Finite Discontinuity Research Articles

On the Singular Behavior of the Inverse Laplace Transforms of the Functions

AbstractExact analytical expressions for the inverse Laplace transforms of the functions are obtained in the form of trigonometric series. The convergence of the series is analyzed theoretically, and it is proven that those diverge on an infinite denumerable set of points. Therefore it is shown that the inverse transforms have an infinite number of singular points. This result, to the best of the author’s knowledge, is new, as the inverse transforms of have previously been considered to be piecewise smooth and continuous. It is also found that the inverse transforms have an infinite number of points of finite discontinuity with different left- and right-side limits. The points of singularity and points of finite discontinuity alternate, and the sign of the infinity at the singular points also alternates depending on the order n. The behavior of the inverse transforms in the proximity of the singular points and the points of finite discontinuity is addressed as well.

Two-dimensional Heisenberg model with nonlinear interactions.

We investigate a two-dimensional classical N-vector model with a nonlinear interaction (1+sigma(i) x sigma(j))(p) in the large-N limit. As observed for N=3 by Blöte et al. [Phys. Rev. Lett. 88, 047203 (2002)], we find a first-order transition for p>p(c) and no finite-temperature phase transitions for p<p(c). For p>p(c), both phases have short-range order, the correlation length showing a finite discontinuity at the transition. For p=p(c), there is a peculiar transition, where the spin-spin correlation length is finite while the energy-energy correlation length diverges.

Nonuniform slot injection (suction) into a compressible flow

The steady nonsimilar compressible laminar boundary-layer flow over a yawed infinite circular cylinder with nonuniform slot injection (suction) has been studied up to the point of separation. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) are removed by choosing appropriate nonuniform mass transfer distributions in the slot. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is found that the nonuniform slot injection moves the point of separation downstream but the nonuniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The yaw angle has very little effect on the location of the point of separation.

Optimized effective potential for the extended Hubbard model

Antiferromagnetic and charge ordered Hartree-Fock solutions of the one-band Hubbard model with on-site and nearest-neighbor Coulomb repulsions are exactly mapped onto an auxiliary local Kohn-Sham (KS) problem within a density-functional theory. The mapping provides a new insight into the interpretation of the KS equations. (i) With an appropriate choice of the basic variable, there is a universal form of the KS potential, which is applicable both for the antiferromagnetic and the charge ordered solutions. (ii) The Kohn-Sham and Hartree-Fock eigenvalues are interconnected by a scaling transformation. (iii) The band-gap problem is attributed to the derivative discontinuity of the basic variable as the function of the electron number, rather than a finite discontinuity of the KS potential. (iv) It is argued that the conductivity gap and the energies of spin-wave excitations can be entirely defined by the parameters of the ground state and the KS eigenvalues.

Hard soliton excitation regime: Stability investigation

The problem of the stability of one-dimensional solitons in the hard regime of soliton excitation, where the matrix element of the four-wave interaction has an additional smallness, is studied. It is that shown for optical solitons striction can weaken the Kerr nonlinearity. It is shown that solitons with a finite amplitude discontinuity at the critical soliton velocity, equal to the minimum phase velocity of linear waves, are unstable while solitons with a soft transition remain stable with respect to one-dimensional perurbations. Two-and three-dimensional solitons near threshold are unstable with respect to modulation perturbations.

Origin of Blazar Activity

Models of Blazars based on the propagation of finite discontinuities or fronts in the Poynting flux jet from the innermost regions of an accretion disk around a black hole are discussed. Such fronts may be responsible for short time–scale (from less than hours to days) flares in different wavebands from high frequency radioband to TeV, with delay in low radio frequencies as a result of synchrotron self-absorption. The cases of magnetic fields of one and opposite polarities across the front are investigated. We find that annihilation of magnetic field in the front leads to higher energy spectrum of leptons and possibility of strong TeV flares. Electron–positron pairs form in most cases as a result of interaction between numerous synchrotron photons and SSC photons, and constitute the majority species, compared with the ions at subparsec scales. Frequent weak outbursts may be responsible for flickering core radiation in all wavebands, while the stronger outbursts may be observed as short time–scale flares.

Effect of Collector-Base Barrier on GaInP/GaAs Double Heterojunction Bipolar Transistor and Further Improvement by Doping-Spike

We report the effects of a collector-base barrier on GaInP/GaAs double heterojunction bipolar transistors (DHBT's). A potential barrier exists at the collector-base heterointerface due to a small yet finite conduction band discontinuity. The voltage-dependent barrier that blocks the electrons results in a large collector current saturation voltage (knee voltage). We found, through theoretical calculation, that the potential barrier is much higher and less sensitive to the external bias when the collector doping density is low. If the conduction band discontinuity of ΔE c=0.2 eV is employed in the calculation, the collector-base voltage used to totally suppress the existing potential barrier varies from 2.5 V for N C=1×1017 cm-3 to 17 V for N C=2×1016 cm-3. Further improvement in eliminating the barrier was achieved using the doping spike located at the heterointerface. A zero potential barrier was obtained even if the base collector was forward biased. Experimentally, we have successfully fabricated GaInP/GaAs DHBT's with and without doping spikes at the B–C heterointerface. Large knee voltages are observed in DHBT's without a doping spike. The improved DHBT's exhibit a high current gain of 280 and a small knee voltage smaller than 1.8 V, supporting the very low potential barrier at the B–C junction.

Thermal Expansion Coefficient of BaCo1-xNixS2

Measurements of the linear thermal expansion coefficient α have been carried out on both polycrystalline pellets and single crystals of BaCo 1- x Ni x S 2 , which has a layered structure and exhibits the Mott transition with varying x . In the region of x ≤0.22, where antiferromagnetic state exists below T N , α exhibits the finite discontinuity Δα at T N , as is expected in ordinary cases of second order phase transition. The sign of the discontinuity Δα{≡α( T N -0)-α( T N +0)} changes from positive to negative at x ∼0.07 with increasing x , which can consistently be explained by considering the x -dependence of the electronic structure of this system.

UV-Regularization of Field Discontinuities

A nonperturbative regularization of uv-divergencies, caused by finite discontinuities in the field configuration, is discussed in the context of (1+1)-dimensional kink models. The relationship between this procedure and the appearance of "quantum copies" of classical kink solutions is studied in detail and confirmed by conventional methods of soliton quantization.

On the connection between discontinuous step-like and smooth kink-type classical solutions in quantum field theory

A nonperturbative procedure for subtracting singularities caused by finite discontinuities of the field configurations is suggested. This procedure is applied to the Lorentz-covariant quantization of(1+1)-dimensional topological kinks. In the course of this procedure, “quantum copies” of a classical kink naturally appear. These copies have the same topological charge but have negligibly small sizes and masses because the subtraction procedure eliminates divergences caused by the field differentiations at the discontinuity points. These effects are investigated in detail for those(1+1)-dimensional scalar field models where classical kinks exist.

Ray splitting and quantum chaos.

Ray splitting is the phenomenon whereby a ray incident on a boundary splits into more than one ray traveling away from the boundary. The most common example of this is the situation, originally considered by Snell in 1621, in which an incident light ray splits into reflected and transmitted rays at a discontinuity in refractive index. This paper seeks to extend techniques and results from quantum chaos to short wavelength problems in which ray splitting surfaces are present. These extensions are tested using a simple model problem for the Schr\"odinger equation in two dimensions with a finite step potential discontinuity. Numerical solutions for the energy spectrum and eigenfunctions in this system are then compared with predictions based on quasiclassical theoretical results suitably extended to include ray splitting. Among the topics treated are the ray orbits for our problem, energy level statistics, scars, trace formulas, the quasiclassical transfer operator technique, and the effect of lateral waves. It is found that these extensions of quantum chaos are very effective for treating problems with ray splitting.

Ray splitting and quantum chaos.

Ray splitting is the phenomenon whereby a ray incident on a boundary splits into more than one ray traveling away from the boundary. The most common example of this is the situation, originally considered by Snell in 1621, in which an incident light ray splits into reflected and transmitted rays at a discontinuity in refractive index. This paper seeks to extend techniques and results from quantum chaos to short wavelength problems in which ray splitting surfaces are present. These extensions are tested using a simple model problem for the Schr\odinger equation in two dimensions with a finite step potential discontinuity. Numerical solutions for the energy spectrum and eigenfunctions in this system are then compared with predictions based on quasiclassical theoretical results suitably extended to include ray splitting. Among the topics treated are the ray orbits for our problem, energy level statistics, scars, trace formulas, the quasiclassical transfer operator technique, and the effect of lateral waves. It is found that these extensions of quantum chaos are very effective for treating problems with ray splitting.

Finite element solution of electron waveguide discontinuities and its application to quantum field effect directional couplers

A numerical approach based on the finite element method is described for the solution of electron waveguide discontinuities with arbitrary potential and effective-mass distributions. Analytical solutions are introduced for the uniform waveguide regions. The approach is applied to a quantum field effect directional coupler with finite coupling length and longitudinal discontinuities. The effects of the longitudinal interference due to the discontinuities and of the transverse interference due to the even and odd supermodes in the coupling region are studied. The influence of the shape of the wire-tip on the transmission properties is also investigated.

Quantum Interference Phenomena in an Electron-Wave Directional Coupler with Finite Coupling Length

A new type of quantum field effect directional coupler with finite coupling length is studied with the equivalent network approach. The coupler analyzed is composed of GaAs/Ga1-xAlxAs and has finite external potential barriers and longitudinal discontinuities. Although this structure is analogous to that in an optical counterpart, there is no radiation loss. Numerical results show that the effects of the longitudinal interference appear as a short-periodic behavior of the transmission probability and the effects of the beat of two normal modes appear as a long-periodic behavior of the transmission probability.

Compression and rarefaction waves in granular flow

The propagation of finite one-dimensional discontinuities of particulate-phase pressure in dry granular flow is examined. These discontinuities are classified depending on whether the granular pressure behind the discontinuity is larger or smaller than that in front of it. If the speed of propagation of infinitesimal discontinuities is regarded as ‘sonic’, the former propagate ‘supersonically’, while the latter propagate ‘subsonically’. Rarefaction and compression waves are also analyzed, and we show that, based on realistic constitutive assumptions on the density dependence of particulate-phase pressure, rarefaction waves smooth out as they propagate, while compression waves reinforce each other to become shocks.

An effective approach for study of multiple discontinuities of transmission lines

In this paper, a novel approach for calculation of discontinuities of transmission lines is presented. This approach is flexible, simple and effective. For calculation of multiple discontinuities or to take into account the thickness of the obstacles, it is only necessary to transfer the relationship between the electric and magnetic field components from one discontinuity to another and match them on the last one. The method of transfer may be arbitrary, it may also be realized by using the well-known method of lines or others methods, Both single and multiple waveguide discontinuities are calculated and the computed results are in good agreement with the literature. Examples of finite thickness waveguide discontinuities are also given. The proposed method may be readily used to calculate microstrip discontinuities. Extension to discontinuities of other types of transmission lines can also be performed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Thermodynamics of spin [formula omitted] reduced s-d model with application to (LaCe)Al 2 alloys

The Hamiltonian H K( B ) of the spin 1 2 s-d exchange model in a uniform magnetic field B is reduced by a method previously applied to H K( 0). The reduced s-d Hamiltonian H r( B ) is asymptotically equivalent in the thermodynamic limit to a mean-field h r( B ), which exhibits a 2nd order phase transition at T c if B is weak. h r( B ) is applied to (LaCe)Al 2 alloys. There is correspondence between theoretical and experimental curves of zero-field susceptibility χi(0, T): the theoretical χi(0, T) has a first-order pole at T c, below the Kondo temperature T K; the experimental χie(0, T) curve has a finite maximum below T K. The zero-field theoretical specific heat of (LaCe)Al 2 exhibits a finite discontinuity at T c. Above T c the expression for resistivity coincides with the one given by Kondo and the limiting T → 0 resistivity is finite.

Non-uniform slot injection (suction) or wall enthalpy into a steady nonsimilar compressible laminar boundary layer

Steady two-dimensional and axisymmetric compressible nonsimilar laminar boundary-layer flows with non-uniform slot injection (or suction) and non-uniform wall enthalpy have been studied from the starting point of the streamwise co-ordinate to the exact point of separation. The effect of different free stream Mach number has also been considered. The finite discontinuities arising at the leading and trailing edges of the slot for the uniform slot injection (suction) or wall enthalpy are removed by choosing appropriate non-uniform slot injection (suction) or wall enthalpy. The difficulties arising at the starting point of the streamwise co-ordinate, at the edges of the slot and at the point of separation are overcome by applying the method of quasilinear implicit finite difference scheme with an appropriate selection of finer step size along the streamwise direction. It is observed that the non-uniform slot injection moves the point of separation downstream but the non-uniform slot suction has the reverse effect. The increase of Mach number shifts the point of separation upstream due to the adverse pressure gradient. The increase of total enthalpy at the wall causes the separation to occur earlier while cooling delays it. The non-uniform total enthalpy at the wall (i.e., the cooling or heating of the wall in a slot) along the streamwise co-ordinate has very little effect on the skin friction and thus on the point of separation.

Three‐dimensional finite element analysis of N‐port waveguide junctions using edge‐elements

AbstractThe finite element method is formulated in such a way that the electromagnetic solution of an excited cavity formed from an N‐port waveguides junction leads directly and naturally to circuit characteristics of this junction. The use of edge‐elements eliminates nonphysical solutions. The reliability of the method is assured compared to a penalty method. Accuracy of the method is demonstrated through the presentation of results for a waveguide T‐junction, while its efficiency is proven through the presentation of results for two case studies of a finite step discontinuity and a finline T‐junction. © 1993 John Wiley &amp; Sons, Inc.

THE PARAMAGNETIC SUSCEPTIBILITY AND CROSSOVER TRANSITION IN U=∞ HUBBARD MODEL

Paramagnetic susceptibility χ(0, 0)=dR(H)/dH in (H→0, U=∞) Hubbard model has been calculated in the second order of a kinematic field. The final result changes cardinally the conclusion about paramagnetic’s instability which was derived from the theory of the first order in kinematic field at T=0 and ρ=1/2W.1 The obtained expression for χ(0, 0) possesses Pauli limit for n→0 with factor 2, has strong correlated enhancement (≈5 times as large) in the region of intermediate filling of the band (n≈0.5), and determines the paramagnetic-ferromagnetic transition as a crossover transition (i.e. without finite or infinite discontinuity).