Infinite Extension Research Articles

Metal-Organic Framework [Cd(LTP)2]n for Improved Enantioseparations on a Chiral Cyclodextrin Stationary Phase in GC.

Metal-organic frameworks (MOFs) are a class of novel porous materials consisting of clusters or chains of metal ions and organic linkers. The chiral MOF [Cd(LTP)2]n (LTP = l(-)-thiazolidine-4-carboxylic acid) possesses infinite extension three-dimensional supramolecular reticular structure with right-handed helix. In this work, three capillary columns (A, B and C) containing MOF [Cd(LTP)2]n, permethylated β-cyclodextrin (CD) and sodium chloride, and MOF [Cd(LTP)2]n and permethylated β-CD, respectively, have been prepared and their respective enantioseparation abilities have been investigated. The polarities of all of the MOFs and permethylated β-CDs are moderate. The numbers of theoretical plates (plate m-1) of the three columns have been measured using n-dodecane at 120°C, which followed an increasing order of A (3100) < B (3800) < C (4300). Some racemates were separated with different resolutions on Columns A, B and C. The results indicated that the incorporated MOF [Cd(LTP)2]n enhanced the separations of racemates on a permethylated β-CD stationary phase with high column efficiency and good reproducibility in gas chromatography.

Numerical analysis of natural convection heat transfer from a fin in parallel enclosure

A fin of finite width with infinitely small thickness is assumed to be placed horizontally between two horizontal parallel plates of infinite extension in the exactly central position. The lower plate and the half of the upper plate are kept at a constant lower temperature, and the remaining upper plate is kept at a constant higher temperature. The fin is also kept at a constant temperature (variable). Steady-state two-dimensional laminar natural convection is analyzed as a problem of boundary value under a boundary-fitted conformal mapping system, using a spectral finite difference scheme, with a condition of doubly-connectedness. The steady-state solution is obtained as a limit of the transient solution.

Markov word patterns and a relation on [formula omitted]-words

We prove that all suffixes of a two-way infinite extension of an irrational characteristic word can be represented as Markov word patterns (MWPs) of type 1 and under some conditions, as MWPs of type 2. For each of these MWPs, the pairs of seed words are identified and are described in several different ways. We prove that the simple Sturmian words are the only Sturmian words that are representable as MWPs, each pair of seed words of which is either a pair of adjacent α-words or adjacent α-words with reverse order.

Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency

We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.

Automatic coupling of ABAQUS and a boundary element code for dynamic elastoplastic problems

Based on a FE–BE coupling algorithm, an automatic implementation procedure for the coupling of the ABAQUS with a self-written linear elastic BE code is introduced for dynamic elastoplastic problems. User subroutine (UEL) is developed to enable the incorporation of the BE capabilities within the ABAQUS. Each closed BE domain in the mixed FEM/BEM model is defined as a finite super-element for which the effective stiffness and effective forces are generated by the BE code and hence can be assembled to the global FE formulation. The user can not only benefit from the powerful pre- and post-disposal functions of the ABAQUS, but also deal with systems with infinite extension by using the BEM as a supplement. Basic steps of the automatic coupling procedure are explained and necessary background information is provided. The analysis is conducted through several examples regarding 2D time domain responses. The results of the analysis document a very good agreement between the present solutions and analytical and other numerical results, confirming thus a successful implementation of the developed automatic coupling procedure.

Some Statistical and Spatial Properties of Signal Scattering by 2-D Slightly Rough Random Surfaces

Within the framework of the first-order small perturbation method (SPM), we establish some statistical and spatial properties of signal scattering by 2-D slightly rough random surfaces. The work concerns the total field within the intermediate field-zone for an ergodic and stationary Gaussian surface under illumination by a monochromatic plane wave. For infinite extension surfaces, we obtain the probability density functions (pdfs) for the modulus and phase of the total field components. The modulus pdf is expressed as an infinite sum of modified Bessel functions while the phase pdf is expressed in terms of the error function. Under oblique illumination, the total field is not wide-sense stationary. From a spatial point of view, for a given elevation and under all incidences, we show that the total field is ergodic to the second order. Under oblique incidence, the spatial distribution of the total field modulus is a Rayleigh law and the phase is uniform. Under normal incidence, we establish that the spatial and statistical distributions are interchangeable.

NSIFs estimation based on the averaged strain energy density under in-plane mixed mode loading

In this work three methods for the rapid calculation of the NSIFs, based on the averaged strain energy density (SED), are compared. The first method was proposed by Lazzarin et al. and it is based on the calculation of the SED averaged in two different control volumes centred at the notch tip. The second one instead was recently presented by Treifi and Oyadiji and it takes advantage of the strain energy density averaged within two control volumes (semi-circular sector) centred at the notch tip. Then a new method based on the evaluation of the total and deviatoric strain energy density averaged over a control volume has been proposed.Finally, the described methods have been applied to plates weakened by different V-notch geometries: diamond-shaped notch, square hole and central crack in plates of finite and infinite extension. The values ​​of the NSIFs derived according to Gross and Mendelson have been compared with those obtained by means of the approximate methods, by using coarse FE meshes.

Boosting Shape Classifiers Accuracy by Considering the Inverse Shape

Many techniques exist for describing shapes. These techniques almost exclusively consider the contour or the inside of the shape; the major problem for describing the outside of a shape, or inverse shape, being that it has an infinite extension. In this paper, we show how to adapt two shape descriptors , one region based, the Cover By Rectangles, and one transform based, the Zernike moments, to be applicable to the inverse shape. We analyze their properties, and show how to deal with the infinite extension of the inverse shape. Then, we apply these descriptors to shape classification and compare representations that use the shape, its inverse, or both. Our experiments establish that, for shape classification, a representation integrating the inverse shape often outperforms a representation restricted to the shape. This opens the path for better techniques that could use, as a rule of thumb, both the representations of a shape and its inverse for the purpose of classification.

Magneto-Thermosolutal Convection in Couple-Stress Fluid in a Porous Medium

Thermosolutal instability of Veronis(1965) type in a couple-stress fluid in the presence of uniform vertical magnetic field in a porous medium is considered. Following the linearized stability theory and normal mode analysis, the paper mathematically established the condition for characterizing the oscillatory motions which may be neutral or unstable, for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. It is proved analytically that all non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth in a porous medium, which is acted upon by uniform vertical magnetic field opposite to force field of gravity and a constant vertical adverse temperature gradient, are necessarily nonoscillatory, in the regime established, the result is important since the exact solutions of the problem investigated are not obtainable in closed form, for any arbitrary combination of free and rigid boundaries. A similar characterization theorem is also established for Stern (1960) type of configuration.

Unbiased simulation of stochastic differential equations using parametrix expansions

In this article, we consider an unbiased simulation method for multidimensional diffusions based on the parametrix method for solving partial differential equations with Holder continuous coefficients. This Monte Carlo method which is based on an Euler scheme with random time steps, can be considered as an infinite dimensional extension of the Multilevel Monte Carlo method for solutions of stochastic differential equations with Holder continuous coefficients. In particular, we study the properties of the variance of the proposed method. In most cases, the method has infinite variance and therefore we propose an importance sampling method to resolve this issue.

Closure planes

We introduce a simple algebraic method for constructing infinite affine (and projective) planes from an infinite set of finite planes of prime power order stemming from a "root" plane. The construction uses finite fields and infinite extensions of finite fields in a critical way. We obtain a classical-looking result which states that if the construction succeeds over the algebraic closure of a finite field, then both the infinite plane and the original root plane must be Desarguesian. The Lenz---Barlotti types for these planes are then linked to the Lenz---Barlotti type of the root plane. Examples are then given. These show that under suitable conditions, the method can yield infinitely many non-isomorphic infinite planes. These examples are of Lenz---Barlotti types II.1 and V.1.

Formation of a Prismatic Dislocation Loop in the Interface of a Circular Cylindrical Inclusion Embedded in a Thin Slab

The introduction of a prismatic dislocation loop in the interface of an axisymmetric precipitate embedded in a thin slab of infinite lateral extension has been theoretically investigated. The critical misfit strain resulting from the lattice mismatch between the inclusion and the slab has been characterized for the loop formation versus the thickness of the slab and the radius of the inclusion. The case where the precipitate is embedded in a semi-infinite matrix is also discussed and a stability diagram of the structure is displayed with respect to the loop introduction versus the geometric and misfit parameters.

Surface elasticity revisited in the context of second strain gradient theory

Surface/interface stresses, when notable, are closely associated with a surface/interface layer in which the interatomic bond lengths and charge density distribution differ remarkably from those of the bulk. The presence of such topographical defects as edges and corners amplifies the noted phenomena by large amounts. If the principal features of interest are such studies as the physics and mechanics of evolving microscopic-/nanoscopic-interfaces and the behavior of nano-sized structures which have a very large surface-to-volume ratio, traditional continuum theories cease to hold. It is for the treatment of such problems that augmented continuum approaches like second strain gradient and surface elasticity theories have been developed by Mindlin (1965) and Gurtin and Murdoch (1975), respectively. In the mathematical framework of the former theory, the surface effect is explicitly revealed through surface characteristic length and modulus of cohesion, whereas within the latter theory, which views the bulk material and its complementary surface as separate interacting entities, the critical role of surfaces/interfaces is directly incorporated through the introduction of the notions of tangential surface strain tensor, surface stress tensor, and surface elastic modulus tensor into the formulation. In the realm of the experimentations, evaluation of the above-mentioned surface parameters poses serious difficulties. One of the objectives of the current study is to provide a remedy as how to calculate, not only these parameters, but also Mindlin’s bulk characteristic lengths as well as Lame constants with the aids of first principles density functional theory (DFT). To this end, surface elasticity is reformulated by maintaining the first and second gradients of the strain tensor for the bulk; as a result two new key equations are obtained. One of these equations is an expression for the net surface stress, needed to relate the surface parameters in surface elasticity to the Mindlin’s second gradient theory parameters. The other equation is for the total elastic energy which is utilized to find an analytical expression for the surface energy. The available data on surface relaxation obtained experimentally and computationally are in good correspondence with the results of the current theory. Moreover, employing the present theory, an estimate for the effective elastic constants of films with infinite extension is provided.

On Vector Perturbation Precoding for the MIMO Gaussian Broadcast Channel

Precoding schemes in the framework of vector perturbation (VP) for the multiple-input multiple-output (MIMO) Gaussian broadcast channel (GBC) are investigated. The VP scheme, originally a “one-shot” technique, is generalized to encompass processing over multiple time instances. Using lattice-based extended alphabets (“perturbations”), and considering the infinite time-span extension limit, a lower bound on the achievable sum-rate using the generalized VP scheme is analytically obtained. The lower bound is shown to asymptotically achieve the optimum sum-rate in the high signal-to-noise ratio (SNR) regime (both in terms of degrees-of-freedom and power offset), for any number of users and transmit antennas. For the two-user cases, it is shown that the lower bound coincides with the sum-capacity for low SNR. The above lower bound is constructively obtained by means of an efficient practically oriented suboptimal transmit energy minimization algorithm, which exhibits a polynomial complexity in the number of users. The proposed precoding scheme demonstrates that the “shaping gain” is achievable for VP schemes, when employing “good” multidimensional lattices. It is also shown that the suboptimum algorithm has its merits, even when processing over multiple time instances is not employed. For the $2\times 2$ MIMO GBC, the VP scheme is generalized further, and an inner bound for the entire achievable rate region is obtained, by which an interesting correspondence is identified with the ultimate capacity region, as obtained by “dirty paper coding”.

A spatial bioeconomic model of the harvest of wild plants and animals

The intensity of harvest of wild plants and animals often varies with the distance from human settlements, processing facilities, markets, and transportation routes such as roads and rivers, resulting in marked spatial gradients in the abundance of such resources. Spatial modeling of the harvest of wild species has therefore emerged as an important research approach. The literature on such modeling is, however, fragmented between different resource types, and empirical validation of the models is often weak or absent. This paper presents a model that is intended to have validity for a wide variety of wild plant and animal resources. It combines a logistic model of resource growth with an economic model assuming that costs associated with harvest consist of three components, namely transport, search, and handling, and a one-dimensional spatial structure where resource harvesters are based at a “central place” surrounded by infinite extensions of habitat for the harvested resource. Model outcomes show that the spatial distribution of harvest heavily depends on the carrying capacity and the catchability coefficient, i.e. the ease of finding and harvesting a resource unit. An empirical study of wildlife hunting and palm leaf harvest in indigenous villages in Ecuadorian Amazonia confirmed the validity of model outcomes.

Interference Alignment Using Finite and Dependent Channel Extensions: The Single Beam Case

Vector space interference alignment (IA) is known to achieve high degrees of freedom (DoF) with infinite independent channel extensions, but its performance is largely unknown for a finite number of possibly dependent channel extensions. In this paper, we consider a $K$-user $M_t \times M_r$ MIMO interference channel (IC) with arbitrary number of channel extensions $T$ and arbitrary channel diversity order $L$ (i.e., each channel matrix is a generic linear combination of $L$ fixed basis matrices). We study the maximum DoF achievable via vector space IA in the single beam case (i.e. each user sends one data stream). We prove that the total number of users $K$ that can communicate interference-free using linear transceivers is upper bounded by $NL+N^2/4$, where $N = \min\{M_tT, M_rT \}$. An immediate consequence of this upper bound is that for a SISO IC the DoF in the single beam case is no more than $\min\left\{\sqrt{ 5K/4}, L + T/4\right\}$. When the channel extensions are independent, i.e. $ L$ achieves the maximum $M_r M_t T $, we show that this maximum DoF lies in $[M_r+M_t-1, M_r+M_t]$ regardless of $T$. Unlike the well-studied constant MIMO IC case, the main difficulty is how to deal with a hybrid system of equations (zero-forcing condition) and inequalities (full rank condition). Our approach combines algebraic tools that deal with equations with an induction analysis that indirectly considers the inequalities.

Effect of Wave Number on the Onset of Instability in Couple-Stress Fluid and its Characterization in The Presence of Magnetic Field

Thermal instability of couple-stress fluid in the presence of uniform vertical magnetic field is considered. Following the linearized stability theory and normal mode analysis, the paper established the regime for all oscillatory and non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth in the presence of uniform vertical magnetic field, the necessary condition for the existence of ‘overstability’ and the sufficient condition for the validity of the ‘exchange principle’ is derived. The result is important since it hold for all wave numbers and for any arbitrary combination of free and rigid boundaries at the top and bottom of the fluid. Further, the stationary convection at marginal state with free horizontal boundaries is analyzed numerically and graphically, showing that the couple-stress parameter and magnetic field has stabilizing effect on the system. However, for the constant magnitude of couple-stress parameter and magnetic field, the wave number has a destabilizing effect for a value less than a critical value, which varies with the magnitude of the couple-stress parameter and magnetic field and for higher value than the critical value of the wave number; it has a stabilizing effect on the system.

Bio‐inspired propulsion: Downstream travelling wave motion of a surface with finite &amp; infinite extension

AbstractThe thrust force on a surface that performs a fish‐like travelling wave motion downstream to an oncoming flow is discussed. Unsteady potential flow, with vortex shedding from the trailing edge, is known to explain the generation of thrust. Contrarily, fish swimming has been related to the flow over an infinitely extended surface. To interlink both problems, the potential flow over the surface of finite length is considered in the limit of high wave numbers. It turns out that the leading order, space‐periodic pressure does not contribute to thrust. Thus, the perturbation pressure is essential for propulsion. Besides, laminar flow is considered in the space‐periodic setting. The present results reveal – in contrast to literature – that the surface force is always drag. (© 2014 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Distributed Dislocation Method for Determining Elastic Fields of 2D and 3D Volume Misfit Particles in Infinite Space and Extension of the Method for Particles in Half Space

AbstractA multitude of researchers have utilized a variety of techniques to formulate the stresses and deformations caused by volume misfit inclusions in infinite host media. Few of such techniques can also be extended to derive solutions for inclusions in a half space. In this manuscript we present a novel computational method for determining the elastic fields of two and three-dimensional inclusions of arbitrary shape in an infinite host matrix. The misfit strain is treated by a distribution of prismatic dislocation loops. A systematic numerical assessment illustrates that the discretization can yield excellent agreement with existing analytical solutions for certain particle geometries. This method is then further developed to solve for two-dimensional problems in a half space.

Modelos relativistas de discos de polvo magnetizados en un espaciotiempo conformestático axialmente simétrico

An infinite family of new solutions of the Einstein-Maxwell equations for axially symmetric conformastatic spacetimes is presented. This family of solutions describe thin dust disks made of material sources with a surface conduction current. The solutions are obtained by expressing the metric function and the magnetic potential in terms of an auxiliary function which satisfies the Laplace equation, a characteristic property of the conformastatic spacetimes. By introducing then a finite discontinuity on the first derivatives of the metric tensor, solutions with a delta function type singularity with support on the hypersurface z = 0 are obtained, describing so infinitesimally thin disks of infinite extension. Then, the surface energy-momentum and the surface current density of the disk are obtained by using the formalism of tensorial distributions and their physical content is analyzed. It was found that the energy density behaves well everywhere, that the energy-momentum tensor satisfies all the energy conditions and that, although the discs are of infinite extension, their total mass is finite. Furthermore, it is found that the curvature quadratic scalars and the electromagnetic invariants are regular everywhere, so that the spacetime is free of singularities. Finally, in order to illustrate the behavior of the family of thin disks, we consider the model for the first family member and graphically analyzes the behavior of the surface energy density and the surface current density. © 2014. Acad. Colomb. Cienc. Ex. Fis. Nat. All rights reserved.