^{b}) walls, we find domains in (D_{s}^{b},D_{s}^{t}) space in which particle alignment is uniform planar (UP), uniform homeotropic (UH), or varies linearly from planar at one wall to homeotropic at the other (L), but no bistable or tristable regions are identified between these domains. Most importantly, there appears never to occur an abrupt change of the LC orientation when the walls strongly favor different anchorings, in general agreement with the scenario proposed by Velasco and co-workers [D. de las Heras et al., Phys. Rev. E 79, 011712 (2009)1539-375510.1103/PhysRevE.79.011712], but in contrast to the behavior of equivalent calamitic systems [F. Barmes et al., Phys. Rev. E 69, 061705 (2004)1539-375510.1103/PhysRevE.69.061705; Phys. Rev. E, 71, 021705 (2005)1539-375510.1103/PhysRevE.71.021705; C. Anquetil-Deck et al., Phys. Rev. E 86, 041707 (2012)1539-375510.1103/PhysRevE.86.041707]. However, for the thinnest films investigated (L_{z}=2σ_{0}), the system is unable to accommodate a rotation of the preferred particle orientation from one wall to the other and adopts instead a tilted configuration, similar to that reported earlier for Gay-Berne films in symmetric confinement [T. Gruhn et al., Thin Solid Films 330, 46 (1998)0040-609010.1016/S0040-6090(98)00799-8; Mol. Phys. 93, 681 (1998)10.1080/002689798169014] but which, as far as we know, has been missed in most earlier work.

Garrett approximation for quantum dots

An approximation previously proposed by Garrett to evaluate the en- ergy level of a particle in a finite square well using the expression of the corresponding level in an infinite one is extended to a spherical well. In this way, simple analytical approximations are obtained for the energy levels of a particle in a spherical cavity with penetrable walls, knowing the exact values of the corresponding levels in a similar cav- ity, with impenetrable walls. The relative errors of this approximation are of order of about 10−3. This approach can be extended to slightly deformed spherical dots (ellip- soidal dots with a small eccentricity), with interesting applications in nanophysics and nanotechnology.

Interstitial space and the Spiritualist séance: psychical geography, telephonic imaginary and social possibility in 1870s Britain

ABSTRACT As the key site in extending the territoriology of Victorian Spiritualism, the domestic séance harboured multiple interstices or interstitial spaces, most notably evident in the spaces in-between sitters and mediums, the various particularities of the séance room (such as spirit cabinets and penetrable walls for spirit materialisation and transport), and the thresholds between the world sitters inhabited and the one with which they sought intimate contact. Notions of interstitial space extended into Spiritualist philosophy when Anna Blackwell wrote in 1871 of a proto-quantum mechanics model of inter-cellular connec-tivity, linking humans to spirits that predated twentieth-century quantum notions of entanglement and nonlocality. The introduction of telephony in Britain further expanded the psychical geography of a Spiritualist imaginary of longdistance communication and provided a new means for spirit contact. In addition, the appearance of the telephone silence cabinet, an interstitial communicative device functioning in a manner similar to that of the séance spirit cabinet, provided conversation privacy through the mediumistic assistance of postal employees. This article contends that interstitial space served as a key component of Spiritualist thought and practice furthering an imaginary of social possibility in 1870s Britain.

Ground state energy of the hydrogen atom inside penetrable spherical cavities; variational approach

In this work we calculate the ground state energy of the hydrogen atom confined in a sphere of penetrable walls of radius Rc. Inside the sphere the system is subject to a Coulomb potential, whereas outside of it the potential is a finite constant V0. The energy is obtained as a function of Rc and V0 by means of the Rayleigh-Ritz variational method, in which, the trial function is proposed as a free particle wave function within a finite square well potential but including an exponential factor that takes into account the electron-nucleus Coulomb attraction. For an impenetrable sphere, , the energy grows fast as Rc approaches zero. On the other hand, when the height of the barrier V0 is finite, the energy increases slowly as Rc goes to zero. We also compute the Fermi contact term, nuclear magnetic screening, polarizability, pressure and tunneling as a function of Rc and V0. As expected, these physical quantities approach the corresponding values of the free hydrogen atom as Rc grows. We also discuss the pressure-induced ionization of the hydrogen atom. The present results are found in good agreement with those previously published in the literature.

On uniform asymptotic approximations of whispering gallery modes propagating along curved penetrable interfaces

While in the classical theory of whispering gallery waves it is assumed that they propagate along a cylindrical perfectly reflecting wall, in many real situations it is important to consider similar waves propagating along penetrable interfaces or curvilinear level sets of the refractive index. An example of waves of the latter kind are whispering gallery modes formed in a shallow-water waveguide due to the horizontal refraction. Such modes are counterpart of quasistationary states in quantum mechanics, as they do not exponentially decay at infinity, and their respective eigenvalues are complex. Recently it was shown that Maslov canonical operator (MCO) theory can be used to compute uniform asymptotic expansions of the solutions to various wave propagation problems. Such approximations admit convenient analytical representation in terms of special functions that can be used for investigating their properties and for other purposes. The MCO theory is applicable only in cases where the solution exponentially decays at infinity, e.g., for computing bound states of a given quantum system. Nevertheless, the technique outlined here allows to obtain analytical expressions for the radial profiles of whispering gallery modes propagating along a penetrable wall or along a curvilinear level set of the refractive index.

Quantum carpets in leaky boxes

Quantum waves evolving or propagating inside one-dimensional boxes generate ‘quantum carpets’: intricate patterns in spacetime. The formally equivalent patterns in classical paraxial optics are observed as the Talbot effect. Boxes that are leaky, i.e. with penetrable walls, can be modelled by representing the walls as nonhermitian boundaries. The waves are superpositions of discrete eigenmodes with complex eigenvalues. Several different boundary conditions are explored, in which the Robin parameter—ratio of the mode derivatives and their values at the walls—may or may not depend on the eigenvalue. Nonhermitian models, which ignore the waves leaking outside the box, or represent them in simplified form, are approximations. For one physical model, the evolving wave in the full space can be calculated exactly, indicating that the nonhermitian model for the wave inside is highly accurate. Leaky boxes can be useful pedagogically: as introductory examples of nonhermiticity and biorthogonality (left and right eigenvectors), and as a rich source of postgraduate or advanced undergraduate student projects, exploring many variants.

Ordering of oblate hard particles between symmetric penetrable walls

ABSTRACT We find the structure of a model discotic liquid crystal (DLC) confined between symmetric walls of controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle-substrate interactions are modelled as follows: each substrate sees a particle as a disc of zero thickness and diameter less than or equal to that of the actual particle, , embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for to homeotropic (face-on) for . This system is investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager’s second-virial approximation with Parsons-Lee rescaling. We find that the agreement between theory and simulation is substantially less good than for prolate HGOs; in particular, the crossover from edge-on to face-on alignment is predicted by theory to occur at , but simulation finds it for . These discrepancies are likely a consequence of the fact that Onsager’s theory is less accurate for discs than for rods. We quantify this by computing the bulk isotropic-nematic phase diagram of oblate HGOs.

Ordering of Oblate Hard Particles between Hybrid Penetrable Walls.

We report a Monte Carlo (MC) simulation study of a model discotic liquid crystal (DLC) confined between hybrid walls with controllable penetrability. The model consists of oblate hard Gaussian overlap (HGO) particles. Particle–substrate interactions are modeled as follows: each substrate sees a particle as a disc of zero thickness and diameter D less than or equal to that of the actual particle, σ0, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This allows us to control the anchoring properties of the substrates, from planar (edge-on) for D ≈ 0 to homeotropic (face-on) for D ≈ σ0, which can be done independently at either substrate. Depending on the values of Ds ≡ D/σ0 at the top (Dst) and bottom (Dsb) substrates, we find domains in (Dsb, Dst) space in which particle alignment is uniform planar (UP), is uniform homeotropic (UH), or varies linearly from planar at one substrate to homeotropic at the other (Lin). These domains are separated by regions of bistability (P–Lin and H–Lin), which appear to be wider than for prolate HGOs, and there may be also a small tristable (P–H–Lin) region. Results are compared with the predictions of density functional theory, implemented at the level of Onsager’s second-virial approximation with Parsons-Lee rescaling. As in the case of symmetric confinement studied previously, the agreement between theory and simulation is substantially less good than for prolate HGOs: in particular, for the investigated substrate separation L = 6σ0, the Lin configuration is never predicted. These discrepancies are likely a consequence of the fact that Onsager’s theory is less accurate for discs than for rods.

Testing one-parameter hybrid exchange functionals in confined atomic systems

In this work the Perdew–Burke–Ernzerhof exchange functional coupled with the exact-exchange is applied on closed-shell atoms confined by impenetrable and penetrable walls. When the Hartree–Fock method is used as the reference, one-parameter hybrid exchange functionals qualitatively give a good description of atoms enclosed by a sphere surrounded by an infinite potential. For atoms confined by a finite potential, however, the same hybrid exchange functionals predict results appreciably different to the reference for small confinement radii. The main reason of this result is the Laplacian of the electron density involved in the exchange potential and, consequently, the effective potential diverges at the nucleus, which cannot be remedied by the inclusion of the exact exchange. Localization and delocalization exhibited by the electron density are used as arguments to explain the differences found between various exchange functionals tested in this article. We show that generalized-gradient functionals are unable to give a good description of the corresponding system when the electron density is squeezed by finite potentials over small regions and how one-parameter hybrid exchange functionals alleviate some of the encountered problems. Although the model of the confined atom is extremely simple, it can reproduce some features predicted by sophisticated methods of electronic structure designed for crystal systems, therefore, this model can be useful to test exchange functionals defined within the Kohn–Sham density functional-theory.

Numerical simulation of ice accretion in supercooled large droplet conditions

The simulated methods for ice accretion on two-dimensional airfoil surface are established completely under the Eulerian framework in supercooled large droplet (SLD) conditions. The two-dimensional code to solve the partial differential equations (PDEs) of droplet phase is derived to simulate the impingement characteristic of SLD. Also, several semi-empirical models which explain the droplet-wall interaction are compared and discussed to show respective features when simulating the splashing phenomenon. In particular, a new boundary condition for wall called penetrable wall for splashing droplet (PWSD) is proposed to deal with the impingement of SLD on solid surface, which efficiently improves the accuracy of simulation. Then the improved impingement characteristic of SLD is input into the extended mass and heat transfer model to simulate the ice growth on airfoil surface. The multistep advanced method is carried out to better match the physical phenomenon of ice growth. At last, the simulated results of critical parameters: local droplet collection efficiency and the height of ice growth are compared with the experimental data which verify the applicability of proposed models.

Vacua and walls of mass-deformed Kähler nonlinear sigma models on Sp(N)/U(N)

We study vacua and walls of mass-deformed K\"ahler nonlinear sigma models on $Sp(N)/U(N)$. We identify elementary walls with the simple roots of $USp(2N)$ and discuss compressed walls, penetrable walls and multiwalls by using the moduli matrix formalism.

Micropolar nanofluid flow and heat transfer between penetrable walls in the presence of thermal radiation and magnetic field

Flow and heat transfer of MHD micro-polar nanofluid in a channel with penetrable walls and considering thermal radiation impact are investigated. A similarity transformation is utilized to transmute the governing momentum and energy equations into non-linear ordinary differential equations with the appropriate boundary conditions. The gained non-linear ordinary differential equations are solved by Duan–Rach Approach (DRA). This method allows us to detect a solution without applying numerical methods to evaluate the unspecified coefficients. The impacts of diverse active parameters such as the micro-polar parameter, the magnetic parameter, the volume fraction of nanofluid and the radiation parameter on the velocity and temperature profiles are examined. Furthermore, the value of the Nusselt number is calculated and presented through figures.

New rotary piercing process for an AZ31 magnesium alloy seamless tube

ABSTRACTTo address the existing defects in the processing of magnesium alloy seamless tubes (MASTs), a new technology for producing AZ31 alloy tubes using a rotary piercing process was studied. Through the finite-element method and experimental analyses, the distributions of stress and strain and the temperature fields were analysed. The effects of temperature, radial reduction, plug diameter, and advance on the penetration rate, diameter, and wall thickness of the tube were studied. The results showed that temperature is the most important parameter; the penetration rate of the tube was >90% for rolling temperatures of 350–450°C. There was complete dynamic recrystallisation and a uniform distribution of equiaxed grains. This process can potentially replace the traditional extrusion process to produce MASTs.

Electron‐density delocalization in many‐electron atoms confined by penetrable walls: A Hartree–Fock study

AbstractThe electronic structure of several many‐electron atoms, confined within a penetrable spherical box, was studied using the Hartree–Fock (HF) method, coupling the Roothaan's approach with a new basis set to solve the corresponding one‐electron equations. The resulting HF wave‐function was employed to evaluate the Shannon entropy, , in configuration space. Confinements imposed by impenetrable walls induce decrements on when the confinement radius, Rc, is reduced and the electron‐density is localized. For confinements commanded by penetrable walls, exhibits an entirely different behavior, because when an atom starts to be confined, delivers values less than those observed for the free system, in the same way that the results presented by impenetrable walls. However, from a confinement radius, shows increments, and precisely in these regions, the spatial restrictions spread to the electron density. Thus, from results presented in this work, the Shannon entropy can be used as a tool to measure the electron density delocalization for many‐electron atoms, as the hydrogen atom confined in similar conditions.

Vacua and walls of mass-deformed Kähler nonlinear sigma models on SO(2N)/U(N)

We construct walls of mass-deformed K\"{a}hler nonlinear sigma models on $SO(2N)/U(N)$, by using the moduli matrix formalism and the simple roots of $SO(2N)$. Penetrable walls are observed in the nonlinear sigma models on $SO(2N)/U(N)$ with $N>3$.

Numerical Simulation of a Single-Phase Flow Through Fractures with Permeable, Porous and Non-Ductile Walls

This paper attempts to study flows within fractures through a set of numerical simulations. In addition, a special care is given to hydraulic features and characteristics of fractures. The research is performed through the application of calculative fluid dynamics and a finite volume discrete schema. The investigated flows are laminar, single-phase and stable flows of water and air through fractures with penetrable walls. The selected fracture geometry is inspired from the tomographic scan of a stone fracture. Water and air are modeled in fractures with permeable walls and different permeability levels. It has been observed that in case of permeable matrixes, the friction coefficient is lower compared to impermeable matrixes. In fact permeability reduced friction. In addition, highest pressure drops were observed in areas with smaller fracture diaphragms. Nonetheless, the surrounding area of the fracture is analyzed with the consideration of Darcy's rule.

Self-propulsion against a moving membrane: Enhanced accumulation and drag force.

Self-propulsion (SP) is a main feature of active particles (AP), such as bacteria or biological micromotors, distinguishing them from passive colloids. A renowned consequence of SP is accumulation at static interfaces, even in the absence of hydrodynamic interactions. Here we address the role of SP in the interaction between AP and a moving semipermeable membrane. In particular, we implement a model of noninteracting AP in a channel crossed by a partially penetrable wall, moving at a constant velocity c. With respect to both the cases of passive colloids with c>0 and AP with c=0, the AP with finite c show enhancement of accumulation in front of the obstacle and experience a largely increased drag force. This effect is understood in terms of an effective potential localised at the interface between particles and membrane, of height proportional to cτ/ξ, where τ is the AP's reorientation time and ξ the width characterizing the surface's smoothness (ξ→0 for hard core obstacles). An approximate analytical scheme is able to reproduce the observed density profiles and the measured drag force, in very good agreement with numerical simulations. The effects discussed here can be exploited for automatic selection and filtering of AP with desired parameters.

Solution of the Kohn–Sham equations for many-electron atoms confined by penetrable walls

The solution of the Kohn–Sham equations in the Roothaan’s context is presented for atoms confined by penetrable walls. A new basis set is employed in this work, which was designed within the Hartree–Fock approach to ensure a correct decay on the electron density. Exchange-correlation functionals from local density and generalized gradient approximation are considered in the implementation of the Kohn–Sham method. The confinement effects on energies (total and orbital) and on the exchange potential are discussed when two exchange-only functionals are compared with the Hartree–Fock method, for closed-shell atoms confined by finite potentials. Clearly, the wrong asymptotic behavior exhibited by the exchange-only Kohn–Sham potentials, considered in this work, has a large impact on orbital energies when several confinements are tested. In fact, such exchange potentials predict orbital energies which are drastically different than those predicted by the Hartree–Fock method. These differences are not restricted just to absolute values, also the trend observed for exchange and orbital energies is quite different than that predicted by Hartree–Fock. Effects of the correlation contribution are also discussed on total and orbital energies, which show same trends than those obtained by exchange-only functionals. Unfortunately, there are no implementations of correlated methods based on the wave-function for this kind of problems, and consequently our results for correlation energy cannot be compared with a reference. With this implementation there is one possibility to test the performance of approximate exchange-correlation functionals, in addition to the sets commonly used in the design of new functionals.

Roothaan's approach to solve the Hartree-Fock equations for atoms confined by soft walls: Basis set with correct asymptotic behavior.

In this report, we use a new basis set for Hartree-Fock calculations related to many-electron atoms confined by soft walls. One- and two-electron integrals were programmed in a code based in parallel programming techniques. The results obtained with this proposal for hydrogen and helium atoms were contrasted with other proposals to study just one and two electron confined atoms, where we have reproduced or improved the results previously reported. Usually, an atom enclosed by hard walls has been used as a model to study confinement effects on orbital energies, the main conclusion reached by this model is that orbital energies always go up when the confinement radius is reduced. However, such an observation is not necessarily valid for atoms confined by penetrable walls. The main reason behind this result is that for atoms with large polarizability, like beryllium or potassium, external orbitals are delocalized when the confinement is imposed and consequently, the internal orbitals behave as if they were in an ionized atom. Naturally, the shell structure of these atoms is modified drastically when they are confined. The delocalization was an argument proposed for atoms confined by hard walls, but it was never verified. In this work, the confinement imposed by soft walls allows to analyze the delocalization concept in many-electron atoms.

NMR characterization of PAMAM_G5.NH2 entrapped atomic and molecular assemblies.

High resolution NMR spectroscopy, NMR diffusiometry, and NMR cryoporometry have been used to investigate aqueous solution (D2O) of PAMAM_G5.NH2-(Au)(25-100) and PAMAM_G5.NH2-(H2O)1000-(H2O)4000 systems. In the case of dendrimer entrapped gold nanoparticles, the detailed analysis of high resolution NMR spectra has shown that no precursor complex formation happens under the circumstances applied for reduction. Further PGSE results verify that gold nanoparticles of 1.9-2.6 nm size are entrapped in the outermost part of the dendrimers and probably more than one dendrimer molecule takes part in the stabilization process. This system looks like a transition state between dendrimer encapsulated nanoparticles (DENs) and dendrimer stabilized nanoparticles (DSNs), and we deal with it in details for what this means. NMR cryoporometry experiments were performed to detect the encapsulation of water molecules. The results show that, in the swelling PAMAM_G5.NH2 dendrimers, by adding water step by step, there are specific cavities for water with diameters of 3.6 and 5.2 nm. These cavities have a penetrable wall for water molecules and probably exist very close to the terminal groups. The permeability of the cavities is increasing with the increase of the water content. In dilute solution, the formation of nanoparticles is determined by the ratio of the rate of nucleation and aggregation and the latter is affected by the PAMAM_G5.NH2.