Sphere Matrices Research Articles

Patterns of Nanoporous Spherical Packing Emerging under Influence of Curvature and Confinement

Nanoporous membranes are popular in nanotechnology due to biomedical and industrial applications. During the past decade, experimental, theoretical and computational research into porous membranes and soft materials has opened up new mathematical dimensions. In bulk, diblock copolymers exhibit ordered morphologies such as parallel matrices of lamellae, bicontinuous matrices of gyroids, hexagonal matrices of cylinders and body-centred cubic matrices of spheres. In melt, confinement plays an essential role in tuning the frustration of the diblock copolymer system to predict more nanostructures. These nanostructures depend on the composition of the copolymers, their confining geometries and the degree of structural frustration. An isotropic 9-point stencil for Laplacian is constructed. The discrete finite-difference technique is used in polar grids to discretize the macromolecule of the diblock copolymer system to study spherical patterns to study the effect of curvature and confinement with a well-known and efficient cell dynamic simulation model. Intel FORTRAN (IFORT) codes are generated to run the CDS model and visualisation of simulation results is observed with the help of OPENDX. A comparison of the proposed study with existing experimental and computational studies is also presented.

Elucidation of the physical factors that control activated transport of penetrants in chemically complex glass-forming liquids

Understanding the activated transport of penetrant or tracer atoms and molecules in condensed phases is a challenging problem in chemistry, materials science, physics, and biophysics. Many angstrom- and nanometer-scale features enter due to the highly variable shape, size, interaction, and conformational flexibility of the penetrant and matrix species, leading to a dramatic diversity of penetrant dynamics. Based on a minimalist model of a spherical penetrant in equilibrated dense matrices of hard spheres, a recent microscopic theory that relates hopping transport to local structure has predicted a novel correlation between penetrant diffusivity and the matrix thermodynamic dimensionless compressibility, S0(T) (which also quantifies the amplitude of long wavelength density fluctuations), as a consequence of a fundamental statistical mechanical relationship between structure and thermodynamics. Moreover, the penetrant activation barrier is predicted to have a factorized/multiplicative form, scaling as the product of an inverse power law of S0(T) and a linear/logarithmic function of the penetrant-to-matrix size ratio. This implies an enormous reduction in chemical complexity that is verified based solely on experimental data for diverse classes of chemically complex penetrants dissolved in molecular and polymeric liquids over a wide range of temperatures down to the kinetic glass transition. The predicted corollary that the penetrant diffusion constant decreases exponentially with inverse temperature raised to an exponent determined solely by how S0(T) decreases with cooling is also verified experimentally. Our findings are relevant to fundamental questions in glassy dynamics, self-averaging of angstrom-scale chemical features, and applications such as membrane separations, barrier coatings, drug delivery, and self-healing.

Non-topological Vortex Configurations in the ABJM Model

In this paper we study the existence of vortex-type solutions for a system of self-dual equations deduced from the mass-deformed Aharony--Bergman--Jafferis--Maldacena (ABJM) model. The governing equations, derived by Mohammed, Murugan, and Nastse under suitable ansatz involving fuzzy sphere matrices, have the new feature that they can support only non-topological vortex solutions. After transforming the self-dual equations into a nonlinear elliptic $2\times 2$ system we prove first an existence result by means of a perturbation argument based on a new and appropriate scaling for the solutions. Subsequently, we prove a more complete existence result by using a dynamical analysis together with a blow-up argument. In this way we establish that, any positive energy level is attained by a 1-parameter family of vortex solutions which also correspond to (constraint) energy minimizers. In other words, we register the exceptional fact in a BPS-setting that, neither a "quantization" effect nor an energy gap is induced upon the system by the rigid "critical" coupling of the self-dual regime.

Abelian-Higgs and vortices from ABJM: towards a string realization of AdS/CMT

We present ans\"{a}tze that reduce the mass-deformed ABJM model to gauged Abelian scalar theories, using the fuzzy sphere matrices $G^\alpha$. One such reduction gives a Toda system, for which we find a new type of nonabelian vortex. Another gives the standard Abelian-Higgs model, thereby allowing us to embed all the usual (multi-)vortex solutions of the latter into the ABJM model. By turning off the mass deformation at the level of the reduced model, we can also continuously deform to the massive $\phi^4$ theory in the massless ABJM case. In this way we can embed the Landau-Ginzburg model into the AdS/CFT correspondence as a consistent truncation of ABJM. In this context, the mass deformation parameter $\mu$ and a field VEV $<\phi>$ act as $g$ and $g_c$ respectively, leading to a well-motivated AdS/CMT construction from string theory. To further this particular point, we propose a simple model for the condensed matter field theory that leads to an approximate description for the ABJM abelianization. Finally, we also find some BPS solutions to the mass-deformed ABJM model with a spacetime interpretation as an M2-brane ending on a spherical M5-brane.

Fluids in random porous media: Scaled particle theory

The scaled particle theory (SPT) is applied to describe thermodynamic properties of a hard sphere (HS) fluid in random porous media. To this purpose, we extended the SPT2 approach, which has been developed previously. The analytical expressions for the chemical potential of an HS fluid in HS and overlapping hard sphere (OPH) matrices, sponge matrix, and hard convex body (HCB) matrix are obtained and analyzed. A series of new approximations for SPT2 are proposed. The grand canonical Monte Carlo (GGMC) simulations are performed to verify an accuracy of the SPT2 approach combined with the new approximations. A possibility of mapping between thermodynamic properties of an HS fluid in random porous media of different types is discussed. It is shown that thermodynamic properties of a fluid in the different matrices tend to be equal if the probe particle porosities and the specific surface pore areas of considered matrices are identical. The obtained results for an HS fluid in random porous media as reference systems are used to extend the van der Waals equation of state to the case of a simple fluid in random porous media. It is observed that a decrease of matrix porosity leads to lowering of the critical temperature and the critical density of a confined fluid, while an increase of a size of matrix particles causes an increase of these critical parameters.

Lennard-Jones binary mixture in disordered matrices: exploring the mode coupling scenarioat increasing confinement

We present results of molecular dynamics simulations performed on a Lennard-Jones liquidbinary mixture confined in matrices of soft spheres at increasing packing fraction. We studythe dynamical properties of the liquid at a given density upon supercooling. Our aim is totest the validity of the mode coupling theory in predicting the behaviour of the glassforming liquid when it is under confinement in a disordered matrix. We use two differentmethods to build up the confining environment. We focus in particular on thebehaviour of the single particle density correlators. We find a close agreement with themode coupling theory at least for all the range of packing fractions examined.Discrepancies between the theory and the computer simulation results can beattributed to hopping effects which are more important at increasing confinement.

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.

Analytical theory of one- and two-dimensional hard sphere fluids in random porous media

The recently proposed scaled particle theory SPT2 approach to the description of three-dimensional hard sphere fluids in random porous media is extended for oneand two-dimensional cases. Analytical expressions for the chemical potential and pressure of oneand two-dimensional hard sphere fluids in hard sphere and overlapping hard sphere matrices are obtained and discussed. Some improvements and modifications of the obtained results are proposed.

Mode-coupling behavior of a Lennard-Jones binary mixture upon increasing confinement

Molecular dynamics simulations are performed on a Lennard Jones binary mixture confined in off lattice matrices of soft spheres with increasing radius. We focus on dynamics upon supercooling and in particular on testing the mode coupling theory properties of the confined mixture. Parameters of mode coupling theory in going from bulk to weak confinement, and from weak to strong confinement are extracted from simulations and analyzed. We focus on the study of the behavior of the single particle density correlators. We find that the mode coupling theory retains its validity also in the case of strong confinement, with a reduction of range of validity. The role of hopping is discussed in relation with the differences between the results obtained from the diffusion coefficients and the mode coupling theory predictions.

From Websites to Wal-Mart: Youth, Identity Work, and the Queering of Boundary Publics in Small Town, USA

Drawing from a larger ethnographic project, this paper discusses rural young people's construction of “boundary publics” as a strategy for space making and locations for what I describe as queer identity work. Building off of the rich literature theorizing both the public sphere and responsive counterpublics, the notion of a boundary public is offered to better address the infrastructural constraints of rural communities and as a critical site to explore young people’s experiences crafting queer sexual and gender identities. Contrary to the presumed invisibility of queer genders and sexualities in rural spaces, I argue that youth assert their presence in fabulously conspicuous ways. Youth pieced together resources in and beyond their communities, carving out what I call “boundary publics”—from personal and organizational websites created by and for other rural queer young people to drag outings at the local Wal-Mart and a local church’s SkatePark. This paper provides a rich account of what rural queer youth do with and in the spaces around them. Their social interactions challenge the expectation that rural queer publics are unsustainable or poor imitations when compared to an urban queer scene. Arguing that late modern identities call for publics, this paper analyzes how rural queer and questioning youth craft such spaces in ways and locations one might not likely expect. Rather than counter or rebuff the mainstream or rural public sphere, the boundary publics of rural young people necessarily move among both the centers and margins of their rural communities. These occupations are activities of what I describe as queer identity work. Youth crisscross the commercial zones of chain stores and the nonprofit corporate structures of non-governmental LGBT advocacy organizations. They also occupy and work the spaces of public parks and meeting halls of organized religions. Rural queer young people absorb, recycle, and recuperate these spaces to make them their own—if only temporarily so. And, in increasingly complicated ways, these youth take up what I shall call new mediascapes such as personal and group websites and listservs. Each of these types of occupation or moments of queer identity work can be understood as liberating and impermanent. Indeed, it is the fragility of these competing qualities that make boundary publics such productive locations of rural queer youth identity work.The fragility of boundary publics also illustrates the elemental entanglements between these publics and the broader public sphere.The examples of queer rural youth boundary publics argue against theorizing that new media can produce independent publics insolated or removed from their offline contexts. In highlighting the constitutive matrices of boundary publics and public spheres, rural queer young people’s experiences of public-ness brings into question divisions of public and private spaces more broadly.

Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material

We present a grand canonical Monte Carlo simulation study of the phase diagram of a Lennard-Jones fluid adsorbed in a fractal and highly porous aerogel. The gel environment is generated from an off-lattice diffusion limited cluster-cluster aggregation process. Simulations have been performed with the multicanonical ensemble sampling technique. The biased sampling function has been obtained by histogram reweighting calculations. Comparing the confined and the bulk system liquid-vapor coexistence curves we observe a decrease of both the critical temperature and density in qualitative agreement with experiments and other Monte Carlo studies on Lennard-Jones fluids confined in random matrices of spheres. At variance with these numerical studies we do not observe upon confinement a peak on the liquid side of the coexistence curve associated with a liquid-liquid phase coexistence. In our case only a shouldering of the coexistence curve appears upon confinement. This shoulder can be associated with high density fluctuations in the liquid phase. The coexisting vapor and liquid phases in our system show a high degree of spatial disorder and inhomogeneity.

Isotropic-nematic transition of hard rods immersed in random sphere matrices

Using replica density functional theory and Monte Carlo computer simulations we investigate a system of annealed hard spherocylinders adsorbed in a matrix of quenched hard spheres. Theoretical predictions for the partition coefficient, defined as the ratio of density of rods in the matrix and that in a reservoir, agree well with simulation results. Theory predicts the isotropic-nematic transition to remain first order upon increasing sphere packing fraction, and to shift towards lower rod densities. This scenario is consistent with our simulation results that clearly show a jump in the nematic order parameter upon increasing the rod density at constant matrix packing fraction, corresponding to the isotropic-nematic transition, even for sphere matrix packing fractions < or approximately equal to 0.3.

Nonadditive Binary Hard Sphere Mixture in Disordered Hard Sphere Matrices: Integral Equations and Computer Simulation

We have studied adsorption of nonadditive binary symmetric hard sphere mixtures in hard sphere matrices and in templated hard sphere matrices. Adsorption is described by using replica Ornstein−Zernike integral equations complemented by Martynov−Sarkisov closure relations. This theory permits straightforward calculation of the chemical potential of fluid species and to describe equilibrium between the bulk phase in a model adsorbent body. Theoretical results for adsorption isotherms agree well with Monte Carlo computer simulation data. On the other hand, we have captured the effect of matrix modification on adsorption via templating. Finally, we have described the coexistence curve (in terms of concentration vs density and in terms of concentration vs chemical potentials of fluid species) for the demixing transition by using theoretical procedure and by semigrand computer simulation in hard sphere matrices and in corresponding templated matrices. We have shown that the explanation of the phase behavior is ...

Adsorption of a Hard Sphere Fluid in a Disordered Polymerized Matrix: Application of the Replica Ornstein–Zernike Equations

A model of hard spheres adsorbed in disordered porous media is studied using the associative replica Ornstein–Zernike (ROZ) equations. Extending previous studies of adsorption in a hard sphere matrices, we investigate a polymerized matrix. We consider an associating fluid of hard spheres with two intracore attractive sites per particle; consequently chains consisting of overlapping hard spheres can be formed due to the chemical association. This is the generalization of the model with sites on the surface of Wertheim that has been studied in the bulk by Chang and Sandler. The matrix structure is obtained in the polymer Percus–Yevick approximation. We solve the ROZ equations in the associative hypernetted chain approximation. The pair distribution functions, the fluid compressibility, the equation of state and chemical potential of the adsorbed fluid are obtained and discussed. It is shown that the adsorption of a hard sphere fluid in a matrix at given density, but consisting of longer chains of overlapping hard spheres, is higher than the adsorption of this fluid in a hard sphere matrix.

Adsorption of Fluids in Disordered Porous Media from the Multidensity Integral Equation Theory. Associative Analogue of the Madden−Glandt Ornstein−Zernike Approximation

The associative analogue of the integral equation theory developed by Madden and Glandt is applied to a model of methane adsorbed in a silica xerogel. The integral equations are solved in the associative Percus−Yevick approximation. The associative treatment of strong attraction between fluid particles and matrix species in this model yields a better description of the pair distribution functions at intermediate fluid densities and at low temperatures in comparison with the Percus−Yevick approximation. In contrast to the Percus−Yevick approximation, the associative Percus−Yevick theory gives solutions for some subcritical temperatures of the bulk fluid. The adlayer structure is discussed in terms of the fraction of bonded species and coordination numbers. The behavior of the distribution functions and internal energy coincides with the Monte Carlo simulation data of Kaminsky and Monson. It is shown that the model can be used for the description of different Lennard-Jones fluids in hard sphere matrices. Possible refinements of the theory by using the replica Ornstein−Zernike equations of Given and Stell are discussed briefly.

Thermodynamics of fluids in random microporous materials from scaled particle theory

The thermodynamic properties of fluids confined to disordered porous solids are studied using a scaled particle theory approach. For simple hard sphere fluids in matrices of hard spheres, this method is of comparable accuracy to those previously introduced. In past studies of such systems, a strong thermodynamic similarity between the partly quenched and fully annealed cases has been evident; an exception to this behavior occurs when the diameters are nonadditive. For adsorbed polymeric molecules, on the other hand, the scaled particle theory introduced in this paper is the only route to the thermodynamics yet presented. The partition coefficients for polymers at infinite dilution in matrices of various porosities agree well with simulation over many orders of magnitude. For bulk polymers, the scaled polymer predictions are in much closer agreement with simulation than those of the traditional pressure and compressibility equations.

A calibration technique for polarimetric coherent-on-receive radar systems

A new technique for calibrating a coherent-on-receive polarimetric radar system is proposed. A coherent-on-receive polarimetric radar is capable of measuring the Mueller matrix of point or distributed targets directly by transmitting at least four independent polarizations and measuring the vertical and horizontal components of the backscatter signal simultaneously. The technique requires the use of two calibration targets, a target with known scattering matrix (such as a metallic sphere or a trihedral corner reflector) and any depolarizing target (for which knowledge of its scattering matrix is not required) to determine the system distortion parameters. The system distortion parameters, which include the channel imbalances, the cross-talk factors of both the transmit and the receive antennas, and the phase shifts and amplitude variations of the transmitter polarizers, are determined by measuring the calibration targets for four different transmit polarizations. The validity of the new calibration technique is examined by measuring the scattering matrices of spheres and cylinders as test targets using a coherent-on-receive radar operating at 34.5 GHz. Excellent agreement between the theoretical and the measured scattering matrices for the test targets are obtained. >

Light polarization: A geometric-algebra approach

The geometric algebra of three-dimensional space (the ‘‘Pauli algebra’’) is known to provide an efficient geometric description of electromagnetic phenomena. Here, it is applied to the three-dimensional Stokes subspace to describe the polarization of an approximately monochromatic collimated beam of electromagnetic radiation. The coherency density ρ is a real element of the algebra whose components are the four Stokes parameters: a scalar representing the total photon flux density plus a three-dimensional vector whose direction and length in the Poincaré sphere give the type and degree of polarization. The detection of the radiation and the incoherent and coherent modification of the polarization by various optical elements are calculated by algebraic multiplication which has faithful representations in 2×2 matrices. One matrix representation of ρ is the coherency matrix with which Jones and Mueller matrices are related whereas another representation is the spin density matrix. However, the calculations are simplest to perform and interpret in the algebraic form independent of any particular matrix representation. It is shown that any possible change in the Stokes parameters can be treated algebraically by a combination of attenuation, depolarization, polarization, and rotation transformations of ρ. The geometric algebra thus unifies Stokes parameters, the Poincaré sphere, Jones and Mueller matrices, and the coherency and density matrices in a single, simple formalism.

Regenerator performance with sinusoidal flow

The ineffectiveness of regenerators with sinusoidal laminar flow through parallel plate, screen and packed sphere matrices is evaluated in the limit of infinite matrix heat capacity. Increases in ineffectiveness of up to 23% over the constant flow values result for parallel plate regenerators.

Visual Examinations of Fluid Behavior in Porous Media - Part I

Abstract An exploratory study was made to examine the possibilities of a visual approach in investigations into microscopic mechanisms of fluid behavior in porous media. Appropriate apparatus and techniques were developed so that microscopic phenomena could he recorded on color movie film as well as be observed visually. The observation flow cells in which the fluid behavior studies were made were essentially single-layered matrices of spheres between plates, sometimes all-glass, sometimes all-Lucite and sometimes a combination of the two. The fluids were limited to water and a filtered crude oil. Two flow regimes were observed during the flow of the immiscible liquids: channel flow and slug flow. In the former, transport was effected through stable networks of interconnecting channels; and in the latter, part of the movement took place in the form of slugs. Under certain conditions, flood-front patterns were found to be different depending upon which liquids were the displacing and displaced phases and not depending upon whether the matrix was water-wet glass or oil-wet Lucite. Residual formations of oil and water were observed and are described. Some of the ramifications and significance of the observed phenomena are discussed. Introduction In recent years considerations of microscopic mechanisms of fluid flow in porous media have taken on greater significance. Much needs to be learned before the fundamentals of petroleum technology are completely established. For example, many unanswered questions exist in connection with relative permeability, displacement phenomena, residual fluid formations, flow structure, etc.; and further analytical mathematical formulations are seriously indicated. It is hoped that systematic investigations into the microscopic mechanisms connected with the behavior of fluids in porous media will shed some light on some of the problems extant. Until recently microscopic mechanisms have been considered almost exclusively as speculative hypotheses. Within the past few years, however, the problem has been submitted to a limited number of experimental investigations. Nuss and Whiting made some studies on the pore-space geometry of sandstones and limestones by impregnating cores with an inert plastic and leaching the solid matrices to leave behind plastic models of the pore spaces. Schaefer traced pore spaces microscopically through lengths of limestone cores by cutting away thin sections from the exposed faces normal to the line of view.