Milne's problem for two-dimensional transport in a quarter space

Double Fourier transformation of the one-speed transport equation is used to determine a family of solutions to the homogeneous (Milne's) problem for the quarter space. All contributions to the density asymptotically away from the corner are determined explicitly by considering two appropriate half-space problems and by extensive use of contour integration in two complex variables. An iterative scheme previously derived may be used to determine the correction near the corner.     

Viscous Slip MHD Flow over a Moving Sheet with an Arbitrary Surface Velocity

The magnetohydrodynamic(MHD) flow induced by a stretching or shrinking sheet under slip conditions is studied.Analytical solutions based on the boundary layer assumption are obtained in a closed form and can be applied to a flow configuration with any arbitrary velocity distributions. Seven typical sheet velocity profiles are employed as illustrating examples. The solutions to the slip MHD flow are derived from the general solution and discussed in detail. Different from self-similar boundary layer flows, the flows studied in this work have solutions in explicit analytical forms. However, the current flows require special mass transfer at the wall, which is determined by the moving velocity of the sheet. The effects of the slip parameter, the mass transfer at the wall, and the magnetic field on the flow are also demonstrated.     

Viscous fingering as a first step toward understanding dendrites

The development of viscous fingering patterns has been observed for Hele-Shaw flows with both planar and circular initial interfaces. These flows have close formal connection with dendritic growth. Local curvature as a function of interfacial arclength has been extracted for all cases and modal analyses have been performed on these curvature functions. A crude measure of the content of the modal analyses comes from the behavior of the average wavenumber, , which at first increases during an initial ramifying flow period and then decreases with time as the pattern coarsens in the quiet regions behind the advancing fingers faster than it ramifies at the front.     

Numerical modelling of free interaction of shock waves in corner flows

The inviscid supersonic flows in corners between intersecting compression wedges were studied numerically. Under usual conditions, the flows in such corner configurations are conically self-similar. Besides, shock waves formed by wedges are plane and they interact with one another in these flows and the downstream development of the shock interaction structure at that occurs in a region which is bounded in cross-sectional directions by the walls and contracts towards the corner rib, and in this sense the above interaction of shocks may be subjected to influence of the rib. The corner flows of another type with an interaction of shocks not subjected to the “rib effect”, in other words free, were considered. This was ensured by that the corner configurations were designed with a gradually expanding gap along the rib in a way that the reflected shocks arising as a result of interaction passed through the gap without falling onto the walls. This eliminated the influence of a local flow near the corner rib on the interaction of plane shock waves formed by the wedges. The inviscid flows symmetric with respect to the bisector plane of the corner dihedral angle were considered. The computations showed that, in the gapped corner configurations with the free interaction of shocks, if these interactions were irregular, the cross-flow patterns were practically the same as in the original corner configurations without a gap. The conditions for the flows over corner configurations were also considered under which the interaction of shocks corresponded to the Neumann criterion of mechanical equilibrium. These conditions are equivalent to those, which take place in two-dimensional steady flows, when a hysteresis phenomenon is possible, which manifests itself in changing the moment of transition from a regime of regular reflection of shocks to an irregular one and conversely at a direct and inverse courses of varying the flow parameters—the Mach number and the inclination angle of the wedges. The conducted computations showed that a hysteresis is possible for considered corner flows in gapped configurations, but it must be followed by a detachment of shocks from the corner apex and a breakdown of the conical flow structure.     

Active control of intermittent noise in a room

I.IntroductionThereverberantnoisesmaybereducedwithanactivenoisecontrol(ANC)systcmformedbyacornermicrophonc-amplifier-1oudspcakersystemina.oom.lllThismeth-odbascdonthenormalmodccancelingprincip1chasalreadybeenclarifiedbothinthco-ryandexperimcnts,andthclimitationandpotcntialityofitsapp1icationalsodiscussedinapreviouspaper.Thediscussionsinthepastlimitedmost1ytothesteadyconditionofnoiscfield,andthisisextendedtothetransientcondihoninthcprcsentwork,viz.thein-llucnceofthecornerANCsystemwhenthenois…     

Theory of corner reflectors in electron waveguides

The transport properties of corner reflectors have been studied using a method derived from the embedding method for confined quantum systems. The method is used to calculate the eigenstates and Green function which are expanded in any convenient basis set and then used to calculate the transmission and reflection coefficients. The results for the reflectors are compared to the results for a right-angled corner and a circular corner. Current flow studies have been done to clarify the transmission results. The local density of states for the corners are calculated to study bound states and resonances. The reflectors have both one-dimensional and two-dimensional densities of states depending on the size of the reflector.     

Bose-Einstein condensate of cavity exciton polaritons in a trap

The properties of traps for exciton polaritons in a semiconductor microcavity with an embedded quantum well have been considered. The behavior of the two-component Bose-Einstein condensate of photons and excitons described by the coupled system of Gross-Pitaevskii equations has been investigated. The analytical solutions for weak-confinement traps have been found in the Thomas-Fermi approximation. In the case of strong confinement, the behavior of the condensate has been investigated and constraints on the possible values of the chemical potential of the system have been obtained. The wavefunctions and generally different spatial profiles of the coupled photon and exciton condensates have been found.     

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

~~Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation1. Feynman, R., There's plenty of room at the bottom, Journal of Microelectromechanical Systems, 1992, 1: 60 -66. 2. Piekos, E. S., Breuer, K. S., Numerical modeling of micromechanical devices using the direct simulation Monte Carlo method, Transactions of the ASME, Journal of Fluids Engineering, 1996, 118: 464-469. 3. Beskok, A., Karniadakis, G. E., Trimmer, W., Rarefaction and …     

Finding Solutions to Equations for the Longitudinal Components of an Electromagnetic Field in a Biisotropic Medium in the Neighborhood of a Regular Singular Point as Generalized Power Series

For a system of equations that describe electromagnetic fields in a biisotropic medium, particular solutions have been constructed in the neighborhood of a regular singular point. The solutions are written in the form of generalized power series. For the coefficients of the power series, exponents and recursion relations have been found. It has been shown that the solutions of the wave equations are generalizations of well-known special cylindrical functions. The behavior of the particular solutions have been examined for varied material parameters of the medium. The solutions obtained allow one to formulate mathematical models which could be used to calculate and optimize the parameters of a wide spectrum of functional devices based on waveguide structures with biisotropic inserts.     

Improved modeling of flows down inclined planes

New models of film flows down inclined planes have been derived by combining a gradient expansion at first or second order to weighted residual techniques with polynomials as test functions. The two-dimensional formulation has been extended to account for three-dimensional flows as well. The full second-order two-dimensional model can be expressed as a set of four coupled evolution equations for four slowly varying fields, the thickness h, the flow rate q and two other quantities measuring the departure from the flat-film semi-parabolic velocity profile. A simplified model has been obtained in terms of h and q only. Including viscous dispersion effects properly, it closely sticks to the asymptotic expansion in the appropriate limit. Our new models improve over previous ones in that they remain valid deep into the strongly nonlinear regime, as shown by the comparison of our results relative to travelling-wave and solitary-wave solutions with those of both direct numerical simulations and experiments. Received 14 September 1999 and Received in final form 6 January 2000     

角锥棱镜阵列谐振腔的输出特性

 角锥棱镜阵列具有溯源反射和准相位共轭两大特点,可在一定程度上补偿高平均功率固体激光器的热畸变。但由于这种角锥棱镜阵列自身的缺陷和由它构成的谐振腔输出激光模式众多的特点,限制了其在谐振腔中的应用。分析了角锥棱镜阵列谐振腔产生多模输出的原因,提出了采用腔内滤波的方法实现单模输出。理论模拟和实验研究结果表明：利用该方法可较好地改善阵列角锥棱镜谐振腔的输出特性,获得了近5倍衍射极限的输出。     

Two-phase electrohydrodynamic simulations using a volume-of-fluid approach

A numerical methodology to simulate two-phase electrohydrodynamic flows under the volume-of-fluid paradigm is proposed. The electric force in such systems acts only at the interface and is zero elsewhere in the two fluids. Continuum surface force representations are derived for the electric field force in a system of dielectric–dielectric and conducting–conducting fluids. On the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region (interface). It is shown that a wrong choice of interpolation scheme (weighted arithmetic mean) may lead to a transition region thickness dependent electric field in the bulk. We simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed. A coupled level set and volume-of-fluid (CLSVOF) algorithm has been used for simulations presented here.     

Two-phase electrohydrodynamic simulations using a volume-of-fluid approach

A numerical methodology to simulate two-phase electrohydrodynamic flows under the volume-of-fluid paradigm is proposed. The electric force in such systems acts only at the interface and is zero elsewhere in the two fluids. Continuum surface force representations are derived for the electric field force in a system of dielectric–dielectric and conducting–conducting fluids. On the basis of analytical calculations for simple flow problems we propose a weighted harmonic mean interpolation scheme to smoothen the electric properties in the diffused transition region (interface). It is shown that a wrong choice of interpolation scheme (weighted arithmetic mean) may lead to a transition region thickness dependent electric field in the bulk. We simulate a set of problems with exact or approximate analytical solutions to validate the numerical model proposed. A coupled level set and volume-of-fluid (CLSVOF) algorithm has been used for simulations presented here.     

Calibrating cellular automaton models for pedestrians walking through corners

Cellular Automata (CA) based pedestrian simulation models have gained remarkable popularity as they are simpler and easier to implement compared to other microscopic modeling approaches. However, incorporating traditional floor field representations in CA models to simulate pedestrian corner navigation behavior could result in unrealistic behaviors. Even though several previous studies have attempted to enhance CA models to realistically simulate pedestrian maneuvers around bends, such modifications have not been calibrated or validated against empirical data. In this study, two static floor field (SFF) representations, namely ‘discrete representation’ and ‘continuous representation’, are calibrated for CA-models to represent pedestrians' walking behavior around 90° bends. Trajectory data collected through a controlled experiment are used to calibrate these model representations. Calibration results indicate that although both floor field representations can represent pedestrians' corner navigation behavior, the ‘continuous’ representation fits the data better. Output of this study could be beneficial for enhancing the reliability of existing CA-based models by representing pedestrians' corner navigation behaviors more realistically.     

Monte Carlo Renormalization Group Study of Φ4 Theory on 4-Dimensional Random Triangle Laticte

A Monte Carlo renormalization group investigation of 4-dimensional Φ⁴ theory is performed. Using special block method, the Ising renormalization flows and the Gaussian renormalization flows have been obtained, and the critical exponent v has been measured. The critical behavior supports the prediction of the triviality of the 4-dimensional iP4 theory.     

Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganism for rotating disk of variable thickness

Here heat, concentration and motile microorganism transfer rates in radiative flow of nanofluid are investigated. Variable thicked surface of rotating disk is examined. Concept of microorganisms suspended nanoparticles is stabilized through bioconvection which has been induced by combined effects of magnetic field and buoyancy forces. For obtained nonlinear differential systems the convergent series solutions are derived. Fluid flow, temperature, concentration and motile density behaviors for different parameters are analyzed through graphs. Skin friction and Nusselt number are analyzed numerically. Clearly temperature and concentration have opposite behavior for larger Brownian motion parameter. Motile density reduces for bioconvection Peclet number and bioconvection Lewis number.     

Measurement and study of the embedding impedance presented by the whisker antenna of a schottky diode corner cube mixer

A 250× scale model of a Schottky diode corner cube mixer designed for operation in the terahertz region has been built and tested. It has been successfully used to measure the embedding impedance presented to the diode at the whisker tip and also determine the impedance of the whisker antenna itself. The results have been input into a computer analysis to determine as to how the performance may be improved. With regards to improving the physical ruggedness of such mixers, a simple equivalent whisker structure has been determined and a new technique that may be used to fabricate a space qualifiable corner cube mixer intended for terahertz operation is disclosed.     

Exact solutions for the flow of non-Newtonian fluid with fractional derivative in an annular pipe

Generally speaking, rheological properties of materials are specified by their so-called constitutive equations. The simplest constitutive equation for a fluid is a Newtonian one, on which the classical Navier-Stokes theory is based. The mechanical behavior of many fluids is well described by this theory. However, there are many rheologically compli- cated fluids such as polymer solutions, blood and heavy oils which are inadequately de- scribed by a Newtonian constitutive equation that does …     

Soft Billiards with Corners

We develop a framework for dealing with smooth approximations to billiards with corners in the two-dimensional setting. Let a polygonal trajectory in a billiard start and end up at the same billiard's corner point. We prove that smooth Hamiltonian flows which limit to this billiard have a nearby periodic orbit if and only if the polygon angles at the corner are acceptable. The criterion for a corner polygon to be acceptable depends on the smooth potential behavior at the corners, which is expressed in terms of a scattering function. We define such an asymptotic scattering function and prove the existence of it, explain how can it be calculated and predict some of its properties. In particular, we show that it is non-monotone for some potentials in some phase space regions. We prove that when the smooth system has a limiting periodic orbit it is hyperbolic provided the scattering function is not extremal there. We then prove that if the scattering function is extremal, the smooth system has elliptic periodic orbits limiting to the corner polygon, and, furthermore, that the return map near these periodic orbits is conjugate to a small perturbation of the Hénon map and therefore has elliptic islands. We find from the scaling that the island size is typically algebraic in the smoothing parameter and exponentially small in the number of reflections of the polygon orbit.     

Flow of a Jeffery-Six Constant Fluid Between Coaxial Cylinders withHeat Transfer Analysis

In the present investigation we have discussed the flow of a Jeffrey-six constant incompressible fluid between two infinite coaxial cylinders in the presence of heat transfer analysis. The governing equations of Jeffrey-six constant fluid along with energy equation have been derived in cylindrical coordinates. The highly nonlinear equations are simplified with the help of non-dimensional parameters and then solved analytically with the help of homotopy analysis method (HAM) for two fundamental flows namely Couette and Generalized Couette flow. The effects of emerging parameters are discussed through graphs. The convergence of the HAM solution has been discussed by plotting h-curves.