Infinite Length Research Articles

Unexpected Dependence of Photonic Band Gap Size on Randomness in Self-Assembled Colloidal Crystals.

Using computer simulations, we explore how thermal noise-induced randomness in a self-assembled photonic crystal affects its photonic band gaps (PBGs). We consider a two-dimensional photonic crystal composed of a self-assembled array of parallel dielectric hard rods of infinite length with circular or square cross section. We find that PBGs can exist over a large range of intermediate packing densities and the largest band gap does not always appear at the highest packing density studied. Remarkably, for rods with square cross section at intermediate packing densities, the transverse magnetic (TM) band gap of the self-assembled (i.e., thermal) system can be larger than that of identical rods arranged in a perfect square lattice. By considering hollow rods, we find the band gap of transverse electric modes can be substantially increased while that of TM modes show no obvious improvement over solid rods. Our study suggests that particle shape and internal structure can be used to engineer the PBG of a self-assembled system despite the positional and orientational randomness arising from thermal noise.

Complex WGM frequencies of gyroelectric cylindrical resonators

Asymptotic closed-form expressions for calculating complex transverse electric (TE)/transverse magnetic (TM) whispering gallery mode (WGM) frequencies in homogeneous gyroelectric circular cylindrical resonators of infinite length are derived. In addition, a volume integral equation (VIE)-cylindrical Dini series expansion method is extended to support the prediction of complex WGMs for continuously varying highly inhomogeneous gyroelectric circular cylindrical resonators. To this end, the entire domain orthogonal vectorial basis of VIE is extended to support very large indices of the involved Dini-type cylindrical vector wave functions via asymptotic closed-form expressions. This way, the eigenbasis required to solve the VIE becomes free of numerical instabilities arising when very large orders of the involved Bessel functions are employed. The complex frequencies obtained by the asymptotic closed-form expressions for the case of the homogeneous gyroelectric resonator, as well as those obtained by the VIE when the multilayered gyroelectric resonator is reduced to one layer, are validated by comparisons with the complex roots extracted by numerically solving the TE/TM characteristic equations obtained from the separation of variables method, using complex root finding techniques. We demonstrate the calculation of very high-order WGM frequencies for cylindrical resonators composed of homogeneous and highly inhomogeneous permittivity profiles. This asymptotic theory constitutes a rigorous tool that may serve for verifying method of analytical regularisation–based numerical solutions for other non-circular inhomogeneous cylinders, and for interpreting experimental data for applications such as WGM lasing, refractometric sensing, and magneto-optic coupling.

Kapitza thermal resistance in linear and nonlinear chain models: Isotopic defect.

Kapitza resistance in the chain models with internal defects is considered. For the case of the linear chain, the exact analytic solution for the boundary resistance is derived for arbitrary linear time-independent conservative inclusion or defect. A simple case of isolated isotopic defects is explored in more detail. Contrary to the bulk conductivity in the linear chain, the Kapitza resistance is finite. However, the universal thermodynamic limit does not exist in this case. In other terms, the exact value of the resistance is not uniquely defined, and depends on the way of approaching the infinite lengths of the chain fragments. By this reason, and also due to the explicit dependence on the parameters of the thermostats, the resistance cannot be considered as a local property of the defect. Asymptotic scaling behavior of the heat flux in the case of very heavy defect is explored and compared to the nonlinear counterparts; similarities in the scaling behavior are revealed. For the lightweight isotopic defect in the linear chain, one encounters a typical dip of the temperature profile, related to weak excitation of the localized mode in the attenuation zone. If the nonlinear interactions are included, this dip can still appear at a relatively short timescale, with subsequent elimination due to the nonlinear interactions. This observation implies that even in the nonlinear chains, the linear dynamics can predict the main features of the short-time evolution of the thermal profile if the temperature is low enough.

Dual polarized engineering the extinction cross-section of a dielectric wire using graphene-based oligomers

In this paper, graphene-coated spherical nanoparticles are arranged around an infinite length dielectric cylinder to enhance its extinction cross-section. Initially, a single longitudinal one-dimensional periodic array is considered in different loci concerning the transverse electric (TE) incident plane wave. It is observed that regardless of the position of the particles, the extinction cross-section of the dielectric cylinder is considerably enhanced with respect to the bare one. Later, by increasing the number of longitudinal plasmonic arrays around the cylinder, each residing in a different azimuthal direction, the extinction cross-section is further manipulated to observe double pronounced Fano resonances. The origin of the Fano resonances is described by considering their planar counterparts constructed by the periodic assembly of plasmonic oligomers. Finally, the hexamer configuration is considered as the prototype, and the effect of various optical, geometrical, and material parameters on the optical response is investigated in detail. Interestingly, due to the spherical symmetry of the cells, the extinction cross-section is also enhanced for the transverse magnetic (TM) incident wave, which is unattainable using a continuous plasmonic cover made of metal or graphene. The potential application of our proposed structure is in the design of reconfigurable conformal optical absorbers and sensors.

Heat transfer analysis of micropolar hybrid nanofluid over an oscillating vertical plate and Newtonian heating

The unsteady flow of micropolar hybrid nanofluids through an oscillating vertical plate having infinite length has been analyzed in this study. This flow goes through Newtonian heating and thermal radiation. To enrich the thermal properties, we add copper and alumina nanoparticles to micropolar fluid. For the enhancement of heat transfer, water is taken as base liquid. The dimensionless reduced form of the governing equations for velocity, temperature and microrotation is formed by using dimensional analysis. We used Laplace transform method to have the exact solutions of these governing equations. MathCad’s software has been used to visualize the effects on the flow of fluid graphically. We found that microrotation, velocity and temperature are inversely proportional to Prandtl number but directly proportional to Grashof number. Further, temperature can be enhanced for increasing value of Newtonian heating, radiation and volume fraction of nanoparticles copper and alumina.

A Literature Review on Dynamic Analysis of Concrete Gravity and Arch Dams

This paper is devoted to a literature review for various treatments of dynamic analysis of concrete gravity and arch dams. The dynamic analysis of dams can be carried out by using analytical, semi-analytical, and numerical approaches, which may include nonlinear effects or ignore them. This kind of analysis can be conducted in the time or frequency domain. Different parameters significantly affect the dynamic behavior of dams, such as dam-water interaction, water compressibility, mass and damping of the foundation, sediments at the reservoir bottom, free surface waves, the infinite length of the foundation rock, reservoir and so on. As the analysis methods of dams developed, these parameters were gradually included in the process. Consequently, their capability enhanced in a more realistic investigation of the dams' behavior. This paper aims to illustrate these achievements by briefly reviewing the available published articles. Corresponding researches are categorizing based on the analysis techniques and considering or neglecting the dam-water interaction, sediments, and free surface motions. Assessing the current studies and suggesting future research are carried out. Expressing positive or negative aspects of the existing investigations are also offered.

Numerical simulation platform for slab track systems subjected to a moving vehicle

With the rapid development of high-speed and urban rail transit, ballastless slab tracks have been widely used in many areas. The work on construction, design, and mechanics of ballastless slab tracks is abundant and achievements have been made. However, a platform for numerical simulation and dynamic analysis of slab track systems subjected to a moving train still needs to be probed into. In the MATLAB®, effective and easily programable methods are presented to guide the construction of the vehicle-slab track interaction system and the realization of long length computation in this present study. Based on previous studies, the formulation of slab track dynamics in the framework of finite element theory is founded with simplicities, and then the wheel-rail coupling matrices totally derived from the nonlinear wheel-rail normal contact/tangential creep forces using the energy variation method are presented. Following the dynamics modeling construction, an improved method for long or infinite length computation is proposed. With an implementation of this method, the effect of the spatial variability of track properties on vehicle-track system dynamic performance can be evaluated conveniently. Using this numerical simulation platform, extensive studies have been conducted to model and analyze the influence of spatial variability of filling layer support stiffness, the track slab finite element type and support type of steel spring for floating-slab tracks, etc.

Mitigating the Effect of Nanoscale Porosity on Thermoelectric Power Factor of Si

The addition of porosity to thermoelectric materials can significantly increase the figure of merit, ZT, by reducing the thermal conductivity. Unfortunately, porosity is also detrimental to the thermoelectric power factor in the numerator of the figure of merit ZT. In this manuscript we derive strategies to recoup electrical performance in nanoporous Si by fine tuning the carrier concentration and through judicious design of the pore size and shape so as to provide energy selective electron filtering. In this study, we considered phosphorus doped silicon containing discrete pores that are either spheres, cylinders, cubes, or triangular prisms. The effects from these pores are compared with those from extended pores with circular, square and triangular cross sectional shape, and infinite length perpendicular to the electrical current. A semiclassical Boltzmann transport equation is used to model Si thermoelectric power factor. This model reveals three key results: The largest enhancement in Seebeck coefficient occurs with cubic pores. The fractional improvement is about 15% at low carrier concentration ($< 10^{20}\ \mathrm{1/cm^3}$) up to 60% at high carrier population with characteristic length around $\sim 1\ \mathrm{nm}$. To obtain the best energy filtering effect at room temperature, nanoporous Si needs to be doped to higher carrier concentration than is optimal for bulk Si. Finally, in $n$-type Si thermoelectrics the electron filtering effect that can be generated with nanoscale porosity is significantly lower than the ideal filtering effect; nevertheless, the enhancement in the Seebeck coefficient that can be obtained is large enough to offset the reduction in electrical conductivity caused by porosity.

Input-Distribution-Aware Successive Cancellation List Decoding of Polar Codes

Polar codes are linear block codes that can achieve channel capacity at infinite code length. Successive cancellation list (SCL) decoding relies on a set of parallel decoders; it yields good error-correction performance at finite code length, at the cost of increased implementation complexity and power consumption. Current efforts in literature focus on design-time decoder complexity reduction, while lacking practical run-time power reduction methods. In this work, input-distribution-aware SCL (IDA-SCL) decoding is proposed, that allows to determine the parallelism to adopt by performing simple observations on the input of the decoder. This technique guarantees fixed, short latency and allows hardware SCL decoders to dynamically shut down part of the internal parallelism before each decoding process. It can be combined with existing complexity- and power- reduction techniques. Simulation results show that IDA-SCL can reduce the run-time complexity of SCL of up to 50%.

Infinite Ergodic Walks in Finite Connected Undirected Graphs.

The micro-canonical, canonical, and grand canonical ensembles of walks defined in finite connected undirected graphs are considered in the thermodynamic limit of infinite walk length. As infinitely long paths are extremely sensitive to structural irregularities and defects, their properties are used to describe the degree of structural imbalance, anisotropy, and navigability in finite graphs. For the first time, we introduce entropic force and pressure describing the effect of graph defects on mobility patterns associated with the very long walks in finite graphs; navigation in graphs and navigability to the nodes by the different types of ergodic walks; as well as node’s fugacity in the course of prospective network expansion or shrinking.

Huffman-Coded Sphere Shaping for Extended-Reach Single-Span Links

Huffman-coded sphere shaping (HCSS) is an algorithm for finite-length probabilistic constellation shaping, which provides nearly optimal energy efficiency at low implementation complexity. In this paper, we experimentally study the nonlinear performance of HCSS employing dual-polarization 64-ary quadrature amplitude modulation (DP-64QAM) in an extended-reach single-span link comprising 200 km of standard single-mode fiber (SSMF). We investigate the effects of shaping sequence length, dimensionality of symbol mapping, and shaping rate. We determine that the naive approach of Maxwell–Boltzmann distribution matching — which is optimal in the additive white Gaussian noise channel — provides a maximum achievable information rate (AIR) gain of 0.18 bits/4D-symbol with respect to uniform signaling at optimum launch power in the infinite length regime. Conversely, HCSS can achieve a gain of 0.37 bits/4D-symbol over uniform signaling using amplitude sequence length of 32, which may be implemented without multiplications, using integer comparison and addition operations only. Coded system performance, with a net data rate of approximately 425 Gb/s for both shaped and uniform inputs, is also analyzed.

Mathematical model of a micropolar lubricating stuff

The article is devoted to the mathematical analysis model of the radial bearing of infinite length, lubricated with lubricating stuff and molten low-melting metal coating on the surface of the bearing bush, having the general rheological properties in the laminar condition of micro-polar lubrication properties, taking into account the dependence of viscosity rheological properties of micro-polar lubricating stuff, and the permeability of the porous coating from the pressure. The authors on the basis of the motion equations of a viscous incompressible fluid having micro-polar properties, and for “lamina”, of the continuity equation, Darcy equation and determining from the expression for the dissipation rate of mechanical energy, the profile of molten contour of the bearing bush, while taking account of the dependence of the overall rheological properties of the lubricating stuff and melt the low-melting metal coating having the micro-polar properties and the permeability of the porous coating of the pressure found the asymptotic and exact self-similar solution of the differential equation system on the parameter, due to the melt and the dissipation rate of mechanical energy to zero (without melt) and first (including melt) approximation.

The cloaking method in non-uniform static fields of cylindrical and spherical invisibility cloaks

The cloaking methods of infinite length coaxial cylindrical and concentric spherical invisibility cloaks in the non-uniform static field are investigated. First, the arbitrary potential function at the infinite boundary is expanded into a series of orthogonal potential functions. When there is only the nth order orthogonal potential function distribution at the infinite boundary, the analytical cloaking conditions of both the infinite length coaxial cylindrical and concentric spherical cloaks are derived. Furthermore, based on the analytical cloaking conditions, the approaching cloaking method is proposed in a complex non-uniform static field which composed of multiple orders potential functions. This method can acquire the optimal cloaking condition and avoid the iteration process by using numerical methods such as the finite element method etc. Finally, three examples are given to verify the correctness of the analytical cloaking conditions and the effectiveness of the approaching cloaking method proposed in this paper.

Length-Based fishery status of Yellowfin tuna (Thunnus albacares Bonnaterre, 1788) in the northern waters of the Oman Sea

In the present study, population characteristics of Thunnus albacares were evaluated by sampling at five fish landing sites in the northern Oman Sea including Beris, Ramin, Pozm, Konarak and Jask from March 2017 to March 2018. The biometric analysis was performed on more than twenty-six thousand fish. Population dynamic parameters were calculated including infinite length (L∞=171 cm), growth coefficient (K=0.54 (yr-1)), growth performance index (Ф'=4.19), natural mortality (M= 0.71(yr-1)), fishing mortality (F=1.57 (yr-1)), total mortality (Z=2.28±0.19 (yr-1)), exploitation coefficient (E=0.68 (yr-1)) and initial condition parameter (-0.18 yr-1). Relative production per recruitment, relative biomass per recruitment and exploitation rate of this species were Y'/ Rp = 0.04, B'/ Rp=0.23(yr-1) and U=0.62 (yr-1), respectively. The Pobj value is 0, and F/Fmsy>1. The results indicated that regarding length frequencies of this species in the northern part of the Oman Sea, yellowfin tuna stock has good conditions, but overfishing of this species is happening, now. Therefore, specific measures should be taken to reduce catch and fishing effort.

Semi-supervised classification on data streams with recurring concept drift and concept evolution

Mining non-stationary stream is a challenging task due to its unique property of infinite length and dynamic characteristics let alone the issues of concept drift, concept evolution and limited labeled data. Although more attention has been attracted on the issues of concept drift and evolution in data streams, however, most of existing methods are supervised in nature, which probably result in a worse classification performance and lower efficiency in the case with scarcity of labeled data. Thus, in this paper, we proposed a semi-supervised framework with recurring concept drift and novel class detection called ESCR, which aims to detect recurring concept drift and concept evolution in data streams with partially labeled data. It is firstly built on an ensemble model consisted of several clustering-based classifiers. In terms of this framework, we adopt Jensen–Shannon divergence based change detection technique on classifier confidence score instead of classification error rate to detect recurring concept drifts. Meanwhile, we take concept evolution into consideration by monitoring the outliers with strong cohesion. Moreover, we further improve the execution efficiency of our framework by exploiting the recursive function and dynamic programming. Finally, extensive experiments conducted on both benchmark and synthetic data sets demonstrate the effectiveness and efficiency of our proposed semi-supervised framework in the handling of data streams with recurring concept drifts and concept evolution, as compared to several well-known semi-supervised data stream classification methods.

The diffusing-velocity random walk: a spatial-Markov formulation of heterogeneous advection and diffusion

Abstract

Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA.

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length.

АНАЛІЗ МЕХАНІЗМА ПІДКРІПЛЕННЯ ПЛИТОЮ КОНСТРУКЦІЇ ДОРОГИ З РОЗВАНТАЖУЮЧИМ РОЗРІЗОМ

The problem posed is about the mechanism for reinforcing the road structure with a slab with an unloading cut. The reasons for the appearance of transverse cracks in the upper layer of the road surface in winter have been investigated. Solvable equations are formulated, their finite element analogs are constructed. Cases of loads at different values of elastic module and plate sizes are considered. At low temperatures, the upper layers of the road try to reduce their length, however, due to their almost infinite length, they cannot do this and transverse disordered cracks appear in the upper layer, which, due to the action of transport loads and the forces of frozen water, lead to further delamination and destruction of the road structure. Therefore, the introduction into another layer of a reinforced slab made of a stiffer and more durable material that is capable of absorbing increased stresses allows the upper layer to shorten and lengthen freely and removes the arising longitudinal thermal stress. Due to the fact that this plate is located in the zone of stress concentration, these stresses become less dangerous. KEYWORDS: AUTOMOBILE ROAD, ASPHALT-CONCRETE COATING, LOADING RISK, TRACKED TRACKS, TRANSPORT LOADS, STRESS FIELD, THERMO ELASTIC STATE

Temperature distribution in an elliptical body with an internal heat source with partial adiabatic isolation

The article calculates the temperature field in an elliptical body with internal heat dissipation. In this case, the boundary conditions are boundary conditions of the third kind. The solution is located at the transition to the elliptic coordinate system. The author has obtained an analytical solution for the distribution of the temperature field in a body with an elliptical cross-section of infinite length with zero ambient temperature with partial adiabatic isolation in the form of a functional series using hypergeometric functions.

Longitudinal wave analysis of infinite length piezoelectric circular rod based on temperature effect

Piezoelectric elements have been commonly used because of their wide applications in sensors, transducers, and some micro intelligent structures. However, in the fields of aviation, aerospace, and automation, some relevant equipment works in a harsh environment and is susceptible to the temperature change, thereby leading its performances to be greatly affected. Therefore, the problem of nonlinear wave relating to piezoelectric circular rods in different temperature fields is studied by modeling and numerical analysis. Firstly, based on the theory of finite deformation, we take infinite piezoelectric circular rod as a research object and consider the effects of transverse inertia and equivalent Poisson's ratio under the thermoelectric coupling action. Using the Hamilton principle and introducing the Euler equation, the longitudinal wave equation of piezoelectric circular rod is obtained. Secondly, Jacobi elliptic cosine function and Jacobi elliptic sine function expansion method are used to solve the wave equation of the piezoelectric circular rod, and the solitary wave solution and the exact periodic solution of the wave equation are obtained. It is found that the periodic solution can be reduced into a solitary wave solution under certain conditions, and it is proved theoretically that there may be solitary wave stably propagating in a piezoelectric circular rod. Finally, the dispersion curves of different wave velocity ratios and the curves about influences of temperature field on the waveform, amplitude and wave number of the piezoelectric rod are obtained by Matlab. The numerical results show that the wave velocity decreases with the increase of temperature when the wave velocity ratio is constant. Given the temperature is constant, it can be found that with the increase of the ratio, the amplitude of solitary wave gradually increases while the wavelength gradually decreases. In addition, the images obtained show that although temperature change can cause the characteristics of solitary waves to change, the solitary waves are always symmetrical bell shaped waves in the propagation process, reflecting the stability characteristics under the combined action of nonlinear and dispersion effects. Therefore, the variation of temperature field can influence and control some propagation characteristics of solitary waves. Moreover, the wave theory has been widely used in the nondestructive testing of structures and the improving of information transmission quality due to its special stability.