One dimensional Newton's equation with variable mass
Mazharimousavi, S Habib
2013-01-01
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a 1+1-dimensional spacetime. As a reflection of the equivalence principle geodesics equation gives the Newton's law of motion leaving the right hand side to be supplemented by the external forces. The resulting equation involves the speed of light so that our equation of motion addresses a wider scope than the customary classical mechanics. In the limit of infinite light speed which amounts to instantaneous interaction we recover the classical results.
One Dimensional Quasi-Exactly Solvable Differential Equations
Fasihi, Mohammad A.
2006-01-01
In this paper by means of similarity transformation we find some one-dimensional quasi-exactly solvable differential equations and their related Hamiltonians which appear in physical problems. We have provided also two examples with application of these differential equations.
Intertwining technique for the one-dimensional stationary Dirac equation
Nieto, L M; Samsonov, B F; Samsonov, Boris F.
2003-01-01
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac Hamiltonians, quadratic supersymmetry, closed extension of transformation operators, chains of transformations, and finally particular cases of pseudoscalar and scalar potentials. The method is widely illustrated by numerous examples.
Solution of One-dimensional Dirac Equation via Poincare Map
Bahlouli, Hocine; Jellal, Ahmed
2011-01-01
We solve the general one-dimensional Dirac equation using a "Poincare Map" approach which avoids any approximation to the spacial derivatives and reduces the problem to a simple recursive relation which is very practical from the numerical implementation point of view. To test the efficiency and rapid convergence of this approach we apply it to a vector coupling Woods--Saxon potential, which is exactly solvable. Comparison with available analytical results is impressive and hence validates the accuracy and efficiency of this method.
Nonlocal separable potential in the one-dimensional Dirac equation
Calkin, M.G.; Kiang, D.; Nogami, Y.
1988-08-01
The one-dimensional Dirac equation is solved for a separable potential of the form of Lorentz scalar plus vector, (..beta..g+h)v(x)v(x'). Exact analytic solutions are obtained for bound and scattering states for arbitrary v(x). For a particular combination of the values of g and h, degeneracy of the bound state occurs, and total reflection also takes place for a certain incident energy. The limiting case, in which v(x) becomes a delta function, is discussed in detail.
Singularity formation for one dimensional full Euler equations
Pan, Ronghua; Zhu, Yi
2016-12-01
We investigate the basic open question on the global existence v.s. finite time blow-up phenomena of classical solutions for the one-dimensional compressible Euler equations of adiabatic flow. For isentropic flows, it is well-known that the solutions develop singularity if and only if initial data contain any compression (the Riemann variables have negative spatial derivative). The situation for non-isentropic flow is not quite clear so far, due to the presence of non-constant entropy. In [4], it is shown that initial weak compressions do not necessarily develop singularity in finite time, unless the compression is strong enough for general data. In this paper, we identify a class of solutions of the full (non-isentropic) Euler equations, developing singularity in finite time even though their initial data do not contain any compression. This is in sharp contrast to the isentropic flow.
Steen-Ermakov-Pinney equation and integrable nonlinear deformation of one-dimensional Dirac equation
Prykarpatskyy, Yarema
2017-01-01
The paper deals with nonlinear one-dimensional Dirac equation. We describe its invariants set by means of the deformed linear Dirac equation, using the fact that two ordinary differential equations are equivalent if their sets of invariants coincide.
Conjugated Molecules Described by a One-Dimensional Dirac Equation.
Ernzerhof, Matthias; Goyer, Francois
2010-06-08
Starting from the Hückel Hamiltonian of conjugated hydrocarbon chains (ethylene, allyl radical, butadiene, pentadienyl radical, hexatriene, etc.), we perform a simple unitary transformation and obtain a Dirac matrix Hamiltonian. Thus already small molecules are described exactly in terms of a discrete Dirac equation, the continuum limit of which yields a one-dimensional Dirac Hamiltonian. Augmenting this Hamiltonian with specially adapted boundary conditions, we find that all the orbitals of the unsaturated hydrocarbon chains are reproduced by the continuous Dirac equation. However, only orbital energies close to the highest occupied molecular orbital/lowest unoccupied molecular orbital energy are accurately predicted by the Dirac equation. Since it is known that a continuous Dirac equation describes the electronic structure of graphene around the Fermi energy, our findings answer the question to what extent this peculiar electronic structure is already developed in small molecules containing a delocalized π-electron system. We illustrate how the electronic structure of small polyenes carries over to a certain class of rectangular graphene sheets and eventually to graphene itself. Thus the peculiar electronic structure of graphene extends to a large degree to the smallest unsaturated molecule (ethylene).
Boltzmann equations for a binary one-dimensional ideal gas.
Boozer, A D
2011-09-01
We consider a time-reversal invariant dynamical model of a binary ideal gas of N molecules in one spatial dimension. By making time-asymmetric assumptions about the behavior of the gas, we derive Boltzmann and anti-Boltzmann equations that describe the evolution of the single-molecule velocity distribution functions for an ensemble of such systems. We show that for a special class of initial states of the ensemble one can obtain an exact expression for the N-molecule velocity distribution function, and we use this expression to rigorously prove that the time-asymmetric assumptions needed to derive the Boltzmann and anti-Boltzmann equations hold in the limit of large N. Our results clarify some subtle issues regarding the origin of the time asymmetry of Boltzmann's H theorem.
A Large Class of Exact Solutions to the One-Dimensional Schrodinger Equation
Karaoglu, Bekir
2007-01-01
A remarkable property of a large class of functions is exploited to generate exact solutions to the one-dimensional Schrodinger equation. The method is simple and easy to implement. (Contains 1 table and 1 figure.)
LIU Shi-Kuo; GAO Bin; FU Zun-Tao; LIU Shi-Da
2009-01-01
In this paper, applying the dependent and independent variables transformations as well as the Jacobi elliptic function expansion method, the envelope periodic solutions to one-dimensional Gross-Pitaevskii equation in Bose-Einstein condensates are obtained.
Exact solution to the one-dimensional Dirac equation of linear potential
Long Chao-Yun; Qin Shui-Jie
2007-01-01
In this paper the one-dimensional Dirac equation with linear potential has been solved by the method of canonical transformation. The bound-state wavefunctions and the corresponding energy spectrum have been obtained for all bound states.
Note on Invariance of One-Dimensional Lattice-Boltzmann Equation
RAN Zheng
2007-01-01
Invariance of the one-dimensional lattice Boltzmann model is proposed together with its rigorous theoretical background.It is demonstrated that the symmetry inherent in Navier-Stokes equations is not really recovered in the one-dimensional lattice Boltzmann equation (LBE),especially for shock calculation.Symmetry breaking may be the inherent cause for the non-physical oscillations in the vicinity of the shock for LBE calculation.
Lagrangian formulation of the one-dimensional Vlasov equation. [in plasma physics
Lewak, G. J.
1974-01-01
A new formulation of the one-dimensional Vlasov equation is derived which is analogous to the Kalman-transformed cold-plasma equations. The equations are shown to yield nonsecular, nonlinear approximations to a source or boundary-value problem. It is suggested that the formulation may have other applications in nonlinear plasma theory.
Extended Wronskian Determinant Approach and Iterative Solutions of One-Dimensional Dirac Equation
XU Ying; LU Meng; SU Ru-Keng
2004-01-01
An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation, which can be solved by iterative procedure to find the wave functions, is established. We employ this approach to study the one-dimensional Dirac equation with one-well potential,and give the energy levels and wave functions up to the first order iterative approximation. For double-well potential,the energy levels up to the first order approximation are given.
Hesthaven, Jan
1997-01-01
This paper presents asymptotically stable schemes for patching of nonoverlapping subdomains when approximating the compressible Navier-Stokes equations given on conservation form. The scheme is a natural extension of a previously proposed scheme for enforcing open boundary conditions and as a res...... for quasi-one-dimensional transonic nozzle flows and for flows around an infinitely long circular cylinder....
Hydrodynamical form for the one-dimensional Gross-Pitaevskii equation
Haidar Mohamad
2014-06-01
Full Text Available We establish a well-posedness result for the hydrodynamical form (HGP of the one dimensional Gross-Pitaevskii equation (GP via the classical form of this equation. The result established in this way proves that (HGP is locally well-posed since the solution of (GP can vanished at some $t\
$C_{0}$-semigroups for hyperbolic partial differential equations on a one-dimensional spatial domain
Jacob, Birgit; Morris, Kirsten; Zwart, Hans
2015-01-01
Hyperbolic partial differential equations on a one-dimensional spatial domain are studied. This class of systems includes models of beams and waves as well as the transport equation and networks of nonhomogeneous transmission lines. The main result of this paper is a simple test for $C_{0}$-semigrou
Solution to the one-dimensional Rayleigh-Plesset equation by the Differential Transform method
Narendranath, Aneet Dharmavaram
2016-01-01
The differential transform method (DTM) is a relatively new technique that may be used to find a series solution to differential equations (both linear and nonlinear) through an iterative process. This brief manuscript is an initial effort in applying the DTM to provide a series solution to the one-dimensional Rayleigh-Plesset equation (RPE).
Computational method for the quantum Hamilton-Jacobi equation: one-dimensional scattering problems.
Chou, Chia-Chun; Wyatt, Robert E
2006-12-01
One-dimensional scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. First, the pole structure of the quantum momentum function for scattering wave functions is analyzed. The significant differences of the pole structure of this function between scattering wave functions and bound state wave functions are pointed out. An accurate computational method for the quantum Hamilton-Jacobi equation for general one-dimensional scattering problems is presented to obtain the scattering wave function and the reflection and transmission coefficients. The computational approach is demonstrated by analysis of scattering from a one-dimensional potential barrier. We not only present an alternative approach to the numerical solution of the wave function and the reflection and transmission coefficients but also provide a computational aspect within the quantum Hamilton-Jacobi formalism. The method proposed here should be useful for general one-dimensional scattering problems.
Performance of parallel computation using CUDA for solving the one-dimensional elasticity equations
Darmawan, J. B. B.; Mungkasi, S.
2017-01-01
In this paper, we investigate the performance of parallel computation in solving the one-dimensional elasticity equations. Elasticity equations are usually implemented in engineering science. Solving these equations fast and efficiently is desired. Therefore, we propose the use of parallel computation. Our parallel computation uses CUDA of the NVIDIA. Our research results show that parallel computation using CUDA has a great advantage and is powerful when the computation is of large scale.
Johannessen, Kim
2014-01-01
The exact solution to the one-dimensional Poisson–Boltzmann equation with asymmetric boundary conditions can be expressed in terms of the Jacobi elliptic functions. The boundary conditions determine the modulus of the Jacobi elliptic functions. The boundary conditions can not be solved analytically...
Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass
YANG Jin; XIANG An-Ping; YU Wan-Lun
2003-01-01
We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable forthe case with time-independence mass.
Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass
YANGJin; XIANGAn-Ping; YUWan-Lun
2003-01-01
We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable for the case with time-independence mass.
Levchenko, E. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2017-06-01
The one-dimensional Fokker-Planck-Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.
Traveling wave solutions of the one-dimensional Boussinesq paradigm equation
Vassilev, V. M.; Djondjorov, P. A.; Hadzhilazova, M. Ts.; Mladenov, I. M.
2013-10-01
The one-dimensional quasi-stationary flow of inviscid liquid in a shallow layer with free surface is described by the so-called Boussinesq Paradigm Equation (BPE). Slightly generalized this equation appears also in the theory of longitudinal vibrations of rods and in the continuum limit for lattices. It is well known that the one-dimensional (1-D) BPE admits a one-parameter family of traveling wave solutions expressed in an analytic form through the "sech" function. In the present contribution, new analytic solutions to the 1-D BPE representing traveling waves are obtained. These solutions are expressed through Weierstrass and Jacobi elliptic functions, which in some cases reduce to elementary functions.
Exact solutions of the one-dimensional generalized modified complex Ginzburg-Landau equation
Yomba, E
2003-01-01
The one-dimensional (1D) generalized modified complex Ginzburg-Landau (MCGL) equation for the traveling wave systems is analytically studied. Exact solutions of this equation are obtained using a method which combines the Painleve test for integrability in the formalism of Weiss-Tabor-Carnevale and Hirota technique of bilinearization. We show that pulses, fronts, periodic unbounded waves, sources, sinks and solution as collision between two fronts are the important coherent structures that organize much of the dynamical properties of these traveling wave systems. The degeneracies of the 1D generalized MCGL equation are examined as well as several of their solutions. These degeneracies include two important equations: the 1D generalized modified Schroedinger equation and the 1D generalized real modified Ginzburg-Landau equation. We obtain that the one parameter family of traveling localized source solutions called 'Nozaki-Bekki holes' become a subfamily of the dark soliton solutions in the 1D generalized modif...
Numerical Solution of One-dimensional Telegraph Equation using Cubic B-spline Collocation Method
J. Rashidinia
2014-02-01
Full Text Available In this paper, a collocation approach is employed for the solution of the one-dimensional telegraph equation based on cubic B-spline. The derived method leads to a tri-diagonal linear system. Computational efficiency of the method is confirmed through numerical examples whose results are in good agreement with theory. The obtained numerical results have been compared with the results obtained by some existing methods to verify the accurate nature of our method.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh; Ahmad Abd. Majid; Ahmad Izani Md. Ismail
2012-01-01
Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
Solutions of multidimensional partial differential equations representable as a one-dimensional flow
Zenchuk, A. I.
2014-03-01
We propose an algorithm for reducing an (M+ 1)-dimensional nonlinear partial differential equation (PDE) representable in the form of a one-dimensional flow ut + (u, ux uxx,…) = 0 (where w is an arbitrary local function of u and its xi derivatives, i = 1,…, M) to a family of M-dimensional nonlinear PDEs F(u,w) = 0, where F is a general (or particular) solution of a certain second-order two-dimensional nonlinear PDE. In particular, the M-dimensional PDE might turn out to be an ordinary differential equation, which can be integrated in some cases to obtain explicit solutions of the original (M+ 1)-dimensional equation. Moreover, a spectral parameter can be introduced in the function F, which leads to a linear spectral equation associated with the original equation. We present simplest examples of nonlinear PDEs together with their explicit solutions.
Eigenmode Analysis of Boundary Conditions for One-Dimensional Preconditioned Euler Equations
Darmofal, David L.
1998-01-01
An analysis of the effect of local preconditioning on boundary conditions for the subsonic, one-dimensional Euler equations is presented. Decay rates for the eigenmodes of the initial boundary value problem are determined for different boundary conditions. Riemann invariant boundary conditions based on the unpreconditioned Euler equations are shown to be reflective with preconditioning, and, at low Mach numbers, disturbances do not decay. Other boundary conditions are investigated which are non-reflective with preconditioning and numerical results are presented confirming the analysis.
Soliton solution for the Landau-Lifshitz equation of a one-dimensional bicomponent magnonic crystal.
Giridharan, D; Sabareesan, P; Daniel, M
2016-09-01
We investigate nonlinear localized magnetic excitations in a one-dimensional bicomponent magnonic crystal under a periodic magnetic field of spatially varying strength. The governing Landau-Lifshitz equation is transformed into a variable coefficient nonlinear Schrödinger (VCNLS) equation using stereographic projection. In general, the VCNLS equation is nonintegrable and by using Painlevé analysis, we obtain necessary conditions for the VCNLS equation to pass the Weiss-Tabor-Carnevale Painlevé test. A sufficient integrability condition is obtained by further exploring a transformation, which can map the VCNLS equation into the well-known standard nonlinear Schrödinger equation. The transformation builds a systematic connection between the solution of the standard nonlinear Schrödinger equation and VCNLS equation. The results show that the excitation of magnetization in the form of a soliton exists on the oscillatory background with a structure similar to the form of spin Bloch waves. Such a solution exists only when certain conditions on the coefficient of the VCNLS equation are satisfied. To corroborate the analytical results, we performed the numerical simulation by solving the governing VCNLS equation with integrability conditions using the split step Fourier method and the result agrees well with analytical results, and it suggests a way to control the dynamics of magnetization in the form of solitons by an appropriate spatial modulation of the nonlinearity coefficient in the governing VCNLS equation, which depends on the ferromagnetic materials which form the bicomponent magnonic crystal.
An Exact, Compressible One-Dimensional Riemann Solver for General, Convex Equations of State
Kamm, James Russell [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-03-05
This note describes an algorithm with which to compute numerical solutions to the one- dimensional, Cartesian Riemann problem for compressible flow with general, convex equations of state. While high-level descriptions of this approach are to be found in the literature, this note contains most of the necessary details required to write software for this problem. This explanation corresponds to the approach used in the source code that evaluates solutions for the 1D, Cartesian Riemann problem with a JWL equation of state in the ExactPack package [16, 29]. Numerical examples are given with the proposed computational approach for a polytropic equation of state and for the JWL equation of state.
Xie, Jiaquan; Huang, Qingxue; Yang, Xia
2016-01-01
In this paper, we are concerned with nonlinear one-dimensional fractional convection diffusion equations. An effective approach based on Chebyshev operational matrix is constructed to obtain the numerical solution of fractional convection diffusion equations with variable coefficients. The principal characteristic of the approach is the new orthogonal functions based on Chebyshev polynomials to the fractional calculus. The corresponding fractional differential operational matrix is derived. Then the matrix with the Tau method is utilized to transform the solution of this problem into the solution of a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via examples. It is shown that the proposed algorithm yields better results. Finally, error analysis shows that the algorithm is convergent.
An Inverse Source Problem for a One-dimensional Wave Equation: An Observer-Based Approach
Asiri, Sharefa M.
2013-05-25
Observers are well known in the theory of dynamical systems. They are used to estimate the states of a system from some measurements. However, recently observers have also been developed to estimate some unknowns for systems governed by Partial differential equations. Our aim is to design an observer to solve inverse source problem for a one dimensional wave equation. Firstly, the problem is discretized in both space and time and then an adaptive observer based on partial field measurements (i.e measurements taken form the solution of the wave equation) is applied to estimate both the states and the source. We see the effectiveness of this observer in both noise-free and noisy cases. In each case, numerical simulations are provided to illustrate the effectiveness of this approach. Finally, we compare the performance of the observer approach with Tikhonov regularization approach.
Cubic B-Spline Collocation Method for One-Dimensional Heat and Advection-Diffusion Equations
Joan Goh
2012-01-01
Full Text Available Numerical solutions of one-dimensional heat and advection-diffusion equations are obtained by collocation method based on cubic B-spline. Usual finite difference scheme is used for time and space integrations. Cubic B-spline is applied as interpolation function. The stability analysis of the scheme is examined by the Von Neumann approach. The efficiency of the method is illustrated by some test problems. The numerical results are found to be in good agreement with the exact solution.
CAUCHY PROBLEM FOR THE ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS
Lian Ruxu; Liu Jian; Li Hailiang; Xiao Ling
2012-01-01
We consider the Cauchy problem for one-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosity coefficient.For regular initial data,we show that the unique strong solution exits globally in time and converges to the equilibrium state time asymptotically.When initial density is piecewise regular with jump discontinuity,we show that there exists a unique global piecewise regular solution. In particular,the jump discontinuity of the density decays exponentially and the piecewise regular solution tends to the equilibrium state as t→ +∞.
Modeling digital pulse waveforms by solving one-dimensional Navier-stokes equations.
Fedotov, Aleksandr A; Akulova, Anna S; Akulov, Sergey A
2016-08-01
Mathematical modeling for composition distal arterial pulse wave in the blood vessels of the upper limbs was considered. Formation of distal arterial pulse wave is represented as a composition of forward and reflected pulse waves propagating along the arterial vessels. The formal analogy between pulse waves propagation along the human arterial system and the propagation of electrical oscillations in electrical transmission lines with distributed parameters was proposed. Dependencies of pulse wave propagation along the human arterial system were obtained by solving the one-dimensional Navier-Stokes equations for a few special cases.
Prozorov, A. A.; Trifonov, A. Yu.; Shapovalov, A. V.
2015-07-01
Asymptotic solutions of the nonlocal, one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with fractional derivatives in the diffusion operator are constructed. The fractional derivative is defined in accordance with the approaches of Weyl, Grünwald-Letnilkov, and Liouville. Asymptotic solutions are constructed in a class of functions that are a perturbation of the found exact quasistationary solution and tend at large times to this quasistationary solution. It is shown that the presence of fractional derivatives leads to drift of the center of mass of the initial distribution and breaks its symmetry.
Dispersion estimates for one-dimensional Schrödinger and Klein-Gordon equations revisited
Egorova, I. E.; Kopylova, E. A.; Marchenko, V. A.; Teschl, G.
2016-06-01
It is shown that for a one-dimensional Schrödinger operator with a potential whose first moment is integrable the elements of the scattering matrix are in the unital Wiener algebra of functions with integrable Fourier transforms. This is then used to derive dispersion estimates for solutions of the associated Schrödinger and Klein-Gordon equations. In particular, the additional decay conditions are removed in the case where a resonance is present at the edge of the continuous spectrum. Bibliography: 29 titles.
A FINITE DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL VARIATIONAL BOUSSINESQ EQUATIONS
A. Suryanto
2012-06-01
Full Text Available The variational Boussinesq equations derived by Klopman et. al. (2005 con-verse mass, momentum and positive-definite energy. Moreover, they were shown to have significantly improved frequency dispersion characteristics, making it suitable for wave simulation from relatively deep to shallow water. In this paper we develop a numerica lcode for the variational Boussinesq equations. This code uses a fourth-order predictor-corrector method for time derivatives and fourth-order finite difference method for the first-order spatial derivatives. The numerical method is validated against experimen-tal data for one-dimensional nonlinear wave transformation problems. Furthermore, the method is used to illustrate the dispersive effects on tsunami-type of wave propagation.
Pérez Guerrero, J. S.; Skaggs, T. H.
2010-08-01
SummaryMathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-dispersion equation with distance-dependent coefficients. An integrating factor is employed to obtain a transport equation that has a self-adjoint differential operator, and a solution is found using the generalized integral transform technique (GITT). It is demonstrated that an analytical expression for the integrating factor exists for several transport equation formulations of practical importance in groundwater transport modeling. Unlike nearly all solutions available in the literature, the current solution is developed for a finite spatial domain. As an illustration, solutions for the particular case of a linearly increasing dispersivity are developed in detail and results are compared with solutions from the literature. Among other applications, the current analytical solution will be particularly useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.
One-Dimensional Optimal System and Similarity Reductions of Wu—Zhang Equation
Xiong, Na; Li, Yu-Qi; Chen, Jun-Chao; Chen, Yong
2016-07-01
The one-dimensional optimal system for the Lie symmetry group of the (2+1)-dimensional Wu—Zhang equation is constructed by the general and systematic approach. Based on the optimal system, the complete and inequivalent symmetry reduction systems are presented in the form of table. It is noteworthy that a new Painlevé integrable equation with constant coefficient is in the table besides the classic Boussinesq equation and the steady case of the Wu-Zhang equation. Supported by the Global Change Research Program of China under Grant No. 2015CB953904, National Natural Science Foundation of China under Grant Nos. 11375090, 11275072 and 11435005, Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20120076110024, the Network Information Physics Calculation of Basic Research Innovation Research Group of China under Grant No. 61321064, Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No. ZF1213, and the Zhejiang Provincial Natural Science Foundation of China under Grant No. LY14A010005
Numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory
Ramos, J. I.
1987-01-01
A review of numerical methods for one-dimensional reaction-diffusion equations arising in combustion theory is presented. The methods reviewed include explicit, implicit, quasi-linearization, time linearization, operator-splitting, random walk and finite-element techniques and methods of lines. Adaptive and nonadaptive procedures are also reviewed. These techniques are applied first to solve two model problems which have exact traveling wave solutions with which the numerical results can be compared. This comparison is performed in terms of both the wave profile and computed wave speed. It is shown that the computed wave speed is not a good indicator of the accuracy of a particular method. A fourth-order time-linearized, Hermitian compact operator technique is found to be the most accurate method for a variety of time and space sizes.
Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations
Ducrot, Arnaud; Matano, Hiroshi
2012-01-01
We consider one-dimensional reaction-diffusion equations for a large class of spatially periodic nonlinearities (including multistable ones) and study the asymptotic behavior of solutions with Heaviside type initial data. Our analysis reveals some new dynamics where the profile of the propagation is not characterized by a single front, but by a layer of several fronts which we call a terrace. Existence and convergence to such a terrace is proven by using an intersection number argument, without much relying on standard linear analysis. Hence, on top of the peculiar phenomenon of propagation that our work highlights, several corollaries will follow on the existence and convergence to pulsating traveling fronts even for highly degenerate nonlinearities that have not been treated before.
Amplitude wave in one-dimensional complex Ginzburg-Landau equation
Xie Ling-Ling; Gao Jia-Zhen; Xie Wei-Miao; Gao Ji-Hua
2011-01-01
The wave propagation in the one-dimensional complex Ginzburg-Landau equation (CGLE) is studied by considering a wave source at the system boundary.A special propagation region,which is an island-shaped zone surrounded by the defect turbulence in the system parameter space,is observed in our numerical experiment.The wave signal spreads in the whole space with a novel amplitude wave pattern in the area.The relevant factors of the pattern formation,such as the wave speed,the maximum propagating distance and the oscillatory frequency,are studied in detail.The stability and the generality of the region are testified by adopting various initial conditions.This finding of the amplitude pattern extends the wave propagation region in the parameter space and presents a new signal transmission mode,and is therefore expected to be of much importance.
Peters, Baron; Bolhuis, Peter G; Mullen, Ryan G; Shea, Joan-Emma
2013-02-01
We propose a method for identifying accurate reaction coordinates among a set of trial coordinates. The method applies to special cases where motion along the reaction coordinate follows a one-dimensional Smoluchowski equation. In these cases the reaction coordinate can predict its own short-time dynamical evolution, i.e., the dynamics projected from multiple dimensions onto the reaction coordinate depend only on the reaction coordinate itself. To test whether this property holds, we project an ensemble of short trajectory swarms onto trial coordinates and compare projections of individual swarms to projections of the ensemble of swarms. The comparison, quantified by the Kullback-Leibler divergence, is numerically performed for each isosurface of each trial coordinate. The ensemble of short dynamical trajectories is generated only once by sampling along an initial order parameter. The initial order parameter should separate the reactants and products with a free energy barrier, and distributions on isosurfaces of the initial parameter should be unimodal. The method is illustrated for three model free energy landscapes with anisotropic diffusion. Where exact coordinates can be obtained from Kramers-Langer-Berezhkovskii-Szabo theory, results from the new method agree with the exact results. We also examine characteristics of systems where the proposed method fails. We show how dynamical self-consistency is related (through the Chapman-Kolmogorov equation) to the earlier isocommittor criterion, which is based on longer paths.
One-Dimensional Quasi-Exactly Solvable Schr\\"odinger Equations
Turbiner, Alexander V
2016-01-01
Quasi-Exactly Solvable Schr\\"odinger Equations occupy an intermediate place between exactly-solvable (e.g. the harmonic oscillator and Coulomb problems etc) and non-solvable ones. Their major property is an explicit knowledge of several eigenstates while the remaining ones are unknown. Many of these problems are of the anharmonic oscillator type with a special type of anharmonicity. The Hamiltonians of quasi-exactly-solvable problems are characterized by the existence of a hidden algebraic structure but do not have any hidden symmetry properties. In particular, all known one-dimensional (quasi)-exactly-solvable problems possess a hidden $\\mathfrak{sl}(2,\\bf{R})-$ Lie algebra. They are equivalent to the $\\mathfrak{sl}(2,\\bf{R})$ Euler-Arnold quantum top in a constant magnetic field. Quasi-Exactly Solvable problems are highly non-trivial, they shed light on delicate analytic properties of the Schr\\"odinger Equations in coupling constant. The Lie-algebraic formalism allows us to make a link between the Schr\\"odi...
Stepanov, Nikolay S.; Zelekson, Lev A.
2017-03-01
The exact stationary solution of one-dimensional non-relativistic Vlasov equation is obtained in the article. It is shown that in the energy exchange with the self-consistent longitudinal electric field, both wave trapped charged particles and the passing ones take part. It is proved that the trapped electron distribution is fundamentally different from distribution functions described by other authors, which used the Bernstein, Greene, and Kruskal method. So, the correct distribution function is characterized by its sudden change at the equality of wave and electrons' velocity but not on the edges of the potential well. This jump occurs for any arbitrary small value of wave potential. It was also found that the energy density of fast electrons trapped by the wave is less than the energy density of slow trapped electrons. This leads to the fact that the energy of the self-consistent electric field may both increase and decrease due to the nonlinear Landau damping. The conditions under which a similar effect can be observed are defined. Also for the first time, it is shown that the self-generated strong electric field always produces antitropic electron beams.
Numerical solutions for the one-dimensional heat-conduction equation using a spreadsheet
Gvirtzman, Zohar; Garfunkel, Zvi
1996-12-01
We show how to use a spreadsheet to calculate numerical solutions of the one-dimensional time-dependent heat-conduction equation. We find the spreadsheet to be a practical tool for numerical calculations, because the algorithms can be implemented simply and quickly without complicated programming, and the spreadsheet utilities can be used not only for graphics, printing, and file management, but also for advanced mathematical operations. We implement the explicit and the Crank-Nicholson forms of the finite-difference approximations and discuss the geological applications of both methods. We also show how to adjust these two algorithms to a nonhomogeneous lithosphere in which the thermal properties (thermal conductivity, density, and radioactive heat generation) change from the upper crust to the lower crust and to the mantle. The solution is presented in a way that can fit any spreadsheet (Lotus-123, Quattro-Pro, Excel). In addition, a Quattro-Pro program with macros that calculate and display the thermal evolution of the lithosphere after a thermal perturbation is enclosed in an appendix.
One-dimensional Lippmann-Schwinger equation and its applications%一维Lippmann-Schwinger方程及其应用
陆晓
2001-01-01
The one-dimensional Lippmann-Schwinger equation and its applications in scattering by one-dimensional potential are discussed. The reflection coefficient and transmission coefficient of the symmetry power-function potential are obtained.%讨论了一维Lippmann-Schwinger方程及其在一维散射问题中的应用，并给出了对称幂函数势的反射系数和透射系数.
李玲; 李伯藏
2002-01-01
Extending the approach proposed by Cole and Schieve (1995 Phys. Rev. A 52 4405) for a one-dimensional cavity with one moving mirror, we develop a geometrical method to solve exactly the generalized Moore (GM)equations for a one-dimensional cavity with two moving mirrors. As examples of applying our method, the GM equations are solved in detail when the two mirrors oscillate resonantly, and the dependences of the solutions on the frequency and dephasing of the mirror motions are investigated.
Functional equation for the crossover in the model of one-dimensional Weierstrass random walks
Rudoi, Yu. G.; Kotel'nikova, O. A.
2016-12-01
We consider the problem of one-dimensional symmetric diffusion in the framework of Markov random walks of the Weierstrass type using two-parameter scaling for the transition probability. We construct a solution for the characteristic Lyapunov function as a sum of regular (homogeneous) and singular (nonhomogeneous) solutions and find the conditions for the crossover from normal to anomalous diffusion.
Miyazawa, Toru
2011-01-01
We study the low-energy behavior of the Green function for one-dimensional Fokker-Planck and Schr\\"odinger equations with periodic potentials. We derive a formula for the power series expansion of reflection coefficients in terms of the wave number, and apply it to the low-energy expansion of the Green function.
A. Sakabekov
2016-01-01
Full Text Available We prove existence and uniqueness of the solution of the problem with initial and Maxwell-Auzhan boundary conditions for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations in space of functions continuous in time and summable in square by a spatial variable. In order to obtain a priori estimation of the initial and boundary value problem for nonstationary nonlinear one-dimensional Boltzmann’s six-moment system equations we get the integral equality and then use the spherical representation of vector. Then we obtain the initial value problem for Riccati equation. We have managed to obtain a particular solution of this equation in an explicit form.
Saeid Gholami
2014-01-01
Full Text Available This study presents a numerical method for the solution of one type of PDEs equation. In this study, apply the pseudo-spectral successive integration method to approximate the solution of the one-dimensional parabolic equation. This method is based on El-Gendi pseudo-spectral method. Also the Finite Difference Method (FDM is used as a minor method. The present numerical results are in satisfactory agreement with exact solution.
Kilic Bulent
2016-01-01
Full Text Available This paper integrates dispersive optical solitons in special optical metamaterials with a time dependent coefficient. We obtained some optical solitons of the aforementioned equation. It is shown that the examined dependent coefficients are affected by the velocity of the wave. The first integral method (FIM and ansatz method are applied to reach the optical soliton solutions of the one-dimensional nonlinear Schrödinger’s equation (NLSE with time dependent coefficients.
Debergh, N M; Samsonov, B F; Van den Bossche, B
2002-01-01
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined through the knowledge of only two eigenfunctions of the first Dirac Hamiltonian. Moreover this operator together with its adjoint and the two Hamiltonians generate a quadratic deformation of the superalgebra subtending the usual supersymmetric quantum mechanics. Our developments are illustrated on the free particle case and the generalized Coulomb interaction. In the latter case, a relativistic counterpart of shape-invariance is observed.
Asiri, Sharefa M.
2016-10-20
In this paper, modulating functions-based method is proposed for estimating space–time-dependent unknowns in one-dimensional partial differential equations. The proposed method simplifies the problem into a system of algebraic equations linear in unknown parameters. The well-posedness of the modulating functions-based solution is proved. The wave and the fifth-order KdV equations are used as examples to show the effectiveness of the proposed method in both noise-free and noisy cases.
On one-dimensional compressible Navier-Stokes equations for a reacting mixture in unbounded domains
Li, Siran
2017-10-01
In this paper we consider the one-dimensional Navier-Stokes system for a heat-conducting, compressible reacting mixture which describes the dynamic combustion of fluids of mixed kinds on unbounded domains. This model has been discussed on bounded domains by Chen (SIAM J Math Anal 23:609-634, 1992) and Chen-Hoff-Trivisa (Arch Ration Mech Anal 166:321-358, 2003), among others, in which the reaction rate function is a discontinuous function obeying the Arrhenius' law of thermodynamics. We prove the global existence of weak solutions to this model on one-dimensional unbounded domains with large initial data in H^1. Moreover, the large-time behaviour of the weak solution is identified. In particular, the uniform-in-time bounds for the temperature and specific volume have been established via energy estimates. For this purpose we utilise techniques developed by Kazhikhov-Shelukhin (cf. Kazhikhov in Siber Math J 23:44-49, 1982; Solonnikov and Kazhikhov in Annu Rev Fluid Mech 13:79-95, 1981) and refined by Jiang (Commun Math Phys 200:181-193, 1999, Proc R Soc Edinb Sect A 132:627-638, 2002), as well as a crucial estimate in the recent work by Li-Liang (Arch Ration Mech Anal 220:1195-1208, 2016). Several new estimates are also established, in order to treat the unbounded domain and the reacting terms.
Benseghir, Rym, E-mail: benseghirrym@ymail.com, E-mail: benseghirrym@ymail.com; Benchettah, Azzedine, E-mail: abenchettah@hotmail.com [LANOS Laboratory, Badji Mokhtar University, BP 12, 23000, Annaba (Algeria); Raynaud de Fitte, Paul, E-mail: prf@univ-rouen.fr [Normandie Univ, Laboratoire Raphaël Salem, UMR CNRS 6085, Rouen (France)
2015-11-30
A stochastic equation system corresponding to the description of the motion of a barotropic viscous gas in a discretized one-dimensional domain with a weight regularizing the density is considered. In [2], the existence of an invariant measure was established for this discretized problem in the stationary case. In this paper, applying a slightly modified version of Khas’minskii’s theorem [5], we generalize this result in the periodic case by proving the existence of a periodic measure for this problem.
Junping YIN; Zhong TAN
2008-01-01
The authors prove two global existence results of strong solutions of the isen- tropic compressible Navier-Stokes-Poisson equations in one-dimensional bounded intervals. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition. In this paper the initial vacuum is allowed, and T is bounded.
Guogang LIU; Yi ZHAO
2004-01-01
The one-dimensional linear wave equation with a van der Pol nonlinear boundary condition is one of the simplest models that may cause isotropic or nonisotropic chaotic vibrations.It characterizes the nonisotropic chaotic vibration by means of the total variation theory.Some results are derived on the exponential growth of total variation of the snapshots on the spatial interval in the long-time horizon when the map and the initial condition satisfy some conditions.
Goloviznin, V. M.; Karabasov, S. A.; Kozubskaya, T. K.; Maksimov, N. V.
2009-12-01
A generalization of the CABARET finite difference scheme is proposed for linearized one-dimensional Euler equations based on the characteristic decomposition into local Riemann invariants. The new method is compared with several central finite difference schemes that are widely used in computational aeroacoustics. Numerical results for the propagation of an acoustic wave in a homogeneous field and the refraction of this wave through a contact discontinuity obtained on a strongly nonuniform grid are presented.
One-dimensional heat conduction equation of the polar bear hair
Zhu Wei-Hong
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus possess special membrane-pore structure. The structure enables the polar bear to survive in the harsh Arctic regions. In this paper, the membrane-pore structure be approximately considered as fractal space, 1-D heat conduction equation of the polar bear hair is established and the solution of the equation is obtained.
Vineet K. Srivastava
2014-03-01
Full Text Available In this paper, an implicit logarithmic finite difference method (I-LFDM is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.
Boundary value problem for one-dimensional fractional differential advection-dispersion equation
Khasambiev Mokhammad Vakhaevich
2014-07-01
Full Text Available An equation commonly used to describe solute transport in aquifers has attracted more attention in recent years. After a formal study of some aspects of the advection-diffusion equation, basically from the mathematical point of view with the solution of a differential equation with fractional derivative, the main interest to this problem shifted onto physical aspects of the dynamical system, such as the total energy and the dynamical response. In this regard it should be pointed out that the interaction with environment is expressed in terms of stochastic arrow of time. This allows one also to reach a progress in one more issue. Formerly the equation of advection-diffusion was not obtained from any physical principles. However, mainly the success concerns linear fractional systems. In fact, there are many cases in which linear treatments are not sufficient. The more general systems described by nonlinear fractional differential equations have not been studied enough. The ordinary calculus brings out clearly that essentially new phenomena occur in nonlinear systems, which generally cannot occur in linear systems. Due to vast range of application of the fractional advection-dispersion equation, a lot of work has been done to find numerical solution and fundamental solution of this equation. The research on the analytical solution of initial-boundary problem for space-fractional advection-dispersion equation is relatively new and is still at an early stage of development. In this paper, we will take use of the method of variable separation to solve space-fractional advection-dispersion equation with initial boundary data.
Wronskian Approach and One-Dimensional Schrodinger Equation with Double-Well Potential
QIU Jian; SU Ru-Keng
2003-01-01
A Wronskian determinant approach is suggested to study the energy and the wave function for onedimensional Schrodinger equation. An integral equation and its corresponding Green function are constructed. As an example, we employed this approach to study the problem of double-well potential with strong coupling. A series of expansion of ground state energy up to the second order approximation of iterative procedure is given.
Solution of the equations for one-dimensional, two-phase, immiscible flow by geometric methods
Ivan, Boronin; Andrey, Shevlyakov
2016-12-01
Buckley-Leverett equations describe non viscous, immiscible, two-phase filtration, which is often of interest in modelling of oil production. For many parameters and initial conditions, the solutions of these equations exhibit non-smooth behaviour, namely discontinuities in form of shock waves. In this paper we obtain a novel method for the solution of Buckley-Leverett equations, which is based on geometry of differential equations. This method is fast, accurate, stable, and describes non-smooth phenomena. The main idea of the method is that classic discontinuous solutions correspond to the continuous surfaces in the space of jets - the so-called multi-valued solutions (Bocharov et al., Symmetries and conservation laws for differential equations of mathematical physics. American Mathematical Society, Providence, 1998). A mapping of multi-valued solutions from the jet space onto the plane of the independent variables is constructed. This mapping is not one-to-one, and its singular points form a curve on the plane of the independent variables, which is called the caustic. The real shock occurs at the points close to the caustic and is determined by the Rankine-Hugoniot conditions.
Kmonodium, a Program for the Numerical Solution of the One-Dimensional Schrodinger Equation
Angeli, Celestino; Borini, Stefano; Cimiraglia, Renzo
2005-01-01
A very simple strategy for the solution of the Schrodinger equation of a particle moving in one dimension subjected to a generic potential is presented. This strategy is implemented in a computer program called Kmonodium, which is free and distributed under the General Public License (GPL).
Beddard, Godfrey S.
2011-01-01
A method of solving the Schrodinger equation using a basis set expansion is described and used to calculate energy levels and wavefunctions of the hindered rotation of ethane and the ring puckering of cyclopentene. The calculations were performed using a computer algebra package and the calculations are straightforward enough for undergraduates to…
On the Numerical Solution of One-Dimensional Integral and Differential Equations
1991-12-01
Conditioned Weights 57 3.5 The Analytical Apparatus for Singular Solutions ................... 58 3.5.1 Notation...Algorithm for Singular Solutions .................. 81 3.7.1 Notation ........ .................................. 82 3.7.2 Discretization of the...Restricted Integral Equations ............. 84 3.7.3 Informal Description of the Algorithm for Singular Solutions . . .. 85 3.8 Description of the
On the One-Dimensional Steady and Unsteady Porous Flow Equation
Andersen, O. H.; Burcharth, H. F.
1995-01-01
Porous flow in coarse granular media is discussed theoretically with special concern given to the variation of the flow resistance with the porosity. For steady state flow, the Navier-Stokes equation is applied as a basis for the derivations. A turbulent flow equation is suggested. Alternative...... derivations based on dimensional analysis and a pipe analogy, respectively, are discussed. For non-steady state flow, the derivations are based on a cylinder/sphere analogy leading to a virtual mass coefficient. For the fully turbulent flow regime, existing experimental data values of the quadratic flow...... resistance coefficients are presented. Moreover, a simple formula for estimation of the turbulent flow coefficient is given. Virtual mass coefficients based on existing data are presented, however, no definite conclusions can be given due to the scarce data available....
Robin Boundary Value Problem for One-Dimensional Landau-Lifshitz Equations
Shi Jin DING; Jin Rui HUANG; Xiao E LIU
2012-01-01
In this paper,we are concerned with the existence and uniqueness of global smooth solution for the Robin boundary value problem of Landau-Lifshitz equations in one dimension when the boundary value depends on time t.Furthermore,by viscosity vanishing approach,we get the existence and uniqueness of the problem without Gilbert damping term when the boundary value is independent of t.
Laryunin, O. A.
2016-09-01
The goal of this work is to solve Maxwell equations analytically and numerically in a one-dimensional case under the conditions of a nonstationary medium. Analytical solutions to the Maxwell equations have been obtained in two partial cases of the linear and quadratic time dependence of medium permittivity. Since the number of models for which the wave equation can be solved analytically is limited, it becomes also necessary to apply numerical methods, specifically the method of finite differences, in a time domain Finite Difference Time Domain method. The effects of the decameter wave dynamic reflection from structures with considerable spatial gradients (the scales of which are comparable with the sounding pulse wavelength) have been studied based on this method. It has been shown that the spectrum can broaden and a Doppler frequency shift of a reflected signal can originate can take place.
The one dimensional Schrödinger equation: symmetries, solutions and Feynman propagators
Cerveró, Jose M.; Polo, Pablo P.
2016-09-01
A simple method to find the symmetries of the Schrödinger equation in one dimension with arbitrary potentials is presented. The method hereby used can be of interest to students in quantum mechanics at the undergraduate level. Several physical questions arising from this symmetry analysis are also discussed. Finally, some attention is paid to how the result leads to the explicit description of the exact propagators in the linear and quadratic case without using the more popular method of describing the classical action in the stationary phase approximation.
Hamiltonian reductions of the one-dimensional Vlasov equation using phase-space moments
Chandre, C.; Perin, M.
2016-03-01
We consider Hamiltonian closures of the Vlasov equation using the phase-space moments of the distribution function. We provide some conditions on the closures imposed by the Jacobi identity. We completely solve some families of examples. As a result, we show that imposing that the resulting reduced system preserves the Hamiltonian character of the parent model shapes its phase space by creating a set of Casimir invariants as a direct consequence of the Jacobi identity. We exhibit three main families of Hamiltonian models with two, three, and four degrees of freedom aiming at modeling the complexity of the bunch of particles in the Vlasov dynamics.
Ali S Wadi; Mourad F Dimian; Fayez N Ibrahim
2014-08-01
We present simple analytical solutions for the unsteady advection–dispersion equations describing the pollutant concentration (, ) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions ≤ 0 and ≥0 and the origin at = 0. The variation of (, ) with the time from = 0 up to → ∞ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.
Adaptation of the Euler-Lagrange equation for studying one-dimensional motions in a constant force
Dias, Clenilda F; Silva, Gislene M; Santos, Creuza A S; Barros, Pedro; Carvalho-Santos, Vagson L
2012-01-01
In this work we have shown that the Euler-Lagrange equation (ELE) can be simplified for one-dimensional motions. By using the partial derivative operators definition, we have proposed two operators, here called \\textit{mean delta operators}, which may be used to solve the ELE in a simplest way. We have applied this simplification to solve three known mechanical problems: a free fall body, the Atwood's machine and the inclinated plan. The proposed simplification may be used for introducing the lagrangian formalism for classical mechanics in introductory physics students, e.g., high school or undergraduate students in the beginning of engineering, mathematics and/or physics courses.
Modeling Xenon Tank Pressurization using One-Dimensional Thermodynamic and Heat Transfer Equations
Gilligan, Ryan P.; Tomsik, Thomas M.
2017-01-01
As a first step in understanding what ground support equipment (GSE) is required to provide external cooling during the loading of 5,000 kg of xenon into 4 aluminum lined composite overwrapped pressure vessels (COPVs), a modeling analysis was performed using Microsoft Excel. The goals of the analysis were to predict xenon temperature and pressure throughout loading at the launch facility, estimate the time required to load one tank, and to get an early estimate of what provisions for cooling xenon might be needed while the tanks are being filled. The model uses the governing thermodynamic and heat transfer equations to achieve these goals. Results indicate that a single tank can be loaded in about 15 hours with reasonable external coolant requirements. The model developed in this study was successfully validated against flight and test data. The first data set is from the Dawn mission which also utilizes solar electric propulsion with xenon propellant, and the second is test data from the rapid loading of a hydrogen cylindrical COPV. The main benefit of this type of model is that the governing physical equations using bulk fluid solid temperatures can provide a quick and accurate estimate of the state of the propellant throughout loading which is much cheaper in terms of computational time and licensing costs than a Computation Fluid Dynamics (CFD) analysis while capturing the majority of the thermodynamics and heat transfer.
An Analog of the Fourier Transform Associated with a Nonlinear One-Dimensional Schroedinger Equation
Zhidkov, E P
2001-01-01
We consider an eigenvalue problem which includes a nonlinear Schroedinger equation on the half-line [0,\\infty) and certain boundary conditions. It is shown that the spectrum of this problem fills a half-line and that to each point of the spectrum there corresponds a unique eigenfunction. The main result of the paper is that an arbitrary infinitely differentiable function g(x) rapidly decaying as x\\to\\infty and satisfying suitable boundary conditions at the point x=0 can be uniquely expanded into an integral over eigenfunctions similar to the representation of functions by the Fourier transform (the latter is obviously associated with a linear self-adjoint eigenvalue problem).
Spreading speeds for one-dimensional monostable reaction-diffusion equations
Berestycki, Henri; Nadin, Grégoire
2012-11-01
We establish in this article spreading properties for the solutions of equations of the type ∂tu - a(x)∂xxu - q(x)∂xu = f(x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x, the nonlinearity f is of monostable Kolmogorov, Petrovsky, and Piskunov type between two steady states 0 and 1 and the initial datum is compactly supported. Using homogenization techniques, we construct two speeds wle overline{w} such that lim _{trArr +infty }sup _{0le xle wt} |u(t,x)-1| = 0 for all win (0,w) and lim _{trArr +infty } sup _{x ge wt} |u(t,x)| =0 for all w>overline{w}. These speeds are characterized in terms of two new notions of generalized principal eigenvalues for linear elliptic operators in unbounded domains. In particular, we derive the exact spreading speed when the coefficients are random stationary ergodic, almost periodic or asymptotically almost periodic (where overline{w}=w).
Kulish Vladimir V.
2004-01-01
Full Text Available This paper presents an integral solution of the generalized one-dimensional equation of energy transport with the convective term.The solution of the problem has been achieved by the use of a novel technique that involves generalized derivatives (in particular, derivatives of noninteger orders. Confluent hypergeometric functions, known as Whittaker's functions, appear in the course of the solution procedure upon applying the Laplace transform to the original transport equation.The analytical solution of the problem is written in the integral form and provides a relationship between the local values of the transported property (e.g., temperature, mass, momentum, etc. and its flux.The solution is valid everywhere within the domain, including the domain boundary.
SONG; Yuquan(宋玉泉); LIU; Shumei(刘术梅)
2002-01-01
Superplastic forming has been extensively applied to manufacture parts and components with complex shapes or high-precisions. However, superplastic formation is in multi-stress state. In a long time, uniaxial tensile constitutive equation has been directly generalized to deal with multi-stress state. Whether so doing is feasible or not needs to be proved in theory. This paper first summarizes the establishing processes of superplastic tensile and bulging constitutive equation with variable m, and, using the analytical expressions of equivalent stress ? and equivalent strain rateof free bulge based on the fundamentals of continuum medium plastic mechanics, derives the analytical expressions of optimum loading rules for superplastic free bulge. By comparing the quantitative results on typical superplastic alloy ZnAl22, it is shown that one-dimensional tensile constitutive equations cannot be directly generalized to deal with two-dimensional bulging quantitative mechanical problems; only superplastic bulging constitutive equation based on bulging stress state can be used to treat the quantitative mechanical problems of bulge.
Per-Ole Nyman
2010-01-01
Full Text Available In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR problems in optimal control theory, using a generalized form of Fibonacci numbers. We find the solution R(k of the corresponding discrete-time Riccati equation in terms of ratios of generalized Fibonacci numbers. An explicit Binet type formula for R(k is also found, removing the need for recursively finding the solution at a given timestep. Moreover, we show that it is also possible to express the feedback gain, the penalty functional and the controller state in terms of these ratios. A generalized golden ratio appears in the corresponding infinite horizon problem. Finally, we show the use of the method in a few examples.
Hayek, Mohamed
2016-04-01
This work develops a simple exact and explicit solution of the one-dimensional transient and nonlinear Richards' equation for soils in a special case of exponential water retention curve and power law hydraulic conductivity. The exact solution is obtained as traveling wave based on the approach proposed by Philip (1957, 1967) and adopted by Zlotnik et al. (2007). The obtained solution is novel, and it expresses explicitly the water content as function of the depth and time. It can be useful to model infiltration into semi-infinite soils with time-dependent boundary conditions and infiltration with constant boundary condition but space-dependent initial condition. A complete analytical inverse procedure based on the proposed analytical solution is presented which allows the estimation of hydraulic parameters. The proposed exact solution is also important for the verification of numerical schemes as well as for checking the implementation of time-dependent boundary conditions.
Atul Kumar; Dilip Kumar Jaiswal; Naveen Kumar
2009-10-01
Analytical solutions are obtained for one-dimensional advection –diffusion equation with variable coefficients in a longitudinal ﬁnite initially solute free domain,for two dispersion problems.In the ﬁrst one,temporally dependent solute dispersion along uniform ﬂow in homogeneous domain is studied.In the second problem the velocity is considered spatially dependent due to the inhomogeneity of the domain and the dispersion is considered proportional to the square of the velocity. The velocity is linearly interpolated to represent small increase in it along the ﬁnite domain.This analytical solution is compared with the numerical solution in case the dispersion is proportional to the same linearly interpolated velocity.The input condition is considered continuous of uniform and of increasing nature both.The analytical solutions are obtained by using Laplace transformation technique.In that process new independent space and time variables have been introduced. The effects of the dependency of dispersion with time and the inhomogeneity of the domain on the solute transport are studied separately with the help of graphs.
LIANG Hui; ZHAO Wei; DAI Dejun; ZHANG Jun
2014-01-01
Diapycnal mixing is important in oceanic circulation. An inverse method in which a semi-explicit scheme is applied to discretize the one-dimensional temperature diffusion equation is established to estimate the vertical temperature diffusion coefficient based on the observed temperature profiles. The sensitivity of the inverse model in the idealized and actual conditions is tested in detail. It can be found that this inverse model has high feasibility under multiple situations ensuring the stability of the inverse model, and can be considered as an efficient way to estimate the temperature diffusion coefficient in the weak current regions of the ocean. Here, the hydrographic profiles from Argo floats are used to estimate the temporal and spatial distribution of the vertical mixing in the north central Pacific based on this inverse method. It is further found that the vertical mixing in the upper ocean displays a distinct seasonal variation with the amplitude decreasing with depth, and the vertical mixing over rough topography is stronger than that over smooth topography. It is suggested that the high-resolution profiles from Argo floats and a more reasonable design of the inverse scheme will serve to understand mixing processes.
无
2002-01-01
Because of the strong structural sensitivity of superplasticity, the deformation rule must be affected by stress-state. It is necessary to prove whether one-dimensional tensile constitutive equation can be directly generalized to deal with the two-dimensional mechanical problems or not. In this paper, theoretical results of fill-forming bulge have been derived from both one-dimensional tensile and two-dimensional bulging constitutive equation with variable m value. By comparing theoretical analysis and experimental results made on typical superplastic alloy Zn-wt22%Al, it is shown that one-dimensional tensile constitutive equation cannot be directly generalized to deal with two-dimensional mechanical questions. A method to correct deviation between theoretical and experimental results is also proposed.
Tomchenko, Maksim
2017-02-01
We show that the system of Gaudin’s equations for quasimomenta k j , which describes a one-dimensional system of spinless point bosons with zero boundary conditions, has the unique real solution for each set of quantum numbers n j .
Kamenev, Alex; Meerson, Baruch; Sasorov, Pavel V
2016-09-01
We study the probability distribution P(H,t,L) of the surface height h(x=0,t)=H in the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension when starting from a parabolic interface, h(x,t=0)=x^{2}/L. The limits of L→∞ and L→0 have been recently solved exactly for any t>0. Here we address the early-time behavior of P(H,t,L) for general L. We employ the weak-noise theory-a variant of WKB approximation-which yields the optimal history of the interface, conditioned on reaching the given height H at the origin at time t. We find that at small HP(H,t,L) is Gaussian, but its tails are non-Gaussian and highly asymmetric. In the leading order and in a proper moving frame, the tails behave as -lnP=f_{+}|H|^{5/2}/t^{1/2} and f_{-}|H|^{3/2}/t^{1/2}. The factor f_{+}(L,t) monotonically increases as a function of L, interpolating between time-independent values at L=0 and L=∞ that were previously known. The factor f_{-} is independent of L and t, signaling universality of this tail for a whole class of deterministic initial conditions.
Kamenev, Alex; Meerson, Baruch; Sasorov, Pavel V.
2016-09-01
We study the probability distribution P (H ,t ,L ) of the surface height h (x =0 ,t )=H in the Kardar-Parisi-Zhang (KPZ) equation in 1 +1 dimension when starting from a parabolic interface, h (x ,t =0 ) =x2/L . The limits of L →∞ and L →0 have been recently solved exactly for any t >0 . Here we address the early-time behavior of P (H ,t ,L ) for general L . We employ the weak-noise theory—a variant of WKB approximation—which yields the optimal history of the interface, conditioned on reaching the given height H at the origin at time t . We find that at small H P (H ,t ,L ) is Gaussian, but its tails are non-Gaussian and highly asymmetric. In the leading order and in a proper moving frame, the tails behave as -lnP =f+|H| 5 /2/t1 /2 and f-|H| 3 /2/t1 /2 . The factor f+(L ,t ) monotonically increases as a function of L , interpolating between time-independent values at L =0 and L =∞ that were previously known. The factor f- is independent of L and t , signaling universality of this tail for a whole class of deterministic initial conditions.
Goloviznin, V. M.; Kanaev, A. A.
2011-05-01
For the CABARET finite difference scheme, a new approach to the construction of convective flows for the one-dimensional nonlinear transport equation is proposed based on the minimum principle of partial local variations. The new approach ensures the monotonicity of solutions for a wide class of problems of a fairly general form including those involving discontinuous and nonconvex functions. Numerical results illustrating the properties of the proposed method are discussed.
Bilge Inan; Ahmet Refik Bahadir
2013-10-01
This paper describes two new techniques which give improved exponential finite difference solutions of Burgers’ equation. These techniques are called implicit exponential finite difference method and fully implicit exponential finite difference method for solving Burgers’ equation. As the Burgers’ equation is nonlinear, the scheme leads to a system of nonlinear equations. At each time-step, Newton’s method is used to solve this nonlinear system. The results are compared with exact values and it is clearly shown that results obtained using both the methods are precise and reliable.
Ashyralyev, Allaberen; Gambo, Yusuf Ya'u.
2016-08-01
The nonlocal boundary value problem for viscous Burgers' equation is considered. Solutions to the 1-D equation are presented numerically by Rothe, Crank-Nicholson and r-modified Crank-Nicholson difference schemes. Matlab codes for all the three schemes are designed based on the idea of fixed-point iteration procedure and modified Gauss elimination method. The numerical results are compared.
Hu, Zhang-Mao; Tian, Hong; Li, Ben-Wen; Zhang, Wei; Yin, Yan-Shan; Ruan, Min; Chen, Dong-Lin
2017-10-01
The ray-effect is a major discretization error in the approximate solution method for the radiative transfer equation (RTE). To overcome this problem, the incident energy transfer equation (IETE) is proposed. The incident energy, instead of radiation intensity, is obtained by directly solving this new equation. Good numerical properties are found for the incident energy transfer equation. To show the properties of numerical solution, the collocation spectral method (CSM) is employed to solve the incident energy transfer equation. Three test cases are taken into account to verify the performance of the incident energy transfer equation. The result shows that the radiative heat flux obtained based on IETE is much more accurate than that based on RTE, which means that the IETE is very effective in eliminating the impacts of ray-effect on the heat flux. However, on the contrary, the radiative intensity obtained based on IETE is less accurate than that based on RTE due to the ray-effect. So, this equation is more suitable for those radiative heat transfer problems, in which the radiation heat flux and incident energy are needed rather than the radiation intensity.
Shvetsov-Shilovski, N.I., E-mail: nikolay.shvetsov@tut.fi; Räsänen, E., E-mail: erasanen@tut.fi
2014-12-15
One-dimensional model systems have a particular role in strong-field physics when gaining physical insight by computing data over a large range of parameters, or when performing numerous time propagations within, e.g., optimal control theory. Here we derive a scheme that removes a singularity in the one-dimensional Schrödinger equation in momentum space for a particle in the commonly used soft-core Coulomb potential. By using this scheme we develop two numerical approaches to the time-dependent Schrödinger equation in momentum space. The first approach employs the expansion of the momentum-space wave function over the eigenstates of the field-free Hamiltonian, and it is shown to be more efficient for laser parameters usual in strong field physics. The second approach employs the Crank–Nicolson scheme or the method of lines for time-propagation. The both methods are readily applicable for large-scale numerical simulations in one-dimensional model systems.
Franz, Delbert D.; Melching, Charles S.
1997-01-01
The Full EQuations (FEQ) model is a computer program for solution of the full, dynamic equations of motion for one-dimensional unsteady flow in open channels and through control structures. A stream system that is simulated by application of FEQ is subdivided into stream reaches (branches), parts of the stream system for which complete information on flow and depth are not required (dummy branches), and level-pool reservoirs. These components are connected by special features; that is, hydraulic control structures, including junctions, bridges, culverts, dams, waterfalls, spillways, weirs, side weirs, and pumps. The principles of conservation of mass and conservation of momentum are used to calculate the flow and depth throughout the stream system resulting from known initial and boundary conditions by means of an implicit finite-difference approximation at fixed points (computational nodes). The hydraulic characteristics of (1) branches including top width, area, first moment of area with respect to the water surface, conveyance, and flux coefficients and (2) special features (relations between flow and headwater and (or) tail-water elevations, including the operation of variable-geometry structures) are stored in function tables calculated in the companion program, Full EQuations UTiLities (FEQUTL). Function tables containing other information used in unsteady-flow simulation (boundary conditions, tributary inflows or outflows, gate settings, correction factors, characteristics of dummy branches and level-pool reservoirs, and wind speed and direction) are prepared by the user as detailed in this report. In the iterative solution scheme for flow and depth throughout the stream system, an interpolation of the function tables corresponding to the computational nodes throughout the stream system is done in the model. FEQ can be applied in the simulation of a wide range of stream configurations (including loops), lateral-inflow conditions, and special features. The
Marko Žnidarič
2011-11-01
We discuss recent ﬁndings about properties of quantum nonequilibrium steady states. In particular we focus on transport properties. It is shown that the time-dependent density matrix renormalization method can be used successfully to ﬁnd a stationary solution of Lindblad master equation. Furthermore, for a speciﬁc model an exact solution is presented.
Zhao Guo-Zhong; Yu Xi-Jun; Zhang Rong-Pei
2013-01-01
In this paper,Runge-Kutta Discontinuous Galerkin (RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical flux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical flux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.
Kaernbach, C; König, P; Schillen, T
1987-02-01
Recent experimental observations of otoacoustic emissions suggest the existence of spontaneous emitters of sound on the basilar membrane. These tend to send off waves not only in the normal direction of propagation. It is therefore significant to study the environmental conditions such an emitter finds inside the cochlea. The impedance relations seen by these emitters are described by the Riccati equation for an inhomogeneous transmission line. The results reported in this paper differ considerably for forward and backward excitation. This reflects the quite different behavior of the cochlea pertaining to waves traveling forward and backward. Because of reflections, backward waves cannot be treated with the Liouville-Green approximation.
Carlen, Eric A.; Fröhlich, Jürg; Lebowitz, Joel
2016-02-01
We construct generalized grand-canonical- and canonical Gibbs measures for a Hamiltonian system described in terms of a complex scalar field that is defined on a circle and satisfies a nonlinear Schrödinger equation with a focusing nonlinearity of order p transitions" and regularity properties of field samples, are established. We then study a time evolution of this system given by the Hamiltonian evolution perturbed by a stochastic noise term that mimics effects of coupling the system to a heat bath at some fixed temperature. The noise is of Ornstein-Uhlenbeck type for the Fourier modes of the field, with the strength of the noise decaying to zero, as the frequency of the mode tends to ∞. We prove exponential approach of the state of the system to a grand-canonical Gibbs measure at a temperature and "chemical potential" determined by the stochastic noise term.
Treena Basu
2015-10-01
Full Text Available This paper proposes an approach for the space-fractional diffusion equation in one dimension. Since fractional differential operators are non-local, two main difficulties arise after discretization and solving using Gaussian elimination: how to handle the memory requirement of O(N2 for storing the dense or even full matrices that arise from application of numerical methods and how to manage the significant computational work count of O(N3 per time step, where N is the number of spatial grid points. In this paper, a fast iterative finite difference method is developed, which has a memory requirement of O(N and a computational cost of O(N logN per iteration. Finally, some numerical results are shown to verify the accuracy and efficiency of the new method.
Feng, Zhaosheng
Many physical phenomena can be described by nonlinear models. The last few decades have seen an enormous growth of the applicability of nonlinear models and of the development of related nonlinear concepts. This has been driven by modern computer power as well as by the discovery of new mathematical techniques, which include two contrasting themes: (i) the theory of dynamical systems, most popularly associated with the study of chaos, and (ii) the theory of integrable systems associated, among other things, with the study of solitons. In this dissertation, we study two nonlinear models. One is the 1-dimensional vibrating string satisfying wtt - wxx = 0 with van der Pol boundary conditions. We formulate the problem into an equivalent first order Hyperbolic system, and use the method of characteristics to derive a nonlinear reflection relation caused by the nonlinear boundary conditions. Thus, the problem is reduced to the discrete iteration problem of the type un+1 = F( un). Periodic solutions are investigated, an invariant interval for the Abel equation is studied, and numerical simulations and visualizations with different coefficients are illustrated. The other model is the Korteweg-de Vries-Burgers (KdVB) equation. In this dissertation, we proposed two new approaches: One is what we currently call First Integral Method, which is based on the ring theory of commutative algebra. Applying the Hilbert-Nullstellensatz, we reduce the KdVB equation to a first-order integrable ordinary differential equation. The other approach is called the Coordinate Transformation Method, which involves a series of variable transformations. Some new results on the traveling wave solution are established by using these two methods, which not only are more general than the existing ones in the previous literature, but also indicate that some corresponding solutions presented in the literature contain errors. We clarify the errors and instead give a refined result.
Fernandes, Julio C.L.; Vilhena, Marco T.; Bodmann, Bardo E.J., E-mail: julio.lombaldo@ufrgs.br, E-mail: mtmbvilhena@gmail.com, E-mail: bardo.bodmann@ufrgs.br [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada; Dulla, Sandra; Ravetto, Piero, E-mail: sandra.dulla@polito.it, E-mail: piero.ravetto@polito.it [Dipartimento di Energia, Politecnico di Torino, Piemonte (Italy)
2015-07-01
In this work we generalize the solution of the one-dimensional neutron transport equation to a multi- group approach in planar geometry. The basic idea of this work consists in consider the hierarchical construction of a solution for a generic number G of energy groups, starting from a mono-energetic solution. The hierarchical method follows the reasoning of the decomposition method. More specifically, the additional terms from adding energy groups is incorporated into the recursive scheme as source terms. This procedure leads to an analytical representation for the solution with G energy groups. The recursion depth is related to the accuracy of the solution, that may be evaluated after each recursion step. The authors present a heuristic analysis of stability for the results. Numerical simulations for a specific example with four energy groups and a localized pulsed source. (author)
Mohammad H. Jabbari
2013-01-01
Full Text Available Using one-dimensional Beji & Nadaoka extended Boussinesq equation, a numerical study of solitary waves over submerged breakwaters has been conducted. Two different obstacles of rectangular as well as circular geometries over the seabed inside a channel have been considered in view of solitary waves passing by. Since these bars possess sharp vertical edges, they cannot directly be modeled by Boussinesq equations. Thus, sharply sloped lines over a short span have replaced the vertical sides, and the interactions of waves including reflection, transmission, and dispersion over the seabed with circular and rectangular shapes during the propagation have been investigated. In this numerical simulation, finite element scheme has been used for spatial discretization. Linear elements along with linear interpolation functions have been utilized for velocity components and the water surface elevation. For time integration, a fourth-order Adams-Bashforth-Moulton predictor-corrector method has been applied. Results indicate that neglecting the vertical edges and ignoring the vortex shedding would have minimal effect on the propagating waves and reflected waves with weak nonlinearity.
Kerstein, A.R. [Sandia National Lab., Livermore, CA (United States)
1996-12-31
One-Dimensional Turbulence is a new turbulence modeling strategy involving an unsteady simulation implemented in one spatial dimension. In one dimension, fine scale viscous and molecular-diffusive processes can be resolved affordably in simulations at high turbulence intensity. The mechanistic distinction between advective and molecular processes is thereby preserved, in contrast to turbulence models presently employed. A stochastic process consisting of mapping {open_quote}events{close_quote} applied to a one-dimensional velocity profile represents turbulent advection. The local event rate for given eddy size is proportional to the velocity difference across the eddy. These properties cause an imposed shear to induce an eddy cascade analogous in many respects to the eddy cascade in turbulent flow. Many scaling and fluctuation properties of self-preserving flows, and of passive scalars introduced into these flows, are reproduced.
One-Dimensionality and Whiteness
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
One-Dimensionality and Whiteness
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
Mansoori Kermani, Maryam; Maghari, Ali
2017-06-01
In this work, a system including two neutral atoms confined to an external one-dimensional Morse potential was modelled. The problem can be relevant to cold atom physics, where neutral atoms may be effectively confined in radially tight tubes formed by optical lattices. The atom-atom interaction was considered as a nonlocal separable potential. Analytical expressions for wave-function as well as transition matrix were derived. The contributions of bound states and resonances in the complex energy plane were calculated. For numerical computations, the bound states in a system of argon gas confined in graphite were considered. Since the most important quantity in the low energy quantum scattering problems is "scattering length," considering various values of Morse parameters, the behavior of this parameter was described versus the reduced energy.
Horsten, N., E-mail: niels.horsten@kuleuven.be; Baelmans, M. [KU Leuven, Department of Mechanical Engineering, Celestijnenlaan 300A, 3001 Leuven (Belgium); Dekeyser, W. [ITER Organization, route de Vinon-sur-Verdon, 13067 St. Paul lez Durance Cedex (France); Samaey, G. [KU Leuven, Department of Computer Science, Celestijnenlaan 200A, 3001 Leuven (Belgium)
2016-01-15
We derive fluid neutral approximations for a simplified 1D edge plasma model, suitable to study the neutral behavior close to the target of a nuclear fusion divertor, and compare its solutions to the solution of the corresponding kinetic Boltzmann equation. The plasma is considered as a fixed background extracted from a detached 2D simulation. We show that the Maxwellian equilibrium distribution is already obtained very close to the target, justifying the use of a fluid approximation. We compare three fluid neutral models: (i) a diffusion model; (ii) a pressure-diffusion model (i.e., a combination of a continuity and momentum equation) assuming equal neutral and ion temperatures; and (iii) the pressure-diffusion model coupled to a neutral energy equation taking into account temperature differences between neutrals and ions. Partial reflection of neutrals reaching the boundaries is included in both the kinetic and fluid models. We propose two methods to obtain an incident neutral flux boundary condition for the fluid models: one based on a diffusion approximation and the other assuming a truncated Chapman-Enskog distribution. The pressure-diffusion model predicts the plasma sources very well. The diffusion boundary condition gives slightly better results overall. Although including an energy equation still improves the results, the assumption of equal ion and neutral temperature already gives a very good approximation.
Dembinski, S. T.; Wolniewicz, L.
1996-01-01
It is shown that the 1D Hamiltonian, which is a sum of operators which generate a finite nilpotent Lie algebra and depends explicitly on time existing closed form solutions of the time-dependent Schrödinger equation, cannot fulfil in general boundary and normalization conditions on a positive semi-axis. An explanation of the controversy surrounding the solutions of the quantum bouncer model, which appeared recently in the literature, is given.
Dembinski, S.T.; Wolniewicz, L. [Institute of Physics, Nicholas Copernicus University, Torun (Poland)
1996-01-21
It is shown that the 1 D Hamiltonian, which is a sum of operators which generate a finite nilpotent Lie algebra and depends explicitly on time existing closed form solutions of the time-dependent Schroedinger equation, cannot fulfil in general boundary and normalization conditions on a positive semi-axis. An explanation of the controversy surrounding the solutions of the quantum bouncer model, which appeared recently in the literature, is given. (author)
Hibiki, T. [Kyoto University, Research Reactor Institute, Osaka (Japan); Takamasa, T. [Tokyo University of Marine Science and Technology, Faculty of Marine Science, Tokyo (Japan); Ishii, M. [Purdue University, School of Nuclear Engineering, West Lafayette IN (United States)
2004-07-01
In view of the practical importance of the drift-flux model for two-phase flow analyses at microgravity conditions, the constitutive equations for distribution parameter and drift velocity have been developed for various two-phase flow regimes at microgravity conditions. A comparison of the model with various experimental data over various flow regimes and a wide range of flow parameters taken at microgravity conditions shows a satisfactory agreement. The newly developed drift-flux model has been applied to reduced gravity conditions such as 1.62 and 3.71 cm/s{sup 2}, which correspond to the Lunar and Martian surface gravities, respectively, and the effect of the gravity on the void fraction in two-phase flow systems has been discussed. It appears that the effect of the gravity on the void fraction in 2-phase flow systems is more pronounced for low liquid flow conditions, whereas the gravity effect may be ignored for high liquid velocity conditions.
Momentum Dynamics of One Dimensional Quantum Walks
Fuss, I; Sherman, P J; Naguleswaran, S; Fuss, Ian; White, langord B.; Sherman, Peter J.; Naguleswaran, Sanjeev
2006-01-01
We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z transform in discrete systems theory. The state functions at each time step are expressed as a simple sum of three Chebyshev polynomials. The functions provide an analytic expression for the development of the walks with time.
One-dimensional photonic crystals
Shen, Huaizhong; Wang, Zhanhua; Wu, Yuxin; Yang, Bai
2016-01-01
A one-dimensional photonic crystal (1DPC), which is a periodic nanostructure with a refractive index distribution along one direction, has been widely studied by scientists. In this review, materials and methods for 1DPC fabrication are summarized. Applications are listed, with a special emphasis
Ceolin, Celina
2010-07-01
The objective of this work is to obtain an analytical solution of the neutron diffusion kinetic equation in one-dimensional cartesian geometry, to monoenergetic and multigroup problems. These equations are of the type stiff, due to large differences in the orders of magnitude of the time scales of the physical phenomena involved, which make them difficult to solve. The basic idea of the proposed method is applying the spectral expansion in the scalar flux and in the precursor concentration, taking moments and solving the resulting matrix problem by the Laplace transform technique. Bearing in mind that the equation for the precursor concentration is a first order linear differential equation in the time variable, to enable the application of the spectral method we introduce a fictitious diffusion term multiplied by a positive value which tends to zero. This procedure opened the possibility to find an analytical solution to the problem studied. We report numerical simulations and analysis of the results obtained with the precision controlled by the truncation order of the series. (author)
One Dimensional Ballistic Electron Transport
Thomas K J
2009-10-01
Full Text Available Research in low-dimensional semiconductor systems over the last three decades has been largely responsible for the current progress in the areas of nanoscience and nanotechnology. The ability to control and manipulate the size, the carrier density, and the carrier type in two-, one-, and zero- dimensional structures has been widely exploited to study various quantum transport phenomena. In this article, a brief introduction is given to ballistic electron transport in one-dimensional quantum wires.
One-Dimensional Simulation of Clay Drying
Siljan Siljan
2002-04-01
Full Text Available Drying of clay is simulated by a one-dimensional model. The background of the work is to form a better basis for investigation of the drying process in production of clay-based building materials. A model of one-dimensional heat and mass transfer in porous material is used and modified to simulate drying of clay particles. The convective terms are discretized by first-order upwinding, and the diffusive terms are discretized by central differencing. DASSL was used to solve the set of algebraic and differential equations. The different simulations show the effect of permeability, initial moisture content and different boundary conditions. Both drying of a flat plate and a spherical particle are modelled.
One-dimensional diffusion model in an Inhomogeneous region
Fedotov, I
2006-01-01
Full Text Available A one-dimensional model is developed to describe atomic diffusion in a graphite tube atomizer for electrothermal atomic adsorption spectrometry. The underlying idea of the model is the solution of an inhomogeneous one-dimensional diffusion equation...
Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Pu, Shi; Roy, Victor; Rezzolla, Luciano; Rischke, Dirk H.
2016-04-01
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work Roy et al., [Phys. Lett. B 750, 45 (2015)], we consider the fluid to have a nonzero magnetization. First, we assume a constant magnetic susceptibility χm and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with χm>0 ), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with χmlaw ˜τ-a, two distinct solutions can be found depending on the values of a and χm. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional Bjorken flow with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data. We find that the temperature and energy density decay more slowly because of the nonvanishing magnetization. For values of the magnetic field typical for heavy-ion collisions, this effect is, however, rather small. It is only for magnetic fields about an order of magnitude larger than expected for heavy-ion collisions that the system is substantially reheated and the lifetime of the quark phase might be extended.
Bjorken flow in one-dimensional relativistic magnetohydrodynamics with magnetization
Pu, Shi; Rezzolla, Luciano; Rischke, Dirk H
2016-01-01
We study the one-dimensional, longitudinally boost-invariant motion of an ideal fluid with infinite conductivity in the presence of a transverse magnetic field, i.e., in the ideal transverse magnetohydrodynamical limit. In an extension of our previous work [1], we consider the fluid to have a non-zero magnetization. First, we assume a constant magnetic susceptibility $\\chi_{m}$ and consider an ultrarelativistic ideal gas equation of state. For a paramagnetic fluid (i.e., with $\\chi_{m}>0$), the decay of the energy density slows down since the fluid gains energy from the magnetic field. For a diamagnetic fluid (i.e., with $\\chi_{m}<0$), the energy density decays faster because it feeds energy into the magnetic field. Furthermore, when the magnetic field is taken to be external and to decay in proper time $\\tau$ with a power law $\\sim\\tau^{-a}$, two distinct solutions can be found depending on the values of $a$ and $\\chi_m$. Finally, we also solve the ideal magnetohydrodynamical equations for one-dimensional...
One dimensional Convolutional Goppa Codes over the projective line
Pérez, J A Domínguez; Sotelo, G Serrano
2011-01-01
We give a general method to construct MDS one-dimensional convolutional codes. Our method generalizes previous constructions of H. Gluesing-Luerssen and B. Langfeld. Moreover we give a classification of one-dimensional Convolutional Goppa Codes and propose a characterization of MDS codes of this type.
One-dimensional Vlasov-Maxwell equilibria
Greene, John M.
1993-06-01
The purpose of this paper is to show that the Vlasov equilibrium of a plasma of charged particles in an electromagnetic field is closely related to a fluid equilibrium, where only a few moments of the velocity distribution of the plasma are considered. In this fluid equilibrium the electric field should be calculated from Ohm's law, rather than the Poisson equation. In practice, only one-dimensional equilibria are treated, because the symmetry makes this case tractable. The emphasis here is on gaining a better understanding of the subject, but an alternate way of doing the calculations is suggested. It is shown that particle distributions can be found that are consistent with any reasonable electromagnetic field profile.
Localized chaos in one-dimensional hydrogen
Humm, D.C.; Saltz, D.; Nayfeh, M.H. (Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801 (USA))
1990-08-01
We calculate the response of hydrogen to the presence of both a strong dc electric field (necessary to isolate a nearly one-dimensional motion) and a strong radiation field of higher frequency than the binding energy of the system, a regime that has not previously been examined by theory or experiment. We determine the classical ionization threshold, the quantum-delocalization threshold, and the threshold of {ital n} mixing due to chaotic effects. The analysis indicates that the dc field can have a dramatic effect on the quantum localization of classically chaotic diffusion, changing the delocalization threshold by more than an order of magnitude. Moreover, this system provides a large spectral region in which quantum-mechanical localization inhibits classical chaotic diffusion. This theory is well suited to experimental testing.
One Dimensional Locally Connected S-spaces
Kunen, Joan E Hart Kenneth
2007-01-01
We construct, assuming Jensen's principle diamond, a one-dimensional locally connected hereditarily separable continuum without convergent sequences. The construction is an inverse limit in omega_1 steps, and is patterned after the original Fedorchuk construction of a compact S-space. To make it one-dimensional, each space in the inverse limit is a copy of the Menger sponge.
Quasi-one-dimensional scattering in a discrete model
Valiente, Manuel; Mølmer, Klaus
2011-01-01
that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model...
Lie symmetry algebra of one-dimensional nonconservative dynamical systems
Liu Cui-Mei; Wu Run-Heng; Fu Jing-Li
2007-01-01
Lie symmetry algebra of linear nonconservative dynamical systems is studied in this paper. By using 1-1 mapping,the Lie point and Lie contact symmetry algebras are obtained from two independent solutions of the one-dimensional linear equations of motion.
Nonequilibrium statistical mechanics in one-dimensional bose gases
Baldovin, F.; Cappellaro, A.; Orlandini, E.; Salasnich, L.
2016-06-01
We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann-Vlasov equation with contact interaction, we derive an effective 1D Landau-Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas.
Exactly solvable one-dimensional inhomogeneous models
Derrida, B.; France, M.M.; Peyriere, J.
1986-11-01
The authors present a simple way of constructing one-dimensional inhomogeneous models (random or quasiperiodic) which can be solved exactly. They treat the example of an Ising chain in a varying magnetic field, but their procedure can easily be extended to other one-dimensional inhomogeneous models. For all the models they can construct, the free energy and its derivatives with respect to temperature can be computed exactly at one particular temperature.
One-dimensional XY model: Ergodic properties and hydrodynamic limit
Shuhov, A. G.; Suhov, Yu. M.
1986-11-01
We prove theorems on convergence to a stationary state in the course of time for the one-dimensional XY model and its generalizations. The key point is the well-known Jordan-Wigner transformation, which maps the XY dynamics onto a group of Bogoliubov transformations on the CAR C *-algebra over Z 1. The role of stationary states for Bogoliubov transformations is played by quasifree states and for the XY model by their inverse images with respect to the Jordan-Wigner transformation. The hydrodynamic limit for the one-dimensional XY model is also considered. By using the Jordan-Wigner transformation one reduces the problem to that of constructing the hydrodynamic limit for the group of Bogoliubov transformations. As a result, we obtain an independent motion of "normal modes," which is described by a hyperbolic linear differential equation of second order. For the XX model this equation reduces to a first-order transfer equation.
Stationary one-dimensional dispersive shock waves
Kartashov, Yaroslav V
2011-01-01
We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defect in defocusing media with linear gain and two-photon absorption. We found that in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from defect or generating beam, the competition between gain and two-photon absorption in dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed certain critical value.
Fate of classical solitons in one-dimensional quantum systems.
Pustilnik, M.; Matveev, K. A.
2015-11-23
We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.
An approach to one-dimensional elliptic quasi-exactly solvable models
M A Fasihi; M A Jafarizadeh; M Rezaei
2008-04-01
One-dimensional Jacobian elliptic quasi-exactly solvable second-order differential equations are obtained by introducing the generalized third master functions. It is shown that the solutions of these differential equations are generating functions for a new set of polynomials in terms of energy with factorization property. The roots of these polynomials are the same as the eigenvalues of the differential equations. Some one-dimensional elliptic quasi-exactly quantum solvable models are obtained from these differential equations.
Fast Integration of One-Dimensional Boundary Value Problems
Campos, Rafael G.; Ruiz, Rafael García
2013-11-01
Two-point nonlinear boundary value problems (BVPs) in both unbounded and bounded domains are solved in this paper using fast numerical antiderivatives and derivatives of functions of L2(-∞, ∞). This differintegral scheme uses a new algorithm to compute the Fourier transform. As examples we solve a fourth-order two-point boundary value problem (BVP) and compute the shape of the soliton solutions of a one-dimensional generalized Korteweg-de Vries (KdV) equation.
One-dimensional oscillator in a box
Amore, Paolo [Facultad de Ciencias, Universidad de Colima, Bernal DIaz del Castillo 340, Colima, Colima (Mexico); Fernandez, Francisco M [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)], E-mail: paolo@ucol.mx, E-mail: fernande@quimica.unlp.edu.ar
2010-01-15
We discuss a quantum-mechanical model of two particles that interact by means of a harmonic potential and are confined to a one-dimensional box with impenetrable walls. We apply perturbation theory to the cases of different and equal masses and analyse the symmetry of the states in the latter case. We compare the approximate perturbation results with accurate numerical ones.
QUASI-ONE DIMENSIONAL CLASSICAL FLUIDS
J.K.Percus
2003-01-01
Full Text Available We study the equilibrium statistical mechanics of simple fluids in narrow pores. A systematic expansion is made about a one-dimensional limit of this system. It starts with a density functional, constructed from projected densities, which depends upon projected one and two-body potentials. The nature of higher order corrections is discussed.
Highly conducting one-dimensional solids
Evrard, Roger; Doren, Victor
1979-01-01
Although the problem of a metal in one dimension has long been known to solid-state physicists, it was not until the synthesis of real one-dimensional or quasi-one-dimensional systems that this subject began to attract considerable attention. This has been due in part to the search for high temperature superconductivity and the possibility of reaching this goal with quasi-one-dimensional substances. A period of intense activity began in 1973 with the report of a measurement of an apparently divergent conduc tivity peak in TfF-TCNQ. Since then a great deal has been learned about quasi-one-dimensional conductors. The emphasis now has shifted from trying to find materials of very high conductivity to the many interesting problems of physics and chemistry involved. But many questions remain open and are still under active investigation. This book gives a review of the experimental as well as theoretical progress made in this field over the last years. All the chapters have been written by scientists who have ...
Neutron transmission bands in one dimensional lattices
Monsivais, G.; Moshinsky, M. [Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-364, 01000 Mexico D.F. (Mexico)
1999-07-01
The original Kronig-Penney lattice, which had delta function interactions at the end of each of the equal segments, seems a good model for the motion of neutrons in a linear lattice if the strength b of the {delta} functions depends of the energy of the neutrons, i.e., b(E). We derive the equation for the transmission bands and consider the relations of b(E) with the R(E) function discussed in a previous paper. We note the great difference in the behavior of the bands when b(E) is constant and when it is related with a single resonance of the R function. (Author)
One-dimensional inverse problems of mathematical physics
Lavrent'ev, M M; Yakhno, V G; Schulenberger, J R
1986-01-01
This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are one-dimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the in
One-dimensional nano-interconnection formation.
Ji, Jianlong; Zhou, Zhaoying; Yang, Xing; Zhang, Wendong; Sang, Shengbo; Li, Pengwei
2013-09-23
Interconnection of one-dimensional nanomaterials such as nanowires and carbon nanotubes with other parts or components is crucial for nanodevices to realize electrical contacts and mechanical fixings. Interconnection has been being gradually paid great attention since it is as significant as nanomaterials properties, and determines nanodevices performance in some cases. This paper provides an overview of recent progress on techniques that are commonly used for one-dimensional interconnection formation. In this review, these techniques could be categorized into two different types: two-step and one-step methods according to their established process. The two-step method is constituted by assembly and pinning processes, while the one-step method is a direct formation process of nano-interconnections. In both methods, the electrodeposition approach is illustrated in detail, and its potential mechanism is emphasized.
Self-consistent mode-coupling approach to one-dimensional heat transport.
Delfini, Luca; Lepri, Stefano; Livi, Roberto; Politi, Antonio
2006-06-01
In the present Rapid Communication we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario to accommodate the known results obtained so far for this problem. More precisely, we conjecture that the universality class is determined by the leading order of the nonlinear interaction potential. Moreover, our analysis allows us to determine the memory kernel, whose expression puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.
One-Dimensional Tunable Josephson Metamaterials
Butz, Susanne
2014-01-01
This thesis presents a novel approach to the experimental realization of tunable, superconducting metamaterials. Therefore, conventional resonant meta-atoms are replaced by meta-atoms that contain Josephson junctions, which renders their resonance frequency tunable by an external magnetic field. This tunability is theoretically and experimentally investigated in one-dimensional magnetic and electric metamaterials. For the magnetic metamaterial, the effective, magnetic permeability is determined.
Vectorlike representation of one-dimensional scattering
Sánchez-Soto, L L; Barriuso, A G; Monzon, J J
2004-01-01
We present a self-contained discussion of the use of the transfer-matrix formalism to study one-dimensional scattering. We elaborate on the geometrical interpretation of this transfer matrix as a conformal mapping on the unit disk. By generalizing to the unit disk the idea of turns, introduced by Hamilton to represent rotations on the sphere, we develop a method to represent transfer matrices by hyperbolic turns, which can be composed by a simple parallelogramlike rule.
One-Dimensional Anisotropic Band Gap Structure
无
2000-01-01
The band gap structure of one-dimensional anisotropic photonic crystal has been studied by means of the transfer matrix formalism. From the analytic expressions and numeric calculations we see some general characteristics of the band gap structure of anisotropic photonic crystals, each band separates into two branches and the two branches react to polarization sensitively. In the practical case of oblique incidence, gaps move towards high frequency when the angle of incidence increases. Under some special conditions, the two branches become degenerate again.
One-dimensional nanostructures principles and applications
Zhai, Tianyou
2012-01-01
Reviews the latest research breakthroughs and applications Since the discovery of carbon nanotubes in 1991, one-dimensional nanostructures have been at the forefront of nanotechnology research, promising to provide the building blocks for a new generation of nanoscale electronic and optoelectronic devices. With contributions from 68 leading international experts, this book reviews both the underlying principles as well as the latest discoveries and applications in the field, presenting the state of the technology. Readers will find expert coverage of all major classes of one-di
Distibines, New One-Dimensional Materials.
2014-09-26
Diarsines, Distibines * and Dibismuthines," XI International Conference on Organometallic * Chemistry , Pine Mountain, Georgia, October 1983. (vi...D-R158 534 DISTIINES NEW ONE-DIMENSIONAL MTERILS(U) ICHIGAN i/UNJY ANN ARBOR DEPT OF CHEMISTRY A J ASHE 17 NAY 85 RFOSR-TR-85-9592 RFOSR-81-909 N...ADDRESS (Ci, Stett, and ZIP Code) Department of Chemistry , University Building 410, Bolling AFS, D.C. of Michigan, Ann Arbor, MI 48109 20332-6448 Sa
One-dimensional hypersonic phononic crystals.
Gomopoulos, N; Maschke, D; Koh, C Y; Thomas, E L; Tremel, W; Butt, H-J; Fytas, G
2010-03-10
We report experimental observation of a normal incidence phononic band gap in one-dimensional periodic (SiO(2)/poly(methyl methacrylate)) multilayer film at gigahertz frequencies using Brillouin spectroscopy. The band gap to midgap ratio of 0.30 occurs for elastic wave propagation along the periodicity direction, whereas for inplane propagation the system displays an effective medium behavior. The phononic properties are well captured by numerical simulations. The porosity in the silica layers presents a structural scaffold for the introduction of secondary active media for potential coupling between phonons and other excitations, such as photons and electrons.
Quasi-one-dimensional scattering in a discrete model
Valiente, Manuel; Moelmer, Klaus [Lundbeck Foundation Theoretical Center for Quantum System Research, Department of Physics and Astronomy, Aarhus University, DK-8000 Aarhus C (Denmark)
2011-11-15
We study quasi-one-dimensional scattering of one and two particles with short-range interactions on a discrete lattice model in two dimensions. One of the directions is tightly confined by an arbitrary trapping potential. We obtain the collisional properties of these systems both at finite and zero Bloch quasimomenta, considering as well finite sizes and transversal traps that support a continuum of states. This is made straightforward by using the exact ansatz for the quasi-one-dimensional states from the beginning. In the more interesting case of genuine two-particle scattering, we find that more than one confinement-induced resonances appear due to the nonseparability of the center-of-mass and relative coordinates on the lattice. This is done by solving its corresponding Lippmann-Schwinger-like equation. We characterize the effective one-dimensional interaction and compare it with a model that includes only the effect of the dominant, broadest resonance, which amounts to a single-pole approximation for the interaction coupling constant.
Study on pile drivability with one dimensional wave propagation theory
陈仁朋; 王仕方; 陈云敏
2003-01-01
Pile drivability is a key problem during the stage of design and construction installation of pile foundations. The solution to the one dimensional wave equation was used to determine the impact force at the top of a concrete pile for a given ram mass, cushion stiffness, and pile impedance. The kinematic equation of pile toe was established and solved based on wave equation theory. The movements of the pile top and pile toe were presented, which clearly showed the dynamic displacement, including rebound and penetration of pile top and toe. A parametric study was made with a full range of practical values of ram weight, cushion stiffness, dropheight, and pile impedance. Suggestions for optimizing the parameters were also presented. Comparisons between the results obtained by the present solution and in-situ measurements indicated the reliability and validity of the method.
Well-posedness of one-dimensional Korteweg models
Sylvie Benzoni-Gavage
2006-05-01
Full Text Available We investigate the initial-value problem for one-dimensional compressible fluids endowed with internal capillarity. We focus on the isothermal inviscid case with variable capillarity. The resulting equations for the density and the velocity, consisting of the mass conservation law and the momentum conservation with Korteweg stress, are a system of third order nonlinear dispersive partial differential equations. Additionally, this system is Hamiltonian and admits travelling solutions, representing propagating phase boundaries with internal structure. By change of unknown, it roughly reduces to a quasilinear Schrodinger equation. This new formulation enables us to prove local well-posedness for smooth perturbations of travelling profiles and almost-global existence for small enough perturbations. A blow-up criterion is also derived.
One-dimensional hydrodynamic model generating turbulent cascade
Matsumoto, Takeshi
2016-01-01
As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analogue (enstrophy) in the inviscid case. With a large-scale forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency and self-similarity in the dynamical system structure.
One-dimensional hydrodynamic model generating a turbulent cascade
Matsumoto, Takeshi; Sakajo, Takashi
2016-05-01
As a minimal mathematical model generating cascade analogous to that of the Navier-Stokes turbulence in the inertial range, we propose a one-dimensional partial-differential-equation model that conserves the integral of the squared vorticity analog (enstrophy) in the inviscid case. With a large-scale random forcing and small viscosity, we find numerically that the model exhibits the enstrophy cascade, the broad energy spectrum with a sizable correction to the dimensional-analysis prediction, peculiar intermittency, and self-similarity in the dynamical system structure.
Spiral Magnetic Order in the One-Dimensional Kondo Lattice
LIU Zhen-Rong; LI Zheng-Zhong; SHEN Rui
2001-01-01
The effects of c-f (conduction-f electrons) hybridization on the spiral spin magnetism in the one dimensional Kondo lattice are studied. By using the mean-field approximation, a close set of equations of the Green's functions with arbitrary wave vector Q for the spiral ordering of spins is deduced. The magnetic phase boundary between the spiral magnetism and ferromagnetism has been calculated approximately. From our qualitative results, one can find that the ferromagnetic region is enlarged due to the c f hybridization. Moreover, some new results reflecting the Kondo effect, such as the modified dispersion relation and the weakening of the localized magnetic moments are also obtained.
Fourier's law for quasi-one-dimensional chaotic quantum systems
Seligman, Thomas H.; Weidenmüller, Hans A.
2011-05-01
We derive Fourier's law for a completely coherent quasi-one-dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.
ABOUT OF SOME ONE-DIMENSIONAL OPTIMIZATION ALGORITHMS WITH ECONOMIC APPLICATIONS
Radu R. Şerban
2012-12-01
Full Text Available In this paper, a new algorithm for one dimensional optimization is presented. The algorithm is based on the “parabola tangent” method for solving a class of equations, without divergence points.
Goloviznin, V. M.; Kanaev, A. A.
2012-03-01
The CABARET computational algorithm is generalized to one-dimensional scalar quasilinear hyperbolic partial differential equations with allowance for inequality constraints on the solution. This generalization can be used to analyze seepage of liquid radioactive wastes through the unsaturated zone.
One-dimensional spinon spin currents
Hirobe, Daichi; Sato, Masahiro; Kawamata, Takayuki; Shiomi, Yuki; Uchida, Ken-Ichi; Iguchi, Ryo; Koike, Yoji; Maekawa, Sadamichi; Saitoh, Eiji
2017-01-01
Quantum spin fluctuation in a low-dimensional or frustrated magnet breaks magnetic ordering while keeping spin correlation. Such fluctuation has been a central topic in magnetism because of its relevance to high-Tc superconductivity and topological states. However, utilizing such spin states has been quite difficult. In a one-dimensional spin-1/2 chain, a particle-like excitation called a spinon is known to be responsible for spin fluctuation in a paramagnetic state. Spinons behave as a Tomonaga-Luttinger liquid at low energy, and the spin system is often called a quantum spin chain. Here we show that a quantum spin chain generates and carries spin current, which is attributed to spinon spin current. This is demonstrated by observing an anisotropic negative spin Seebeck effect along the spin chains in Sr2CuO3. The results show that spin current can flow even in an atomic channel owing to long-range spin fluctuation.
Collapsing of chaos in one dimensional maps
Yuan, Guocheng; Yorke, James A.
2000-02-01
In their numerical investigation of the family of one dimensional maps f l(x)=1-2∣x∣ l, where l>2 , Diamond et al. [P. Diamond et al., Physica D 86 (1999) 559-571] have observed the surprising numerical phenomenon that a large fraction of initial conditions chosen at random eventually wind up at -1, a repelling fixed point. This is a numerical artifact because the continuous maps are chaotic and almost every (true) trajectory can be shown to be dense in [-1,1]. The goal of this paper is to extend and resolve this obvious contradiction. We model the numerical simulation with a randomly selected map. While they used 27 bit precision in computing f l, we prove for our model that this numerical artifact persists for an arbitrary high numerical prevision. The fraction of initial points eventually winding up at -1 remains bounded away from 0 for every numerical precision.
Superfluid helium-4 in one dimensional channel
Kim, Duk Y.; Banavar, Samhita; Chan, Moses H. W.; Hayes, John; Sazio, Pier
2013-03-01
Superfluidity, as superconductivity, cannot exist in a strict one-dimensional system. However, the experiments employing porous media showed that superfluid helium can flow through the pores of nanometer size. Here we report a study of the flow of liquid helium through a single hollow glass fiber of 4 cm in length with an open id of 150 nm between 1.6 and 2.3 K. We found the superfluid transition temperature was suppressed in the hollow cylinder and that there is no flow above the transition. Critical velocity at temperature below the transition temperature was determined. Our results bear some similarity to that found by Savard et. al. studying the flow of helium through a nanohole in a silicon nitrite membrane. Experimental study at Penn State is supported by NSF Grants No. DMR 1103159.
One-dimensional reduction of viscous jets
Pitrou, Cyril
2015-01-01
We build a general formalism to describe thin viscous jets as one-dimensional objects with an internal structure. We present in full generality the steps needed to describe the viscous jets around their central line, and we argue that the Taylor expansion of all fields around that line is conveniently expressed in terms of symmetric trace-free tensors living in the two dimensions of the fiber sections. We recover the standard results of axisymmetric jets and we report the first and second corrections to the lowest order description, also allowing for a rotational component around the axis of symmetry. When applied to generally curved fibers, the lowest order description corresponds to a viscous string model whose sections are circular. However, when including the first corrections we find that curved jets generically develop elliptic sections. Several subtle effects imply that the first corrections cannot be described by a rod model, since it amounts to selectively discard some corrections. However, in a fast...
Spectral (Finite) Volume Method for One Dimensional Euler Equations
Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)
2002-01-01
Consider a mesh of unstructured triangular cells. Each cell is called a Spectral Volume (SV), denoted by Si, which is further partitioned into subcells named Control Volumes (CVs), indicated by C(sub i,j). To represent the solution as a polynomial of degree m in two dimensions (2D) we need N = (m+1)(m+2)/2 pieces of independent information, or degrees of freedom (DOFs). The DOFs in a SV method are the volume-averaged mean variables at the N CVs. For example, to build a quadratic reconstruction in 2D, we need at least (2+1)(3+1)/2 = 6 DOFs. There are numerous ways of partitioning a SV, and not every partition is admissible in the sense that the partition may not be capable of producing a degree m polynomial. Once N mean solutions in the CVs of a SV are given, a unique polynomial reconstruction can be obtained.
Goal Adaptive Discretization of a One-Dimensional Boltzmann Equation
Hoitinga, W.
2011-01-01
Fluid-flow problems in the transitional molecular/continuum regime play an important role in many engineering applications. Such problems are gaining further prominence with the perpetual trend towards miniaturization in science and engineering. The numerical simulation of flows in the transitional
One-dimensional modeling of piping flow erosion
Lachouette, Damien; Golay, Frédéric; Bonelli, Stéphane
2008-09-01
A process called "piping", which often occurs in water-retaining structures (earth-dams, dykes, levees), involving the formation and progression of a continuous tunnel between the upstream and downstream sides, is one of the main cause of structure failure. Starting with the diphasic flow volume equations and the jump equations including the erosion processes, a simplified one-dimensional model for two-phase piping flow erosion was developed. The numerical simulation based on constant input and output pressures showed that the particle concentration can be a significant factor at the very beginning of the process, resulting in the enlargement of the hole at the exit. However, it was concluded that this influence is a secondary factor: the dilute flow assumption, which considerably simplifies the description, is relevant here. To cite this article: D. Lachouette et al., C. R. Mecanique 336 (2008).
Few quantum particles on one dimensional lattices
Valiente Cifuentes, Manuel
2010-06-18
There is currently a great interest in the physics of degenerate quantum gases and low-energy few-body scattering due to the recent experimental advances in manipulation of ultracold atoms by light. In particular, almost perfect periodic potentials, called optical lattices, can be generated. The lattice spacing is fixed by the wavelength of the laser field employed and the angle betwen the pair of laser beams; the lattice depth, defining the magnitude of the different band gaps, is tunable within a large interval of values. This flexibility permits the exploration of different regimes, ranging from the ''free-electron'' picture, modified by the effective mass for shallow optical lattices, to the tight-binding regime of a very deep periodic potential. In the latter case, effective single-band theories, widely used in condensed matter physics, can be implemented with unprecedent accuracy. The tunability of the lattice depth is nowadays complemented by the use of magnetic Feshbach resonances which, at very low temperatures, can vary the relevant atom-atom scattering properties at will. Moreover, optical lattices loaded with gases of effectively reduced dimensionality are experimentally accessible. This is especially important for one spatial dimension, since most of the exactly solvable models in many-body quantum mechanics deal with particles on a line; therefore, experiments with one-dimensional gases serve as a testing ground for many old and new theories which were regarded as purely academic not so long ago. The physics of few quantum particles on a one-dimensional lattice is the topic of this thesis. Most of the results are obtained in the tight-binding approximation, which is amenable to exact numerical or analytical treatment. For the two-body problem, theoretical methods for calculating the stationary scattering and bound states are developed. These are used to obtain, in closed form, the two-particle solutions of both the Hubbard and
Gonzalez, Arnulfo
2016-01-01
The problem of monoenergetic neutral particle transport in a duct, where particles travel inside the duct walls, is treated using an approximate one-dimensional model. The one-dimensional model uses three-basis functions, as part of a previously derived weighted-residual procedure, to account for the geometry of particle transport in a duct system (where particle migration into the walls is not considered). Our model introduces two stochastic parameters to account for particle-wall interactions: an albedo approximation yielding the fraction of particles that return to the duct after striking the walls, and a mean-distance travelled in the walls transverse to the duct by particles that re-enter the duct. Our model produces a set of three transport equations with a non-local scattering kernel. We solve these equations using discrete ordinates with source iteration. Numerical results for the reflection and transmission probabilities of neutron transport in ducts of circular cross section are compared to Monte Ca...
One-Dimensional (1-D) Nanoscale Heterostructures
Guozhen SHEN; Di CHEN; Yoshio BANDO; Dmitri GOLBERG
2008-01-01
One-dimensional (1-D) nanostructures have been attracted much attention as a result of their exceptional properties, which are different from bulk materials. Among 1-D nanostructures, 1-D heterostructures with modulated compositions and interfaces have recently become of particular interest with respect to potential applications in nanoscale building blocks of future optoelectronic devices and systems. Many kinds of methods have been developed for the synthesis of 1-D nanoscale heterostructures. This article reviews the most recent development, with an emphasize on our own recent efforts, on 1-D nanoscale heterostructures, especially those synthesized from the vapor deposition methods, in which all the reactive precursors are mixed together in the reaction chamber. Three types of 1-D nanoscale heterostructures, defined from their morphologies characteristics, are discussed in detail, which include 1-D co-axial core-shell heterostructures, 1-D segmented heterostructures and hierarchical heterostructures. This article begins with a brief survey of various methods that have been developed for synthesizing 1-D nanoscale heterostructures and then mainly focuses on the synthesis, structures and properties of the above three types of nanoscale heterostructures. Finally, this review concludes with personal views towards the topic of 1-D nanoscale heterostructures.
Energy in one-dimensional linear waves
Repetto, C E; Roatta, A; Welti, R J, E-mail: welti@fceia.unr.edu.ar [Laboratorio de Vibraciones y Ondas, Departamento de Fisica, Escuela de Formacion Basica, Facultad de Ciencias Exactas, IngenierIa y Agrimensura (UNR), Pellegrini 250, S2000BTP Rosario (Argentina)
2011-11-15
This work is based on propagation phenomena that conform to the classical wave equation. General expressions of power, the energy conservation equation in continuous media and densities of the kinetic and potential energies are presented. As an example, we study the waves in a string and focused attention on the case of standing waves. The treatment is applicable to introductory science textbooks. (letters and comment)
Strongly anisotropic wetting on one-dimensional nanopatterned surfaces.
Xia, Deying; Brueck, S R J
2008-09-01
This communication reports strongly anisotropic wetting behavior on one-dimensional nanopatterned surfaces. Contact angles, degree of anisotropy, and droplet distortion are measured on micro- and nanopatterned surfaces fabricated with interference lithography. Both the degree of anisotropy and the droplet distortion are extremely high as compared with previous reports because of the well-defined nanostructural morphology. The surface is manipulated to tune with the wetting from hydrophobic to hydrophilic while retaining the structural wetting anisotropy with a simple silica nanoparticle overcoat. The wetting mechanisms are discussed. Potential applications in microfluidic devices and evaporation-induced pattern formation are demonstrated.
One-dimensional nanomaterials: Synthesis and applications
Lei, Bo
My research mainly covers three types of one-dimensional (1D) nanomaterials: metal oxide nanowires, transition metal oxide core-shell nanowires and single-walled carbon nanotubes. This new class of nanomaterials has generated significant impact in multiple fields including electronics, medicine, computing and energy. Their peculiar, fascinating properties are promising for unique applications on electronics, spintronics, optical and chemical/biological sensing. This dissertation will summarize my research work on these three 1D nanomaterials and propose some ideas that may lead to further development. Chapter 1 will give a brief introduction of nanotechnology journey and 1D nanomaterials. Chapter 2 and 3 will discuss indium oxide nanowires, as the representative of metal oxide nanwires. More specifically, chapter 2 is focused on the synthesis, material characterization, transport studies and doping control of indium oxide nanowires; Chapter 3 will give a comprehensive review of our systematic studies on molecular memory applications based on molecule/indium oxide nanowire heterostructures. Chapter 4 will introduce another 1D nanomaterial-transition metal oxide (TMO) core-shell nanowires. The discuss will focus on the synthesis of TMO nanowires, material analysis and their electronic properties as a function of temperature and magnetic field. Chapter 5 is dedicated to aligned single-walled carbon nanotubes (SWNTs) on synthesis with rational control of position and orientation, detailed characterization and construction of scaled top-gated transistors. This chapter presents a way to produce the p- and n-type nanotube transistors based on gate voltage polarity control during electrical breakdown. Finally, chapter 6 summarizes the above discussions and proposes some suggestions for future studies.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A.
2016-11-01
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
One-Dimensional Forward–Forward Mean-Field Games
Gomes, Diogo A., E-mail: diogo.gomes@kaust.edu.sa; Nurbekyan, Levon; Sedjro, Marc [King Abdullah University of Science and Technology (KAUST), CEMSE Division (Saudi Arabia)
2016-12-15
While the general theory for the terminal-initial value problem for mean-field games (MFGs) has achieved a substantial progress, the corresponding forward–forward problem is still poorly understood—even in the one-dimensional setting. Here, we consider one-dimensional forward–forward MFGs, study the existence of solutions and their long-time convergence. First, we discuss the relation between these models and systems of conservation laws. In particular, we identify new conserved quantities and study some qualitative properties of these systems. Next, we introduce a class of wave-like equations that are equivalent to forward–forward MFGs, and we derive a novel formulation as a system of conservation laws. For first-order logarithmic forward–forward MFG, we establish the existence of a global solution. Then, we consider a class of explicit solutions and show the existence of shocks. Finally, we examine parabolic forward–forward MFGs and establish the long-time convergence of the solutions.
Analytical solution of one dimensional temporally dependent ...
user
The models involve the one-site, two-site, and two-region ... (2005) presented an analytical solution to advection-dispersion equation ... transfer of heat in fluids, flow through porous media, and the spread of contaminants in fluids and in ...
Multi-symplectic, Lagrangian, one-dimensional gas dynamics
Webb, G. M.
2015-05-01
The equations of Lagrangian, ideal, one-dimensional, compressible gas dynamics are written in a multi-symplectic form using the Lagrangian mass coordinate m and time t as independent variables, and in which the Eulerian position of the fluid element x = x(m, t) is one of the dependent variables. This approach differs from the Eulerian, multi-symplectic approach using Clebsch variables. Lagrangian constraints are used to specify equations for xm, xt, and St consistent with the Lagrangian map, where S is the entropy of the gas. We require St = 0 corresponding to advection of the entropy S with the flow. We show that the Lagrangian Hamiltonian equations are related to the de Donder-Weyl multi-momentum formulation. The pullback conservation laws and the symplecticity conservation laws are discussed. The pullback conservation laws correspond to invariance of the action with respect to translations in time (energy conservation) and translations in m in Noether's theorem. The conservation law due to m-translation invariance gives rise to a novel nonlocal conservation law involving the Clebsch variable r used to impose ∂S(m, t)/∂t = 0. Translation invariance with respect to x in Noether's theorem is associated with momentum conservation. We obtain the Cartan-Poincaré form for the system, and use it to obtain a closed ideal of two-forms representing the equation system.
Explicit Solutions for One-Dimensional Mean-Field Games
Prazeres, Mariana
2017-04-05
In this thesis, we consider stationary one-dimensional mean-field games (MFGs) with or without congestion. Our aim is to understand the qualitative features of these games through the analysis of explicit solutions. We are particularly interested in MFGs with a nonmonotonic behavior, which corresponds to situations where agents tend to aggregate. First, we derive the MFG equations from control theory. Then, we compute explicit solutions using the current formulation and examine their behavior. Finally, we represent the solutions and analyze the results. This thesis main contributions are the following: First, we develop the current method to solve MFG explicitly. Second, we analyze in detail non-monotonic MFGs and discover new phenomena: non-uniqueness, discontinuous solutions, empty regions and unhappiness traps. Finally, we address several regularization procedures and examine the stability of MFGs.
Properties of surface modes in one dimensional plasma photonic crystals
Shukla, S.; Prasad, S., E-mail: prasad.surendra@gmail.com; Singh, V. [Department of Physics, Faculty of Science, Banaras Hindu University, Varanasi 221005 (India)
2015-02-15
Properties of surface modes supported at the interface of air and a semi-infinite one dimensional plasma photonic crystal are analyzed. The surface mode equation is obtained by using transfer matrix method and applying continuity conditions of electric fields and its derivatives at the interface. It is observed that with increase in the width of cap layer, frequencies of surface modes are shifted towards lower frequency side, whereas increase in tangential component of wave-vector increases the mode frequency and total energy carried by the surface modes. With increase in plasma frequency, surface modes are found to shift towards higher frequency side. The group velocity along interface is found to control by cap layer thickness.
Benchmarking high order finite element approximations for one-dimensional boundary layer problems
Malagu, M.; Benvenuti, E.; Simone, A.
2013-01-01
In this article we investigate the application of high order approximation techniques to one-dimensional boundary layer problems. In particular, we use second order differential equations and coupled second order differential equations as case studies. The accuracy and convergence rate of numerical
Imploding ignition waves: I. one dimensional analysis
Kushnir, Doron; Waxman, Eli
2011-01-01
We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R_c. An approximate analytic expression for R_c is derived for an ideal gas equation of state and a simple (power-law-Arrhenius) reaction law, and shown to reproduce the results of numerical solutions. For typical acetylene-air experiments we find R_c~0.1 mm (spherical) and R_c~1 mm (cylindrical). We suggest that the deflagration to detonation transition (DDT) observed in these systems may be due to converging shocks produced by the turbulent deflagration flow, which reaches sub (but near) sonic velocities on scales >>R_c. Our suggested mechanism differs from that proposed by Zel'dovich et al. (1970), in which a fine tuned spatial gradient in the chemical induction time is required to be maintained within the turbulent deflagration flow. Our analysis may be readily extended to more complicated equations of state and...
Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.
Li, Ben; Stenstrom, M K
2014-01-01
One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.
MARCUSE’S ONE-DIMENSIONAL SOCIETY IN ONE-DIMENSIONAL MAN
MILOS RASTOVIC
2013-05-01
Full Text Available Nowadays, Marcuse’s main book One-Dimensional Man is almost obsolete, or rather passé. However, there are reasons to renew the reading of his book because of “the crisis of capitalism,” and the prevailing framework of technological domination in “advanced industrial society” in which we live today. “The new forms of control” in “advanced industrial societies” have replaced traditional methods of political and economic administration. The dominant structural element of “advanced industrial society” has become a technical and scientific apparatus of production and distribution of technology and administrative practice based on application of impersonal rules by a hierarchy of associating authorities. Technology has been liberated from the control of particular interests, and it has become the factor of domination in itself. Technological domination stems from the technical development of the productive apparatus that reproduces its ability into all spheres of social life (cultural, political, and economic. Based upon this consideration, in this paper, I will examine Marcuse’s ideas of “the new forms of control,” which creates a one–dimensional society. Marcuse’s fundamental thesis in One-Dimensional Man is that technological rationality is the most dominant factor in an “advanced industrial society,” which unites two earlier opposing forces of dissent: the bourgeoisie and the proletariat.
Gibbs measures and phase transitions in one-dimensional models
Mallak, Saed
2000-01-01
Ankara : Department of Mathematics and the Institute of Engineering and Sciences of Bilkent University, 2000. Thesis (Ph.D.) -- Bilkent University, 2000. Includes bibliographical references leaves 63-64 In this thesis we study the problem of limit Gibbs measures in one-dimensional models. VVe investigate uniqueness conditions for the limit Gibbs measures for one-dimensional models. VVe construct a one-dimensional model disproving a uniqueness conjecture formulated before for...
One-dimensional semirelativistic Hamiltonian with multiple Dirac delta potentials
Erman, Fatih; Gadella, Manuel; Uncu, Haydar
2017-02-01
In this paper, we consider the one-dimensional semirelativistic Schrödinger equation for a particle interacting with N Dirac delta potentials. Using the heat kernel techniques, we establish a resolvent formula in terms of an N ×N matrix, called the principal matrix. This matrix essentially includes all the information about the spectrum of the problem. We study the bound state spectrum by working out the eigenvalues of the principal matrix. With the help of the Feynman-Hellmann theorem, we analyze how the bound state energies change with respect to the parameters in the model. We also prove that there are at most N bound states and explicitly derive the bound state wave function. The bound state problem for the two-center case is particularly investigated. We show that the ground state energy is bounded below, and there exists a self-adjoint Hamiltonian associated with the resolvent formula. Moreover, we prove that the ground state is nondegenerate. The scattering problem for N centers is analyzed by exactly solving the semirelativistic Lippmann-Schwinger equation. The reflection and the transmission coefficients are numerically and asymptotically computed for the two-center case. We observe the so-called threshold anomaly for two symmetrically located centers. The semirelativistic version of the Kronig-Penney model is shortly discussed, and the band gap structure of the spectrum is illustrated. The bound state and scattering problems in the massless case are also discussed. Furthermore, the reflection and the transmission coefficients for the two delta potentials in this particular case are analytically found. Finally, we solve the renormalization group equations and compute the beta function nonperturbatively.
Generalized Hasimoto Transform of One-Dimensional Dispersive Flows into Compact Riemann Surfaces
Eiji Onodera
2008-05-01
Full Text Available We study the structure of differential equations of one-dimensional dispersive flows into compact Riemann surfaces. These equations geometrically generalize two-sphere valued systems modeling the motion of vortex filament. We define a generalized Hasimoto transform by constructing a good moving frame, and reduce the equation with values in the induced bundle to a complex valued equation which is easy to handle. We also discuss the relationship between our reduction and the theory of linear dispersive partial differential equations.
Integral Transport Theory in One-dimensional Geometries
Carlvik, I.
1966-06-15
A method called DIT (Discrete Integral Transport) has been developed for the numerical solution of the transport equation in one-dimensional systems. The characteristic features of the method are Gaussian integration over the coordinate as described by Kobayashi and Nishihara, and a particular scheme for the calculation of matrix elements in annular and spherical geometry that has been used for collision probabilities in earlier Flurig programmes. The paper gives a general theory including such things as anisotropic scattering and multi-pole fluxes, and it gives a brief description of the Flurig scheme. Annular geometry is treated in some detail, and corresponding formulae are given for spherical and plane geometry. There are many similarities between DIT and the method of collision probabilities. DIT is in many cases faster, because for a certain accuracy in the fluxes DIT often needs fewer space points than the method of collision probabilities needs regions. Several computer codes using DIT, both one-group and multigroup, have been written. It is anticipated that experience gained in calculations with these codes will be reported in another paper.
Eilbeck, J. C; Lomdahl, P.S.; Olsen, O.H.
1985-01-01
A two-dimensional model of Josephson junction of overlap type is presented. The energy input is provided through induced magnetic fields modeled by a set of boundary conditions. In the limit of a very narrow junction, this model reduces to the one-dimensional model. Further, an equation derived f...
Aleutdinova, V. A.; Borisov, A. V.; Shaparev, V. É.; Shapovalov, A. V.
2011-09-01
Numerical solutions of the generalized one-dimensional Fisher-Kolmogorov-Petrovskii-Piskunov equation with nonlocal competitive losses and convection are constructed. The influence function for nonlocal losses is chosen in the form of a Gaussian distribution. The effect of convection on the dynamics of the spatially inhomogeneous distribution of the population density is investigated.
Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface
Fernandez, Francisco M.
2010-01-01
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…
Simple One-Dimensional Quantum-Mechanical Model for a Particle Attached to a Surface
Fernandez, Francisco M.
2010-01-01
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schrodinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships…
Rotvig, J.; Smith, H.; Jauho, Antti-Pekka
1996-01-01
We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model an....... 74, 1831 (1995)], where a set of numerical simulations was presented....
Well-posedness for one-dimensional anisotropic Cahn-Hilliard and Allen-Cahn systems
Ahmad Makki
2015-01-01
Full Text Available Our aim is to prove the existence and uniqueness of solutions for one-dimensional Cahn-Hilliard and Allen-Cahn type equations based on a modification of the Ginzburg-Landau free energy proposed in [8]. In particular, the free energy contains an additional term called Willmore regularization and takes into account strong anisotropy effects.
Yu Daren; Wu Zhiwen; Wu Xiaoling
2005-01-01
Based on the analysis of the physical mechanism of the Stationary Plasma Thruster (SPT), an integral equation describing the ion density of the steady SPT and the ion velocity distribution function at an arbitrary axial position of the steady SPT channel are derived. The integral equation is equivalent to the Vlasov equation, but the former is simpler than the latter. A one dimensional steady quasineutral hybrid model is established. In this model, ions are described by the above integral equation, and neutrals and electrons are described by hydrodynamic equations. The transferred equivalency to the differential equation and the integral equation, together with other equations, are solved by an ordinary differential equation (ODE) solver in the Matlab.The numerical simulation results show that under various circumstances, the ion average velocity would be different and needs to be deduced separately.
Generalization of the one-dimensional ideal plasma flow with spherical waves
Golovin, Sergey V [Queen' s University, Kingston, Ontario K7 L 3N6 (Canada)
2006-06-09
We give a description of the ideal plasma flow, which is governed by an exact partially invariant solution of the magnetohydrodynamics equations. The solution generalizes known one-dimensional flow with spherical waves. The generalization consists in addition of the special tangent vector components of the velocity and the magnetic field at any plasma particle. In the special case of zeroth tangential component the solution coincides with the classical one-dimensional one. This paper describes a three-dimensional picture of the plasma flow, governed by the obtained solution.
Torsional Detwinning Domino in Nanotwinned One-Dimensional Nanostructures.
Zhou, Haofei; Li, Xiaoyan; Wang, Ying; Liu, Zishun; Yang, Wei; Gao, Huajian
2015-09-09
How to maintain sustained deformation in one-dimensional nanostructures without localized failure is an important question for many applications of nanotechnology. Here we report a phenomenon of torsional detwinning domino that leads to giant rotational deformation without localized failure in nanotwinned one-dimensional metallic nanostructures. This mechanism is demonstrated in nanotwinned Cu nanorods via molecular dynamics simulations, where coherent twin boundaries are transformed into twist boundaries and then dissolved one by one, resulting in practically unlimited rotational deformation. This finding represents a fundamental advance in our understanding of deformation mechanisms in one-dimensional metallic nanostructures.
A kinetic model for the one-dimensional electromagnetic solitons in an isothermal plasmapdf
tajima, Toshi
2002-02-22
Two nonlinear second order differential equations for the amplitude of the vector potential and for the electromagnetic potential are derived, starting from the full Maxwell equations where the field sources are calculated by integrating in the momentum space the particle distribution function, which is an exact solution of the relativistic Vlasov equation. The resulting equations are exact in describing a hot one-dimensional plasma sustaining a relativistically intense, circularly polarized electromagnetic polarized electromagnetic radiation. The case of standing soliton-like structures in an electron-positron plasma is then investigated. It is demonstrated that at ultrarelativistic temperatures extremely large amplitude solitons can be formed in a strongly overdense plasma.
A NEW ONE-DIMENSIONAL CHAOTIC MAP WITH INFINITE COLLAPSES
Qiu Yuehong; He Chen; Zhu Hongwen
2002-01-01
This letter presents a new one-dimensional chaotic map with infinite collapses. Theoretical analyses show that the map has complicated dynamical behavior and ideal distribution.The map can be applied in chaotic spreading spectrum communication and chaotic cipher.
One-dimensional spatially dependent solute transport in semi ...
One-dimensional spatially dependent solute transport in semi-infinite porous media: an analytical solution. ... Journal Home > Vol 9, No 4 (2017) > ... In this mathematical model the dispersion coefficient is considered spatially dependent while ...
One-Dimensional Tunable Photonic-Crystal IR Filter Project
National Aeronautics and Space Administration — MetroLaser proposes to design and develop an innovative narrowband tunable IR filter based on the properties of a one-dimensional photonic crystal structure with a...
One-Dimensional Tunable Photonic-Crystal IR Filter Project
National Aeronautics and Space Administration — MetroLaser proposes to design and develop an innovative narrowband tunable IR filter based on the properties of a one-dimensional photonic crystal structure with a...
Digital noise generators using one-dimensional chaotic maps
Martínez-Ñonthe, J. A; Palacios-Luengas, L.; Cruz-Irisson, M.; Vazquez Medina, R. [Instituto Politécnico Nacional, ESIME-Culhuacan, Santa Ana 1000, 04430, D.F. (Mexico); Díaz Méndez, J. A. [Instituto Nacional de Astrofísica, Óptica y Electrónica, Luis Enrique Erro 1, Tonantzintla, Puebla (Mexico)
2014-05-15
This work shows how to improve the statistical distribution of signals produced by digital noise generators designed with one-dimensional (1-D) chaotic maps. It also shows that in a digital electronic design the piecewise linear chaotic maps (PWLCM) should be considered because they do not have stability islands in its chaotic behavior region, as it occurs in the case of the logistic map, which is commonly used to build noise generators. The design and implementation problems of the digital noise generators are analyzed and a solution is proposed. This solution relates the output of PWLCM, usually defined in the real numbers' domain, with a codebook of S elements, previously defined. The proposed solution scheme produces digital noise signals with a statistical distribution close to a uniform distribution. Finally, this work shows that it is possible to have control over the statistical distribution of the noise signal by selecting the control parameter of the PWLCM and using, as a design criterion, the bifurcation diagram.
One dimensional models of excitons in carbon nanotubes
Cornean, Horia Decebal; Duclos, P.; Pedersen, Thomas Garm
Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.......Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable....
An investigation of dopping profile for a one dimensional heterostructure
Huang, Zhaohui
2005-03-01
A one-dimensional junction is formed by joining two silicon nanowires whose surfaces are terminated with capping groups of different electronegativity and polarizability. If this heterostructure is doped (with e.g. phosphorous) on the side with the higher bandgap, the system becomes a modulation doped heterostructure with novel one-dimensional electrostatics. We use density functional theory calculations in the pseudopotential approximation, plus empirical model calculations, to investigate doping profiles in this new class of nanostructures.
Fidelity of an electron in one-dimensional determined potentials
Song Wen-Guang; Tong Pei-Qing
2009-01-01
We numerically study the fidelity of an electron in the one-dimensional Harper model and in the one-dimensional slowly varying potential model. Our results show that many properties of the two models can be well reflected by the fidelity: (i) the mobility edge and metal-insulator transition can be characterized by the static fidelity; (ii) the extended state and localized state can be identified by the dynamic fidelity. Therefore, it may broaden the applied areas of the fidelity.
Spatial modes in one-dimensional models for capillary jets
Guerrero, J.; González, H.; García, F. J.
2016-03-01
One-dimensional (1D) models are widely employed to simplify the analysis of axisymmetric capillary jets. These models postulate that, for slender deformations of the free surface, the radial profile of the axial velocity can be approximated as uniform (viscous slice, averaged, and Cosserat models) or parabolic (parabolic model). In classical works on spatial stability analysis with 1D models, considerable misinterpretation was generated about the modes yielded by each model. The already existing physical analysis of three-dimensional (3D) axisymmetric spatial modes enables us to relate these 1D spatial modes to the exact 3D counterparts. To do so, we address the surface stimulation problem, which can be treated as linear, by considering the effect of normal and tangential stresses to perturb the jet. A Green's function for a spatially local stimulation having a harmonic time dependence provides the general formalism to describe any time-periodic stimulation. The Green's function of this signaling problem is known to be a superposition of the spatial modes, but in fact these modes are of fundamental nature, i.e., not restricted to the surface stimulation problem. The smallness of the wave number associated with each mode is the criterion to validate or invalidate the 1D approaches. The proposed axial-velocity profiles (planar or parabolic) also have a remarkable influence on the outcomes of each 1D model. We also compare with the classical 3D results for (i) conditions for absolute instability, and (ii) the amplitude of the unstable mode resulting from both normal and tangential surface stress stimulation. Incidentally, as a previous task, we need to re-deduce 1D models in order to include eventual stresses of various possible origins (electrohydrodynamic, thermocapillary, etc.) applied on the free surface, which were not considered in the previous general formulations.
Simple Two-Dimensional Corrections for One-Dimensional Pulse Tube Models
Lee, J. M.; Kittel, P.; Timmerhaus, K. D.; Radebaugh, R.
2004-01-01
One-dimensional oscillating flow models are very useful for designing pulse tubes. They are simple to use, not computationally intensive, and the physical relationship between temperature, pressure and mass flow are easy to understand when used in conjunction with phasor diagrams. They do not possess, however, the ability to directly calculate thermal and momentum diffusion in the direction transverse to the oscillating flow. To account for transverse effects, lumped parameter corrections, which are obtained though experiment, must be used. Or two-dimensional solutions of the differential fluid equations must be obtained. A linear two-dimensional solution to the fluid equations has been obtained. The solution provides lumped parameter corrections for one-dimensional models. The model accounts for heat transfer and shear flow between the gas and the tube. The complex Nusselt number and complex shear wall are useful in describing these corrections, with phase relations and amplitudes scaled with the Prandtl and Valensi numbers. The calculated ratio, a, between a two-dimensional solution of the oscillating temperature and velocity and a one-dimensional solution for the same shows a scales linearly with Va for Va less than 30. In this region alpha less than 0.5, that is, the enthalpy flow calculated with a two-dimensional model is 50% of a calculation using a one-dimensional model. For Va greater than 250, alpha = 0.8, showing that diffusion is still important even when it is confined to a thing layer near the tube wall.
UNIVERSAL THEORY OF STEADY-STATE ONE-DIMENSIONAL PHOTOREFRACTIVE SOLITONS
刘劲松
2001-01-01
A universal theory of steady-state one-dimensional photorefractive spatial solitons is developed which applies to the steady-state one-dimensional photorefractive solitons under various realizations, including the screening solitons in a biased photorefractive medium, the photovoltaic solitons in open- and closed-circuit photovoltaic-photorefractive media and the screening-photovoltaic solitons in biased photovoltaic-photorefractive media. Previous theories advanced individually elsewhere for these solitons can be obtained by simplifying the universal theory under the appropriate conditions.
One dimensional speckle fields generated by three phase level diffusers
Cabezas, L.; Amaya, D.; Bolognini, N.; Lencina, A.
2015-02-01
Speckle patterns have usually been obtained by using ground glass as random diffusers. Liquid-crystal spatial light modulators have opened the possibility of engineering tailored speckle fields obtained from designed diffusers. In this work, one-dimensional Gaussian speckle fields with fully controllable features are generated. By employing a low-cost liquid-crystal spatial light modulator, one-dimensional three phase level diffusers are implemented. These diffusers make it possible to control average intensity distribution and statistical independence among the generated patterns. The average speckle size is governed by an external slit pupil. A theoretical model to describe the generated speckle patterns is developed. Experimental and theoretical results confirming the generation of one-dimensional speckle fields are presented. Some possible applications of these speckles, such as atom trapping and super-resolution imaging, are briefly envisaged.
Analysis of one dimensional and two dimensional fuzzy controllers
Ban Xiaojun; Gao Xiaozhi; Huang Xianlin; Wu Tianbao
2006-01-01
The analytical structures and the corresponding mathematical properties of the one dimensional and two dimensional fuzzy controllers are first investigated in detail.The nature of these two kinds of fuzzy controllers is next probed from the perspective of control engineering. For the one dimensional fuzzy controller, it is concluded that this controller is a combination of a saturation element and a nonlinear proportional controller, and the system that employs the one dimensional fuzzy controller is the combination of an open-loop control system and a closedloop control system. For the latter case, it is concluded that it is a hybrid controller, which comprises the saturation part, zero-output part, nonlinear derivative part, nonlinear proportional part, as well as nonlinear proportional-derivative part, and the two dimensional fuzzy controller-based control system is a loop-varying system with varying number of control loops.
A review on one dimensional perovskite nanocrystals for piezoelectric applications
Li-Qian Cheng
2016-03-01
Full Text Available In recent years, one-dimensional piezoelectric nanomaterials have become a research topic of interest because of their special morphology and excellent piezoelectric properties. This article presents a short review on one dimensional perovskite piezoelectric materials in different systems including Pb(Zr,TiO3, BaTiO3 and (K,NaNbO3 (KNN. We emphasize KNN as a promising lead-free piezoelectric compound with a high Curie temperature and high piezoelectric properties and describe its synthesis and characterization. In particular, details are presented for nanoscale piezoelectricity characterization of a single KNN nanocrystal by piezoresponse force microscopy. Finally, this review describes recent progress in applications based on one dimensional piezoelectric nanostructures with a focus on energy harvesting composite materials.
One-dimensional models of excitons in carbon nanotubes
Cornean, Horia Decebal; Duclos, Pierre; Pedersen, Thomas Garm
2004-01-01
Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable.......Excitons in carbon nanotubes may be modeled by two oppositely charged particles living on the surface of a cylinder. We derive three one-dimensional effective Hamiltonians which become exact as the radius of the cylinder vanishes. Two of them are solvable....
One-dimensional Nanostructured Materials From Organic Precursor
K. F. Cai
2005-01-01
@@ 1Introduction One-dimensional nanostructured materials, such as nanowires, nanobelts, nanotubes and nanocables have been attracting a great research interest in the last decade due to their superior electrical, optical, mechanical and thermal properties, and many methods have been explored to synthesis of the materials, e.g., arc discharge, laser ablation, chemical vapor deposition, thermal evaporation, sol-gel method, template method and so on. In this work, we present a novel and simple method to one-dimensional nanostructured materials by pyrolysis of organic precursor.
Branching solutions to one-dimensional variational problems
Ivanov, A O
2001-01-01
This book deals with the new class of one-dimensional variational problems - the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Contents: Preliminary Results; Networks Extremality Criteria; Linear Networks in R N; Extremals of Length Type Functionals: The
The kink-soliton and antikink-soliton in quasi-one-dimensional nonlinear monoatomic lattice
XU; Quan; TIAN; Qiang
2005-01-01
The quasi-one-dimensional nonlinear monoatomic lattice is analyzed. The kink-soliton and antikink-soliton are presented. When the interaction of the lattice is strong in the x-direction and weak in the y-direction, the two-dimensional (2D) lattice changes to a quasi-one-dimensional lattice. Taking nearest-neighbor interaction into account, the vibration equation can be transformed into the KPI, KPII and MKP equation. Considering the cubic nonlinear potential of the vibration in the lattice, the kink-soliton solution is presented. Considering the quartic nonlinear potential and the cubic interaction potential, the kink-soliton and antikink-soliton solutions are presented.
Stable One-Dimensional Periodic Wave in Kerr-Type and Quadratic Nonlinear Media
Roxana Savastru
2012-01-01
Full Text Available We present the propagation of optical beams and the properties of one-dimensional (1D spatial solitons (“bright” and “dark” in saturated Kerr-type and quadratic nonlinear media. Special attention is paid to the recent advances of the theory of soliton stability. We show that the stabilization of bright periodic waves occurs above a certain threshold power level and the dark periodic waves can be destabilized by the saturation of the nonlinear response, while the dark quadratic waves turn out to be metastable in the broad range of material parameters. The propagation of (1+1 a dimension-optical field on saturated Kerr media using nonlinear Schrödinger equations is described. A model for the envelope one-dimensional evolution equation is built up using the Laplace transform.
Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms
Schmittfull, Marcel; Vlah, Zvonimir; McDonald, Patrick
2016-05-01
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e., Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g., the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.
One-dimensional simulation of lake and ice dynamics during winter
Ali Oveisy
2014-04-01
Full Text Available An ice formation model, based on the solution of the heat conduction equation across blue ice, white ice and snow cover, is integrated into the Dynamic Reservoir Simulation Model (DYRESM to allow for one-dimensional (vertical winter simulation of lake dynamics during periods of ice cover. This is an extension of a previous three-layer snow and ice model to include two-way coupling between the ice and the water column. The process-based ice formation is suitable for application to mid-latitude regions and includes: snowmelt due to rain; formation of white ice; and variability in snow density, snow conductivity, and ice and snow albedo. The model was validated against published observations from Harmon lake, British Columbia, and new observations from Eagle lake, Ontario. The ice thickness and water column temperature profile beneath the ice were predicted with Root Mean Square Deviations (RMSD of 1 cm and 0.38°C, respectively, during the winter of 1990-91in Harmon lake. In Eagle lake the 2011-12 year-round water column temperature profile was predicted with an RMSD of 1.8°C. Improved prediction of under-ice lake temperature, relative to published results from simpler models, demonstrates the need for models that accurately capture ice-formation processes, including ice to water column coupling, formation of both blue and white ice layers, and process-based ice and snow parameters (density, conductivity and albedo.
Phase Space Compression in One-Dimensional Complex Ginzburg-Landau Dquation
GAO Ji-Hua; PENG Jian-Hua
2007-01-01
The transition from stationary to oscillatory states in dynamical systems under phase space compression is investigated. By considering the model for the spatially one-dimensional complex Ginzburg-Landau equation, we find that defect turbulence can be substituted with stationary and oscillatory signals by applying system perturbation and confining variable into various ranges. The transition procedure described by the oscillatory frequency is studied via numerical simulations in detail.
Generalized Theory of One-Dimensional Steady-State Optical Spatial Solitons
WANG Hong-Cheng; WANG Xiao-Sheng; SHE Wei-Long
2004-01-01
@@ We present a generalized soliton theory based on the one-dimensional generalized nonlinear Schrodinger equation,from which one can easily obtain the bright, dark, and grey soliton waveforms, and their existence curves. We show that the forming conditions of spatial solitons are directly dependent on the relationship between the index perturbation and the intensity, no matter whether the index perturbation is positive or negative. Some relevant examples are presented when the solitons are supported by the photoisomerization nonlinearity.
Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem
Baiyu Wang
2014-01-01
Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.
Herrebout, D.; Bogaerts, A.; Yan, M.; Gijbels, R.; W. Goedheer,; Dekempeneer, E.
2001-01-01
A one-dimensional (1D) model for a methane rf plasma consisting of 20 species (neutrals, radicals, ions, and electrons) is presented. The equations solved are the particle balances, assuming a drift-diffusion approximation for the fluxes, and the electron energy balance equation. The self-consistent
Symmetricity of Distribution for One-Dimensional Hadamard Walk
Konno, N; Soshi, T; Konno, Norio; Namiki, Takao; Soshi, Takahiro
2002-01-01
In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetricity of probability distributions for the Hadamard walk.
The electromagnetic Brillouin precursor in one-dimensional photonic crystals
Uitham, R.; Hoenders, B. J.
2008-01-01
We have calculated the electromagnetic Brillouin precursor that arises in a one-dimensional photonic crystal that consists of two homogeneous slabs which each have a single electron resonance. This forerunner is compared with the Brillouin precursor that arises in a homogeneous double-electron reson
Time correlation functions for the one-dimensional Lorentz gas
Mazo, R.M.; Beijeren, H. van
1983-01-01
The velocity autocorrelation function and related quantities are investigated for the one-dimensional deterministic Lorentz gas, consisting of randomly distributed fixed scatterers and light particles moving back and forth between two of these at a constant given speed. An expansion for the velocity
Current-Voltage Characteristics of Quasi-One-Dimensional Superconductors
Vodolazov, D.Y.; Peeters, F.M.; Piraux, L.
2003-01-01
The current-voltage (I-V) characteristics of quasi-one-dimensional superconductors were discussed. The I-V characteristics exhibited an unusual S behavior. The dynamics of superconducting condensate and the existence of two different critical currents resulted in such an unusual behavior....
The Long Decay Model of One-Dimensional Projectile Motion
Lattery, Mark Joseph
2008-01-01
This article introduces a research study on student model formation and development in introductory mechanics. As a point of entry, I present a detailed analysis of the Long Decay Model of one-dimensional projectile motion. This model has been articulated by Galileo ("in De Motu") and by contemporary students. Implications for instruction are…
The electromagnetic Brillouin precursor in one-dimensional photonic crystals
Uitham, R.; Hoenders, B. J.
2008-01-01
We have calculated the electromagnetic Brillouin precursor that arises in a one-dimensional photonic crystal that consists of two homogeneous slabs which each have a single electron resonance. This forerunner is compared with the Brillouin precursor that arises in a homogeneous double-electron
One-dimensional Bose gas on an atom chip
van Amerongen, A.H.
2008-01-01
We describe experiments investigating the (coherence) properties of a finite-temperature one-dimensional (1D) Bose gas with repulsive interactions. The confining magnetic field is generated with a micro-electronic circuit. This microtrap for atoms or `atom chip' is particularly suited to generate a
Quantum Dynamics of One-Dimensional Nanocrystalline Solids
丁建文; 颜晓红; 曹觉先; 王登龙
2002-01-01
A novel ballistic-nonballistic dynamic transition in one-dimensional nanocrystalline solids is found upon varyingthe strength of the composition modulation and the grain-boundary effect. This can contribute to the under-standing of the strange electronic transport properties of nanostructured systems.
One-dimensional models of thermal activation under shear stress
Nabarro, FRN
2003-01-01
Full Text Available The analysis of thermal activation under shear stress in three- and even two-dimensional models presents unresolved problems. The analysis of one-dimensional models presented here may illuminate the study of more realistic models. For the model...
How good are one-dimensional Josephson junction models?
Lomdahl, P. S.; Olsen, O.H.; Eilbeck, J. C.
1985-01-01
A two-dimensional model of Josephson junctions of overlap type is presented and shown to reduce to the usual one-dimensional (1D) model in the limit of a very narrow junction. Comparisons between the stability limits for fluxon reflection obtained from the two models suggest that the many results...
Quasi-one-dimensional intermittent flux behavior in superconducting films
Qviller, A. J.; Yurchenko, V. V.; Galperin, Y. M.
2012-01-01
. The intermittent behavior shows no threshold value in the applied field, in contrast to conventional flux jumping. The results strongly suggest that the quasi-one-dimensional flux jumps are of a different nature than the thermomagnetic dendritic (branching) avalanches that are commonly found in superconducting...
Radiative decay of the one-dimensional large acoustic polaron
Ivic, Zoran; Zekovic, Slobodan; Przulj, Zeljko
2002-12-30
Finite temperature dynamics and stability of the adiabatic large acoustic polaron in one-dimensional systems have been examined by means of the perturbation method based upon the inverse scattering transform. Polaron life-time was estimated in dependence of temperature and electron (exciton)-phonon coupling constant.
An algebraic study of unitary one dimensional quantum cellular automata
Arrighi, P
2005-01-01
We provide algebraic characterizations of unitary one dimensional quantum cellular automata. We do so both by algebraizing existing decision procedures, and by adding constraints into the model which do not change the quantum cellular automata's computational power. The configurations we consider have finite but unbounded size.
Novel Progress in One-Dimensional Carbon Nanotubes Studies
无
2004-01-01
@@ One-dimensional carbon nanotubes (CNT) have received considerable attention from researchers worldwide. It is not only because of their unique physical properties, but also their potential applications. Recently, researchers of the CAS Institute of Physics have made new progress in the field.
Quantum transport in strongly interacting one-dimensional nanostructures
Agundez, R. R.
2015-01-01
In this thesis we study quantum transport in several one-dimensional systems with strong electronic interactions. The first chapter contains an introduction to the concepts treated throughout this thesis, such as the Aharonov-Bohm effect, the Kondo effect, the Fano effect and quantum state transfer.
Bloch oscillations in an aperiodic one-dimensional potential
de Moura, FABF; Lyra, ML; Dominguez-Adame, F; Malyshev, V.A.
2005-01-01
We study the dynamics of an electron subjected to a static uniform electric field within a one-dimensional tight-binding model with a slowly varying aperiodic potential. The unbiased model is known to support phases of localized and extended one-electron states separated by two mobility edges. We sh
Quantum dynamics of one-dimensional nanocrystalline solids
Ding Jian Wen; Cao Jue Xian; Wang Deng Long
2002-01-01
A novel ballistic-non-ballistic dynamic transition in one-dimensional nanocrystalline solids is found upon varying the strength of the composition modulation and the grain-boundary effect. This can contribute to the understanding of the strange electronic transport properties of nano-structured systems
Exact results for one dimensional fluids through functional integration
Fantoni, Riccardo
2016-01-01
We review some of the exactly solvable one dimensional continuum fluid models of equilibrium classical statistical mechanics under the unified setting of functional integration in one dimension. We make some further developments and remarks concerning fluids with penetrable particles. We then apply our developments to the study of the Gaussian core model for which we are unable to find a well defined thermodynamics.
Transport through a Finite One-Dimensional Crystal
Kouwenhoven, L.P.; Hekking, F.W.J.; Wees, B.J. van; Harmans, C.J.P.M.; Timmering, C.E.; Foxon, C.T.
1990-01-01
We have studied the magnetotransport properties of an artificial one-dimensional crystal. The crystal consists of a sequence of fifteen quantum dots, defined in the two-dimensional electron gas of a GaAs/AlGaAs heterostructure by means of a split-gate technique. At a fixed magnetic field of 2 T, two
Vázquez, Marco-Vinicio; Dagdug, Leonardo
2010-12-01
Computer simulations of the diffusion of a Brownian particle, in a hemispherical shaped tube, were carried out to assess the range of applicability of the reduction of the three-dimensional diffusion to an effective one-dimensional description. Previously Berezhkovskii et al. [21] founded that the one-dimensional description centered in the Fick-Jacobs' equation with a position dependent diffusion coefficients, D(x) (one due to R. Zwanzig [14], and another by Reguera-Rubí [15]), has a restricted range of applicability, for a conical tube. Remarkably, our results have shown that applying the Zwanzig's formula one can predict variation of τ in the whole range of a/R in n→w direction, while the Reguera-Rubí's formula fits simulations' data in the w→n direction. This is an important result since it is known that Reguera-Rubí's predicts better the mean first-passage time's behavior without regard of direction in other geometries, and this is our principal result.
Humbird, David; Trendewicz, Anna; Braun, Robert; Dutta, Abhijit
2017-01-27
A biomass fast pyrolysis reactor model with detailed reaction kinetics and one-dimensional fluid dynamics was implemented in an equation-oriented modeling environment (Aspen Custom Modeler). Portions of this work were detailed in previous publications; further modifications have been made here to improve stability and reduce execution time of the model to make it compatible for use in large process flowsheets. The detailed reactor model was integrated into a larger process simulation in Aspen Plus and was stable for different feedstocks over a range of reactor temperatures. Sample results are presented that indicate general agreement with experimental results, but with higher gas losses caused by stripping of the bio-oil by the fluidizing gas in the simulated absorber/condenser. This integrated modeling approach can be extended to other well-defined, predictive reactor models for fast pyrolysis, catalytic fast pyrolysis, as well as other processes.
A Dynamical Formulation of One-Dimensional Scattering Theory and Its Applications in Optics
Mostafazadeh, Ali
2013-01-01
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrodinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, anti-lasing, and unidirectional invisibility.
Coupled mode analysis of a periodic one-dimensional multimodal fiber bundle
Shlivinski, Amir
2016-10-01
This contribution is a mathematical analysis of the coupled mode equations of a one dimensional infinite periodic lattice of multimodal adjacent fibers that are fused together (a "fiber bundle"). As such, it provides a systematic and detailed derivation of the coupled mode equations and their eigen (modal) solutions within a matrix-based framework and using Z -transform spectral-based formulation. The resulting solution is general in the sense that it is not restricted to a particular dielectric profile of the fibers. Moreover, under a weak coupling assumption, the modal solution clearly identifies the physical building blocks of the solution.
One-Dimensional Stationary Mean-Field Games with Local Coupling
Gomes, Diogo A.
2017-05-25
A standard assumption in mean-field game (MFG) theory is that the coupling between the Hamilton–Jacobi equation and the transport equation is monotonically non-decreasing in the density of the population. In many cases, this assumption implies the existence and uniqueness of solutions. Here, we drop that assumption and construct explicit solutions for one-dimensional MFGs. These solutions exhibit phenomena not present in monotonically increasing MFGs: low-regularity, non-uniqueness, and the formation of regions with no agents.
Direct Current Hopping Conductivity in One-Dimensional Nanometre Systems
宋祎璞; 徐慧; 罗峰
2003-01-01
A one-dimensional random nanocrystalline chain model is established. A dc electron-phonon-field conductance model of electron tunnelling transfer is set up, and a new dc conductance formula in one-dimensional nanometre systems is derived. By calculating the dc conductivity, the relationship among the electric field, temperature and conductivity is analysed, and the effect of the crystalline grain size and the distortion of interfacial atoms on the dc conductance is discussed. The result shows that the nanometre system appears the characteristic of negative differential dependence of resistance and temperature at low temperature. The dc conductivity of nanometre systems varies with the change of electric field and trends to rise as the crystalline grain size increases and to decrease as the distorted degree of interfacial atoms increases.
True Bilayer Exciton Condensate of One-Dimensional Electrons
Kantian, A.; Abergel, D. S. L.
2017-07-01
We theoretically predict that a true bilayer exciton condensate, characterized by off-diagonal long-range order and global phase coherence, can be created in one-dimensional solid state electron systems. The mechanism by which this happens is to introduce a single particle hybridization of electron and hole populations, which locks the phase of the relevant mode and hence invalidates the Mermin-Wagner theorem. Electron-hole interactions then amplify this tendency towards off-diagonal long-range order, enhancing the condensate properties by more than an order of magnitude over the noninteracting limit. We show that the temperatures below which a substantial condensate fraction would form could reach hundreds of Kelvin, a benefit of the weak screening in one-dimensional systems.
Resonance Raman spectroscopy in one-dimensional carbon materials
Dresselhaus Mildred S.
2006-01-01
Full Text Available Brazil has played an important role in the development and use of resonance Raman spectroscopy as a powerful characterization tool for materials science. Here we present a short history of Raman scattering research in Brazil, highlighting the important contributions to the field coming from Brazilian researchers in the past. Next we discuss recent and important contributions where Brazil has become a worldwide leader, that is on the physics of quasi-one dimensional carbon nanotubes. We conclude this article by presenting results from a very recent resonance Raman study of exciting new materials, that are strictly one-dimensional carbon chains formed by the heat treatment of very pure double-wall carbon nanotube samples.
One-dimensional Si nanolines in hydrogenated Si(001)
François, Bianco; Köster, Sigrun A.; Owen, James G. H.; Renner, Christoph; Bowler, David R.
2012-02-01
We present a detailed study of the structural and electronic properties of a self-assembled silicon nanoline embedded in the H-terminated silicon (001) surface, known as the Haiku stripe. The nanoline is a perfectly straight and defect free endotaxial structure of huge aspect ratio; it can grow micrometre long at a constant width of exactly four Si dimers (1.54 nm). Another remarkable property is its capacity to be exposed to air without suffering any degradation. The nanoline grows independently of any step edges at tunable densities, from isolated nanolines to a dense array of nanolines. In addition to these unique structural characteristics, scanning tunnelling microscopy and density functional theory reveal a one-dimensional state confined along the Haiku core. This nanoline is a promising candidate for the long sought after electronic solid-state one-dimensional model system to explore the fascinating quantum properties emerging in such reduced dimensionality. Phys. Rev. B, 84, 035328 (2011)
Luttinger parameter of quasi-one-dimensional para -H2
Ferré, G.; Gordillo, M. C.; Boronat, J.
2017-02-01
We have studied the ground-state properties of para-hydrogen in one dimension and in quasi-one-dimensional configurations using the path-integral ground-state Monte Carlo method. This method produces zero-temperature exact results for a given interaction and geometry. The quasi-one-dimensional setup has been implemented in two forms: the inner channel inside a carbon nanotube coated with H2 and a harmonic confinement of variable strength. Our main result is the dependence of the Luttinger parameter on the density within the stable regime. Going from one dimension to quasi-one dimension, keeping the linear density constant, produces a systematic increase of the Luttinger parameter. This increase is, however, not enough to reach the superfluid regime and the system always remain in the quasicrystal regime, according to Luttinger liquid theory.
Kinetic properties of small one-dimensional Ising magnetic
Udodov, Vladimir; Spirin, Dmitriy; Katanov Khakas State University Team
2011-03-01
Within the framework of a generalized Ising model, a one-dimensional magnetic of a finite length with free ends is considered. The correlation length critical exponent ν and kinetic critical exponent z of the magnet is calculated taking into account the next nearest neighbor interactions and the external field. Of special interest are non-equilibrium processes taking place within the critical temperature interval, which are characterized critical exponent y and dynamic critical index z . Due to significant difficulties encountered in the experimental investigations (e.g., measurement of z) , a natural solution to this complex problem would be modeling of those non-eqilibrium processes. This work addresses non-equilibrium processes in one-dimensional magnetics. Using the Monte Carlo method, an equilibrium critical exponent of the correlation length ν and the dynamic critical index z are calculated for a finite-size magnetic.
Dark Matter in a One-dimensional Universe
Sigismondi, C
2003-01-01
A computer code to simulate temporal evolution of overdensities in a one-dimensional Universe is presented for didactic purposes. The formation of large scale structures in this one-dimensional universe can be studied both in matter or radiation dominated eras. Since large scale structures are already observed at z > 7, primordial dark matter overdensities delta_DM which are 90 times larger than the observed barionic delta_B in the cosmic microwave background are required at z~1000. This makes possible non-linear gravitational collapse at redshift z >7 and the formation of the structures. Primordial perturbations delta_B~10^-5 do not leave the linear regime of growth without the aid of dark matter's potential wells. This code is suitable for commercial worksheets like MSExcel, StarOffice, or OpenOffice.
The Quantum Well of One-Dimensional Photonic Crystals
Xiao-Jing Liu
2015-01-01
Full Text Available We have studied the transmissivity of one-dimensional photonic crystals quantum well (QW with quantum theory approach. By calculation, we find that there are photon bound states in the QW structure (BA6(BBABBn(AB6, and the numbers of the bound states are equal to n+1. We have found that there are some new features in the QW, which can be used to design optic amplifier, attenuator, and optic filter of multiple channel.
Bose gases in one-dimensional harmonic trap
JI-XUAN HOU; JING YANG
2016-10-01
Thermodynamic quantities, occupation numbers and their fluctuations of a one-dimensional Bose gas confined by a harmonic potential are studied using different ensemble approaches. Combining number theory methods, a new approach is presented to calculate the occupation numbers of different energy levels in microcanonical ensemble. The visible difference of the ground state occupation number in grand-canonical ensemble and microcanonical ensemble is found to decrease by power law as the number of particles increases.
ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Nikola Stefanović
2007-01-01
In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic ...
Butz, Susanne
2014-01-01
This thesis presents a novel approach to the experimental realization of tunable, superconducting metamaterials. Therefore, conventional resonant meta-atoms are replaced by meta-atoms that contain Josephson junctions, which renders their resonance frequency tunable by an external magnetic field. This tunability is theoretically and experimentally investigated in one-dimensional magnetic and electric metamaterials. For the magnetic metamaterial, the effective, magnetic permeability is determined.
Few interacting fermions in one-dimensional harmonic trap
Sowiński, Tomasz; Dutta, Omjyoti; Lewenstein, Maciej
2013-01-01
We study spin-1/2 fermions, interacting via a two-body contact potential, in a one-dimensional harmonic trap. Applying exact diagonalization, we investigate the behavior at finite interaction strength, and discuss the role of a ground state degeneracy which occurs for sufficiently strong repulsive interaction. Even low temperature or a completely depolarizing channel may then dramatically influence the system's behavior. We calculate level occupation numbers as signatures of thermalization, and we discuss the mechanisms to break the degeneracy.
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
Alexander A. Andrianov
2009-06-01
Full Text Available When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.
Thermal breakage of a discrete one-dimensional string.
Lee, Chiu Fan
2009-09-01
We study the thermal breakage of a discrete one-dimensional string, with open and fixed ends, in the heavily damped regime. Basing our analysis on the multidimensional Kramers escape theory, we are able to make analytical predictions on the mean breakage rate and on the breakage propensity with respect to the breakage location on the string. We then support our predictions with numerical simulations.
PT-invariant one-dimensional Coulomb problem
Sinha, A K; Sinha, Anjana; Roychoudhury, Rajkumar
2002-01-01
The one-dimensional Coulomb-like potential with a real coupling constant beta, and a centrifugal-like core of strength G = alpha^2 - {1/4}, viz. V(x) = {alpha^2 - (1/4)}/{(x-ic)^2} + beta/|x-ic|, is discussed in the framework of PT-symmetry. The PT-invariant exactly solvable model so formed, is found to admit a double set of real and discrete energies, numbered by a quasi-parity q = +/- 1.
Impurity modes in the one-dimensional XXZ Heisenberg model
Sousa, J.M. [Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portella, 57072-970 Teresina, Piauí (Brazil); Leite, R.V. [Centro de Ciências Exatas e Tecnologia, Curso de Física, Universidade Estadual Vale do Acaraú, Av. Dr. Guarany 317, Campus Cidao, 62040-730 Sobral, Ceará (Brazil); Landim, R.R. [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil); Costa Filho, R.N., E-mail: rai@fisica.ufc.br [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil)
2014-04-01
A Green's function formalism is used to calculate the energy of impurity modes associated with one and/or two magnetic impurities in the one-dimensional Heisenberg XXZ magnetic chain. The system can be tuned from the Heisenberg to the Ising model varying a parameter λ. A numerical study is performed showing two types of localized modes (s and p). The modes depend on λ and the degeneracy of the acoustic modes is broken.
Universal correlations of one-dimensional electrons at low density
Göhmann, F.
2000-01-01
We summarize results on the asymptotics of the two-particle Green functions of interacting electrons in one dimension. Below a critical value of the chemical potential the Fermi surface vanishes, and the system can no longer be described as a Luttinger liquid. Instead, the non-relativistic Fermi gas with infinite point-like repulsion becomes the universal model for the long-wavelength, low temperature physics of the one-dimensional electrons. This model, which we call the impenetrable electro...
One Dimensional Polymeric Organic Photonic Crystals for DFB Lasers
F. Scotognella
2008-01-01
Full Text Available We present a very simple method to realize a one-dimensional photonic crystal (1D PC, consisting of a dye-doped polymeric multilayer. Due to the high photonic density of states at the edges of the photonic band-gap (PBG, a surface emitting distributed feedback (DFB laser is obtained with this structure. Furthermore, the incidence angle dependence of the PBG of the polymeric multilayer is reported.
PERIODIC SOLUTIONS IN ONE-DIMENSIONAL COUPLED MAP LATTICES
郑永爱; 刘曾荣
2003-01-01
It is proven that the existence of nonlinear solutions with time period in one-dimensional coupled map lattice with nearest neighbor coupling. This is a class of systemswhose behavior can be regarded as infinite array of coupled oscillators. A method forestimating the critical coupling strength below which these solutions with time period persistis given. For some particular nonlinear solutions with time period, exponential decay inspace is proved.
One-dimensional photonic crystals bound by light
Cui, Liyong; Li, Xiao; Chen, Jun; Cao, Yongyin; Du, Guiqiang; Ng, Jack
2017-08-01
Through rigorous simulations, the light scattering induced optical binding of one-dimensional (1D) dielectric photonic crystals is studied. The optical forces corresponding to the pass band, band gap, and band edge are qualitatively different. It is shown that light can induce self-organization of dielectric slabs into stable photonic crystals, with its lower band edge coinciding with the incident light frequency. Incident light at normal and oblique incidence and photonic crystals with parity-time symmetry are also considered.
One-dimensional contact process: duality and renormalization.
Hooyberghs, J; Vanderzande, C
2001-04-01
We study the one-dimensional contact process in its quantum version using a recently proposed real-space renormalization technique for stochastic many-particle systems. Exploiting the duality and other properties of the model, we can apply the method for cells with up to 37 sites. After suitable extrapolation, we obtain exponent estimates that are comparable in accuracy with the best known in the literature.
Correlation functions of one-dimensional bosons at low temperature
Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M. [CNRS, ENS Lyon (France). Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Institute, Moscow (Russian Federation)
2010-12-15
We consider the low-temperature limit of the long-distance asymptotic behavior of the finite temperature density-density correlation function in the one-dimensional Bose gas derived recently in the algebraic Bethe Ansatz framework. Our results confirm the predictions based on the Luttinger liquid and conformal field theory approaches. We also demonstrate that the amplitudes arising in this asymptotic expansion at low-temperature coincide with the amplitudes associated with the so-called critical form factors. (orig.)
The one-dimensional extended Bose-Hubbard model
Ramesh V Pai; Rahul Pandit
2003-10-01
We use the finite-size, density-matrix-renormalization-group (DMRG) method to obtain the zero-temperature phase diagram of the one-dimensional, extended Bose-Hubbard model, for mean boson density ρ = 1, in the - plane ( and are respectively, onsite and nearest-neighbour repulsive interactions between bosons). The phase diagram includes superfluid (SF), bosonic-Mott-insulator (MI), and mass-density-wave (MDW) phases. We determine the natures of the quantum phase transitions between these phases.
Statistics of resonances in one-dimensional continuous systems
Joshua Feinberg
2009-09-01
We study the average density of resonances (DOR) of a disordered one-dimensional continuous open system. The disordered system is semi-infinite, with white-noise random potential, and it is coupled to the external world by a semi-infinite continuous perfect lead. Our main result is an integral representation for the DOR which involves the probability density function of the logarithmic derivative of the wave function at the contact point.
Negative Refraction Angular Characterization in One-Dimensional Photonic Crystals
Jesus Eduardo Lugo; Rafael Doti; Jocelyn Faubert
2011-01-01
BACKGROUND: Photonic crystals are artificial structures that have periodic dielectric components with different refractive indices. Under certain conditions, they abnormally refract the light, a phenomenon called negative refraction. Here we experimentally characterize negative refraction in a one dimensional photonic crystal structure; near the low frequency edge of the fourth photonic bandgap. We compare the experimental results with current theory and a theory based on the group velocity d...
Exchange effects in a quasi-one-dimensional electron gas
Gold, A.; Ghazali, A.
1990-04-01
We calculate the electron exchange of a quasi-one-dimensional electron gas in a quantum-well wire of radius R0. A two-subband model is considered and the exchange self-energy for the first and second subband is calculated under the assumption that only the lowest subband is partially filled with electrons. Band-bending effects are also discussed. Results for the total energy per electron including kinetic and exchange energy are presented.
Topological modes in one-dimensional solids and photonic crystals
Atherton, Timothy J.; Butler, Celia A. M.; Taylor, Melita C.; Hooper, Ian R.; Hibbins, Alastair P.; Sambles, J. Roy; Mathur, Harsh
2016-03-01
It is shown theoretically that a one-dimensional crystal with time-reversal and particle-hole symmetries is characterized by a topological invariant that predicts the existence or otherwise of edge states. This is confirmed experimentally through the construction and simulation of a photonic crystal analog in the microwave regime. It is shown that the edge mode couples to modes external to the photonic crystal via a Fano resonance.
One-dimensional photonic band gaps in optical lattices
Samoylova, Marina; Holynski, Michael; Courteille, Philippe Wilhelm; Bachelard, Romain
2013-01-01
The phenomenon of photonic band gaps in one-dimensional optical lattices is reviewed using a microscopic approach. Formally equivalent to the transfer matrix approach in the thermodynamic limit, a microscopic model is required to study finite-size effects, such as deviations from the Bragg condition. Microscopic models describing both scalar and vectorial light are proposed, as well as for two- and three-level atoms. Several analytical results are compared to experimental data, showing a good agreement.
Morphology-Controlled Growth of AIN One-Dimensional Nanostructures
Ting XIE; Min YE; Xiaosheng FANG; Zhi JIANG; Li CHEN; Mingguang KONG; Yucheng WU; Lide ZHANG
2008-01-01
Aluminum nitride (AIN) nanowires, serrated nanoribbons, and nanoribbons were selectively obtained through a simple chloride assisted chemical vapor deposition process. The morphologies of the products could be controlled by adjusting the deposition position and the flux of the reactant gas. The morphologies and structures of the AIN products were investigated in detail. The formation mechanism of the as-prepared different morphologies of AIN one-dimensional (1D) nanostructures was discussed on the basis of the experimental results.
Analysis of necking based on a one-dimensional model
Audoly, Basile; Hutchinson, John W.
2016-12-01
Dimensional reduction is applied to derive a one-dimensional energy functional governing tensile necking localization in a family of initially uniform prismatic solids, including as particular cases rectilinear blocks in plane strain and cylindrical bars undergoing axisymmetric deformations. The energy functional depends on both the axial stretch and its gradient. The coefficient of the gradient term is derived in an exact and general form. The one-dimensional model is used to analyze necking localization for nonlinear elastic materials that experience a maximum load under tensile loading, and for a class of nonlinear materials that mimic elastic-plastic materials by displaying a linear incremental response when stretch switches from increasing to decreasing. Bifurcation predictions for the onset of necking from the simplified theory compared with exact results suggest the approach is highly accurate at least when the departures from uniformity are not too large. Post-bifurcation behavior is analyzed to the point where the neck is fully developed and localized to a region on the order of the thickness of the block or bar. Applications to the nonlinear elastic and elastic-plastic materials reveal the highly unstable nature of necking for the former and the stable behavior for the latter, except for geometries where the length of the block or bar is very large compared to its thickness. A formula for the effective stress reduction at the center of a neck is established based on the one-dimensional model, which is similar to that suggested by Bridgman (1952).
Gravitational anomalies and one-dimensional behavior of black holes
Majhi, Bibhas Ranjan, E-mail: bibhas.majhi@iitg.ernet.in [Department of Physics, Indian Institute of Technology Guwahati, 781039, Guwahati, Assam (India)
2015-12-08
It has been pointed out by Bekenstein and Mayo that the behavior of the black hole’s entropy or information flow is similar to information flow through one-dimensional channel. Here I analyze the same issue with the use of gravitational anomalies. The rate of the entropy change (S{sup .}) and the power (P) of the Hawking emission are calculated from the relevant components of the anomalous stress tensor under the Unruh vacuum condition. I show that the dependence of S{sup .} on the power is S{sup .} ∝P{sup 1/2}, which is identical to that for the information flow in a one-dimensional system. This is established by using the (1+1)-dimensional gravitational anomalies first. Then the fact is further bolstered by considering the (1+3)-dimensional gravitational anomalies. It is found that, in the former case, the proportionality constant is exactly identical to the one-dimensional situation, known as Pendry’s formula, while in the latter situation its value decreases.
Gravitational anomalies and one-dimensional behavior of black holes
Majhi, Bibhas Ranjan [Indian Institute of Technology Guwahati, Department of Physics, Guwahati, Assam (India)
2015-12-15
It has been pointed out by Bekenstein and Mayo that the behavior of the black hole's entropy or information flow is similar to information flow through one-dimensional channel. Here I analyze the same issue with the use of gravitational anomalies. The rate of the entropy change (S) and the power (P) of the Hawking emission are calculated from the relevant components of the anomalous stress tensor under the Unruh vacuum condition. I show that the dependence of S on the power is S ∝ P{sup 1/2}, which is identical to that for the information flow in a one-dimensional system. This is established by using the (1+1)-dimensional gravitational anomalies first. Then the fact is further bolstered by considering the (1+3)-dimensional gravitational anomalies. It is found that, in the former case, the proportionality constant is exactly identical to the one-dimensional situation, known as Pendry's formula, while in the latter situation its value decreases. (orig.)
Gravitational anomalies and one dimensional behaviour of black holes
Majhi, Bibhas Ranjan
2015-01-01
It has been pointed out by Bekenstein and Mayo that the behavior of the Black hole's entropy or information flow is similar to that through one-dimensional channel. Here I analyse the same issue with the use of gravitational anomalies. The rate of the entropy change ($\\dot{S}$) and the power ($P$) of the Hawking emission are calculated from the relevant components of the anomalous stress-tensor under the Unruh vacuum condition. I show that the dependence of $\\dot{S}$ on power is $\\dot{S}\\propto P^{1/2}$ which is identical to that for the information flow in one dimensional system. This is established by using the ($1+1$) dimensional gravitational anomalies first. Then the fact is further bolstered by considering the ($1+3$) dimensional gravitational anomalies. It is found that in the former case, the proportionality constant is exactly identical to one dimensional situation, known as Pendry's formula, while in later situation its value decreases.
Hu, Zi-Song; Takahashi, Kengo; Tsuchiya, Yoshimi
1994-02-01
Transient behaviors in self-sustained oscillation of a plasmodial strand of Physarum polycephalum have been investigated for various external loads under isotonic conditions. Synchronization between divisions of the strand has been observed in its formation process, which shows that the plasmodial strand can be considered as a one-dimensionally coupled oscillator system. The synchronization has been found to proceed faster with increasing external load applied to the strand. It has furthermore been found that the rate of increase of the amplitude of oscillation increases with the load, whereas the temporal behavior of its period is independent of the load. These results show that the oscillators themselves in the plasmodial strand do not depend on the external load, but the coupling between these oscillators is strongly affected with the external load. The experimental results have also been simulated on the basis of one-dimensionally coupled van der Pol equations.
Three species one-dimensional kinetic model for weakly ionized plasmas
Gonzalez, J; Tierno, S P
2016-01-01
A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma dynamics evolves in the privileged direction of the field. The energy transmitted to the charges is be channelized to the neutrals thanks to collisions and impacting the plasma dynamics. Charge-charge interactions have been designed as a one dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift diffusion operator in the Doughertys form. The resulting set of coupled drift diffusion equations is solved with the stable and robust Propagator Integral Method. This method feasibility accounts for non-linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions. It is found that charge neutral collisions exert a significant effect sin...
Thermodynamics of a one-dimensional self-gravitating gas with periodic boundary conditions
Kumar, Pankaj; Miller, Bruce N.; Pirjol, Dan
2017-02-01
We study the thermodynamic properties of a one-dimensional gas with one-dimensional gravitational interactions. Periodic boundary conditions are implemented as a modification of the potential consisting of a sum over mirror images (Ewald sum), regularized with an exponential cutoff. As a consequence, each particle carries with it its own background density. Using mean-field theory, we show that the system has a phase transition at a critical temperature. Above the critical temperature the gas density is uniform, while below the critical point the system becomes inhomogeneous. Numerical simulations of the model, which include the caloric curve, the equation of state, the radial distribution function, and the largest Lyapunov exponent, confirm the existence of the phase transition, and they are in good agreement with the theoretical predictions.
Invariant for one-dimensional heat conduction in dielectrics and metals
Sajadi, Seyed Mohammad; Ordonez-Miranda, Jose; Hill, James M.; Ezzahri, Younès; Joulain, Karl; Ghasemi, Hadi
2017-05-01
We theoretically and experimentally demonstrate that the one-dimensional heat conduction in dielectrics and metals is ruled by the invariant T^4(z)+T^4(L-z)=\\text{constant} , where T is the temperature and z an arbitrary position within the heated material of length L. This is achieved using the integral expressions predicted by the Boltzmann transport equation, under the gray relaxation time approximation, for the steady-state temperature and heat flux, and measuring the temperature at three equidistant positions in rods of Si, Cu, and Fe-C excited with temperatures much smaller than their corresponding Debye ones. The obtained temperature invariant for symmetrical positions could be applied to describe the heating of materials supporting one-dimensional heat conduction.
Pikichyan, H. V.
2016-06-01
It is shown that for the nonlinear boundary value problem of determining the radiation field inside a one-dimensional anisotropic medium illuminated from outside at its boundaries on both sides, the formulas for adding layers in semilinear systems of differential equations for radiative transfer, invariant embedding, and total Ambartsumyan invariance can be used to reduce the equations for the problem to separable equations with initial conditions. The fields travelling to the left and right are thereby found independently of one another. In addition, when one of them has been determined, the other can be found directly using an explicit expression. A general equivalence property of operators with respect to a certain mathematical form, expression, or functional is formulated mathematically. New equations, referred to as kinetic equations of equivalency, are derived from the mutual equivalence of the differential operators of the Boltzmann kinetic equation (the equations of radiative transfer) and the functional equation of the Ambartsumian's complete invariance. Besides separability, these new equations also have the property of linearity. Formulas are also introduced for special problems of single sided illumination of a medium that in this case serve as supplementary information in the initial conditions for formulating Cauchy problems.
One-dimensional Transport Simulation of Pollutants in Natural Streams
Mostafa Ramezani
2016-10-01
Full Text Available Rivers are the main sources of freshwater systems which governments need to manage and plan to maintain them as per an acceptable quality. In this research, a numerical scheme was used and implemented in MATLAB to provide a one-dimensional water quality tool. This code then was tested with two datasets of Chattahoochee and Mackinaw rivers. To evaluate the model performance, results and sampled data were checked in terms of conformity by using three metrics: CE, MARE, and RMSE. Results were almost near to observed data and metrics’ values were found satisfactory, showing that the employed numerical approach is an appropriate method for surface water quality planning and management.
Universality of anomalous one-dimensional heat conductivity
Lepri, Stefano; Livi, Roberto; Politi, Antonio
2003-12-01
In one and two dimensions, transport coefficients may diverge in the thermodynamic limit due to long-time correlation of the corresponding currents. The effective asymptotic behavior is addressed with reference to the problem of heat transport in one-dimensional crystals, modeled by chains of classical nonlinear oscillators. Extensive accurate equilibrium and nonequilibrium numerical simulations confirm that the finite-size thermal conductivity diverges with system size L as κ∝Lα. However, the exponent α deviates systematically from the theoretical prediction α=1/3 proposed in a recent paper [O. Narayan and S. Ramaswamy, Phys. Rev. Lett. 89, 200601 (2002)].
On Global One-Dimensionality proposal in Quantum General Relativity
Glinka, L A
2008-01-01
Quantum General Relativity, better known as Quantum Gravity with additional epithets, currently is faraway from phenomenology. This mental crisis leads at most to empty hypotheses, but not to realistic physics. However, there exists the way, investigated by Dirac, which is constructive for experimental data predictions in astrophysics, high energy physics, and condensed matter physics. It is Field Theory. This article presents certain proposal for new discussion. General Relativity in 3+1 metric field gauge and its canonical quantization is developed. Reduction of the quantum geometrodynamics to Global One-Dimensional bosonic field theory, its quantization, and some conclusions are presented.
Exactly integrable analogue of a one-dimensional gravitating system
Miller, Bruce N. [Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129 (United States)]. E-mail: b.miller@tcu.edu; Yawn, Kenneth R. [Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129 (United States); Maier, Bill [Department of Physics and Astronomy, Texas Christian University, Fort Worth, TX 76129 (United States)
2005-10-10
Exchange symmetry in acceleration partitions the configuration space of an N particle one-dimensional gravitational system (OGS) into N{exclamation_point} equivalent cells. We take advantage of the resulting small angular separation between the forces in neighboring cells to construct a related integrable version of the system that takes the form of a central force problem in N-1 dimensions. The properties of the latter, including the construction of trajectories and possible continuum limits, are developed. Dynamical simulation is employed to compare the two models. For some initial conditions, excellent agreement is observed.
Fluctuation dissipation ratio in the one dimensional kinetic Ising model
Lippiello, E.; Zannetti, M.
2000-01-01
The exact relation between the response function $R(t,t^{\\prime})$ and the two time correlation function $C(t,t^{\\prime})$ is derived analytically in the one dimensional kinetic Ising model subjected to a temperature quench. The fluctuation dissipation ratio $X(t,t^{\\prime})$ is found to depend on time through $C(t,t^{\\prime})$ in the time region where scaling $C(t,t^{\\prime}) = f(t/t^{\\prime})$ holds. The crossover from the nontrivial form $X(C(t,t^{\\prime}))$ to $X(t,t^{\\prime}) \\equiv 1$ t...
Enhanced dipolar transport in one-dimensional waveguide arrays
Cantillano, Camilo; Real, Bastián; Rojas-Rojas, Santiago; Delgado, Aldo; Szameit, Alexander; Vicencio, Rodrigo A
2016-01-01
We study the transport properties of fundamental and dipolar (first-excited) modes on one-dimensional coupled waveguide arrays. By modulating an optical beam, we are able to generate fundamental and dipolar modes to study discrete diffraction (single-site excitation) and gaussian beam propagation (multi-site excitation \\& phase gradient). We find that dipolar modes experience a coupling constant more than two times larger than the one for fundamental modes. This implies an enhanced transport of energy for dipoles in a tight-binding lattice. Additionally, we study disordered systems and find that while fundamental modes are already trapped in a weakly disorder array, dipoles still diffract across the lattice.
Impedance of rigid bodies in one-dimensional elastic collisions
Santos, Janilo; de Oliveira, Bruna P. W.; Nelson,Osman Rosso
2012-01-01
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand efficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the probl...
Quantum Simulations of One-Dimensional Nanostructures under Arbitrary Deformations
Koskinen, Pekka
2016-09-01
A powerful technique is introduced for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching. The technique is based on an unconventional control of periodic symmetry which eliminates artifacts due to deformation constraints and quantum finite-size effects and allows transparent electronic-structure analysis. Via density-functional tight-binding implementation, the technique demonstrates its utility by predicting nonlinear electromechanical properties in carbon nanotubes and abrupt behavior in the structural yielding of Au7 and Mo6 S6 nanowires. The technique drives simulations markedly closer to the realistic modeling of these slender nanostructures under experimental conditions.
Beam interactions in one-dimensional saturable waveguide arrays
Stepic, M; Rueter, C E; Shandarov, V; Kip, D; Stepic, Milutin; Smirnov, Eugene; Rueter, Christian E.; Shandarov, Vladimir; Kip, Detlef
2006-01-01
The interaction between two parallel beams in one-dimensional discrete saturable systems has been investigated using lithium niobate nonlinear waveguide arrays. When the beams are separated by one channel and in-phase it is possible to observe soliton fusion at low power levels. This new result is confirmed numerically. By increasing the power, soliton-like propagation of weakly-coupled beams occurs. When the beams are out-of-phase the most interesting result is the existence of oscillations which resemble the recently discovered Tamm oscillations.
Waves and instability in a one-dimensional microfluidic array
Liu, Bin; Feng, Yan
2012-01-01
Motion in a one-dimensional (1D) microfluidic array is simulated. Water droplets, dragged by flowing oil, are arranged in a single row, and due to their hydrodynamic interactions spacing between these droplets oscillates with a wave-like motion that is longitudinal or transverse. The simulation yields wave spectra that agree well with experiment. The wave-like motion has an instability which is confirmed to arise from nonlinearities in the interaction potential. The instability's growth is spatially localized. By selecting an appropriate correlation function, the interaction between the longitudinal and transverse waves is described.
Fragmented one dimensional man / El hombre unidimensional fragmentado
Juan Antonio Rodríguez del Pino
2013-10-01
Full Text Available Paraphrase the title of the famous essay by Herbert Marcuse, since the image has traditionally been generated of man, masculinity, has been one-dimensional. I mean, the man was characterized by traits and behaviors established and entrenched since ancient time, considering all other distinguishing signs as mere deviations from the normative improper. But observe that this undeniable reality, as analyzed various researchers through what has come to be called Men's studies, has proven to be a fallacy difficult to maintain throughout history and today turns into fallacious and ineffective against changes in our current existing corporate models.
Molecular nanostamp based on one-dimensional porphyrin polymers.
Kanaizuka, Katsuhiko; Izumi, Atsushi; Ishizaki, Manabu; Kon, Hiroki; Togashi, Takanari; Miyake, Ryosuke; Ishida, Takao; Tamura, Ryo; Haga, Masa-aki; Moritani, Youji; Sakamoto, Masatomi; Kurihara, Masato
2013-08-14
Surface design with unique functional molecules by a convenient one-pot treatment is an attractive project for the creation of smart molecular devices. We have employed a silane coupling reaction of porphyrin derivatives that form one-dimensional polymer wires on substrates. Our simple one-pot treatment of a substrate with porphyrin has successfully achieved the construction of nanoscale bamboo shoot structures. The nanoscale bamboo shoots on the substrates were characterized by atomic force microscopy (AFM), UV-vis spectra, and X-ray diffraction (XRD) measurements. The uneven and rigid nanoscale structure has been used as a stamp for constructing bamboo shoot structures of fullerene.
Dynamical Structure Factors of quasi-one-dimensional antiferromagnets
Hagemans, Rob; Caux, Jean-Sébastien; Maillet, Jean Michel
2007-03-01
For a long time it has been impossible to accurately calculate the dynamical structure factors (spin-spin correlators as a function of momentum and energy) of quasi-one-dimensional antiferromagnets. For integrable Heisenberg chains, the recently developed ABACUS method (a first-principles computational approach based on the Bethe Ansatz) now yields highly accurate (over 99% of the sum rule) results for the DSF for finite chains, allowing for a very precise description of neutron-scattering data over the full momentum and energy range. We show remarkable agreement between results obtained with ABACUS and experiment.
ONE-DIMENSIONAL AND TWO-DIMENSIONAL LEADERSHIP STYLES
Nikola Stefanović
2007-06-01
Full Text Available In order to motivate their group members to perform certain tasks, leaders use different leadership styles. These styles are based on leaders' backgrounds, knowledge, values, experiences, and expectations. The one-dimensional styles, used by many world leaders, are autocratic and democratic styles. These styles lie on the two opposite sides of the leadership spectrum. In order to precisely define the leadership styles on the spectrum between the autocratic leadership style and the democratic leadership style, leadership theory researchers use two dimensional matrices. The two-dimensional matrices define leadership styles on the basis of different parameters. By using these parameters, one can identify two-dimensional styles.
Obstacle Effects on One-Dimensional Translocation of ATPase
WANG Xian-Ju; AI Bao-Quan; LIU Liang-Gang
2002-01-01
We apply a general random walk model to the study of the ATPase's one-dimensional translocation along obstacle biological environment, and show the effects of random obstacles on the ATPase translocation along single stranded DNA. We find that the obstacle environment can reduce the lifetime of ATPase lattice-bound state which results in the inhibition of ATPase activity. We also carry out the ranges of rate constant of ATPase unidirectonal translocation and bidirectional translocation. Our results are consistent with the experiments and relevant theoretical consideration, and can be used to explain some physiological phenomena.
Longitudinal waves in one dimensional non-uniform waveguides
无
2011-01-01
Wave approach is used to analyze the longitudinal wave motion in one dimensional non-uniform waveguides.With assumptions of constant wave velocity and no wave conversion,there exist four types of non-uniform rods and corresponding traveling wave solutions are investigated.The obtained results indicate that the kinetic energy is preserved as a constant and the wave amplitude is inversely proportional to square root of the cross-sectional area of the rod.Under certain condition,there exists a cut-off frequ...
Bloch oscillations in a one-dimensional spinor gas.
Gangardt, D M; Kamenev, A
2009-02-20
A force applied to a spin-flipped particle in a one-dimensional spinor gas may lead to Bloch oscillations of the particle's position and velocity. The existence of Bloch oscillations crucially depends on the viscous friction force exerted by the rest of the gas on the spin excitation. We evaluate the friction in terms of the quantum fluid parameters. In particular, we show that the friction is absent for integrable cases, such as an SU(2) symmetric gas of bosons or fermions. For small deviations from the exact integrability the friction is very weak, opening the possibility to observe Bloch oscillations.
Black Phosphorus based One-dimensional Photonic Crystals and Microcavities
Kriegel, I
2016-01-01
The latest achievements in the fabrication of black phosphorus thin layers, towards the technological breakthrough of a phosphorene atomically thin layer, are paving the way for a their employment in electronics, optics, and optoelectronics. In this work, we have simulated the optical properties of one-dimensional photonic structures, i.e. photonic crystals and microcavities, in which few-layer black phosphorus is one of the components. The insertion of the 5 nm black phosphorous layers leads to a photonic band gap in the photonic crystals and a cavity mode in the microcavity interesting for light manipulation and emission enhancement.
Coherent Backscattering of Light Off One-Dimensional Atomic Strings
Sørensen, H. L.; Béguin, J.-B.; Kluge, K. W.; Iakoupov, I.; Sørensen, A. S.; Müller, J. H.; Polzik, E. S.; Appel, J.
2016-09-01
We present the first experimental realization of coherent Bragg scattering off a one-dimensional system—two strings of atoms strongly coupled to a single photonic mode—realized by trapping atoms in the evanescent field of a tapered optical fiber, which also guides the probe light. We report nearly 12% power reflection from strings containing only about 1000 cesium atoms, an enhancement of 2 orders of magnitude compared to reflection from randomly positioned atoms. This result paves the road towards collective strong coupling in 1D atom-photon systems. Our approach also allows for a straightforward fiber connection between several distant 1D atomic crystals.
Multiple nonequilibrium steady states for one-dimensional heat flow.
Zhang, F; Isbister, D J; Evans, D J
2001-08-01
A nonequilibrium molecular dynamics model of heat flow in one-dimensional lattices is shown to have multiple steady states for any fixed heat field strength f(e) ranging from zero to a certain positive value. We demonstrate that, depending on the initial conditions, there are at least two possibilities for the system's evolution: (i) formation of a stable traveling wave (soliton), and (ii) chaotic motion throughout the entire simulation. The percentage of the soliton-generating trajectories is zero for small field strength f(e), but increases sharply to unity over a critical region of the parameter f(e).
Lateral shift in one-dimensional quasiperiodic chiral photonic crystal
Da, Jian, E-mail: dajian521@sina.com [Department of Information Engineering, Huaian Senior Vocational and Technical School, Feiyao road, Huaian 223005, Jiangsu Province (China); Mo, Qi, E-mail: moqiyueyang@163.com [School of Software, Yunnan University, Cuihu Bai Road, Kunming City, Yunnan Province 650091 (China); Cheng, Yaokun [Department of Information Engineering, Huaian Senior Vocational and Technical School, Feiyao road, Huaian 223005, Jiangsu Province (China); Liu, Taixiang [Taishan Vocational College of Nursing, Shandong Province 271000 (China)
2015-02-01
We investigate the lateral shift of a one-dimensional quasiperiodic photonic crystal consisting of chiral and conventional dielectric materials. The effect of structural irregularity on lateral shift is evaluated by stationary-phase approach. Our results show that the lateral shift can be modulated by varying the structural irregularity in quasiperiodic structure. Besides, the position of peak in lateral shift spectrum stays sensitive to the chiral factor of chiral materials. In comparison with that of periodic structure, quasiperiodic structure provides an extra degree of freedom to manipulate the lateral shift.
One-Dimensional Metals Conjugated Polymers, Organic Crystals, Carbon Nanotubes
Roth, Siegmar
2004-01-01
Low-dimensional solids are of fundamental interest in materials science due to their anisotropic properties. Written not only for experts in the field, this book explains the important concepts behind their physics and surveys the most interesting one-dimensional systems and discusses their present and emerging applications in molecular scale electronics. The second edition of this successful book has been completely revised to include the remarkable achievements of the last ten years of research and applications. Chemists, polymer and materials scientists as well as students will find this bo
One-dimensional numerical simulation of non-uniform sediment transport under unsteady flows
Hongwei FANG; Minghong CHEN; Qianhai CHEN
2008-01-01
One-dimensional numerical models are popularly used in sediment transport research because they can be easily programmed and cost less time compared with two-and three-dimensional numerical models.In particular,they possess greater capacity to be applied in large river basins with many tributaries.This paper presents a one-dimensional numerical model capable of calculating total-load sediment transport.The cross-section-averaged sediment transport capacity and recovery coefficient are addressed in the suspended load model.This one-dimensional model,therefore,can be applied to fine suspended loads and to hyperconcentrated flows in the Yellow River.Moreover,a new discretization scheme for the equation of unsteady non-uniform suspended sediment transport is proposed.The model is calibrated using data measured from the Yantan Reservoir on the Hongshui River and the Sanmenxia Reservoir on the Yellow River.A comparison of the calculated water level and river bed deformation with field measurements shows that the improved numerical model is capable of predicting flow,sediment transport,bed changes,and bed-material sorting in various situations,with reasonable accuracy and reliability.
A One Dimensional, Time Dependent Inlet/Engine Numerical Simulation for Aircraft Propulsion Systems
Garrard, Doug; Davis, Milt, Jr.; Cole, Gary
1999-01-01
The NASA Lewis Research Center (LeRC) and the Arnold Engineering Development Center (AEDC) have developed a closely coupled computer simulation system that provides a one dimensional, high frequency inlet/engine numerical simulation for aircraft propulsion systems. The simulation system, operating under the LeRC-developed Application Portable Parallel Library (APPL), closely coupled a supersonic inlet with a gas turbine engine. The supersonic inlet was modeled using the Large Perturbation Inlet (LAPIN) computer code, and the gas turbine engine was modeled using the Aerodynamic Turbine Engine Code (ATEC). Both LAPIN and ATEC provide a one dimensional, compressible, time dependent flow solution by solving the one dimensional Euler equations for the conservation of mass, momentum, and energy. Source terms are used to model features such as bleed flows, turbomachinery component characteristics, and inlet subsonic spillage while unstarted. High frequency events, such as compressor surge and inlet unstart, can be simulated with a high degree of fidelity. The simulation system was exercised using a supersonic inlet with sixty percent of the supersonic area contraction occurring internally, and a GE J85-13 turbojet engine.
A refined one-dimensional rotordynamics model with three-dimensional capabilities
Carrera, E.; Filippi, M.
2016-03-01
This paper evaluates the vibration characteristics of various rotating structures. The present methodology exploits the one-dimensional Carrera Unified Formulation (1D CUF), which enables one to go beyond the kinematic assumptions of classical beam theories. According to the component-wise (CW) approach, Lagrange-like polynomial expansions (LE) are here adopted to develop the refined displacement theories. The LE elements make it possible to model each structural component of the rotor with an arbitrary degree of accuracy using either different displacement theories or localized mesh refinements. Hamilton's Principle is used to derive the governing equations, which are solved by the Finite Element Method. The CUF one-dimensional theory includes all the effects due to rotation, namely the Coriolis term, spin softening and geometrical stiffening. The numerical simulations have been performed considering a thin ring, discs and bladed-deformable shafts. The effects of the number and the position of the blades on the dynamic stability of the rotor have been evaluated. The results have been compared, when possible, with the 2D and 3D solutions that are available in the literature. CUF models appear very practical to investigate the dynamics of complex rotating structures since they provide 2D and quasi-3D results, while preserving the computational effectiveness of one-dimensional solutions.
Quasi-Dirac points in one-dimensional graphene superlattices
Chen, C.H.; Tseng, P.; Hsueh, W.J., E-mail: hsuehwj@ntu.edu.tw
2016-08-26
Quasi-Dirac points (QDPs) with energy different from the traditional Dirac points (TDPs) have been found for the first time in one-dimensional graphene superlattices. The angular-averaged conductance reaches a minimum value at the QDPs, at which the Fano factor approaches 1/3. Surprisingly, the minimum conductance at these QDPs may be lower than that at the TDPs under certain conditions. This is remarkable as the minimum conductance attainable in graphene superlattices was believed to appear at TDPs. - Highlights: • Quasi-Dirac points (QDPs) are found for the first time in one-dimensional graphene superlattices. • The QDP is different from the traditional Dirac points (TDPs) in graphene superlattices. • The angular-averaged conductance reaches a minimum value at the QDPs, at which the Fano factor approaches 1/3. • The minimum conductance at these QDPs may be lower than that at the TDPs under certain conditions. • The minimum conductance attainable in graphene superlattices was believed to appear at TDPs.
Neutron scattering studies of three one-dimensional antiferromagnets
Kenzelmann, M
2001-01-01
observed in the disordered phase of spin-1/2 chains. The magnetic order of the one-dimensional spin-1/2 XY antiferromagnet Cs sub 2 CoCl sub 4 was investigated using neutron diffraction. The magnetic structure has an ordering wave-vector (0, 0.5, 0.5) for T < 217 mK and the magnetic structure is a non-linear structure with the magnetic moments at a small angle to the b axis. Above a field of H = 2.1 T the magnetic order collapses in an apparent first order phase transition, suggesting a transition to a spin-liquid phase. Low-dimensional magnets with low-spin quantum numbers are ideal model systems for investigating strongly interacting macroscopic quantum ground states and their non-linear spin excitations. This thesis describes neutron scattering experiments of three one-dimensional low-spin antiferromagnets where strong quantum fluctuations lead to highly-correlated ground states and unconventional cooperative spin excitations. The excitation spectrum of the antiferromagnetic spin-1 Heisenberg chain CsNi...
Hydrogen peroxide stabilization in one-dimensional flow columns
Schmidt, Jeremy T.; Ahmad, Mushtaque; Teel, Amy L.; Watts, Richard J.
2011-09-01
Rapid hydrogen peroxide decomposition is the primary limitation of catalyzed H 2O 2 propagations in situ chemical oxidation (CHP ISCO) remediation of the subsurface. Two stabilizers of hydrogen peroxide, citrate and phytate, were investigated for their effectiveness in one-dimensional columns of iron oxide-coated and manganese oxide-coated sand. Hydrogen peroxide (5%) with and without 25 mM citrate or phytate was applied to the columns and samples were collected at 8 ports spaced 13 cm apart. Citrate was not an effective stabilizer for hydrogen peroxide in iron-coated sand; however, phytate was highly effective, increasing hydrogen peroxide residuals two orders of magnitude over unstabilized hydrogen peroxide. Both citrate and phytate were effective stabilizers for manganese-coated sand, increasing hydrogen peroxide residuals by four-fold over unstabilized hydrogen peroxide. Phytate and citrate did not degrade and were not retarded in the sand columns; furthermore, the addition of the stabilizers increased column flow rates relative to unstabilized columns. These results demonstrate that citrate and phytate are effective stabilizers of hydrogen peroxide under the dynamic conditions of one-dimensional columns, and suggest that citrate and phytate can be added to hydrogen peroxide before injection to the subsurface as an effective means for increasing the radius of influence of CHP ISCO.
Hudritsch, W.W.; Smith, P.D.
1977-11-01
The one-dimensional computer program PADLOC is designed to analyze steady-state and time-dependent plateout of fission products in an arbitrary network of pipes. The problem solved is one of mass transport of impurities in a fluid, including the effects of sources in the fluid and in the plateout surfaces, convection along the flow paths, decay, adsorption on surfaces (plateout), and desorption from surfaces. These phenomena are governed by a system of coupled, nonlinear partial differential equations. The solution is achieved by (a) linearizing the equations about an approximate solution, employing a Newton Raphson iteration technique, (b) employing a finite difference solution method with an implicit time integration, and (c) employing a substructuring technique to logically organize the systems of equations for an arbitrary flow network.
Subharmonic wave transition in a quasi-one-dimensional noisy fluidized shallow granular bed.
Ortega, Ignacio; Clerc, Marcel G; Falcón, Claudio; Mujica, Nicolás
2010-04-01
We present an experimental and theoretical study of the pattern formation process of standing subharmonic waves in a fluidized quasi-one-dimensional shallow granular bed. The fluidization process is driven by means of a time-periodic air flow, analogous to a tapping type of forcing. Measurements of the amplitude of the critical mode close to the transition are in quite good agreement with those inferred from a universal stochastic amplitude equation. This allows us to determine both the bifurcation point of the deterministic system and the corresponding noise intensity. We also show that the probability density distribution is well described by a generalized Rayleigh distribution, which is the stationary solution of the corresponding Fokker-Planck equation of the universal stochastic amplitude equation that describes our system.
Hudritsch, W.W.; Smith, P.D.
1977-11-01
The one-dimensional computer program PADLOC is designed to analyze steady-state and time-dependent plateout of fission products in an arbitrary network of pipes. The problem solved is one of mass transport of impurities in a fluid, including the effects of sources in the fluid and in the plateout surfaces, convection along the flow paths, decay, adsorption on surfaces (plateout), and desorption from surfaces. These phenomena are governed by a system of coupled, nonlinear partial differential equations. The solution is achieved by (a) linearizing the equations about an approximate solution, employing a Newton Raphson iteration technique, (b) employing a finite difference solution method with an implicit time integration, and (c) employing a substructuring technique to logically organize the systems of equations for an arbitrary flow network.
Stability conditions for one-dimensional optical solitons in cubic-quintic-septimal media
Reyna, Albert S; de Araujo, Cid B
2015-01-01
Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear terms are focusing. Conditions for onset of the supercritical collapse of the optical beam are identified too. A variational approximation is used to predict dependence of the soliton propagation constant on the norm, and respective stability regions are identified using the Vakhitov-Kolokolov criterion. Analytical results obtained by means of the variational approximation are corroborated by numerical simulations of the cubic-quintic-septimal nonlinear Schroedinger equation.
On the one-dimensional acoustic propagation in conical ducts with stationary mean flow.
Barjau, Ana
2007-12-01
This paper proposes a direct time-domain calculation of the time-domain responses of anechoic conical tubes with steady weak mean flow. The starting point is the approximated linear one-dimensional wave equation governing the velocity potential for the case of steady flow with low Mach number. A traveling solution with general space-dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained. The results include the well-known responses of conical and cylindrical ducts with zero mean flow.
Extended one-dimensional method for coherent synchrotron radiation including shielding
David Sagan
2009-04-01
Full Text Available Coherent synchrotron radiation can severely limit the performance of accelerators designed for high brightness and short bunch length. Examples include light sources based on energy recovery LINAC or free-electron lasers, and bunch compressors for linear colliders. In order to better simulate coherent synchrotron radiation, a one-dimensional formalism due to Saldin, Schneidmiller, and Yurkov has been implemented in the general beam dynamics code Bmad. Wide vacuum chambers are simulated by means of vertical image charges. Results from Bmad are here compared to analytical approximations, to numerical solutions of the Maxwell equations, and to the simulation code elegant and the code of Agoh and Yokoya.
Extended one-dimensional method for coherent synchrotron radiation including shielding
Sagan, David; Hoffstaetter, Georg; Mayes, Christopher; Sae-Ueng, Udom
2009-04-01
Coherent synchrotron radiation can severely limit the performance of accelerators designed for high brightness and short bunch length. Examples include light sources based on energy recovery LINAC or free-electron lasers, and bunch compressors for linear colliders. In order to better simulate coherent synchrotron radiation, a one-dimensional formalism due to Saldin, Schneidmiller, and Yurkov has been implemented in the general beam dynamics code Bmad. Wide vacuum chambers are simulated by means of vertical image charges. Results from Bmad are here compared to analytical approximations, to numerical solutions of the Maxwell equations, and to the simulation code elegant and the code of Agoh and Yokoya.
TIME-HARMONIC DYNAMIC GREEN'S FUNCTIONS FOR ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS
Wang Xu
2005-01-01
Quasicrystals have additional phason degrees of freedom not found in conventional crystals. In this paper, we present an exact solution for time-harmonic dynamic Green's function of one-dimensional hexagonal quasicrystals with the Laue classes 6/mh and 6/mhmm. Through the introduction of two new functions ψ and ψ, the original problem is reduced to the determination of Green's functions for two independent Helmholtz equations. The explicit expressions of displacement and stress fields are presented and their asymptotic behaviors are discussed. The static Green's function can be obtained by letting the circular frequency approach zero.
A Quasi-One-Dimensional Model for a Solar Flux Tube
杨志良; 张洪起; 张枚; 冯学尚
2002-01-01
We develop the quasi-one-dimensional flux tube model with magnetohydrodynamical equations. In order to know whether the magnetic field can maintain their similar structurefrom photosphere to chromosphere, we suppose that the flux tube is thin in radius relative to the length, and that the quantities in the cross section are averaged.The radii of the flux tube and the magnetic field are numerically simulated. One of the important results shows that the flux tube does not expand as quickly as the existing model when it is out of the photosphere with high velocity. This is consistent with observations of the magnetic field in the photosphere and chromosphere.
Quantum simulations of a particle in one-dimensional potentials using NMR
Shankar, Ravi; Hegde, Swathi S.; Mahesh, T.S.
2014-01-03
A quantum computer made up of a controllable set of quantum particles has the potential to efficiently simulate other quantum systems. In this work we studied quantum simulations of single particle Shrödinger equation for certain one-dimensional potentials. Using a five-qubit NMR system, we achieve space discretization with four qubits, and the other qubit is used for preparation of initial states as well as measurement of spatial probabilities. The experimental relative probabilities compare favourably with the theoretical expectations, thus effectively mimicking a small scale quantum simulator.
Classical Lie Point Symmetry Analysis of a Steady Nonlinear One-Dimensional Fin Problem
R. J. Moitsheki
2012-01-01
Full Text Available We consider the one-dimensional steady fin problem with the Dirichlet boundary condition at one end and the Neumann boundary condition at the other. Both the thermal conductivity and the heat transfer coefficient are given as arbitrary functions of temperature. We perform preliminary group classification to determine forms of the arbitrary functions appearing in the considered equation for which the principal Lie algebra is extended. Some invariant solutions are constructed. The effects of thermogeometric fin parameter and the exponent on temperature are studied. Also, the fin efficiency is analyzed.
Temporal Behaviour of Harmonics from One-Dimensional H2+ in an UltrashortLaser Pulse
屈卫星; 李儒新; 徐至展; 夏宇兴; 甘明龙
2001-01-01
With the method of wavelet transform, we consider the temporal behaviour of high-order harmonic generationfrom one-dimensional H2+ exposed to an ultrashort laser pulse with a duration of tens of femtoseconds. The results, which are calculated by numerically solving the corresponding time-dependent Schrodinger equation with the split-operator method in the non-Born-Oppenheimer approach, show that: (1) the high-order harmonics in the cut-off range emitted as a train of pulses have better coherence than those in the plateau; (2) the harmonics are emitted early in time when the intensity of the laser pulse increases.
Simple one-dimensional quantum-mechanical model for a particle attached to a surface
Fernandez, Francisco M, E-mail: fernande@quimica.unlp.edu.a [INIFTA (UNLP, CCT La Plata-CONICET), Division Quimica Teorica, Blvd 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
2010-07-15
We present a simple one-dimensional quantum-mechanical model for a particle attached to a surface. It leads to the Schroedinger equation for a harmonic oscillator bounded on one side that we solve in terms of Weber functions and discuss the behaviour of the eigenvalues and eigenfunctions. We derive the virial theorem and other exact relationships as well as the asymptotic behaviour of the eigenvalues. We calculate the zero-point energy for model parameters corresponding to H adsorbed on Pd(1 0 0). The model is suitable for an advanced undergraduate or graduate course on quantum mechanics.
Fourier's law for quasi-one-dimensional chaotic quantum systems
Seligman, Thomas H [Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, C.P. 62210 Cuernavaca, Morelos (Mexico); Weidenmueller, Hans A, E-mail: Hans.Weidenmueller@mpi-hd.mpg.de [Max-Planck-Institut fuer Kernphysik, PO Box 103980, 69029 Heidelberg (Germany)
2011-05-20
We derive Fourier's law for a completely coherent quasi-one-dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.
Effect of Temperature on Polaron Stability in a One-Dimensional Organic Lattice
LIU Wen; LI Yuan; QU Zhen; GAO gun; YIN Sun; LIU De-Sheng
2009-01-01
Effect of temperature on the polaron stability in a one-dimensional organic lattice is investigated within the Su-Schrieffer-Heeger model.The temperature effect is simulated by introducing random forces to the equation of the lattice motion.It is found that the localized polaron state becomes delocalized even at low temperatures.The time of polaron keeping localized depends on the magnitude of temperatures.By taking into account the thermal effect,we find that the dissociation field is weaker as compared with earlier works.
Theory of finite-entanglement scaling at one-dimensional quantum critical points.
Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M; Moore, Joel E
2009-06-26
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finite-entanglement scaling in one-dimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.
Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
Gonzales, Marcelo; Khodaee, Sadi; Toppan, Francesco
2012-01-01
"Pure" homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-Extended one-dimensional Supersymmetry Algebra are classified. "Pure" means that they admit at least one graphical presentation (the corresponding graph/graphs are known as "Adinkras"). We further prove the existence of "entangled" linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N=4 supermultiplet with field content (3,8,5). It interpolates between two inequivalent pure N=4 supermultiplets with the same field content. The one-dimensional N=4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented. The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed. Discrete properties such as chirality and coloring can discriminate different supermultiplets. The tools used in our classification have been previously introduced and discu...
杨婷; 黎野平
2012-01-01
We study the stationary solutions of a one-dimensional bipolar quantum drift-diffusion model from semiconductor devices and plasmas.In a bounded interval supplemented by the proper boundary conditions,we first show the existence and uniqueness of the stationary solutions to the onedimensional bipolar quantum drift-diffusion model.The proof can be completed by the Schauder fixed-point principle and the careful energy estimates.Then,we study the classical limit of the stationary solutions to the bipolar quantum drift-diffusion model.Namely,we show that the stationary solution to the quantum drift-diffusion model approaches that to the drift-diffusion model as the scaled Planck constant ε tends to zero.%研究了来自于半导体器件和等离子体中的一维双极量子漂移-扩散模型的稳态解.在有合适边界条件的有界区域里,先利用Schauder不动点定理和能量估计的技巧,证明一维双极量子漂移-扩散模型的稳态解的存在性和唯一性;其次,研究双极量子漂移-扩散模型的稳态解的经典极限,即当普朗克常数ε趋于零时,量子漂移一扩散模型的稳态解趋向于经典漂移-扩散模型的稳态解.
Crystallographic shear mechanisms in Rh one-dimensional oxides
Hernando, María; Boulahya, Khalid; Parras, Marina; González-Calbet, José M.
2005-02-01
Electron diffraction and high resolution electron microscopy have been used to characterize two new one-dimensional superstructures in the A sbnd Rh sbnd O system (A = Ca, Sr) related to the 2H-ABO 3-type. They are formed by the intergrowth of n A 3A'BO 6 blocks, showing the Sr 4RhO 6-type, with A 12A' 2B 8O 30 blocks, constituted by two A 3O 9 and two A 3A'O 6 layers alternating in the stacking sequence 1:1, leading to the A 27A' 7B 13O 60 ( n=5) and A 30A' 8B 14O 66 ( n=6) compositions. A crystallographic shear mechanism is proposed to describe the structural relationship between Sr 4RhO 6 (A 3A'BO 6-type) and the new superstructures.
Impedance of rigid bodies in one-dimensional elastic collisions
Santos, Janilo; Nelson, Osman Rosso
2012-01-01
In this work we study the problem of one-dimensional elastic collisions of billiard balls, considered as rigid bodies, in a framework very different from the classical one presented in text books. Implementing the notion of impedance matching as a way to understand eficiency of energy transmission in elastic collisions, we find a solution which frames the problem in terms of this conception. We show that the mass of the ball can be seen as a measure of its impedance and verify that the problem of maximum energy transfer in elastic collisions can be thought of as a problem of impedance matching between different media. This approach extends the concept of impedance, usually associated with oscillatory systems, to system of rigid bodies.
Strongly interacting photons in one-dimensional continuum
Roy, Dibyendu; Firstenberg, Ofer
2016-01-01
The photon-photon scattering in vacuum is extremely weak. However, strong effective interactions between single photons can be realized by employing strong light-matter coupling. These interactions are a fundamental building block for quantum optics, bringing many-body physics to the photonic world and providing important resources for quantum photonic devices and for optical metrology. In this Colloquium, we review the physics of strongly-interacting photons in one-dimensional systems with no optical confinement along the propagation direction. We focus on two recently-demonstrated experimental realizations: (i) superconducting qubits coupled to open transmission lines, and (ii) interacting Rydberg atoms in a cold gas. Advancements in the theoretical understanding of these systems are presented in complementary formalisms and compared to experimental results. The experimental achievements are summarized alongside of a systematic description of the quantum optical effects and quantum devices emerging from the...
One-dimensional long-range percolation: A numerical study
Gori, G.; Michelangeli, M.; Defenu, N.; Trombettoni, A.
2017-07-01
In this paper we study bond percolation on a one-dimensional chain with power-law bond probability C /rd +σ , where r is the distance length between distinct sites and d =1 . We introduce and test an order-N Monte Carlo algorithm and we determine as a function of σ the critical value Cc at which percolation occurs. The critical exponents in the range 0 introduction of a suitably defined effective dimension deff relating the long-range model with a short-range one in dimension deff. We finally present a formulation of our algorithm for bond percolation on general graphs, with order N efficiency on a large class of graphs including short-range percolation and translationally invariant long-range models in any spatial dimension d with σ >0 .
Configurational and energy landscape in one-dimensional Coulomb systems.
Varela, Lucas; Téllez, Gabriel; Trizac, Emmanuel
2017-02-01
We study a one-dimensional Coulomb system, where two charged colloids are neutralized by a collection of point counterions, with global neutrality. With temperature being given, two situations are addressed: Either the colloids are kept at fixed positions (canonical ensemble) or the force acting on the colloids is fixed (isobaric-isothermal ensemble). The corresponding partition functions are worked out exactly, in view of determining which arrangement of counterions is optimal. How many counterions should be in the confined segment between the colloids? For the remaining ions outside, is there a left-right symmetry breakdown? We evidence a cascade of transitions as system size is varied in the canonical treatment or as pressure is increased in the isobaric formulation.
The statistical distributions of one-dimensional “turbulence”
Peyrard, Michel
2004-06-01
We study a one-dimensional discrete analog of the von Kármán flow widely investigated in turbulence, made of a lattice of anharmonic oscillators excited by both ends in the presence of a dissipative term proportional to the second-order finite difference of the velocities, similar to the viscous term in a fluid. The dynamics of the model shows striking similarities with an actual turbulent flow, both at local and global scales. Calculations of the probability distribution function of velocity increments, extensively studied in turbulence, with a very large number of points in order to determine accurately the statistics of rare events, allow us to provide a meaningful comparison of different theoretical expressions of the PDFs.
Scale dependent partitioning of one-dimensional aperiodic set diffraction
Elkharrat, A.
2004-06-01
We give a multiresolution partition of pure point parts of diffraction patterns of one-dimensional aperiodic sets. When an aperiodic set is related to the Golden Ratio, denoted by tau, it is well known that the pure point part of its diffractive measure is supported by the extension ring of tau, denoted by mathbb{Z}[tau]. The partition we give is based on the formalism of the so called tau-integers, denoted by mathbb{Z}_tau. The set of tau-integers is a selfsimilar set obeying mathbb{Z}_tau/tau^{j-1}subsetmathbb{Z}_tau/tau^j subset mathbb{Z}_tau/tau^{j + 1} subsetmathbb{Z}[tau], jinmathbb{Z}. The pure point spectrum is then partitioned with respect to this “Russian doll” like sequence of subsets mathbb{Z}_tau/tau^j. Thus we deduce the partition of the pure point part of the diffractive measure of aperiodic sets.
Numerical method of characteristics for one-dimensional blood flow
Acosta, Sebastian; Riviere, Beatrice; Penny, Daniel J; Rusin, Craig G
2014-01-01
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time-step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the ...
Testing of a one dimensional model for Field II calibration
Bæk, David; Jensen, Jørgen Arendt; Willatzen, Morten
2008-01-01
to the calibrated Field II program for 1, 4, and 10 cycle excitations. Two parameter sets were applied for modeling, one real valued Pz27 parameter set, manufacturer supplied, and one complex valued parameter set found in literature, Alguer´o et al. [11]. The latter implicitly accounts for attenuation. Results show......Field II is a program for simulating ultrasound transducer fields. It is capable of calculating the emitted and pulse-echoed fields for both pulsed and continuous wave transducers. To make it fully calibrated a model of the transducer’s electro-mechanical impulse response must be included. We...... examine an adapted one dimensional transducer model originally proposed by Willatzen [9] to calibrate Field II. This model is modified to calculate the required impulse responses needed by Field II for a calibrated field pressure and external circuit current calculation. The testing has been performed...
Automated quantification of one-dimensional nanostructure alignment on surfaces
Dong, Jianjin; Abukhdeir, Nasser Mohieddin
2016-01-01
A method for automated quantification of the alignment of one-dimensional nanostructures from microscopy imaging is presented. Nanostructure alignment metrics are formulated and shown to able to rigorously quantify the orientational order of nanostructures within a two-dimensional domain (surface). A complementary image processing method is also presented which enables robust processing of microscopy images where overlapping nanostructures might be present. Scanning electron microscopy (SEM) images of nanowire-covered surfaces are analyzed using the presented methods and it is shown that past single parameter alignment metrics are insufficient for highly aligned domains. Through the use of multiple parameter alignment metrics, automated quantitative analysis of SEM images is shown to be possible and the alignment characteristics of different samples are able to be rigorously compared using a similarity metric. The results of this work provide researchers in nanoscience and nanotechnology with a rigorous metho...
Coherent backscattering of light off one-dimensional atomic strings
Sørensen, H L; Kluge, K W; Iakoupov, I; Sørensen, A S; Müller, J H; Polzik, E S; Appel, J
2016-01-01
Bragg scattering, well known in crystallography, has become a powerful tool for artificial atomic structures such as optical lattices. In an independent development photonic waveguides have been used successfully to boost quantum light-matter coupling. We combine these two lines of research and present the first experimental realisation of coherent Bragg scattering off a one-dimensional (1D) system - two strings of atoms strongly coupled to a single photonic mode - realised by trapping atoms in the evanescent field of a tapered optical fibre (TOF), which also guides the probe light. We report nearly 12% power reflection from strings containing only about one thousand caesium atoms, an enhancement of more than two orders of magnitude compared to reflection from randomly positioned atoms. This result paves the road towards collective strong coupling in 1D atom-photon systems. Our approach also allows for a straightforward fibre connection between several distant 1D atomic crystals.
A Reduced Order, One Dimensional Model of Joint Response
DOHNER,JEFFREY L.
2000-11-06
As a joint is loaded, the tangent stiffness of the joint reduces due to slip at interfaces. This stiffness reduction continues until the direction of the applied load is reversed or the total interface slips. Total interface slippage in joints is called macro-slip. For joints not undergoing macro-slip, when load reversal occurs the tangent stiffness immediately rebounds to its maximum value. This occurs due to stiction effects at the interface. Thus, for periodic loads, a softening and rebound hardening cycle is produced which defines a hysteretic, energy absorbing trajectory. For many jointed sub-structures, this hysteretic trajectory can be approximated using simple polynomial representations. This allows for complex joint substructures to be represented using simple non-linear models. In this paper a simple one dimensional model is discussed.
One-dimensional topological edge states of bismuth bilayers
Drozdov, Ilya K.; Alexandradinata, A.; Jeon, Sangjun; Nadj-Perge, Stevan; Ji, Huiwen; Cava, R. J.; Andrei Bernevig, B.; Yazdani, Ali
2014-09-01
The hallmark of a topologically insulating state of matter in two dimensions protected by time-reversal symmetry is the existence of chiral edge modes propagating along the perimeter of the sample. Among the first systems predicted to be a two-dimensional topological insulator are bilayers of bismuth. Here we report scanning tunnelling microscopy experiments on bulk Bi crystals that show that a subset of the predicted Bi-bilayers' edge states are decoupled from the states of the substrate and provide direct spectroscopic evidence of their one-dimensional nature. Moreover, by visualizing the quantum interference of edge-mode quasi-particles in confined geometries, we demonstrate their remarkable coherent propagation along the edge with scattering properties consistent with strong suppression of backscattering as predicted for the propagating topological edge states.
Spin accumulation on a one-dimensional mesoscopic Rashba ring
Zhang Zhiyong [Department of Physics, Nanjing University, Nanjing 210093 (China)
2006-04-26
The nonequilibrium spin accumulation on a one-dimensional (1D) mesoscopic Rashba ring is investigated with unpolarized current injected through ideal leads. Due to the Rashba spin-orbit (SO) coupling and back-scattering at the interfaces between the leads and the ring, a beating pattern is formed in the fast oscillation of spin accumulation. If every beating period is complete, a plateau is formed, where the variation of spin accumulation with the external voltage is slow, but if new incomplete periods emerge in the envelope function, a transitional region appears. This plateau structure and the beating pattern are related to the tunnelling through spin-dependent resonant states. Because of the Aharonov-Casher (AC) effect, the average spin accumulation oscillates quasi-periodically with the Rashba SO coupling and has a series of zeros. In some situations, the direction of the average spin accumulation can be reversed by the external voltage in this 1D Rashba ring.
Spin accumulation on a one-dimensional mesoscopic Rashba ring.
Zhang, Zhi-Yong
2006-04-26
The nonequilibrium spin accumulation on a one-dimensional (1D) mesoscopic Rashba ring is investigated with unpolarized current injected through ideal leads. Due to the Rashba spin-orbit (SO) coupling and back-scattering at the interfaces between the leads and the ring, a beating pattern is formed in the fast oscillation of spin accumulation. If every beating period is complete, a plateau is formed, where the variation of spin accumulation with the external voltage is slow, but if new incomplete periods emerge in the envelope function, a transitional region appears. This plateau structure and the beating pattern are related to the tunnelling through spin-dependent resonant states. Because of the Aharonov-Casher (AC) effect, the average spin accumulation oscillates quasi-periodically with the Rashba SO coupling and has a series of zeros. In some situations, the direction of the average spin accumulation can be reversed by the external voltage in this 1D Rashba ring.
SUSY-inspired one-dimensional transformation optics
Miri, Mohammad-Ali; Christodoulides, Demetrios N
2014-01-01
Transformation optics aims to identify artificial materials and structures with desired electromagnetic properties by means of pertinent coordinate transformations. In general, such schemes are meant to appropriately tailor the constitutive parameters of metamaterials in order to control the trajectory of light in two and three dimensions. Here we introduce a new class of one-dimensional optical transformations that exploits the mathematical framework of supersymmetry (SUSY). This systematic approach can be utilized to synthesize photonic configurations with identical reflection and transmission characteristics, down to the phase, for all incident angles, thus rendering them perfectly indistinguishable to an external observer. Along these lines, low-contrast dielectric arrangements can be designed to fully mimic the behavior of a given high-contrast structure that would have been otherwise beyond the reach of available materials and existing fabrication techniques. Similar strategies can also be adopted to re...
Characterizing high- n quasi-one-dimensional strontium Rydberg atoms
Hiller, Moritz; Yoshida, Shuhei; Burgdörfer, Joachim; Ye, Shuzhen; Zhang, Xinyue; Dunning, F. Barry
2014-05-01
The production of high- n, n ~ 300 , quasi-one-dimensional strontium Rydberg atoms by two-photon excitation of selected extreme Stark states in the presence of a weak dc field is examined using a crossed laser-atom beam geometry. The polarization of the product states is probed using three independent techniques which are analyzed with the aid of classical-trajectory Monte Carlo simulations that employ initial ensembles based on quantum calculations using a two-active-electron model. Comparisons between theory and experiment demonstrate that the product states have large dipole moments, ~ 1 . 0 - 1 . 2n2 a . u . and that they can be engineered using pulsed electric fields to create a wide variety of target states. Research supported by the NSF, the Robert A Welch Foundation, and the FWF (Austria).
Topologically protected states in one-dimensional systems
Fefferman, C L; Weinstein, M I
2017-01-01
The authors study a class of periodic Schrödinger operators, which in distinguished cases can be proved to have linear band-crossings or "Dirac points". They then show that the introduction of an "edge", via adiabatic modulation of these periodic potentials by a domain wall, results in the bifurcation of spatially localized "edge states". These bound states are associated with the topologically protected zero-energy mode of an asymptotic one-dimensional Dirac operator. The authors' model captures many aspects of the phenomenon of topologically protected edge states for two-dimensional bulk structures such as the honeycomb structure of graphene. The states the authors construct can be realized as highly robust TM-electromagnetic modes for a class of photonic waveguides with a phase-defect.
One-dimensional hybrid nanostructures for heterogeneous photocatalysis and photoelectrocatalysis.
Xiao, Fang-Xing; Miao, Jianwei; Tao, Hua Bing; Hung, Sung-Fu; Wang, Hsin-Yi; Yang, Hong Bin; Chen, Jiazang; Chen, Rong; Liu, Bin
2015-05-13
Semiconductor-based photocatalysis and photoelectrocatalysis have received considerable attention as alternative approaches for solar energy harvesting and storage. The photocatalytic or photoelectrocatalytic performance of a semiconductor is closely related to the design of the semiconductor at the nanoscale. Among various nanostructures, one-dimensional (1D) nanostructured photocatalysts and photoelectrodes have attracted increasing interest owing to their unique optical, structural, and electronic advantages. In this article, a comprehensive review of the current research efforts towards the development of 1D semiconductor nanomaterials for heterogeneous photocatalysis and photoelectrocatalysis is provided and, in particular, a discussion of how to overcome the challenges for achieving full potential of 1D nanostructures is presented. It is anticipated that this review will afford enriched information on the rational exploration of the structural and electronic properties of 1D semiconductor nanostructures for achieving more efficient 1D nanostructure-based photocatalysts and photoelectrodes for high-efficiency solar energy conversion.
Polaron and bipolaron of uniaxially strained one dimensional zigzag ladder
Yavidov, B.Ya., E-mail: bakhrom.yavidov@gmail.com
2016-09-15
An influence of the uniaxial strains in one dimensional zigzag ladder (1DZL) on the properties of polarons and bipolarons is considered. It is shown that strain changes all the parameters of the system, in particular, spectrum, existing bands and the masses of charge carriers. Numerical results obtained by taking into an account the Poisson effect clearly indicate that the properties of the (bi)polaronic system can be tuned via strain. Mass of bipolaron can be manipulated by the strain too which in turn leads to the way of tuning Bose–Einstein condensation temperature T{sub BEC} of bipolarons. It is shown that T{sub BEC} of bipolarons in strained 1DZL reasonably correlates with the values of critical temperature of superconductivity of certain perovskites.
Thermal radiation in one-dimensional photonic quasicrystals with graphene
Costa, C. H.; Vasconcelos, M. S.; Fulco, U. L.; Albuquerque, E. L.
2017-10-01
In this work we investigate the thermal power spectra of the electromagnetic radiation through one-dimensional stacks of dielectric layers, with graphene at their interfaces, arranged according to a quasiperiodic structure obeying the Fibonacci (FB), Thue-Morse (TM) and double-period (DP) sequences. The thermal radiation power spectra are determined by means of a theoretical model based on a transfer matrix formalism for both normal and oblique incidence geometries, considering the Kirchhoff's law of thermal radiation. A systematic study of the consequences of the graphene layers in the thermal emittance spectra is presented and discussed. We studied also the radiation spectra considering the case where the chemical potential is changed in order to tune the omnidirectional photonic band gap.
One-dimensional quasi-relativistic particle in the box
Kaleta, Kamil; Malecki, Jacek
2011-01-01
Two-term Weyl-type asymptotic law for the eigenvalues of one-dimensional quasi-relativistic Hamiltonian (-h^2 c^2 d^2/dx^2 + m^2 c^4)^(1/2) + V_well(x) (the Klein-Gordon square-root operator with electrostatic potential) with the infinite square well potential V_well(x) is given: the n-th eigenvalue is equal to (n pi/2 - pi/8) h c/a + O(1/n), where 2a is the width of the potential well. Simplicity of eigenvalues is proved. Some L^2 and L^infinity properties of eigenfunctions are also studied. Eigenvalues represent energies of a `massive particle in the box' quasi-relativistic model.
Novel superconducting phenomena in quasi-one-dimensional Bechgaard salts
Jerome, Denis; Yonezawa, Shingo
2016-03-01
It is the saturation of the transition temperature Tc in the range of 24 K for known materials in the late sixties that triggered the search for additional materials offering new coupling mechanisms leading in turn to higher Tc's. As a result of this stimulation, superconductivity in organic matter was discovered in tetramethyl-tetraselenafulvalene-hexafluorophosphate, (TMTSF)2PF6, in 1979, in the laboratory founded at Orsay by Professor Friedel and his colleagues in 1962. Although this conductor is a prototype example for low-dimensional physics, we mostly focus in this article on the superconducting phase of the ambient-pressure superconductor (TMTSF)2ClO4, which has been studied most intensively among the TMTSF salts. We shall present a series of experimental results supporting nodal d-wave symmetry for the superconducting gap in these prototypical quasi-one-dimensional conductors. xml:lang="fr"
One-Dimensional Time to Explosion (Thermal Sensitivity) of ANPZ
Hsu, P. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Hust, G. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); McClelland, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Gresshoff, M. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2014-11-12
Incidents caused by fire and combat operations can heat energetic materials that may lead to thermal explosion and result in structural damage and casualty. Some explosives may thermally explode at fairly low temperatures (< 100 C) and the violence from thermal explosion may cause a significant damage. Thus it is important to understand the response of energetic materials to thermal insults. The One Dimensional Time to Explosion (ODTX) system at the Lawrence Livermore National Laboratory has been used for decades to measure times to explosion, threshold thermal explosion temperature, and determine kinetic parameters of energetic materials. Samples of different configurations (pressed part, powder, paste, and liquid) can be tested in the system. The ODTX testing can also provide useful data for assessing the thermal explosion violence of energetic materials. This report summarizes the recent ODTX experimental data and modeling results for 2,6-diamino-3,5-dintropyrazine (ANPZ).
Capillary condensation in one-dimensional irregular confinement
Handford, Thomas P.; Pérez-Reche, Francisco J.; Taraskin, Sergei N.
2013-07-01
A lattice-gas model with heterogeneity is developed for the description of fluid condensation in finite sized one-dimensional pores of arbitrary shape. Mapping to the random-field Ising model allows an exact solution of the model to be obtained at zero-temperature, reproducing the experimentally observed dependence of the amount of fluid adsorbed in the pore on external pressure. It is demonstrated that the disorder controls the sorption for long pores and can result in H2-type hysteresis. Finite-temperature Metropolis dynamics simulations support analytical findings in the limit of low temperatures. The proposed framework is viewed as a fundamental building block of the theory of capillary condensation necessary for reliable structural analysis of complex porous media from adsorption-desorption data.
Compaction of quasi-one-dimensional elastoplastic materials
Shaebani, M. Reza; Najafi, Javad; Farnudi, Ali; Bonn, Daniel; Habibi, Mehdi
2017-06-01
Insight into crumpling or compaction of one-dimensional objects is important for understanding biopolymer packaging and designing innovative technological devices. By compacting various types of wires in rigid confinements and characterizing the morphology of the resulting crumpled structures, here, we report how friction, plasticity and torsion enhance disorder, leading to a transition from coiled to folded morphologies. In the latter case, where folding dominates the crumpling process, we find that reducing the relative wire thickness counter-intuitively causes the maximum packing density to decrease. The segment size distribution gradually becomes more asymmetric during compaction, reflecting an increase of spatial correlations. We introduce a self-avoiding random walk model and verify that the cumulative injected wire length follows a universal dependence on segment size, allowing for the prediction of the efficiency of compaction as a function of material properties, container size and injection force.
One-dimensional photonic crystal fishbone hybrid nanocavity with nanoposts
Lu, Tsan-Wen; Lin, Pin-Tso; Lee, Po-Tsung, E-mail: potsung@mail.nctu.edu.tw [Department of Photonics and Institute of Electro-Optical Engineering, National Chiao Tung University, Rm. 413 CPT Building, 1001 Ta-Hsueh Road, Hsinchu 30010, Taiwan (China)
2014-05-12
We propose and investigate a one-dimensional photonic crystal (PhC) fishbone (FB) hybrid nanocavity lying on silver substrate with a horizontal air slot. With very few PhC periods, the confined transverse-magnetic, TM{sub 10} hybrid mode concentrated within the air slot shows high quality factor over effective mode volume ratio larger than 10{sup 5}λ{sup −3}. Most importantly, this FB hybrid nanocavity allows formation of low-index nanoposts within the air slot without significantly affecting the mode properties. These nanoposts guarantee the structural stabilities under different environmental perturbations. Furthermore, capabilities of our proposed design in serving as optical sensors and tweezers for bio-sized nanoparticles are also investigated.
Reprint of : Absorbing/Emitting Phonons with one dimensional MOSFETs
Bosisio, Riccardo; Gorini, Cosimo; Fleury, Geneviève; Pichard, Jean-Louis
2016-08-01
We consider nanowires in the field effect transistor device configuration. Modeling each nanowire as a one dimensional lattice with random site potentials, we study the heat exchanges between the nanowire electrons and the substrate phonons, when electron transport is due to phonon-assisted hops between localized states. Shifting the nanowire conduction band with a metallic gate induces different behaviors. When the Fermi potential is located near the band center, a bias voltage gives rise to small local heat exchanges which fluctuate randomly along the nanowire. When it is located near one of the band edges, the bias voltage yields heat currents which flow mainly from the substrate towards the nanowire near one boundary of the nanowire, and in the opposite direction near the other boundary. This opens interesting perspectives for heat management at submicron scales: arrays of parallel gated nanowires could be used for a field control of phonon emission/absorption.
Charge diffusion in the one-dimensional Hubbard model
Steinigeweg, R.; Jin, F.; De Raedt, H.; Michielsen, K.; Gemmer, J.
2017-08-01
We study the real-time and real-space dynamics of charge in the one-dimensional Hubbard model in the limit of high temperatures. To this end, we prepare pure initial states with sharply peaked density profiles and calculate the time evolution of these nonequilibrium states, by using numerical forward-propagation approaches to chains as long as 20 sites. For a class of typical states, we find excellent agreement with linear-response theory and unveil the existence of remarkably clean charge diffusion in the regime of strong particle-particle interactions. We additionally demonstrate that, in the half-filling sector, this diffusive behavior does not depend on certain details of our initial conditions, i.e., it occurs for five different realizations with random and nonrandom internal degrees of freedom, single and double occupation of the central site, and displacement of spin-up and spin-down particles.
Analytical models of optical response in one-dimensional semiconductors
Pedersen, Thomas Garm, E-mail: tgp@nano.aau.dk
2015-09-04
The quantum mechanical description of the optical properties of crystalline materials typically requires extensive numerical computation. Including excitonic and non-perturbative field effects adds to the complexity. In one dimension, however, the analysis simplifies and optical spectra can be computed exactly. In this paper, we apply the Wannier exciton formalism to derive analytical expressions for the optical response in four cases of increasing complexity. Thus, we start from free carriers and, in turn, switch on electrostatic fields and electron–hole attraction and, finally, analyze the combined influence of these effects. In addition, the optical response of impurity-localized excitons is discussed. - Highlights: • Optical response of one-dimensional semiconductors including excitons. • Analytical model of excitonic Franz–Keldysh effect. • Computation of optical response of impurity-localized excitons.
A one-dimensional toy model of globular clusters
Fanelli, D; Ruffo, S; Fanelli, Duccio; Merafina, Marco; Ruffo, Stefano
2001-01-01
We introduce a one-dimensional toy model of globular clusters. The model is a version of the well-known gravitational sheets system, where we take additionally into account mass and energy loss by evaporation of stars at the boundaries. Numerical integration by the "exact" event-driven dynamics is performed, for initial uniform density and Gaussian random velocities. Two distinct quasi-stationary asymptotic regimes are attained, depending on the initial energy of the system. We guess the forms of the density and velocity profiles which fit numerical data extremely well and allow to perform an independent calculation of the self-consistent gravitational potential. Some power-laws for the asymptotic number of stars and for the collision times are suggested.
Magnons in one-dimensional k-component Fibonacci structures
Costa, C. H.; Vasconcelos, M. S.
2014-05-01
We have studied the magnon transmission through of one-dimensional magnonic k-component Fibonacci structures, where k different materials are arranged in accordance with the following substitution rule: Sn(k)=Sn-1(k)Sn-k(k) (n ≥k=0,1,2,…), where Sn(k) is the nth stage of the sequence. The calculations were carried out in exchange dominated regime within the framework of the Heisenberg model and taking into account the RPA approximation. We have considered multilayers composed of simple cubic spin-S Heisenberg ferromagnets, and, by using the powerful transfer-matrix method, the spin wave transmission is obtained. It is demonstrated that the transmission coefficient has a rich and interesting magnonic pass- and stop-bands structures, which depends on the frequency of magnons and the k values.
Magnons in one-dimensional k-component Fibonacci structures
Costa, C. H., E-mail: carloshocosta@hotmail.com [Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil); Vasconcelos, M. S. [Escola de Ciências e Tecnologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal-RN (Brazil)
2014-05-07
We have studied the magnon transmission through of one-dimensional magnonic k-component Fibonacci structures, where k different materials are arranged in accordance with the following substitution rule: S{sub n}{sup (k)}=S{sub n−1}{sup (k)}S{sub n−k}{sup (k)} (n≥k=0,1,2,…), where S{sub n}{sup (k)} is the nth stage of the sequence. The calculations were carried out in exchange dominated regime within the framework of the Heisenberg model and taking into account the RPA approximation. We have considered multilayers composed of simple cubic spin-S Heisenberg ferromagnets, and, by using the powerful transfer-matrix method, the spin wave transmission is obtained. It is demonstrated that the transmission coefficient has a rich and interesting magnonic pass- and stop-bands structures, which depends on the frequency of magnons and the k values.
Liu Yang; Tang Yi
2008-01-01
By means of the Glauber's coherent state method combined with multiple-scale method,this paper investigates the localized modes in a quantum one-dimensional Klein-Gordon chain and finds that the equation of motion of annihilation operator is reduced to the nonlinear Schr(o)dinger equation.Interestingly,the model can support both bright and dark small amplitude travelling and non-travelling nonlinear localized modes in different parameter spaces.
Magnetic properties of manganese based one-dimensional spin chains.
Asha, K S; Ranjith, K M; Yogi, Arvind; Nath, R; Mandal, Sukhendu
2015-12-14
We have correlated the structure-property relationship of three manganese-based inorganic-organic hybrid structures. Compound 1, [Mn2(OH-BDC)2(DMF)3] (where BDC = 1,4-benzene dicarboxylic acid and DMF = N,N'-dimethylformamide), contains Mn2O11 dimers as secondary building units (SBUs), which are connected by carboxylate anions forming Mn-O-C-O-Mn chains. Compound 2, [Mn2(BDC)2(DMF)2], contains Mn4O20 clusters as SBUs, which also form Mn-O-C-O-Mn chains. In compound 3, [Mn3(BDC)3(DEF)2] (where DEF = N,N'-diethylformamide), the distorted MnO6 octahedra are linked to form a one-dimensional chain with Mn-O-Mn connectivity. The magnetic properties were investigated by means of magnetization and heat capacity measurements. The temperature dependent magnetic susceptibility of all the three compounds could be nicely fitted using a one-dimensional S = 5/2 Heisenberg antiferromagnetic chain model and the value of intra-chain exchange coupling (J/k(B)) between Mn(2+) ions was estimated to be ∼1.1 K, ∼0.7 K, and ∼0.46 K for compounds 1, 2, and 3, respectively. Compound 1 does not undergo any magnetic long-range-order down to 2 K while compounds 2 and 3 undergo long-range magnetic order at T(N) ≈ 4.2 K and ≈4.3 K, respectively, which are of spin-glass type. From the values of J/k(B) and T(N) the inter-chain coupling (J(⊥)/k(B)) was calculated to be about 0.1J/k(B) for both compounds 2 and 3, respectively.
A One-Dimensional Synthetic-Aperture Microwave Radiometer
Doiron, Terence; Piepmeier, Jeffrey
2010-01-01
A proposed one-dimensional synthetic- aperture microwave radiometer could serve as an alternative to either the two-dimensional synthetic-aperture radiometer described in the immediately preceding article or to a prior one-dimensional one, denoted the Electrically Scanned Thinned Array Radiometer (ESTAR), mentioned in that article. The proposed radiometer would operate in a pushbroom imaging mode, utilizing (1) interferometric cross-track scanning to obtain cross-track resolution and (2) the focusing property of a reflector for along-track resolution. The most novel aspect of the proposed system would be the antenna (see figure), which would include a cylindrical reflector of offset parabolic cross section. The reflector could be made of a lightweight, flexible material amenable to stowage and deployment. Other than a stowage/deployment mechanism, the antenna would not include moving parts, and cross-track scanning would not entail mechanical rotation of the antenna. During operation, the focal line, parallel to the cylindrical axis, would be oriented in the cross-track direction, so that placement of receiving/radiating elements at the focal line would afford the desired along-track resolution. The elements would be microwave feed horns sparsely arrayed along the focal line. The feed horns would be oriented with their short and long cross-sectional dimensions parallel and perpendicular, respectively, to the cylindrical axis to obtain fan-shaped beams having their broad and narrow cross-sectional dimensions parallel and perpendicular, respectively, to the cylindrical axis. The interference among the beams would be controlled in the same manner as in the ESTAR to obtain along-cylindrical- axis (cross-track) resolution and cross-track scanning.
Itsuki Banno; Kazumi Fujima
2007-01-01
A determinantal formula is developed for direct evaluation of transition amplitude without solving the wave equation in a one-dimensional potential scattering system. Our formulation is based on the principle that a desired quantity can be extracted from the wave operator, which is the master operator maintaining all the information of the system. This principle is tested in a simplified system, I.e., in a one-dimensional potential scattering system. We are now developing a formula for direct evaluation of near-field amplitude to design a system, in which local Geld enhancement is desired.
Jiménez Pérez, J. L.; Sakanaka, P. H.; Algatti, M. A.; Mendoza-Alvarez, J. G.; Cruz Orea, A.
2001-05-01
This paper presents the theoretical and experimental results for oxide thin film growth on titanium films previously deposited over glass substrate. Ti films of thickness 0.1 μm were heated by Nd:YAG laser pulses in air. The oxide tracks were created by moving the samples with a constant speed of 2 mm/s, under the laser action. The micro-topographic analysis of the tracks was performed by a microprofiler. The results taken along a straight line perpendicular to the track axis revealed a Gaussian profile that closely matches the laser's spatial mode profile, indicating the effectiveness of the surface temperature gradient on the film's growth process. The sample's micro-Raman spectra showed two strong bands at 447 and 612 cm -1 associated with the TiO 2 structure. This is a strong indication that thermo-oxidation reactions took place at the Ti film surface that reached an estimated temperature of 1160 K just due to the action of the first pulse. The results obtained from the numerical integration of the analytical equation which describes the oxidation rate (Wagner equation) are in agreement with the experimental data for film thickness in the high laser intensity region. This shows the partial accuracy of the one-dimensional model adopted for describing the film growth rate.
Berezhkovskii, A. M.; Pustovoit, M. A.; Bezrukov, S. M.
2007-04-01
Brownian dynamics simulations of the particle diffusing in a long conical tube (the length of the tube is much greater than its smallest radius) are used to study reduction of the three-dimensional diffusion in tubes of varying cross section to an effective one-dimensional description. The authors find that the one-dimensional description in the form of the Fick-Jacobs equation with a position-dependent diffusion coefficient, D(x ), suggested by Zwanzig [J. Phys. Chem. 96, 3926 (1992)], with D(x ) given by the Reguera-Rubí formula [Phys. Rev. E 64, 061106 (2001)], D(x )=D/√1+R'(x)2, where D is the particle diffusion coefficient in the absence of constraints, and R(x ) is the tube radius at x, is valid when ∣R'(x)∣⩽1. When ∣R'(x)∣>1, higher spatial derivatives of the one-dimensional concentration in the effective diffusion equation cannot be neglected anymore as was indicated by Kalinay and Percus [J. Chem. Phys. 122, 204701 (2005)]. Thus the reduction to the effective one-dimensional description is a useful tool only when ∣R'(x)∣⩽1 since in this case one can apply the powerful standard methods to analyze the resulting diffusion equation.
A dynamical formulation of one-dimensional scattering theory and its applications in optics
Mostafazadeh, Ali, E-mail: amostafazadeh@ku.edu.tr
2014-02-15
We develop a dynamical formulation of one-dimensional scattering theory where the reflection and transmission amplitudes for a general, possibly complex and energy-dependent, scattering potential are given as solutions of a set of dynamical equations. By decoupling and partially integrating these equations, we reduce the scattering problem to a second order linear differential equation with universal initial conditions that is equivalent to an initial-value time-independent Schrödinger equation. We give explicit formulas for the reflection and transmission amplitudes in terms of the solution of either of these equations and employ them to outline an inverse-scattering method for constructing finite-range potentials with desirable scattering properties at any prescribed wavelength. In particular, we construct optical potentials displaying threshold lasing, antilasing, and unidirectional invisibility. -- Highlights: • Proposes a dynamical theory of scattering in one dimension. • Derives and solves dynamical equations for scattering data. • Gives a new inverse scattering prescription. • Constructs optical potentials with desired scattering properties.
A universal solution to one-dimensional oscillatory integrals
LI JianBing; WANG XueSong; WANG Tao
2008-01-01
How to calculate the highly oscillatory integrals is the bottleneck that restraints the research of light wave and electromagnetic wave's propagation and scattering.Levin method is a classical quadrature method for this type of integrals.Unfortunately it is susceptible to the system of linear equations' ill-conditioned behavior.We bring forward a universal quadrature method in this paper,which adopts Chebyshev differential matrix to solve the ordinary differential equation (ODE).This method can not only obtain the indefinite integral' function values directly,but also make the system of linear equations well-conditioned for general oscillatory integrals.Furthermore,even if the system of linear equations in our method is ill-conditioned,TSVD method can be adopted to solve them properly and eventually obtain accurate integral results,thus making a breakthrough in Levin method's susceptivity to the system of linear equations' ill-conditioned behavior.
One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium
Sanjay K Yadav; Atul Kumar; Dilip K Jaiswal; Naveen Kumar
2011-04-01
The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.
Corrections to the Eckhaus' stability criterion for one-dimensional stationary structures
Malomed, B. A.; Staroselsky, I. E.; Konstantinov, A. B.
1989-01-01
Two amendments to the well-known Eckhaus' stability criterion for small-amplitude non-linear structures generated by weak instability of a spatially uniform state of a non-equilibrium one-dimensional system against small perturbations with finite wavelengths are obtained. Firstly, we evaluate small corrections to the main Eckhaus' term which, on the contrary so that term, do not have a universal form. Comparison of those non-universal corrections with experimental or numerical results gives a possibility to select a more relevant form of an effective nonlinear evolution equation. In particular, the comparison with such results for convective rolls and Taylor vortices gives arguments in favor of the Swift-Hohenberg equation. Secondly, we derive an analog of the Eckhaus criterion for systems degenerate in the sense that in an expansion of their non-linear parts in powers of dynamical variables, the second and third degree terms are absent.
Vectorial coupled-mode solitons in one-dimensional photonic crystals
朱善华; 黄国翔; 崔维娜
2002-01-01
We study the dynamics of vectorial coupled-mode solitons in one-dimensional photonic crystals with quadraticand cubic nonlinearities. Starting from Maxwell's equations, the vectorial coupled-mode equations for the envelopesof two fundamental-frequency optical mode and one low-frequency mode components due to optical rectification arederived by means of the method of multiple scales. A set of coupled soliton solutions of the vectorial coupled-modeequations is provided. The results show that a modulation of the fundamental-frequency optical modes occurs due tothe optical rectification field resulting from the quadratic nonlinearity. The optical rectification field disappears whenthe frequency of the fundamental-frequency optical fields approaches the edge of the photonic bands.
Derrida, Bernard; Meerson, Baruch; Sasorov, Pavel V.
2016-04-01
Consider a one-dimensional branching Brownian motion and rescale the coordinate and time so that the rates of branching and diffusion are both equal to 1. If X1(t ) is the position of the rightmost particle of the branching Brownian motion at time t , the empirical velocity c of this rightmost particle is defined as c =X1(t ) /t . Using the Fisher-Kolmogorov-Petrovsky-Piscounov equation, we evaluate the probability distribution P (c ,t ) of this empirical velocity c in the long-time t limit for c >2 . It is already known that, for a single seed particle, P (c ,t ) ˜exp[-(c2/4 -1 ) t ] up to a prefactor that can depend on c and t . Here we show how to determine this prefactor. The result can be easily generalized to the case of multiple seed particles and to branching random walks associated with other traveling-wave equations.
MULTI-IFE-A one-dimensional computer code for Inertial Fusion Energy (IFE) target simulations
Ramis, R.; Meyer-ter-Vehn, J.
2016-06-01
The code MULTI-IFE is a numerical tool devoted to the study of Inertial Fusion Energy (IFE) microcapsules. It includes the relevant physics for the implosion and thermonuclear ignition and burning: hydrodynamics of two component plasmas (ions and electrons), three-dimensional laser light ray-tracing, thermal diffusion, multigroup radiation transport, deuterium-tritium burning, and alpha particle diffusion. The corresponding differential equations are discretized in spherical one-dimensional Lagrangian coordinates. Two typical application examples, a high gain laser driven capsule and a low gain radiation driven marginally igniting capsule are discussed. In addition to phenomena relevant for IFE, the code includes also components (planar and cylindrical geometries, transport coefficients at low temperature, explicit treatment of Maxwell's equations) that extend its range of applicability to laser-matter interaction at moderate intensities (<1016 W cm-2). The source code design has been kept simple and structured with the aim to encourage user's modifications for specialized purposes.
Levy-Feldgeim distributions for one-dimensional analysis of the Bose-Einstein correlations
Okorokov, V A
2016-01-01
The paper presents the study of relations between parameters of the two central-symmetrical Levy - Feldgeim distributions which can be used for investigation of one-dimensional Bose - Einstein correlations (1D BEC). The systems of equations are suggested for femtoscopic 1D parameters, strength of correlations and radius, in the case of two general view stable distributions for the first time. The relations take into account possible various finite ranges of the Lorentz invariant four-momentum difference for two central-symmetrical Levy - Feldgeim distributions. The systems of transcendental equations are derived for specific case of general view stable distributions most used for experimental study of 1D BEC, namely, for Cauchy and Gauss parameterizations. The mathematical formalism is verified with help of available experimental results for 1D BEC in various processes of strong interaction. The estimations for 1D femtoscopic parameters agree well with experiments in cases of the pair of general central-symme...
Negative refraction angular characterization in one-dimensional photonic crystals.
Jesus Eduardo Lugo
Full Text Available BACKGROUND: Photonic crystals are artificial structures that have periodic dielectric components with different refractive indices. Under certain conditions, they abnormally refract the light, a phenomenon called negative refraction. Here we experimentally characterize negative refraction in a one dimensional photonic crystal structure; near the low frequency edge of the fourth photonic bandgap. We compare the experimental results with current theory and a theory based on the group velocity developed here. We also analytically derived the negative refraction correctness condition that gives the angular region where negative refraction occurs. METHODOLOGY/PRINCIPAL FINDINGS: By using standard photonic techniques we experimentally determined the relationship between incidence and negative refraction angles and found the negative refraction range by applying the correctness condition. In order to compare both theories with experimental results an output refraction correction was utilized. The correction uses Snell's law and an effective refractive index based on two effective dielectric constants. We found good agreement between experiment and both theories in the negative refraction zone. CONCLUSIONS/SIGNIFICANCE: Since both theories and the experimental observations agreed well in the negative refraction region, we can use both negative refraction theories plus the output correction to predict negative refraction angles. This can be very useful from a practical point of view for space filtering applications such as a photonic demultiplexer or for sensing applications.
Charge transport through one-dimensional Moiré crystals
Bonnet, Roméo; Lherbier, Aurélien; Barraud, Clément; Rocca, Maria Luisa Della; Lafarge, Philippe; Charlier, Jean-Christophe
2016-01-01
Moiré superlattices were generated in two-dimensional (2D) van der Waals heterostructures and have revealed intriguing electronic structures. The appearance of mini-Dirac cones within the conduction and valence bands of graphene is one of the most striking among the new quantum features. A Moiré superstructure emerges when at least two periodic sub-structures superimpose. 2D Moiré patterns have been particularly investigated in stacked hexagonal 2D atomic lattices like twisted graphene layers and graphene deposited on hexagonal boron-nitride. In this letter, we report both experimentally and theoretically evidence of superlattices physics in transport properties of one-dimensional (1D) Moiré crystals. Rolling-up few layers of graphene to form a multiwall carbon nanotube adds boundaries conditions that can be translated into interference fringes-like Moiré patterns along the circumference of the cylinder. Such a 1D Moiré crystal exhibits a complex 1D multiple bands structure with clear and robust interband quantum transitions due to the presence of mini-Dirac points and pseudo-gaps. Our devices consist in a very large diameter (>80 nm) multiwall carbon nanotubes of high quality, electrically connected by metallic electrodes acting as charge reservoirs. Conductance measurements reveal the presence of van Hove singularities assigned to 1D Moiré superlattice effect and illustrated by electronic structure calculations.
Negative refraction angular characterization in one-dimensional photonic crystals.
Lugo, Jesus Eduardo; Doti, Rafael; Faubert, Jocelyn
2011-04-06
Photonic crystals are artificial structures that have periodic dielectric components with different refractive indices. Under certain conditions, they abnormally refract the light, a phenomenon called negative refraction. Here we experimentally characterize negative refraction in a one dimensional photonic crystal structure; near the low frequency edge of the fourth photonic bandgap. We compare the experimental results with current theory and a theory based on the group velocity developed here. We also analytically derived the negative refraction correctness condition that gives the angular region where negative refraction occurs. By using standard photonic techniques we experimentally determined the relationship between incidence and negative refraction angles and found the negative refraction range by applying the correctness condition. In order to compare both theories with experimental results an output refraction correction was utilized. The correction uses Snell's law and an effective refractive index based on two effective dielectric constants. We found good agreement between experiment and both theories in the negative refraction zone. Since both theories and the experimental observations agreed well in the negative refraction region, we can use both negative refraction theories plus the output correction to predict negative refraction angles. This can be very useful from a practical point of view for space filtering applications such as a photonic demultiplexer or for sensing applications.
One-dimensional consolidation in unsaturated soils under cyclic loading
Lo, Wei-Cheng; Sposito, Garrison; Lee, Jhe-Wei; Chu, Hsiuhua
2016-05-01
The one-dimensional consolidation model of poroelasticity of Lo et al. (2014) for an unsaturated soil under constant loading is generalized to include an arbitrary time-dependent loading. A closed-form solution for the pore water and air pressures along with the total settlement is derived by employing a Fourier series representation in the spatial domain and a Laplace transformation in the time domain. This solution is illustrated for the important example of a fully-permeable soil cylinder with an undrained initial condition acted upon by a periodic stress. Our results indicate that, in terms of a dimensionless time scale, the transient solution decays to zero most slowly in a water-saturated soil, whereas for an unsaturated soil, the time for the transient solution to die out is inversely proportional to the initial water saturation. The generalization presented here shows that the diffusion time scale for pore water in an unsaturated soil is orders of magnitude greater than that in a water-saturated soil, mainly because of the much smaller hydraulic conductivity of the former.
Solitary Wave in One-dimensional Buckyball System at Nanoscale
Xu, Jun; Zheng, Bowen; Liu, Yilun
2016-01-01
We have studied the stress wave propagation in one-dimensional (1-D) nanoscopic buckyball (C60) system by molecular dynamics (MD) simulation and quantitative modeling. Simulation results have shown that solitary waves are generated and propagating in the buckyball system through impacting one buckyball at one end of the buckyball chain. We have found the solitary wave behaviors are closely dependent on the initial temperature and impacting speed of the buckyball chain. There are almost no dispersion and dissipation of the solitary waves (stationary solitary wave) for relatively low temperature and high impacting speed. While for relatively high temperature and low impacting speed the profile of the solitary waves is highly distorted and dissipated after propagating several tens of buckyballs. A phase diagram is proposed to describe the effect of the temperature and impacting speed on the solitary wave behaviors in buckyball system. In order to quantitatively describe the wave behavior in buckyball system, a simple nonlinear-spring model is established, which can describe the MD simulation results at low temperature very well. The results presented in this work may lay a solid step towards the further understanding and manipulation of stress wave propagation and impact energy mitigation at nanoscale. PMID:26891624
Correlation effects for a quasi-one-dimensional polaron gas
Machado, Paulo Cesar Miranda [Escola de Engenharia Eletrica e de Computacao, Universidade Federal de Goias, Goiania (Brazil); Borges, Antonio Newton; Osorio, Francisco Aparecido Pinto [Instituto de Fisica, Universidade Federal de Goias, Goiania (Brazil); Nucleo de Pesquisa em Fisica, Pontificia Universidade Catolica de Goias, Goiania (Brazil)
2011-04-15
In this work, we investigate the plasmon-LO phonon interaction effects on the intrasubband structure factor, electron-electron effective potential, and plasmon energy associated with the lowest subband in a GaAs-AlGaAs rectangular quantum-well wire (QWW) as a function of the electronic density. Our calculations are performed using the self-consistent field approximation, which includes the local-field correction (LFC) within the Singwi, Tosi, Land, and Sjolander (STLS) theory, at zero temperature and assuming a three-subband model, where only the first subband is occupied by electrons. We report for the first time dips in the structure factor spectra as a function of the quasi-one-dimensional (Q1D) plasmon-LO phonon wavevector that are directly related with the resonant split of the collective excitation energy into two branches due to the polaronic effects. (Copyright copyright 2011 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Solution-phase Synthesis of One-dimensional Semiconductor Nanostructures
Jianfeng YE; Limin QI
2008-01-01
The synthesis of one-dimensional (1D) semiconductor nanostructures has been studied intensively for a wide range of materials due to their unique structural and physical properties and promising potential for future technological applications. Among various strategies for synthesizing 1D semiconductor nanostructures, solution-phase synthetic routes are advantageous in terms of cost, throughput, modulation of composition, and the potential for large-scale and environmentally benign production. This article gives a concise review on the recent developments in the solution-phase synthesis of 1D semiconductor nanostructures of different compositions, sizes, shapes, and architectures. We first introduce several typical solution-phase synthetic routes based on controlled precipitation from homogeneous solutions, including hydrothermal/solvothermal process, solution-liquid-solid (SLS) process, high-temperature organic-solution process, and low-temperature aqueous-solution process. Subsequently, we discuss two solution-phase synthetic strategies involving solid templates or substrates, such as the chemical transformation of 1D sacrificial templates and the oriented growth of 1D nanostructure arrays on solid substrates. Finally, prospects of the solution-phase approaches to 1D semiconductor nanostructures will be briefly discussed.
Controlled Growth of One-Dimensional Oxide Nanomaterials
Xiaosheng FANG; Lide ZHANG
2006-01-01
This article reviews the recent developments in the controlled growth of one-dimensional (1D) oxide nanomaterials, including ZnO, SnO2, In2O3, Ga2O3, SiOx, MgO, and Al2O3. The growth of 1D oxide nanomaterials was carried out in a simple chemical vapor transport and condensation system. This article will begin with a survey of nanotechnology and 1D nanomaterials achieved by many researchers, and then mainly discuss on the controlled growth of 1D oxide nanomaterials with their morphologies, sizes, compositions, and microstructures controlled by altering experimental parameters, such as the temperature at the source material and the substrate, temperature gradient in the tube furnace, the total reaction time, the heating rate of the furnace, the gas flow rate, and the starting material. Their roles in the formation of various morphologies are analyzed and discussed. Finally, this review will be concluded with personal perspectives on the future research directions of this area.
Approximate Relativistic Solutions for One-Dimensional Cylindrical Coaxial Diode
曾正中; 刘国治; 邵浩
2002-01-01
Two approximate analytical relativistic solutions for one-dimensional, space-chargelimited cylindrical coaxial diode are derived and utilized to compose best-fitting approximate solutions. Comparison of the best-fitting solutions with the numerical one demonstrates an error of about 11% for cathode-inside arrangement and 12% in the cathode-outside case for ratios of larger to smaller electrode radius from 1.2 to 10 and a voltage above 0.5 MV up to 5 MV. With these solutions the diode lengths for critical self-magnetic bending and for the condition under which the parapotential model validates are calculated to be longer than 1 cm up to more than 100 cm depending on voltage, radial dimensions and electrode arrangement. The influence of ion flow from the anode on the relativistic electron-only solution is numerically computed, indicating an enhancement factor of total diode current of 1.85 to 4.19 related to voltage, radial dimension and electrode arrangement.
Negativity spectrum of one-dimensional conformal field theories
Ruggiero, Paola; Calabrese, Pasquale
2016-01-01
The partial transpose $\\rho_A^{T_2}$ of the reduced density matrix $\\rho_A$ is the key object to quantify the entanglement in mixed states, in particular through the presence of negative eigenvalues in its spectrum. Here we derive analytically the distribution of the eigenvalues of $\\rho_A^{T_2}$, that we dub negativity spectrum, in the ground sate of gapless one-dimensional systems described by a Conformal Field Theory (CFT), focusing on the case of two adjacent intervals. We show that the negativity spectrum is universal and depends only on the central charge of the CFT, similarly to the entanglement spectrum. The precise form of the negativity spectrum depends on whether the two intervals are in a pure or mixed state, and in both cases, a dependence on the sign of the eigenvalues is found. This dependence is weak for bulk eigenvalues, whereas it is strong at the spectrum edges. We also investigate the scaling of the smallest (negative) and largest (positive) eigenvalues of $\\rho_A^{T_2}$. We check our resu...
One-Dimensional Electron Transport Layers for Perovskite Solar Cells
Ujwal K. Thakur
2017-04-01
Full Text Available The electron diffusion length (Ln is smaller than the hole diffusion length (Lp in many halide perovskite semiconductors meaning that the use of ordered one-dimensional (1D structures such as nanowires (NWs and nanotubes (NTs as electron transport layers (ETLs is a promising method of achieving high performance halide perovskite solar cells (HPSCs. ETLs consisting of oriented and aligned NWs and NTs offer the potential not merely for improved directional charge transport but also for the enhanced absorption of incoming light and thermodynamically efficient management of photogenerated carrier populations. The ordered architecture of NW/NT arrays affords superior infiltration of a deposited material making them ideal for use in HPSCs. Photoconversion efficiencies (PCEs as high as 18% have been demonstrated for HPSCs using 1D ETLs. Despite the advantages of 1D ETLs, there are still challenges that need to be overcome to achieve even higher PCEs, such as better methods to eliminate or passivate surface traps, improved understanding of the hetero-interface and optimization of the morphology (i.e., length, diameter, and spacing of NWs/NTs. This review introduces the general considerations of ETLs for HPSCs, deposition techniques used, and the current research and challenges in the field of 1D ETLs for perovskite solar cells.
A Smart Colorful Supercapacitor with One Dimensional Photonic Crystals
Liu, Cihui; Liu, Xing; Xuan, Hongyun; Ren, Jiaoyu; Ge, Liqin
2015-12-01
To meet the pressing demands for portable and flexible equipment in contemporary society, developing flexible, lightweight, and sustainable supercapacitor systems with large power densities, long cycle life, and ease of strongly required. However, estimating the state-of-charge of existing supercapacitors is difficult, and thus their service life is limited. In this study, we fabricate a flexible color indicative supercapacitor device with mesoporous polyaniline (mPANI)/Poly(N-Isopropyl acrylamide-Graphene Oxide-Acrylic Acid) (P(NiPPAm-GO-AA)) one dimensional photonic crystals (1DPCs) as the electrode material through a low-cost, eco-friendly, and scalable fabrication process. We found that the state-of-charge could be monitored by the structural color oscillation due to the change in the photonic band gap position of the 1DPCs. The flexible 1DPCs supercapacitor is thin at 3 mm and exhibits good specific capacitance of 22.6 F g-1 with retention of 91.1% after 3,000 cycles. This study shows the application of the 1DPCs supercapacitor as a visual ultrathin power source. The technology may find many applications in future wearable electronics.
Cooperative eigenmodes and scattering in one-dimensional atomic arrays
Bettles, Robert J.; Gardiner, Simon A.; Adams, Charles S.
2016-10-01
Collective coupling between dipoles can dramatically modify the optical response of a medium. Such effects depend strongly on the geometry of the medium and the polarization of the light. Using a classical coupled dipole model, here we investigate the simplest case of one-dimensional arrays of interacting atomic dipoles driven by a weak laser field. Changing the polarization and direction of the driving field allows us to separately address superradiant, subradiant, redshifted, and blueshifted eigenmodes, as well as observe strong Fano-like interferences between different modes. The cooperative eigenvectors can be characterized by the phase difference between nearest-neighbor dipoles, ranging from all oscillating in phase to all oscillating out of phase with their nearest neighbors. Investigating the eigenvalue behavior as a function of atom number and lattice spacing, we find that certain eigenmodes of an infinite atomic chain have the same decay rate as a single atom between two mirrors. The effects we observe provide a framework for collective control of the optical response of a medium, giving insight into the behavior of more complicated geometries, as well as providing further evidence for the dipolar analog of cavity QED.
One-Dimensional Electron Transport Layers for Perovskite Solar Cells
Thakur, Ujwal K.; Kisslinger, Ryan; Shankar, Karthik
2017-01-01
The electron diffusion length (Ln) is smaller than the hole diffusion length (Lp) in many halide perovskite semiconductors meaning that the use of ordered one-dimensional (1D) structures such as nanowires (NWs) and nanotubes (NTs) as electron transport layers (ETLs) is a promising method of achieving high performance halide perovskite solar cells (HPSCs). ETLs consisting of oriented and aligned NWs and NTs offer the potential not merely for improved directional charge transport but also for the enhanced absorption of incoming light and thermodynamically efficient management of photogenerated carrier populations. The ordered architecture of NW/NT arrays affords superior infiltration of a deposited material making them ideal for use in HPSCs. Photoconversion efficiencies (PCEs) as high as 18% have been demonstrated for HPSCs using 1D ETLs. Despite the advantages of 1D ETLs, there are still challenges that need to be overcome to achieve even higher PCEs, such as better methods to eliminate or passivate surface traps, improved understanding of the hetero-interface and optimization of the morphology (i.e., length, diameter, and spacing of NWs/NTs). This review introduces the general considerations of ETLs for HPSCs, deposition techniques used, and the current research and challenges in the field of 1D ETLs for perovskite solar cells. PMID:28468280
Nucleation and growth of nanoscaled one-dimensional materials
Cui, Hongtao
Nanoscaled one-dimensional materials have attracted great interest due to their novel physical and chemical properties. The purpose of this dissertation is to study the nucleation and growth mechanisms of carbon nanotubes and silicon nitride nanowires with their field emission applications in mind. As a result of this research, a novel methodology has been developed to deposit aligned bamboo-like carbon nanotubes on substrates using a methane and ammonia mixture in microwave plasma enhanced chemical deposition. Study of growth kinetics suggests that the carbon diffusion through bulk catalyst particles controls growth in the initial deposition process. Microstructures of carbon nanotubes are affected by the growth temperature and carbon concentration in the gas phase. High-resolution transmission electron microscope confirms the existence of the bamboo-like structure. Electron diffraction reveals that the iron-based catalyst nucleates and sustains the growth of carbon nanotubes. A nucleation and growth model has been constructed based upon experimental data and observations. In the study of silicon nitride nanoneedles, a vapor-liquid-solid model is employed to explain the nucleation and growth processes. Ammonia plasma etching is proposed to reduce the size of the catalyst and subsequently produce the novel needle-like nanostructure. High-resolution transmission electron microscope shows the structure is well crystallized and composed of alpha-silicon nitride. Other observations in the structure are also explained.
A disorder-enhanced quasi-one-dimensional superconductor.
Petrović, A P; Ansermet, D; Chernyshov, D; Hoesch, M; Salloum, D; Gougeon, P; Potel, M; Boeri, L; Panagopoulos, C
2016-01-01
A powerful approach to analysing quantum systems with dimensionality d>1 involves adding a weak coupling to an array of one-dimensional (1D) chains. The resultant quasi-1D (q1D) systems can exhibit long-range order at low temperature, but are heavily influenced by interactions and disorder due to their large anisotropies. Real q1D materials are therefore ideal candidates not only to provoke, test and refine theories of strongly correlated matter, but also to search for unusual emergent electronic phases. Here we report the unprecedented enhancement of a superconducting instability by disorder in single crystals of Na2-δMo6Se6, a q1D superconductor comprising MoSe chains weakly coupled by Na atoms. We argue that disorder-enhanced Coulomb pair-breaking (which usually destroys superconductivity) may be averted due to a screened long-range Coulomb repulsion intrinsic to disordered q1D materials. Our results illustrate the capability of disorder to tune and induce new correlated electron physics in low-dimensional materials.
Spin interference in silicon one-dimensional rings
Bagraev, N T [Ioffe Physico-Technical Institute, RAS, 194021 St Petersburg (Russian Federation); Galkin, N G [Ioffe Physico-Technical Institute, RAS, 194021 St Petersburg (Russian Federation); Gehlhoff, W [Institut fuer Festkoerperphysik, TU Berlin, D-10623 Berlin (Germany); Klyachkin, L E [Ioffe Physico-Technical Institute, RAS, 194021 St Petersburg (Russian Federation); Malyarenko, A M [Ioffe Physico-Technical Institute, RAS, 194021 St Petersburg (Russian Federation); Shelykh, I A [Physics and Astronomy School, University of Southampton, Highfield, Southampton, S017 1BJ (United Kingdom)
2006-11-15
We present the first findings of the spin transistor effect in a Rashba gate-controlled ring embedded in a p-type self-assembled silicon quantum well that is prepared on an n-type Si(100) surface. The coherence and phase sensitivity of the spin-dependent transport of holes are studied by varying the values of the external magnetic field and the bias voltage that are applied perpendicularly to the plane of the double-slit ring. First, the amplitude and phase sensitivity of the 0.7 x (2e{sup 2}/h) feature of the hole quantum conductance staircase revealed by the quantum point contact inserted in one of the arms of the double-slit ring are found to result from the interplay of the spontaneous spin polarization and the Rashba spin-orbit interaction. Second, the quantum scatterers connected to two one-dimensional leads and the quantum point contact inserted are shown to define the amplitude and the phase of the Aharonov-Bohm and the Aharonov-Casher conductance oscillations. (letter to the editor)
A Smart Colorful Supercapacitor with One Dimensional Photonic Crystals.
Liu, Cihui; Liu, Xing; Xuan, Hongyun; Ren, Jiaoyu; Ge, Liqin
2015-12-22
To meet the pressing demands for portable and flexible equipment in contemporary society, developing flexible, lightweight, and sustainable supercapacitor systems with large power densities, long cycle life, and ease of strongly required. However, estimating the state-of-charge of existing supercapacitors is difficult, and thus their service life is limited. In this study, we fabricate a flexible color indicative supercapacitor device with mesoporous polyaniline (mPANI)/Poly(N-Isopropyl acrylamide-Graphene Oxide-Acrylic Acid) (P(NiPPAm-GO-AA)) one dimensional photonic crystals (1DPCs) as the electrode material through a low-cost, eco-friendly, and scalable fabrication process. We found that the state-of-charge could be monitored by the structural color oscillation due to the change in the photonic band gap position of the 1DPCs. The flexible 1DPCs supercapacitor is thin at 3 mm and exhibits good specific capacitance of 22.6 F g(-1) with retention of 91.1% after 3,000 cycles. This study shows the application of the 1DPCs supercapacitor as a visual ultrathin power source. The technology may find many applications in future wearable electronics.
Transmission properties of one-dimensional ternary plasma photonic crystals
Shiveshwari, Laxmi [Department of Physics, K. B. Womens' s College, Hazaribagh 825 301 (India); Awasthi, S. K. [Department of Physics and Material Science and Engineering, Jaypee Institute of Information Technology, Noida 201 304 (India)
2015-09-15
Omnidirectional photonic band gaps (PBGs) are found in one-dimensional ternary plasma photonic crystals (PPC) composed of single negative metamaterials. The band characteristics and transmission properties are investigated through the transfer matrix method. We show that the proposed structure can trap light in three-dimensional space due to the elimination of Brewster's angle transmission resonance allowing the existence of complete PBG. The results are discussed in terms of incident angle, layer thickness, dielectric constant of the dielectric material, and number of unit cells (N) for TE and TM polarizations. It is seen that PBG characteristics is apparent even in an N ≥ 2 system, which is weakly sensitive to the incident angle and completely insensitive to the polarization. Finite PPC could be used for multichannel transmission filter without introducing any defect in the geometry. We show that the locations of the multichannel transmission peaks are in the allowed band of the infinite structure. The structure can work as a single or multichannel filter by varying the number of unit cells. Binary PPC can also work as a polarization sensitive tunable filter.
Phonons in a one-dimensional microfluidic crystal
Beatus, Tsevi; Bar-Ziv, Roy; 10.1038/nphys432
2010-01-01
The development of a general theoretical framework for describing the behaviour of a crystal driven far from equilibrium has proved difficult1. Microfluidic crystals, formed by the introduction of droplets of immiscible fluid into a liquid-filled channel, provide a convenient means to explore and develop models to describe non-equilibrium dynamics2, 3, 4, 5, 6, 7, 8, 9, 10, 11. Owing to the fact that these systems operate at low Reynolds number (Re), in which viscous dissipation of energy dominates inertial effects, vibrations are expected to be over-damped and contribute little to their dynamics12, 13, 14. Against such expectations, we report the emergence of collective normal vibrational modes (equivalent to acoustic 'phonons') in a one-dimensional microfluidic crystal of water-in-oil droplets at Reapprox10-4. These phonons propagate at an ultra-low sound velocity of approx100 mum s-1 and frequencies of a few hertz, exhibit unusual dispersion relations markedly different to those of harmonic crystals, and g...
Trapped Atoms in One-Dimensional Photonic Crystals
Kimble, H.
2013-05-01
I describe one-dimensional photonic crystals that support a guided mode suitable for atom trapping within a unit cell, as well as a second probe mode with strong atom-photon interactions. A new hybrid trap is analyzed that combines optical and Casimir-Polder forces to form stable traps for neutral atoms in dielectric nanostructures. By suitable design of the band structure, the atomic spontaneous emission rate into the probe mode can exceed the rate into all other modes by more than tenfold. The unprecedented single-atom reflectivity r0 ~= 0 . 9 for the guided probe field could create new scientific opportunities, including quantum many-body physics for 1 D atom chains with photon-mediated interactions and high-precision studies of vacuum forces. Towards these goals, my colleagues and I are pursuing numerical simulation, device fabrication, and cold-atom experiments with nanoscopic structures. Funding is provided by by the IQIM, an NSF PFC with support of the Moore Foundation, by the AFOSR QuMPASS MURI, by the DoD NSSEFF program (HJK), and by NSF Grant PHY0652914 (HJK). DEC acknowledges funding from Fundacio Privada Cellex Barcelona.
Validation and Comparison of One-Dimensional Graound Motion Methodologies
B. Darragh; W. Silva; N. Gregor
2006-06-28
Both point- and finite-source stochastic one-dimensional ground motion models, coupled to vertically propagating equivalent-linear shear-wave site response models are validated using an extensive set of strong motion data as part of the Yucca Mountain Project. The validation and comparison exercises are presented entirely in terms of 5% damped pseudo absolute response spectra. The study consists of a quantitative analyses involving modeling nineteen well-recorded earthquakes, M 5.6 to 7.4 at over 600 sites. The sites range in distance from about 1 to about 200 km in the western US (460 km for central-eastern US). In general, this validation demonstrates that the stochastic point- and finite-source models produce accurate predictions of strong ground motions over the range of 0 to 100 km and for magnitudes M 5.0 to 7.4. The stochastic finite-source model appears to be broadband, producing near zero bias from about 0.3 Hz (low frequency limit of the analyses) to the high frequency limit of the data (100 and 25 Hz for response and Fourier amplitude spectra, respectively).
Fermion Coherent State Studies of One-Dimensional Hubbard Model
LIN Ji; GAO Xian-Long; WANG Ke-Lin
2007-01-01
We present a comparative study of the ground state of the one-dimensional Hubbard model. We first use a new fermion coherent state method in the framework of Fermi liquid theory by introducing a hole operator and considering the interactions of two pairs electrons and holes. We construct the ground state of the Hubbard model as ｜〉 = [f + ∑′ψc+k1σ1 h+k2σ2 c+k3σ3 h+k4σ4 ∏exp(ρc+k1σ1 h+k2σ2)] [〉0, where ψ and ρ are the coupling constants. Our results are then compared to those of variational methods, density functional theory based on the exact solvable Bethe ansatz solutions, variational Monto-Carlo method (VMC) as well as to the exact result of the infinite system. We find satisfactory agreement between the fermion coherent state scheme and the VMC data, and provide a new picture to deal with the strongly correlated system.
Topological water wave states in a one-dimensional structure
Yang, Zhaoju; Gao, Fei; Zhang, Baile
2016-01-01
Topological concepts have been introduced into electronic, photonic, and phononic systems, but have not been studied in surface-water-wave systems. Here we study a one-dimensional periodic resonant surface-water-wave system and demonstrate its topological transition. By selecting three different water depths, we can construct different types of water waves - shallow, intermediate and deep water waves. The periodic surface-water-wave system consists of an array of cylindrical water tanks connected with narrow water channels. As the width of connecting channel varies, the band diagram undergoes a topological transition which can be further characterized by Zak phase. This topological transition holds true for shallow, intermediate and deep water waves. However, the interface state at the boundary separating two topologically distinct arrays of water tanks can exhibit different bands for shallow, intermediate and deep water waves. Our work studies for the first time topological properties of water wave systems, and paves the way to potential management of water waves. PMID:27373982
Charge transport through one-dimensional Moiré crystals.
Bonnet, Roméo; Lherbier, Aurélien; Barraud, Clément; Della Rocca, Maria Luisa; Lafarge, Philippe; Charlier, Jean-Christophe
2016-01-20
Moiré superlattices were generated in two-dimensional (2D) van der Waals heterostructures and have revealed intriguing electronic structures. The appearance of mini-Dirac cones within the conduction and valence bands of graphene is one of the most striking among the new quantum features. A Moiré superstructure emerges when at least two periodic sub-structures superimpose. 2D Moiré patterns have been particularly investigated in stacked hexagonal 2D atomic lattices like twisted graphene layers and graphene deposited on hexagonal boron-nitride. In this letter, we report both experimentally and theoretically evidence of superlattices physics in transport properties of one-dimensional (1D) Moiré crystals. Rolling-up few layers of graphene to form a multiwall carbon nanotube adds boundaries conditions that can be translated into interference fringes-like Moiré patterns along the circumference of the cylinder. Such a 1D Moiré crystal exhibits a complex 1D multiple bands structure with clear and robust interband quantum transitions due to the presence of mini-Dirac points and pseudo-gaps. Our devices consist in a very large diameter (>80 nm) multiwall carbon nanotubes of high quality, electrically connected by metallic electrodes acting as charge reservoirs. Conductance measurements reveal the presence of van Hove singularities assigned to 1D Moiré superlattice effect and illustrated by electronic structure calculations.
Redshift distortions in one-dimensional power spectra
Desjacques, V; Desjacques, Vincent; Nusser, Adi
2004-01-01
We present a model for one-dimensional (1D) matter power spectra in redshift space as estimated from data provided along individual lines of sight. We derive analytic expressions for these power spectra in the linear and nonlinear regimes, focusing on redshift distortions arising from peculiar velocities. In the linear regime, redshift distortions enhance the 1D power spectra only on small scales, and do not affect the power on large scales. This is in contrast to the effect of distortions on three-dimensional (3D) power spectra estimated from data in 3D space, where the enhancement is independent of scale. For CDM cosmologies, the 1D power spectra in redshift and real space are similar for wavenumbers $q<0.1h/Mpc$ where both have a spectral index close to unity, independent of the details of the 3D power spectrum. Nonlinear corrections drive the 1D power spectrum in redshift space into a nearly universal shape over scale $q<10h/Mpc$, and suppress the power on small scales as a result of the strong velo...
Electron Rydberg wave packets in one-dimensional atoms
Supriya Chatterjee; Amitava Choudhuri; Aparna Saha; B Talukdar
2010-09-01
An expression for the transition probability or form factor in one-dimensional Rydberg atom irradiated by short half-cycle pulse was constructed. In applicative contexts, our expression was found to be more useful than the corresponding result given by Landau and Lifshitz. Using the new expression for the form factor, the motion of a localized quantum wave packet was studied with particular emphasis on its revival and super-revival properties. Closed form analytical expressions were derived for expectation values of the position and momentum operators that characterized the widths of the position and momentum distributions. Transient phase-space localization of the wave packet produced by the application of a single impulsive kick was explicitly demonstrated. The undulation of the uncertainty product as a function of time was studied in order to visualize how the motion of the wave packet in its classical trajectory spreads throughout the orbit and the system becomes nonclassical. The process, however, repeats itself such that the atom undergoes a free evolution from a classical, to a nonclassical, and back to a classical state.
One-dimensional Ising model with multispin interactions
Turban, L
2016-01-01
We study the spin-$1/2$ Ising chain with multispin interactions $K$ involving the product of $m$ successive spins, for general values of $m$. Using a change of spin variables the zero-field partition function of a finite chain is obtained for free and periodic boundary conditions (BC) and we calculate the two-spin correlation function. When placed in an external field $H$ the system is shown to be self-dual. Using another change of spin variables the one-dimensional (1D) Ising model with multispin interactions in a field is mapped onto a zero-field rectangular Ising model with first-neighbour interactions $K$ and $H$. The 2D system, with size $m\\times N/m$, has the topology of a cylinder with helical BC. In the thermodynamic limit $N/m\\to\\infty$, $m\\to\\infty$, a 2D critical singularity develops on the self-duality line, $\\sinh 2K\\sinh 2H=1$.
One dimensional numerical simulation of small scale CFB combustors
Gungor, Afsin [Department of Mechanical Engineering, Faculty of Engineering and Architecture, Nigde University, 51100 Nigde (Turkey)
2009-03-15
In this study, a one-dimensional model which includes volatilization, attrition and combustion of char particles for a circulating fluidized bed (CFB) combustor has been developed. In the modeling, the CFB combustor is analyzed in two regions: bottom zone considering as a bubbling fluidized bed in turbulent fluidization regime and upper zone core-annulus solids flow structure is established. In the bottom zone, a single-phase back-flow cell model is used to represent the solid mixing. Solids exchange, between the bubble phase and emulsion phase is a function of the bubble diameter and varies along the axis of the combustor. In the upper zone, particles move upward in the core and downward in the annulus. Thickness of the annulus varies according to the combustor height. Using the developed simulation program, the effects of operational parameters which are the particle diameter, superficial velocity and air-to-fuel ratio on net solids flux, oxygen and carbon dioxide mole ratios along the bed height and carbon content and bed temperature on the top of the riser are investigated. Simulation results are compared with test results obtained from the 50 kW Gazi University Heat Power Laboratory pilot scale unit and good agreement is observed. (author)
One dimensional coordination polymers: Synthesis, crystal structures and spectroscopic properties
Karaağaç, Dursun; Kürkçüoğlu, Güneş Süheyla; Şenyel, Mustafa; Şahin, Onur
2016-11-01
Two new one dimensional (1D) cyanide complexes, namely [M(4-aepy)2(H2O)2][Pt(CN)4], (4-aepy = 4-(2-aminoethyl)pyridine M = Cu(II) (1) or Zn(II) (2)), have been synthesized and characterized by vibrational (FT-IR and Raman) spectroscopy, single crystal X-ray diffraction, thermal and elemental analyses techniques. The crystallographic analyses reveal that 1 and 2 are isomorphous and isostructural, and crystallize in the monoclinic system and C2 space group. The Pt(II) ions are coordinated by four cyanide-carbon atoms in the square-planar geometry and the [Pt(CN)4]2- ions act as a counter ion. The M(II) ions display an N4O2 coordination sphere with a distorted octahedral geometry, the nitrogen donors belonging to four molecules of the organic 4-aepy that act as unidentate ligands and two oxygen atoms from aqua ligands. The crystal structures of 1 and 2 are similar each other and linked via intermolecular hydrogen bonding, Pt⋯π interactions to form 3D supramolecular network. Vibration assignments of all the observed bands are given and the spectral features also supported to the crystal structures of the complexes.
Automated quantification of one-dimensional nanostructure alignment on surfaces
Dong, Jianjin; Goldthorpe, Irene A.; Mohieddin Abukhdeir, Nasser
2016-06-01
A method for automated quantification of the alignment of one-dimensional (1D) nanostructures from microscopy imaging is presented. Nanostructure alignment metrics are formulated and shown to be able to rigorously quantify the orientational order of nanostructures within a two-dimensional domain (surface). A complementary image processing method is also presented which enables robust processing of microscopy images where overlapping nanostructures might be present. Scanning electron microscopy (SEM) images of nanowire-covered surfaces are analyzed using the presented methods and it is shown that past single parameter alignment metrics are insufficient for highly aligned domains. Through the use of multiple parameter alignment metrics, automated quantitative analysis of SEM images is shown to be possible and the alignment characteristics of different samples are able to be quantitatively compared using a similarity metric. The results of this work provide researchers in nanoscience and nanotechnology with a rigorous method for the determination of structure/property relationships, where alignment of 1D nanostructures is significant.
Stepwise Nanopore Evolution in One-Dimensional Nanostructures
Choi, Jang Wook
2010-04-14
We report that established simple lithium (Li) ion battery cycles can be used to produce nanopores inside various useful one-dimensional (1D) nanostructures such as zinc oxide, silicon, and silver nanowires. Moreover, porosities of these 1D nanomaterials can be controlled in a stepwise manner by the number of Li-battery cycles. Subsequent pore characterization at the end of each cycle allows us to obtain detailed snapshots of the distinct pore evolution properties in each material due to their different atomic diffusion rates and types of chemical bonds. Also, this stepwise characterization led us to the first observation of pore size increases during cycling, which can be interpreted as a similar phenomenon to Ostwald ripening in analogous nanoparticle cases. Finally, we take advantage of the unique combination of nanoporosity and 1D materials and demonstrate nanoporous silicon nanowires (poSiNWs) as excellent supercapacitor (SC) electrodes in high power operations compared to existing devices with activated carbon. © 2010 American Chemical Society.
A one-dimensional theory for Higgs branch operators
Dedushenko, Mykola; Yacoby, Ran
2016-01-01
We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d ${\\cal N} = 4$ superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d ${\\cal N}=4$ theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d ${\\cal N} = 2$ subalgebra of the ${\\cal N}=4$ algebra. The result is a simple model that can be used to calculate correlation functions ...
One-dimensional adhesion model for large scale structures
Kayyunnapara Thomas Joseph
2010-05-01
Full Text Available We discuss initial value problems and initial boundary value problems for some systems of partial differential equations appearing in the modelling for the large scale structure formation in the universe. We restrict the initial data to be bounded measurable and locally bounded variation function and use Volpert product to justify the product which appear in the equation. For more general initial data in the class of generalized functions of Colombeau, we construct the solution in the sense of association.
A New Paradigm of Modeling One-Dimensional River/Stream Watershed Water Quality
Zhang, F.; Yeh, G. G.; Fang, Y.
2002-12-01
This paper presents the development of sediment and reactive chemical transport under non-isotherm condition in one-dimensional river/stream watershed system. We assume that effect of temperature cannot be omitted, so that the distribution of temperature needs to be calculated and biogeochemical parameters can be assigned according to temperature to compute sediment and chemical transport. Through decomposition of reaction network via Gauss-Jordan column reduction, (a) redundant fast reactions and irrelevant kinetic reactions are removed from the system; (b) fast reactions and slow reactions can be decoupled; (c) species reaction equations are transformed into two sets: equilibrium species mass action equations and kinetic-variable reaction equations. This enable our model to include as many types of reactions as possible, choose kinetic-variables instead of chemical species as primary dependent variables, and simplify the reaction terms in transport equations. In our model, production-consumption rate of chemical species is determined by reaction-based formulations, and two options are provided to solve the advection-dispersion transport equation: Lagrangian-Eulerian approach and Finite Element Method in Conservative Form. An example problem is employed to demonstrate the design capability of the model and the robustness of the numerical simulations.
Phase transitions in a one-dimensional multibarrier potential of finite range
Bar, D
2002-01-01
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barries in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend sensitively on the ratio $c$ of spacing to width of the barriers (even in the limit $N \\to \\infty$). We compute here the specific heat of an ensemble of such systems and show that there is critical dependence on this parameter, as well as on the temperature, strongly suggestive of phase transitions.
Encounter distribution of two random walkers on a finite one-dimensional interval
Tejedor, Vincent; Schad, Michaela; Metzler, Ralf [Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching (Germany); Benichou, Olivier; Voituriez, Raphael, E-mail: metz@ph.tum.de [Laboratoire de Physique Theorique de la Matiere Condensee (UMR 7600), Universite Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex (France)
2011-09-30
We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function. (paper)
On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems
J. Hutchinson
2015-01-01
Full Text Available We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.
Temporal coupled mode analysis of one-dimensional magneto-photonic crystals with cavity structures
Saghirzadeh Darki, Behnam; Zeidaabadi Nezhad, Abolghasem; Firouzeh, Zaker Hossein
2016-12-01
In this paper, we propose the time-dependent coupled mode analysis of one-dimensional magneto-photonic crystals including one, two or multiple defect layers. The performance of the structures, namely the total transmission, Faraday rotation and ellipticity, is obtained using the proposed method. The results of the developed analytic approach are verified by comparing them to the results of the exact numerical transfer matrix method. Unlike the widely used numerical method, our proposed analytic method seems promising for the synthesis as well as the analysis purposes. Moreover, the proposed method has not the restrictions of the previously examined analytic methods.
Synthesis and application of one-dimensional nanomaterials
Zhang, Daihua
My research has been focused on the synthesis, characterization and application of three types of one-dimensional (1D) nanostructures, including metal oxide nanowires, transition metal oxide core-shell nanocables, and carbon nanotubes. They represent a new class of materials that have attracted steadily growing interest due to their peculiar properties and unique applications complementary to bulk materials. This dissertation will summarize my studies on these three 1D nanomaterials, as well as propose future research work that may lead to further development of this field. Following a brief introduction to 1D nanomaterials in Chapter 1, Chapter 2 will focus on the first material - metal oxide nanowires. The discussion starts from the synthesis approach and material characterization of metal oxide nanowires, and then shifts to the electron transport properties and potential applications. A series of functional devices based on In2O 3 and SnO2 nanowires will be demonstrated and evaluated, which range from field effect transistors (FETs), nonvolatile memories, to photo-detecting devices and chemical sensors. Chapter 3 will discuss the fabrication of transition metal oxide (TMO) core-shell nanocables and their electron transport properties as a function of temperature and external magnetic field. The discussion will primarily focus on one of the TMO materials---magnetite (Fe3O 4) core-shell nanowires and nanotubes. Chapter 4 focuses on the application of carbon nanotubes (CNTs) in macroelectronics and explores the feasibility of using CNT films as transparent electrodes for organic light emitting diodes (OLEDs). Chapter 5, in the end, summarizes the above discussions and proposes future research directions in 1D nanomaterials.
Filtration-guided assembly for patterning one-dimensional nanostructures
Zhang, Yaozhong; Wang, Chuan; Yeom, Junghoon
2017-04-01
Tremendous progress has been made in synthesizing various types of one-dimensional (1D) nanostructures (NSs), such as nanotubes and nanowires, but some technical challenges still remain in the deterministic assembly of the solution-processed 1D NSs for device integration. In this work we investigate a scalable yet inexpensive nanomaterial assembly method, namely filtration-guided assembly (FGA), to place nanomaterials into desired locations as either an individual entity or ensembles, and form functional devices. FGA not only addresses the assembly challenges but also encompasses the notion of green nanomanufacturing, maximally utilizing nanomaterials and eliminating a waste stream of nanomaterials into the environment. FGA utilizes selective filtration of 1D NSs through the open windows on the nanoporous filter membrane whose surface is patterned by a polymer mask for guiding the 1D NS deposition. The modified soft-lithographic technique called blanket transfer (BT) is employed to create the various photoresist patterns of sub-10-micron resolution on the nanoporous filter membrane like mixed cellulose acetate. We use single-walled carbon nanotubes (SWCNTs) as a model 1D NS and demonstrate the fabrication of an array pattern of homogeneous 1D NS network films over an area of 20 cm2 within 10 min. The FGA-patterned SWCNT network films are transferred onto the substrate using the adhesive-based transfer technique, and show the highly uniform film thickness and resistance measurements across the entire substrate. Finally, the electrical performance of the back-gated transistors made from the FGA and transfer method of 95% pure SWCNTs is demonstrated.
Rashba electron transport in one-dimensional quantum waveguides
无
2010-01-01
The properties of Rashba wave function in the planar one-dimensional waveguide are studied, and the following results are obtained. Due to the Rashba effect, the plane waves of electron with the energy E divide into two kinds of waves with the wave vectors k 1 =k 0 +k δ and k 2 =k 0 -k δ , where k δ is proportional to the Rashba coefficient, and their spin orientations are +π/2 (spin up) and -π/2 (spin down) with respect to the circuit, respectively. If there is gate or ferromagnetic contact in the circuit, the Rashba wave function becomes standing wave form exp(±ik δ l)sin[k 0 (l-L)], where L is the position coordinate of the gate or contact. Unlike the electron without considering the spin, the phase of the Rashba plane or standing wave function depends on the direction angle θ of the circuit. The travel velocity of the Rashba waves with the wave vector k 1 or k 2 are the same hk0/m * . The boundary conditions of the Rashba wave functions at the intersection of circuits are given from the continuity of wave functions and the conservation of current density. Using the boundary conditions of Rashba wave functions we study the transmission and reflection probabilities of Rashba electron moving in several structures, and find the interference effects of the two Rashba waves with different wave vectors caused by ferromagnetic contact or the gate. Lastly we derive the general theory of multiple branches structure. The theory can be used to design various spin polarized devices.
Hardening transition in a one-dimensional model for ferrogels
Annunziata, Mario Alberto; Menzel, Andreas M.; Löwen, Hartmut
2013-05-01
We introduce and investigate a coarse-grained model for quasi one-dimensional ferrogels. In our description the magnetic particles are represented by hard spheres with a magnetic dipole moment in their centers. Harmonic springs connecting these spheres mimic the presence of a cross-linked polymer matrix. A special emphasis is put on the coupling of the dipolar orientations to the elastic deformations of the matrix, where a memory effect of the orientations is included. Although the particles are displaced along one spatial direction only, the system already shows rich behavior: as a function of the magnetic dipole moment, we find a phase transition between "soft-elastic" states with finite interparticle separation and finite compressive elastic modulus on the one hand, and "hardened" states with touching particles and therefore diverging compressive elastic modulus on the other hand. Corresponding phase diagrams are derived neglecting thermal fluctuations of the magnetic particles. In addition, we consider a situation in which a spatially homogeneous magnetization is initially imprinted into the material. Depending on the strength of the magneto-mechanical coupling between the dipole orientations and the elastic deformations, the system then relaxes to a uniaxially ferromagnetic, an antiferromagnetic, or a spiral state of magnetization to minimize its energy. One purpose of our work is to provide a largely analytically solvable approach that can provide a benchmark to test future descriptions of higher complexity. From an applied point of view, our results could be exploited, for example, for the construction of novel damping devices of tunable shock absorbance.
Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals
Costa, C.H.O. [Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Vasconcelos, M.S., E-mail: manoelvasconcelos@yahoo.com.br [Escola de Ciencias e Tecnologia, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Barbosa, P.H.R.; Barbosa Filho, F.F. [Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina-Pi (Brazil)
2012-07-15
In this work we carry out a theoretical analysis of the spectra of magnons in quasiperiodic magnonic crystals arranged in accordance with generalized Fibonacci sequences in the exchange regime, by using a model based on a transfer-matrix method together random-phase approximation (RPA). The generalized Fibonacci sequences are characterized by an irrational parameter {sigma}(p,q), which rules the physical properties of the system. We discussed the magnonic fractal spectra for first three generalizations, i.e., silver, bronze and nickel mean. By varying the generation number, we have found that the fragmentation process of allowed bands makes possible the emergence of new allowed magnonic bulk bands in spectra regions that were magnonic band gaps before, such as which occurs in doped semiconductor devices. This interesting property arises in one-dimensional magnonic quasicrystals fabricated in accordance to quasiperiodic sequences, without the need to introduce some deferent atomic layer or defect in the system. We also make a qualitative and quantitative investigations on these magnonic spectra by analyzing the distribution and magnitude of allowed bulk bands in function of the generalized Fibonacci number F{sub n} and as well as how they scale as a function of the number of generations of the sequences, respectively. - Highlights: Black-Right-Pointing-Pointer Quasiperiodic magnonic crystals are arranged in accordance with the generalized Fibonacci sequence. Black-Right-Pointing-Pointer Heisenberg model in exchange regime is applied. Black-Right-Pointing-Pointer We use a theoretical model based on a transfer-matrix method together random-phase approximation. Black-Right-Pointing-Pointer Fractal spectra are characterized. Black-Right-Pointing-Pointer We analyze the distribution of allowed bulk bands in function of the generalized Fibonacci number.
One-Dimensional Mass-Spring Chains Supporting Elastic Waves with Non-Conventional Topology
2016-04-01
Full Text Available There are two classes of phononic structures that can support elastic waves with non-conventional topology, namely intrinsic and extrinsic systems. The non-conventional topology of elastic wave results from breaking time reversal symmetry (T-symmetry of wave propagation. In extrinsic systems, energy is injected into the phononic structure to break T-symmetry. In intrinsic systems symmetry is broken through the medium microstructure that may lead to internal resonances. Mass-spring composite structures are introduced as metaphors for more complex phononic crystals with non-conventional topology. The elastic wave equation of motion of an intrinsic phononic structure composed of two coupled one-dimensional (1D harmonic chains can be factored into a Dirac-like equation, leading to antisymmetric modes that have spinor character and therefore non-conventional topology in wave number space. The topology of the elastic waves can be further modified by subjecting phononic structures to externally-induced spatio-temporal modulation of their elastic properties. Such modulations can be actuated through photo-elastic effects, magneto-elastic effects, piezo-electric effects or external mechanical effects. We also uncover an analogy between a combined intrinsic-extrinsic systems composed of a simple one-dimensional harmonic chain coupled to a rigid substrate subjected to a spatio-temporal modulation of the side spring stiffness and the Dirac equation in the presence of an electromagnetic field. The modulation is shown to be able to tune the spinor part of the elastic wave function and therefore its topology. This analogy between classical mechanics and quantum phenomena offers new modalities for developing more complex functions of phononic crystals and acoustic metamaterials.
Petkov, K.P.; Puton, M; Madsen, Søren Peder
2014-01-01
A model based on a homogeneous formulation of the governing differential equations (Navier-Stokes equations) describing the process of pressure drop in a simplified geometry of an expansion valve is investigated and simulated. Numerical solutions are compared to experimental results. The model...... is a one dimensional formulation in space and the equations incorporates the change in tubes and orifice diameter as formulated in (S. Madsen et.al., Dynamic Modeling of Phase Crossings in Two-Phase Flow, Communications in Computational Physics 12 (4), 1129-1147). The pressure changes in the flow...
Jiang, Song; Zhang, Jianwen
2017-09-01
We consider an initial-boundary value problem for the one-dimensional equations of compressible isentropic magnetohydrodynamic (MHD) flows. The non-resistive limit of the global solutions with large data is justified. As a by-product, the global well-posedness of the compressible non-resistive MHD equations is established. Moreover, the thickness of the magnetic boundary-layer of the value O(ν^α) with 00 is the resistivity coefficient. The proofs of these results are based on a full use of the so-called ‘effective viscous flux’, the material derivative and the structure of the equations.
van der Laan, Mark; Gruber, Susan
2016-05-01
Consider a study in which one observes n independent and identically distributed random variables whose probability distribution is known to be an element of a particular statistical model, and one is concerned with estimation of a particular real valued pathwise differentiable target parameter of this data probability distribution. The targeted maximum likelihood estimator (TMLE) is an asymptotically efficient substitution estimator obtained by constructing a so called least favorable parametric submodel through an initial estimator with score, at zero fluctuation of the initial estimator, that spans the efficient influence curve, and iteratively maximizing the corresponding parametric likelihood till no more updates occur, at which point the updated initial estimator solves the so called efficient influence curve equation. In this article we construct a one-dimensional universal least favorable submodel for which the TMLE only takes one step, and thereby requires minimal extra data fitting to achieve its goal of solving the efficient influence curve equation. We generalize these to universal least favorable submodels through the relevant part of the data distribution as required for targeted minimum loss-based estimation. Finally, remarkably, given a multidimensional target parameter, we develop a universal canonical one-dimensional submodel such that the one-step TMLE, only maximizing the log-likelihood over a univariate parameter, solves the multivariate efficient influence curve equation. This allows us to construct a one-step TMLE based on a one-dimensional parametric submodel through the initial estimator, that solves any multivariate desired set of estimating equations.
Boukahil, A.; Huber, D. L.
1989-09-01
The harmonic magnon modes in a one-dimensional Heisenberg spin glass having nearest-neighbor exchange interactions of fixed magnitude and random sign are investigated. The Lyapounov exponent is calculated for chains of 107-108 spins over the interval 0<=ω<=4J. In the low-frequency regime, ω<~0.1J, an anomalous behavior for the density of states ρ(ω)~ω-1/3 is established, consistent with earlier results obtained by Stinchcombe and Pimentel using transfer-matrix techniques; at higher frequencies, gaps appear in the spectrum. At low frequencies, the localization length diverges as ω-2/3. A formal connection is established between the spin glass and the one-dimensional discretized Schrödinger equation. By making use of the connection, it is shown that the theory of Derrida and Gardner, which was developed for weak potential disorder, can account quantitatively for the distribution and localization of the low-frequency magnon modes in the spin-glass model.
Analysis and Design of One Dimensional Periodic Foundations for Seismic Base Isolation of Structures
Witarto Witarto
2016-01-01
Full Text Available Periodic foundationis a new type of seismic base isolation system. It is inspired by the periodic material crystal lattice in the solid state physics. This kind of material has a unique property, which is termed as frequency band gap that is capable of blocking incoming waves having frequencies falling within the band gap. Consequently, seismic waves having frequencies falling within the frequency band gap are blocked by the periodic foundation. The ability to block the seismic waveshas put this kind of foundation as a prosperous next generation of seismic base isolators. This paper provides analytical study on the one dimensional (1D type periodic foundations to investigate their seismic performance. The general idea of basic theory of one dimensional (1D periodic foundations is first presented.Then, the parametric studies considering infinite and finite boundary conditions are discussed. The effect of superstructure on the frequency band gap is investigated as well. Based on the analytical study, a set of equations is proposed for the design guidelines of 1D periodic foundations for seismic base isolation of structures.
One-dimensional Turbulence Models of Type I X-ray Bursts
Hou, Chen [Univ. of Minnesota, Minneapolis, MN (United States)
2016-01-06
Type I X-ray bursts are caused by thermonuclear explosions occurring on the surface of an accreting neutron star in a binary star system. Observations and simulations of these phenomena are of great importance for understanding the fundamental properties of neutron stars and dense matter because the equation of state for cold dense matter can be constrained by the mass-radius relationship of neutron stars. During the bursts, turbulence plays a key role in mixing the fuels and driving the unstable nuclear burning process. This dissertation presents one-dimensional models of photospheric radius expansion bursts with a new approach to simulate turbulent advection. Compared with the traditional mixing length theory, the one-dimensional turbulence (ODT) model represents turbulent motions by a sequence of maps that are generated according to a stochastic process. The light curves I obtained with the ODT models are in good agreement with those of the KEPLER model in which the mixing length theory and various diffusive processes are applied. The abundance comparison, however, indicates that the differences in turbulent regions and turbulent diffusivities result in more ^{12}C survival during the bursts in the ODT models, which can make a difference in the superbursts phenomena triggered by unstable carbon burning.
Applying experimental constraints to a one-dimensional model for BiS2 superconductivity
Griffith, M. A.; Foyevtsova, K.; Continentino, M. A.; Martins, G. B.
2016-10-01
Recent ARPES measurements [Sugimoto et al., Phys. Rev. B 92 (2015) 041113] have confirmed the one-dimensional character of the electronic structure of CeO0.5 F0.5 BiS2, a representative of BiS2-based superconductors. In addition, several members of this family present sizable increase in the superconducting transition temperature Tc under application of hydrostatic pressure. Motivated by these two results, we propose an effective one-dimensional three-orbital model, whose kinetic energy part, obtained through ab initio calculations, is supplemented by pair-scattering terms, which are treated at the mean-field level. We solve the gap equations self-consistently and then systematically probe which combination of pair-scattering terms gives results consistent with experiment, namely, a superconducting dome with a maximum Tc at the right chemical potential and a sizable increase in Tc when the magnitude of the hoppings is increased. For these constraints to be satisfied multi-gap superconductivity is required, in agreement with experiments, and one of the hoppings has a dominant influence over the increase of Tc with pressure.
Directly measuring of thermal pulse transfer in one-dimensional highly aligned carbon nanotubes.
Zhang, Guang; Liu, Changhong; Fan, Shoushan
2013-01-01
Using a simple and precise instrument system, we directly measured the thermo-physical properties of one-dimensional highly aligned carbon nanotubes (CNTs). A kind of CNT-based macroscopic materials named super aligned carbon nanotube (SACNT) buckypapers was measured in our experiment. We defined a new one-dimensional parameter, the "thermal transfer speed" to characterize the thermal damping mechanisms in the SACNT buckypapers. Our results indicated that the SACNT buckypapers with different densities have obviously different thermal transfer speeds. Furthermore, we found that the thermal transfer speed of high-density SACNT buckypapers may have an obvious damping factor along the CNTs aligned direction. The anisotropic thermal diffusivities of SACNT buckypapers could be calculated by the thermal transfer speeds. The thermal diffusivities obviously increase as the buckypaper-density increases. For parallel SACNT buckypapers, the thermal diffusivity could be as high as 562.2 ± 55.4 mm(2)/s. The thermal conductivities of these SACNT buckypapers were also calculated by the equation k = Cpαρ.
Three species one-dimensional kinetic model for weakly ionized plasmas
Gonzalez, J.; Donoso, J. M.; Tierno, S. P.
2016-06-01
A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi-analytical method feasibility accounts for non-linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.
Non-periodic one-dimensional ideal conductors and integrable turbulence
Zakharov, Dmitry V.; Zakharov, Vladimir E.; Dyachenko, Sergey A.
2016-12-01
To relate the motion of a quantum particle to the properties of the potential is a fundamental problem of physics, which is far from being solved. Can a medium with a potential which is neither periodic nor quasi-periodic be a conductor? That question seems to have been never addressed, despite being both interesting and having practical importance. Here we propose a new approach to the spectral problem of the one-dimensional Schrödinger operator with a bounded potential. We construct a wide class of potentials having a spectrum consisting of the positive semiaxis and finitely many bands on the negative semiaxis. These potentials, which we call primitive, are reflectionless for positive energy and in general are neither periodic nor quasi-periodic. Moreover, they can be stochastic, and yet allow ballistic transport, and thus describe one-dimensional ideal conductors. Primitive potentials also generate a new class of solutions of the KdV hierarchy. Stochastic primitive potentials describe integrable turbulence, which is important for hydrodynamics and nonlinear optics. We construct the potentials by numerically solving a system of singular integral equations. We hypothesize that finite-gap potentials are a subclass of primitive potentials, and prove this in the case of one-gap potentials.
Three species one-dimensional kinetic model for weakly ionized plasmas
Gonzalez, J., E-mail: jorge.gonzalez@upm.es; Donoso, J. M.; Tierno, S. P. [Department of Applied Physics, Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid (Spain)
2016-06-15
A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.
Qin, C.; Hassanizadeh, S.M.; Rensink, D.; Fell, S.
2012-01-01
The mathematical description of liquid water flooding in the gas channel (GC) of a polymer electrolyte fuel cell (PEFC) at the macro scale has remained a challenge up to now. The mist flow assumption in the GC has been commonly used in previous numerical studies. In this work, a one-dimensional (dow
Betin, A Yu; Bobrinev, V I; Verenikina, N M; Donchenko, S S; Odinokov, S B [Research Institute ' Radiotronics and Laser Engineering' , Bauman Moscow State Technical University, Moscow (Russian Federation); Evtikhiev, N N; Zlokazov, E Yu; Starikov, S N; Starikov, R S [National Reseach Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow (Russian Federation)
2015-08-31
A multiplex method of recording computer-synthesised one-dimensional Fourier holograms intended for holographic memory devices is proposed. The method potentially allows increasing the recording density in the previously proposed holographic memory system based on the computer synthesis and projection recording of data page holograms. (holographic memory)
Strong correlations and topological order in one-dimensional systems
De Gottardi, Wade Wells
This thesis presents theoretical studies of strongly correlated systems as well as topologically ordered systems in 1D. Non-Fermi liquid behavior characteristic of interacting 1D electron systems is investigated with an emphasis on experimentally relevant setups and observables. The existence of end Majorana fermions in a 1D p-wave superconductor subject to periodic, incommensurate and disordered potentials is studied. The Tomonaga-Luttinger liquid (TLL), a model of interacting electrons in one spatial dimension, is considered in the context of two systems of experimental interest. First, a study of the electronic properties of single-walled armchair carbon nanotubes in the presence of transverse electric and magnetic fields is presented. As a result of their effect on the band structure and electron wave functions, fields alter the nature of the (effective) Coulomb interaction in tubes. In particular, it is found that fields couple to nanotube bands (or valleys), a quantum degree of freedom inherited from the underlying graphene lattice. As revealed by a detailed TLL calculation, it is predicted that fields induce electrons to disperse into their spin, band, and charge components. Fields also provide a means of tuning the shell-filling behavior associated with short tubes. The phenomenon of charge fractionalization is investigated in a one-dimensional ring. TLL theory predicts that momentum-resolved electrons injected into the ring will fractionalize into clockwise- and counterclockwise-moving quasiparticles. As a complement to transport measurements in quantum wires connected to leads, non-invasive measures involving the magnetic field profiles around the ring are proposed. Topological aspects of 1D p-wave superconductors are explored. The intimate connection between non-trivial topology (fermions) and spontaneous symmetry breaking (spins) in one-dimension is investigated. Building on this connection, a spin ladder system endowed with vortex degrees of freedom is
Linearized analysis of one-dimensional magnetohydrodynamic flows
Gundersen, Roy M
1964-01-01
Magnetohydrodynamics is concerned with the motion of electrically conducting fluids in the presence of electric or magnetic fields. Un fortunately, the subject has a rather poorly developed experimental basis and because of the difficulties inherent in carrying out controlled laboratory experiments, the theoretical developments, in large measure, have been concerned with finding solutions to rather idealized problems. This lack of experimental basis need not become, however, a multi megohm impedance in the line of progress in the development of a satisfactory scientific theory. While it is true that ultimately a scientific theory must agree with and, in actuality, predict physical phenomena with a reasonable degree of accuracy, such a theory must be sanctioned by its mathematical validity and consistency. Physical phenomena may be expressed precisely and quite comprehensively through the use of differential equations, and the equations formulated by LUNDQUIST and discussed by FRIEDRICHS belong to a class ...
Collective Coordinates in One-Dimensional Soliton Models Revisited
Takyi, I
2016-01-01
We compare numerical solutions to the full field equations to simplified approaches based on implementing three collective coordinates for kink-antikink interactions within the $\\varphi^4$ and $\\phi^6$ models in one time and one space dimensions. We particularly pursue the question whether the collective coordinate approximation substantiates the conjecture that vibrational modes are important for resonance structures to occur in kink-antikink scattering.
Nonlinear Propagation of Light in One Dimensional Periodic Structures
Goodman, Roy H.; Weinstein, Michael I.; Philip J Holmes
2000-01-01
We consider the nonlinear propagation of light in an optical fiber waveguide as modeled by the anharmonic Maxwell-Lorentz equations (AMLE). The waveguide is assumed to have an index of refraction which varies periodically along its length. The wavelength of light is selected to be in resonance with the periodic structure (Bragg resonance). The AMLE system considered incorporates the effects non-instantaneous response of the medium to the electromagnetic field (chromatic or material dispersion...
Collapse of the wave field in a one-dimensional system of weakly coupled light guides
Balakin, A. A.; Litvak, A. G.; Mironov, V. A.; Skobelev, S. A.
2016-12-01
The analytical and numerical study of the radiation self-action in a system of coupled light guides is fulfilled on the basis of the discrete nonlinear Schrödinger equation (DNSE). We develop a variational method for qualitative study of DNSE and classify self-action modes. We show that the diffraction of narrow (in grating scale) wave beams weakens in discrete media and, consequently, the "collapse" of the one-dimensional wave field with power exceeding the critical value occurs. This results in the ability to self-channel radiation in the central fiber. Qualitative analytical results were confirmed by numerical simulation of DNSE, which also shows the stability of the collapse mode.
Distributional approach to point interactions in one-dimensional quantum mechanics
Marcos eCalçada
2014-04-01
Full Text Available We consider the one-dimensional quantum mechanical problem of defining interactions concentrated at a single point in the framework of the theory of distributions. The often ill-defined product which describes the interaction term in the Schrodinger and Dirac equations is replaced by a well-defined distribution satisfying some simple mathematical conditions and, in addition, the physical requirement of probability current conservation is imposed. A four-parameter family of interactions thus emerges as the most general point interaction both in the non-relativistic and in the relativistic theories (in agreement with results obtained by self-adjoint extensions. Since the interaction is given explicitly, the distributional method allows one to carry out symmetry investigations in a simple way, and it proves to be useful to clarify some ambiguities related to the so-called $delta^prime$ interaction.
Impurity effects on the band structure of one-dimensional photonic crystals: Experiment and theory
Luna-Acosta, G A; Kuhl, U; Stoeckmann, H -J
2007-01-01
We study the effects of single impurities on the transmission in microwave realizations of the photonic Kronig-Penney model, consisting of arrays of Teflon pieces alternating with air spacings in a microwave guide. As only the first propagating mode is considered, the system is essentially one dimensional obeying the Helmholtz equation. We derive analytical closed form expressions from which the band structure, frequency of defect modes, and band profiles can be determined. These agree very well with experimental data for all types of single defects considered (e. g. interstitial, substitutional) and shows that our experimental set-up serves to explore some of the phenomena occurring in more sophisticated experiments. Conversely, based on the understanding provided by our formulas, information about the unknown impurity can be determined by simply observing certain features in the experimental data for the transmission. Further, our results are directly applicable to the closely related quantum 1D Kronig-Penn...
One-dimensional motion of a material with a strain theshold
A. Farina
2007-12-01
Full Text Available We consider the one-dimensional shearing motion of a material exhibiting elastic behaviour when the stress is below some threshold. The threshold represents a limit to the deformability, i.e. no further deformation can occur on increasing the stress. The mathematical formulation leads to a free boundary problem for the wave equation, whose structure depends on whether the stress (and the velocity are continuous across the propagating interface for the strain threshold .Local existence and uniqueness are proved for the continuous case (in which the interface propagation is subsonic. Some explicit solutions are calculated for another case (with a supersonic interface. It is shown that the model with strain threshold is never the limit of hyperelastic systems.
An inverse problem for a one-dimensional time-fractional diffusion problem
Jin, Bangti
2012-06-26
We study an inverse problem of recovering a spatially varying potential term in a one-dimensional time-fractional diffusion equation from the flux measurements taken at a single fixed time corresponding to a given set of input sources. The unique identifiability of the potential is shown for two cases, i.e. the flux at one end and the net flux, provided that the set of input sources forms a complete basis in L 2(0, 1). An algorithm of the quasi-Newton type is proposed for the efficient and accurate reconstruction of the coefficient from finite data, and the injectivity of the Jacobian is discussed. Numerical results for both exact and noisy data are presented. © 2012 IOP Publishing Ltd.
S Lakshmi; Swapan K Pati
2003-10-01
We consider an interacting one-dimensional molecular wire attached to two metal electrodes on either side of it. The electrostatic potential profile across the wire-electrode interface has been deduced solving the Schrodinger and Poisson equations self-consistently. Since the Poisson distribution crucially depends on charge densities, we have considered different Hamiltonian parameters to model the nanoscale wire. We find that for very weak electron correlations, the potential gradient is almost zero in the middle of the wire but are large near the chain ends. However, for strong correlations, the potential is essentially a ramp function. The nonlinear current, obtained from the scattering formalism, is found to be less with the ramp potential than for weak correlations. Some of the interesting features in current-voltage characteristics have been explained using one-electron formalism and instabilities in the system.
One dimensional simulation on stability of detached plasma in a tokamak divertor
Nakazawa, Shinji; Nakajima, Noriyoshi; Okamoto, Masao; Ohyabu, Nobuyoshi [National Inst. for Fusion Science, Toki, Gifu (Japan)
1999-06-01
The stability of radiation front in the Scrape-Off-Layer (SOL) of a tokamak is studied with a one dimensional fluid code; the time-dependent transport equations are solved in the direction parallel to a magnetic field line. The simulation results show that stable detached solutions exist, where the plasma temperature near the divertor target is {approx}2 eV. It is found that whenever such stable detached states are attained, the strong radiation front is contact with or at a small distance from the divertor target. When the energy externally injected into the SOL is decreased below a critical value, the radiation front starts to move towards the X-point, cooling the SOL plasma. In such cases, no stationary solutions such that the radiation front rests in the divertor channel are observed in our parameter space. This qualitatively corresponds to the results of tokamak divertor experiments which show the movement of radiation front. (author)
One-Dimensional Modeling of an Entrained Coal Gasification Process Using Kinetic Parameters
Moonkyeong Hwang
2016-02-01
Full Text Available A one-dimensional reactor model was developed to simulate the performance of an entrained flow gasifier under various operating conditions. The model combined the plug flow reactor (PFR model with the well-stirred reactor (WSR model. Reaction kinetics was considered together with gas diffusion for the solid-phase reactions in the PFR model, while equilibrium was considered for the gas-phase reactions in the WSR model. The differential and algebraic equations of mass balance and energy balance were solved by a robust ODE solver, i.e., an semi-implicit Runge–Kutta method, and by a nonlinear algebraic solver, respectively. The computed gasifier performance was validated against experimental data from the literature. The difference in product gas concentration from the equilibrium model, and the underlying mechanisms were discussed further. The optimal condition was found after parameter studies were made for various operating conditions.
An Analytical Solution for One-Dimensional Water Infiltration and Redistribution in Unsaturated Soil
WANG Quan-Jiu; R. HORTON; FAN Jun
2009-01-01
Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.
Non-Bragg-gap solitons in one-dimensional Kerr-metamaterial Fibonacci heterostructures.
Reyes-Gómez, E; Cavalcanti, S B; Oliveira, L E
2015-06-01
A detailed study of non-Bragg-gap solitons in one-dimensional Kerr-metamaterial quasiperiodic Fibonacci heterostructures is performed. The transmission coefficient is numerically obtained by combining the transfer-matrix formalism in the metamaterial layers with a numerical solution of the nonlinear differential equation in the Kerr slabs, and by considering the loss effects in the metamaterial slabs. A switching from states of no transparency in the linear regime to high-transparency states in the nonlinear regime is observed for both zero-order and plasmon-polariton gaps. The spatial localization of the non-Bragg-gap solitons is also examined, and the symmetry properties of the soliton waves are briefly discussed.
Finite element method for one-dimensional rill erosion simulation on a curved slope
Lijuan Yan
2015-03-01
Full Text Available Rill erosion models are important to hillslope soil erosion prediction and to land use planning. The development of rill erosion models and their use has become increasingly of great concern. The purpose of this research was to develop mathematic models with computer simulation procedures to simulate and predict rill erosion. The finite element method is known as an efficient tool in many other applications than in rill soil erosion. In this study, the hydrodynamic and sediment continuity model equations for a rill erosion system were solved by the Galerkin finite element method and Visual C++ procedures. The simulated results are compared with the data for spatially and temporally measured processes for rill erosion under different conditions. The results indicate that the one-dimensional linear finite element method produced excellent predictions of rill erosion processes. Therefore, this study supplies a tool for further development of a dynamic soil erosion prediction model.
Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
Sailer, K; Nagy, S
2013-01-01
A projection method is proposed to treat the one-dimensional Schrodinger equation for a single particle when the Generalized Uncertainty Principle (GUP) generates an ultraviolet (UV) wavevector cutoff. The existence of a unique coordinate representation called the naive one is derived from the one-parameter family of discrete coordinate representations. In this bandlimited Quantum Mechanics a continuous potential is reconstructed from discrete sampled values observed by means of a particle in maximally localized states. It is shown that bandlimitation modifies the speed of the center and the spreading time of a Gaussian wavepacket moving in free space. Indication is found that GUP accompanied by bandlimitation may cause departures of the low-lying energy levels of a particle in a box from those in ordinary Quantum Mechanics much less suppressed than commonly thought when GUP without bandlimitation is in work.
Nonlinear electrodynamics of electrons in a quasi-one-dimensional ballistic ring
Epshtein, E.M. [Institute for Radioengineering and Electronics, Russian Academy of Sciences, Moscow (Russian Federation); Shmelev, G.M.; Maglevanny, I.I. [Volgograd State Pedagogical University, Volgograd (Russian Federation)
2000-09-01
We consider ballistic electron motion in a quasi-one-dimensional ring under the uniform high-frequency electric field induced by an electromagnetic field. The electron satisfies a nonlinear equation of motion which is formally identical to that for a pendulum with a vibrating suspension point. The averaging method of Kapitza is used. The electromagnetic emission spectrum is calculated. The spectrum consists of low-frequency radiation, scattered radiation at the incident radiation frequency and combination scattered radiation; the intensities and frequencies of all components depend nonlinearly on the incident radiation frequency. At a certain value of that intensity the spontaneous symmetry breakdown occurs. As a result, the system acquires some static electric dipole moment. (author)
Nonlinear electrodynamics of electrons in a quasi-one-dimensional ballistic ring
Epshtein, E. M.; Shmelev, G. M.; Maglevanny, I. I.
2000-09-01
We consider ballistic electron motion in a quasi-one-dimensional ring under the uniform high-frequency electric field induced by an electromagnetic field. The electron satisfies a nonlinear equation of motion which is formally identical to that for a pendulum with a vibrating suspension point. The averaging method of Kapitza is used. The electromagnetic emission spectrum is calculated. The spectrum consists of low-frequency radiation, scattered radiation at the incident radiation frequency and combination scattered radiation; the intensities and frequencies of all components depend nonlinearly on the incident radiation frequency. At a certain value of that intensity the spontaneous symmetry breakdown occurs. As a result, the system acquires some static electric dipole moment.
Impurity effects on the band structure of one-dimensional photonic crystals: experiment and theory
Luna-Acosta, G A [Instituto de Fisica, BUAP Apartado Postal J-48, 72570 Puebla (Mexico); Schanze, H; Kuhl, U; Stoeckmann, H-J [Fachbereich Physik der Philipps-Universitaet Marburg, Renthof 5, D-35032 (Germany)], E-mail: gluna@sirio.ifuap.buap.mx
2008-04-15
We study the effects of single impurities on the transmission in microwave realizations of the photonic Kronig-Penney model, consisting of arrays of Teflon pieces alternating with air spacings in a microwave guide. As only the first propagating mode is considered, the system is essentially one-dimensional (1D) obeying the Helmholtz equation. We derive analytical closed form expressions from which the band structure, frequency of defect modes and band profiles can be determined. These agree very well with experimental data for all types of single defects considered (e.g. interstitial and substitutional) and show that our experimental set-up serves to explore some of the phenomena occurring in more sophisticated experiments. Conversely, based on the understanding provided by our formulae, information about the unknown impurity can be determined by simply observing certain features in the experimental data for the transmission. Further, our results are directly applicable to the closely related quantum 1D Kronig-Penney model.
One-Dimensional Discrete Stark Hamiltonian and Resonance Scattering by Impurities
Dmitrieva, L A; Melnikov, Yu B; Kuperin, Yu.A.; Melnikov, Yu.B.
1997-01-01
A one-dimensional discrete Stark Hamiltonian with a continuous electric field is constructed by extension theory methods. In absence of the impurities the model is proved to be exactly solvable, the spectrum is shown to be simple, continuous, filling the real axis; the eigenfunctions, the resolvent and the spectral measure are constructed explicitly. For this (unperturbed) system the resonance spectrum is shown to be empty. The model considering impurity in a single node is also constructed using the operator extension theory methods. The spectral analysis is performed and the dispersion equation for the resolvent singularities is obtained. The resonance spectrum is shown to contain infinite discrete set of resonances. One-to-one correspondence of the constructed Hamiltonian to some Lee-Friedrichs model is established.
Magneto-tunable one-dimensional graphene-based photonic crystal
Jahani, D., E-mail: dariush110@gmail.com; Soltani-Vala, A., E-mail: asoltani@tabrizu.ac.ir; Barvestani, J.; Hajian, H. [Department of Solid State Physics, Faculty of Physics, University of Tabriz, Tabriz (Iran, Islamic Republic of)
2014-04-21
We investigate the effect of a perpendicular static magnetic field on the optical bandgap of a one-dimensional (1D) graphene-dielectric photonic crystal in order to examine the possibility of reaching a rich tunable photonic bandgap. The solution of the wave equation in the presence of the anisotropic Hall situation suggests two decoupled circularly polarized wave each exhibiting different degrees of bandgap tunability. It is also numerically demonstrated that applying different values of field intensity lead to perceptible changes in photonic bandgap of such a structure. Finally, the effect of opening a finite electronic gap in the spectrum of graphene on the optical dispersion solution of such a 1D photonic crystal is reported. It is shown that increasing the value of the electronic gap results in the shrinkage of the associated photonic bandgaps.
Anderson localization and saturable nonlinearity in one-dimensional disordered lattices
Nguyen, Ba Phi
2016-01-01
We investigate numerically the propagation and the Anderson localization of plane waves in a one-dimensional lattice chain, where disorder and saturable nonlinearity are simultaneously present. Using a calculation scheme for solving the stationary discrete nonlinear Schr\\"{o}dinger equation in the fixed input case, the disorder-averaged logarithmic transmittance and the localization length are calculated in a numerically precise manner. The localization length is found to be a nonmonotonic function of the incident wave intensity, acquiring a minimum value at a certain finite intensity, due to saturation effects. For low incident intensities where the saturation effect is ineffective, the enhancement of localization due to Kerr-type nonlinearity occurs in a way similar to the case without saturation. For sufficiently high incident intensities, we find that the localization length is an increasing function of the incident wave intensity, which implies that localization is suppressed for stronger input intensiti...
A variational principle for compressible fluid mechanics. Discussion of the one-dimensional theory
Prozan, R. J.
1982-01-01
The second law of thermodynamics is used as a variational statement to derive a numerical procedure to satisfy the governing equations of motion. The procedure, based on numerical experimentation, appears to be stable provided the CFL condition is satisfied. This stability is manifested no matter how severe the gradients (compression or expansion) are in the flow field. For reasons of simplicity only one dimensional inviscid compressible unsteady flow is discussed here; however, the concepts and techniques are not restricted to one dimension nor are they restricted to inviscid non-reacting flow. The solution here is explicit in time. Further study is required to determine the impact of the variational principle on implicit algorithms.
Serov, Vladislav V.; Kheifets, A. S.
2014-01-01
We analyze a transfer ionization (TI) reaction in the fast proton-helium collision $\\rm H^+ + He \\to H^0 + He^{2+} + e^-$ by solving a time-dependent Schr\\"odinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time independent analogues of our model using lowest order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the Born series calculations, we conclude th...
Methods of Numerical Analysis of One-Dimensional Two-Body Problem in Wheeler-Feynman Electrodynamics
Klimenko, S. V.; Nikitin, I. N.; Urazmetov, W. F.
Numerical methods for solutions of differential equations with deviating arguments describing one-dimensional ultra-relativistic scattering of two identical charged particles in Wheeler-Feynman electrodynamics with half-retarded/half-advanced interaction are developed. Utilization of the methods for the physical problem analysis leads to the discovery of a bifurcation of solutions and breaking of their reflectional symmetry for particles asymptotic velocity v>0.937c in their center-of-mass frame.
Contraction of the Finite One-Dimensional Oscillator
Atakishiyev, Natig M.; Pogosyan, George S.; Wolf, Kurt Bernardo
The finite oscillator model of 2j + 1 points has the dynamical algebra u(2), consisting of position, momentum and mode number. It is a paradigm of finite quantum mechanics where a sequence of finite unitary models contract to the well-known continuum theory. We examine its contraction as the number and density of points increase. This is done on the level of the dynamical algebra, of the Schrödinger difference equation, the (Kravchuk) wave functions, and the Fourier-Kravchuk transformation between position and momentum representations.
One-Dimensional Analysis of Thermal Stratification in AHTR and SFR Coolant Pools
Haihua Zhao; Per F. Peterson
2007-10-01
Thermal stratification phenomena are very common in pool type reactor systems, such as the liquid-salt cooled Advanced High Temperature Reactor (AHTR) and liquid-metal cooled fast reactor systems such as the Sodium Fast Reactor (SFR). It is important to accurately predict the temperature and density distributions both for design optimation and accident analysis. Current major reactor system analysis codes such as RELAP5 (for LWR’s, and recently extended to analyze high temperature reactors), TRAC (for LWR’s), and SASSYS (for liquid metal fast reactors) only provide lumped-volume based models which can only give very approximate results and can only handle simple cases with one mixing source. While 2-D or 3-D CFD methods can be used to analyze simple configurations, these methods require very fine grid resolution to resolve thin substructures such as jets and wall boundaries, yet such fine grid resolution is difficult or impossible to provide for studying the reactor response to transients due to computational expense. Therefore, new methods are needed to support design optimization and safety analysis of Generation IV pool type reactor systems. Previous scaling has shown that stratified mixing processes in large stably stratified enclosures can be described using one-dimensional differential equations, with the vertical transport by free and wall jets modeled using standard integral techniques. This allows very large reductions in computational effort compared to three-dimensional numerical modeling of turbulent mixing in large enclosures. The BMIX++ (Berkeley mechanistic MIXing code in C++) code was originally developed at UC Berkeley to implement such ideas. This code solves mixing and heat transfer problems in stably stratified enclosures. The code uses a Lagrangian approach to solve 1-D transient governing equations for the ambient fluid and uses analytical or 1-D integral models to compute substructures. By including liquid salt properties, BMIX++ code is
A one-dimensional material transfer model for HECTR version 1. 5
Geller, A.S.; Wong, C.C.
1991-08-01
HECTR (Hydrogen Event Containment Transient Response) is a lumped-parameter computer code developed for calculating the pressure-temperature response to combustion in a nuclear power plant containment building. The code uses a control-volume approach and subscale models to simulate the mass, momentum, and energy transfer occurring in the containment during a loss-of-collant-accident (LOCA). This document describes one-dimensional subscale models for mass and momentum transfer, and the modifications to the code required to implement them. Two problems were analyzed: the first corresponding to a standard problem studied with previous HECTR versions, the second to experiments. The performance of the revised code relative to previous HECTR version is discussed as is the ability of the code to model the experiments. 8 refs., 5 figs., 3 tabs.
Ramis, Rafael
2017-02-01
A new one-dimensional hydrodynamic algorithm, specifically developed for Inertial Confinement Fusion (ICF) applications, is presented. The scheme uses a fully conservative Lagrangian formulation in planar, cylindrical, and spherically symmetric geometries, and supports arbitrary equations of state with separate ion and electron components. Fluid equations are discretized on a staggered grid and stabilized by means of an artificial viscosity formulation. The space discretized equations are advanced in time using an implicit algorithm. The method includes several numerical parameters that can be adjusted locally. In regions with low Courant-Friedrichs-Lewy (CFL) number, where stability is not an issue, they can be adjusted to optimize the accuracy. In typical problems, the truncation error can be reduced by a factor between 2 to 10 in comparison with conventional explicit algorithms. On the other hand, in regions with high CFL numbers, the parameters can be set to guarantee unconditional stability. The method can be integrated into complex ICF codes. This is demonstrated through several examples covering a wide range of situations: from thermonuclear ignition physics, where alpha particles are managed as an additional species, to low intensity laser-matter interaction, where liquid-vapor phase transitions occur.
Pittman, C. M.
1994-01-01
This program performs a one-dimensional numerical analysis of the transient thermal response of multi-layer insulative systems. The analysis can determine the temperature distribution through a system consisting of from one to four layers, one of which can be an air gap. Concentrated heat sinks at any interface can be included. The computer program based on the analysis will determine the thickness of a specified layer that will satisfy a temperature limit criterion at any point in the insulative system. The program will also automatically calculate the thickness at several points on a system and determine the total system mass. This program was developed as a tool for designing thermal protection systems for high-speed aerospace vehicles but could be adapted to many areas of industry involved in thermal insulation systems. In this package, the equations describing the transient thermal response of a system are developed. The governing differential equation for each layer and boundary condition are put in finite-difference form using a Taylor's series expansion. These equations yield an essentially tridiagonal matrix of unknown temperatures. A procedure based on Gauss' elimination method is used to solve the matrix. This program is written in FORTRAN IV for the CDC RUN compiler and has been implemented on a CDC 6000 series machine operating under SCOPE 3.0. This program requires a minimum of 44K (octal) of 60 bit words of memory.
A Quasi-One-Dimensional CFD Model for Multistage Turbomachines
Olivier Léonard; Olivier Adam
2008-01-01
The objective of this paper is to present a fast and reliable CFD model that is able to simulate stationary and transient operations of multistage compressors and turbines. This analysis tool is based on an adapted version of the Euler equations solved by a time-marching, finite-volume method. The Euler equations have been extended by including source terms expressing the blade-flow interactions. These source terms are determined using the velocity triangles and a row-by-row representation of the blading at mid-span. The losses and deviations undergone by the fluid across each blade row are supplied by correlations. The resulting flow solver is a performance prediction tool based only on the machine geometry, offering the possibility of exploring the entire characteristic map of a multistage compressor or turbine. Its efficiency in terms of CPU time makes it possible to couple it to an optimization algorithm or to a gas turbine performance tool. Different test-cases are presented for which the calculated characteristic maps are compared to experimental ones.
Imploding Ignition Waves. I. One-dimensional Analysis
Kushnir, Doron; Livne, Eli; Waxman, Eli
2012-06-01
We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R crit. An approximate analytic expression for R crit is derived for an ideal gas equation of state and a simple (power-law-Arrhenius) reaction law, and shown to reproduce the results of numerical solutions. For typical acetylene-air experiments we find R crit ~ 100 μm (spherical) and R crit ~ 1 mm (cylindrical). We suggest that the deflagration to detonation transition (DDT) observed in these systems may be due to converging shocks produced by the turbulent deflagration flow, which reaches sub- (but near) sonic velocities on scales GtR crit. Our suggested mechanism differs from that proposed by Zel'dovich et al., in which a fine-tuned spatial gradient in the chemical induction time is required to be maintained within the turbulent deflagration flow. Our analysis may be readily extended to more complicated equations of state and reaction laws. An order of magnitude estimate of R crit within a white dwarf at the pre-detonation conditions believed to lead to Type Ia supernova explosions is 0.1 km, suggesting that our proposed mechanism may be relevant for DDT initiation in these systems. The relevance of our proposed ignition mechanism to DDT initiation may be tested by both experiments and numerical simulations.
IMPLODING IGNITION WAVES. I. ONE-DIMENSIONAL ANALYSIS
Kushnir, Doron; Waxman, Eli [Department of Particle Physics and Astrophysics, Weizmann Institute of Science, Rehovot 76100 (Israel); Livne, Eli [Racah Institute of Physics, Hebrew University, Jerusalem (Israel)
2012-06-20
We show that converging spherical and cylindrical shock waves may ignite a detonation wave in a combustible medium, provided the radius at which the shocks become strong exceeds a critical radius, R{sub crit}. An approximate analytic expression for R{sub crit} is derived for an ideal gas equation of state and a simple (power-law-Arrhenius) reaction law, and shown to reproduce the results of numerical solutions. For typical acetylene-air experiments we find R{sub crit} {approx} 100 {mu}m (spherical) and R{sub crit} {approx} 1 mm (cylindrical). We suggest that the deflagration to detonation transition (DDT) observed in these systems may be due to converging shocks produced by the turbulent deflagration flow, which reaches sub- (but near) sonic velocities on scales >>R{sub crit}. Our suggested mechanism differs from that proposed by Zel'dovich et al., in which a fine-tuned spatial gradient in the chemical induction time is required to be maintained within the turbulent deflagration flow. Our analysis may be readily extended to more complicated equations of state and reaction laws. An order of magnitude estimate of R{sub crit} within a white dwarf at the pre-detonation conditions believed to lead to Type Ia supernova explosions is 0.1 km, suggesting that our proposed mechanism may be relevant for DDT initiation in these systems. The relevance of our proposed ignition mechanism to DDT initiation may be tested by both experiments and numerical simulations.
Dias, Nuno Costa; Jorge, Cristina; Prata, João Nuno
2016-04-01
Using an extension of the Hörmander product of distributions, we obtain an intrinsic formulation of one-dimensional Schrödinger operators with singular potentials. This formulation is entirely defined in terms of standard Schwartz distributions and does not require (as some previous approaches) the use of more general distributions or generalized functions. We determine, in the new formulation, the action and domain of the Schrödinger operators with arbitrary singular boundary potentials. We also consider the inverse problem, and obtain a general procedure for constructing the singular (pseudo) potential that imposes a specific set of (local) boundary conditions. This procedure is used to determine the boundary operators for the complete four-parameter family of one-dimensional Schrödinger operators with a point interaction. Finally, the δ and δ‧ potentials are studied in detail, and the corresponding Schrödinger operators are shown to coincide with the norm resolvent limit of specific sequences of Schrödinger operators with regular potentials.
Liu, Qihang; Zunger, Alex
2017-04-01
We show that the previously predicted "cubic Dirac fermion," composed of six conventional Weyl fermions including three with left-handed and three with right-handed chirality, is realized in a specific, stable solid state system that has been made years ago, but was not appreciated as a "cubically dispersed Dirac semimetal" (CDSM). We identify the crystal symmetry constraints and find the space group P 63/m as one of the two that can support a CDSM, of which the characteristic band crossing has linear dispersion along the principle axis but cubic dispersion in the plane perpendicular to it. We then conduct a material search using density functional theory, identifying a group of quasi-one-dimensional molybdenum monochalcogenide compounds AI(MoXVI)3 (AI=Na , K, Rb, In, Tl; XVI=S , Se, Te) as ideal CDSM candidates. Studying the stability of the A (MoX) 3 family reveals a few candidates such as Rb (MoTe) 3 and Tl (MoTe) 3 that are predicted to be resilient to Peierls distortion, thus retaining the metallic character. Furthermore, the combination of one dimensionality and metallic nature in this family provides a platform for unusual optical signature—polarization-dependent metallic vs insulating response.
NASA One-Dimensional Combustor Simulation--User Manual for S1D_ML
Stueber, Thomas J.; Paxson, Daniel E.
2014-01-01
The work presented in this paper is to promote research leading to a closed-loop control system to actively suppress thermo-acoustic instabilities. To serve as a model for such a closed-loop control system, a one-dimensional combustor simulation composed using MATLAB software tools has been written. This MATLAB based process is similar to a precursor one-dimensional combustor simulation that was formatted as FORTRAN 77 source code. The previous simulation process requires modification to the FORTRAN 77 source code, compiling, and linking when creating a new combustor simulation executable file. The MATLAB based simulation does not require making changes to the source code, recompiling, or linking. Furthermore, the MATLAB based simulation can be run from script files within the MATLAB environment or with a compiled copy of the executable file running in the Command Prompt window without requiring a licensed copy of MATLAB. This report presents a general simulation overview. Details regarding how to setup and initiate a simulation are also presented. Finally, the post-processing section describes the two types of files created while running the simulation and it also includes simulation results for a default simulation included with the source code.
Quasi-one-dimensional density of states in a single quantum ring
Kim, Heedae; Lee, Woojin; Park, Seongho; Kyhm, Kwangseuk; Je, Koochul; Taylor, Robert A.; Nogues, Gilles; Dang, Le Si; Song, Jin Dong
2017-01-01
Generally confinement size is considered to determine the dimensionality of nanostructures. While the exciton Bohr radius is used as a criterion to define either weak or strong confinement in optical experiments, the binding energy of confined excitons is difficult to measure experimentally. One alternative is to use the temperature dependence of the radiative recombination time, which has been employed previously in quantum wells and quantum wires. A one-dimensional loop structure is often assumed to model quantum rings, but this approximation ceases to be valid when the rim width becomes comparable to the ring radius. We have evaluated the density of states in a single quantum ring by measuring the temperature dependence of the radiative recombination of excitons, where the photoluminescence decay time as a function of temperature was calibrated by using the low temperature integrated intensity and linewidth. We conclude that the quasi-continuous finely-spaced levels arising from the rotation energy give rise to a quasi-one-dimensional density of states, as long as the confined exciton is allowed to rotate around the opening of the anisotropic ring structure, which has a finite rim width.
Synthesis and structure of solution-stable one-dimensional palladium wires.
Campbell, Michael G; Powers, David C; Raynaud, Jean; Graham, Michael J; Xie, Ping; Lee, Eunsung; Ritter, Tobias
2011-11-13
One-dimensional metal wires are valuable materials because of their optical and electronic anisotropy, and they have potential utility in devices such as photovoltaic cells and molecular sensors. However, despite more than a century of research, only a few examples exist of well-defined one-dimensional (1D) metal wires that allow for the rational variation of conductivity. Herein we describe the first examples of 1D molecular wires supported by Pd-Pd bonds, the thin-film conductive properties of which can be altered by controlled molecular changes. Wires based on Pd(III) give semiconducting films with a modifiable bandgap, whereas wires based on Pd(2.5) give films that display metallic conductivity above 200 K: a metallic state has not been reported previously for any polymer composed of 1D metal wires. The wires are infinite in the solid state and maintain 1D structures in solution with lengths of up to 750 nm. Solution stability enables thin film coating, a requisite for device fabrication using molecular wires.
Lime Kiln Modeling. CFD and One-dimensional simulations
Svedin, Kristoffer; Ivarsson, Christofer; Lundborg, Rickard
2009-03-15
The incentives for burning alternative fuels in lime kilns are growing. An increasing demand on thorough investigations of alternative fuel impact on lime kiln performance have been recognized, and the purpose of this project has been to develop a lime kiln CFD model with the possibility to fire fuel oil and lignin. The second part of the project consists of three technical studies. Simulated data from a one-dimensional steady state program has been used to support theories on the impact of biofuels and lime mud dryness. The CFD simulations was carried out in the commercial code FLUENT. Due to difficulties with the convergence of the model the calcination reaction is not included. The model shows essential differences between the two fuels. Lignin gives a different flame shape and a longer flame length compared to fuel oil. Mainly this depends on how the fuel is fed into the combustion chamber and how much combustion air that is added as primary and secondary air. In the case of lignin combustion the required amount of air is more than in the fuel oil case. This generates more combustion gas and a different flow pattern is created. Based on the values from turbulent reaction rate for the different fuels an estimated flame length can be obtained. For fuel oil the combustion is very intense with a sharp peak in the beginning and a rapid decrease. For lignin the combustion starts not as intense as for the fuel oil case and has a smoother shape. The flame length appears to be approximately 2-3 meter longer for lignin than for fuel oil based on turbulent reaction rate in the computational simulations. The first technical study showed that there are many benefits of increasing dry solids content in the lime mud going into a kiln such as increased energy efficiency, reduced TRS, and reduced sodium in the kiln. However, data from operating kilns indicates that these benefits can be offset by increasing exit gas temperature that can limit kiln production capacity. Simulated
Fabrication and characterization of one dimensional zinc oxide nanostructures
Cheng, Chun
In this thesis, one dimensional (1D) ZnO nanostructures with controlled morphologies, defects and alignment have been fabricated by a simple vapor transfer method. The crystal structures, interfaces, growth mechanisms and optical properties of ZnO nanostructures have been investigated by scanning electron microscopy (SEM), transmission electron microscopy (TEM) and photoluminescence (PL) spectroscopy. Great efforts have been devoted to the patterned growth and assembly of ZnO nanostructures as well as the stability of ZnO nanowires (NWs). Using carbonized photoresists, a simple and very effective method has been developed for fabricating and patterning high-quality ZnO NW arrays. ZnO NWs from this method show excellent alignment, crystal quality, and optical properties that are independent of the substrates. The carbonized photoresists provide perfect nucleation sites for the growth of aligned ZnO NWs and also perfectly connect to the NWs to form ideal electrodes. This approach is further extended to realize large area growth of different forms of ZnO NW arrays (e.g., the horizontal growth and multilayered ZnO NW arrays) on other kinds of carbon-based materials. In addition, the as-synthesized vertically aligned ZnO NW arrays show a low weighted reflectance (Rw) and can be used as antireflection coatings. Moreover, non c-axis growth of 1D ZnO nanostructures (e.g., nanochains, nanobrushes and nanobelts) and defect related 1D ZnO nanostructures (e.g., Y-shaped twinned nanobelts and hierarchical nanostructures decorated by flowers induced by screw dislocations) is also present. Using direct oxidization of pure Zn at high temperatures in air, uniformed ZnO NWs and tetrapods have been fabricated. The spatially-resolved PL study on these two kinds of nanostructures suggests that the defects leading to the green luminescence (GL) should originate from the structural changes along the legs of the tetrapods. Surface defects in these ZnO nanostructures play an unimportant
Lime Kiln Modeling. CFD and One-dimensional simulations
Svedin, Kristoffer; Ivarsson, Christofer; Lundborg, Rickard
2009-03-15
The incentives for burning alternative fuels in lime kilns are growing. An increasing demand on thorough investigations of alternative fuel impact on lime kiln performance have been recognized, and the purpose of this project has been to develop a lime kiln CFD model with the possibility to fire fuel oil and lignin. The second part of the project consists of three technical studies. Simulated data from a one-dimensional steady state program has been used to support theories on the impact of biofuels and lime mud dryness. The CFD simulations was carried out in the commercial code FLUENT. Due to difficulties with the convergence of the model the calcination reaction is not included. The model shows essential differences between the two fuels. Lignin gives a different flame shape and a longer flame length compared to fuel oil. Mainly this depends on how the fuel is fed into the combustion chamber and how much combustion air that is added as primary and secondary air. In the case of lignin combustion the required amount of air is more than in the fuel oil case. This generates more combustion gas and a different flow pattern is created. Based on the values from turbulent reaction rate for the different fuels an estimated flame length can be obtained. For fuel oil the combustion is very intense with a sharp peak in the beginning and a rapid decrease. For lignin the combustion starts not as intense as for the fuel oil case and has a smoother shape. The flame length appears to be approximately 2-3 meter longer for lignin than for fuel oil based on turbulent reaction rate in the computational simulations. The first technical study showed that there are many benefits of increasing dry solids content in the lime mud going into a kiln such as increased energy efficiency, reduced TRS, and reduced sodium in the kiln. However, data from operating kilns indicates that these benefits can be offset by increasing exit gas temperature that can limit kiln production capacity. Simulated
Spontaneously stochastic solutions in one-dimensional inviscid systems
Mailybaev, Alexei A
2015-01-01
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a theoretical argument (with a detailed numerical confirmation) showing that a classical deterministic solution before a finite-time blowup, $t t_b$, representing a unique physically relevant description in the inviscid limit. This theory is based on the dynamical system formulation written for the logarithmic time $\\tau = \\log(t-t_b)$, which features a stable traveling wave solution for the inviscid Burgers equation, but a stochastic traveling wave for the Sabra model. The latter describes a universal onset of stochasticity immediately after the blowup.
Spontaneously stochastic solutions in one-dimensional inviscid systems
Mailybaev, Alexei A.
2016-08-01
In this paper, we study the inviscid limit of the Sabra shell model of turbulence, which is considered as a particular case of a viscous conservation law in one space dimension with a nonlocal quadratic flux function. We present a theoretical argument (with a detailed numerical confirmation) showing that a classical deterministic solution before a finite-time blowup, t t b , representing a unique physically relevant description in the inviscid limit. This theory is based on the dynamical system formulation written for the logarithmic time τ =log ≤ft(t-{{t}b}\\right) , which features a stable traveling wave solution for the inviscid Burgers equation, but a stochastic traveling wave for the Sabra model. The latter describes a universal onset of stochasticity immediately after the blowup.
Costanza, E. F.; Costanza, G.
2016-10-01
Continuum partial differential equations are obtained from a set of discrete stochastic evolution equations of both non-Markovian and Markovian processes and applied to the diffusion within the context of the lattice gas model. A procedure allowing to construct one-dimensional lattices that are topologically equivalent to two-dimensional lattices is described in detail in the case of a rectangular lattice. This example shows the general features that possess the procedure and extensions are also suggested in order to provide a wider insight in the present approach.
Li Yeping
2008-01-01
A one-dimensional stationary nonisentropic hydrodynamic model for semicon-ductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron tempera-ture, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.
One-dimensional Arterial Network Model for Bypass Grafts Assessment
Ghigo, Arthur; Wang, Xiaofei; Lagrée, Pierre-Yves; Fullana, Jose-Maria
2016-01-01
We propose an arterial network model based on 1D blood hemodynamic equations to study the behavior of different vascular surgical bypass grafts in case of an arterial occlusive pathology: an obliteration or stenosis of the iliac artery. We investigate the performances of three different bypass grafts (Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree of obliteration of the stenosis. Numerical simulations show that all bypass grafts are efficient since we retrieve in all cases the normal hemodynamics in the stenosed region while ensuring at the same time a global healthy circulation. We analyze in particular the Axillo-Femoral bypass graft by performing hundreds of simulations by varying the values of the Young's modulus [0.1--50 MPa] and the radius [0.01--5 cm] of the bypass graft. We show that the Young's modulus and radius of commercial bypass grafts are optimal in terms of hemodynamic considerations. The numerical findings prove that this approach could be used to optimize or pl...
Lourenço, C. R.; Rocha Filho, T. M.
2015-07-01
The dynamics of quasistationary states of long-range interacting systems with N particles can be described by kinetic equations such as the Balescu-Lenard and Landau equations. In the case of one-dimensional homogeneous systems, two-body contributions vanish as two-body collisions in one dimension only exchange momentum and thus cannot change the one-particle distribution. Using a Kac factor in the interparticle potential implies a scaling of the dynamics proportional to Nδ with δ =1 except for one-dimensional homogeneous systems. For the latter different values for δ were reported for a few models. Recently it was shown by Rocha Filho and collaborators [Phys. Rev. E 90, 032133 (2014)], 10.1103/PhysRevE.90.032133 for the Hamiltonian mean-field model that δ =2 provided that N is sufficiently large, while small N effects lead to δ ≈1.7 . More recently, Gupta and Mukamel [J. Stat. Mech. (2011) P03015, 10.1088/1742-5468/2011/03/P03015] introduced a classical spin model with an anisotropic interaction with a scaling in the dynamics proportional to N1.7 for a homogeneous state. We show here that this model reduces to a one-dimensional Hamiltonian system and that the scaling of the dynamics approaches N2 with increasing N . We also explain from theoretical consideration why usual kinetic theory fails for small N values, which ultimately is the origin of noninteger exponents in the scaling.
Non-periodic one-dimensional ideal conductors and integrable turbulence
Zakharov, Dmitry V. [Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012 (United States); Zakharov, Vladimir E. [Department of Mathematics, University of Arizona, Tucson, AZ, 85791 (United States); Dyachenko, Sergey A., E-mail: sdyachen@math.uiuc.edu [Department of Mathematics, University of Illinois, Urbana-Champaign, IL, 61801 (United States)
2016-12-01
Highlights: • An efficient procedure for construction of non-periodic, non-vanishing reflectionless potentials is presented. • The analytical procedure is reinforced by numerical simulation that presents some of these potentials. • The present work is a key ingredient for the study of integrable turbulence and statistical description of “solitonic gas”. - Abstract: To relate the motion of a quantum particle to the properties of the potential is a fundamental problem of physics, which is far from being solved. Can a medium with a potential which is neither periodic nor quasi-periodic be a conductor? That question seems to have been never addressed, despite being both interesting and having practical importance. Here we propose a new approach to the spectral problem of the one-dimensional Schrödinger operator with a bounded potential. We construct a wide class of potentials having a spectrum consisting of the positive semiaxis and finitely many bands on the negative semiaxis. These potentials, which we call primitive, are reflectionless for positive energy and in general are neither periodic nor quasi-periodic. Moreover, they can be stochastic, and yet allow ballistic transport, and thus describe one-dimensional ideal conductors. Primitive potentials also generate a new class of solutions of the KdV hierarchy. Stochastic primitive potentials describe integrable turbulence, which is important for hydrodynamics and nonlinear optics. We construct the potentials by numerically solving a system of singular integral equations. We hypothesize that finite-gap potentials are a subclass of primitive potentials, and prove this in the case of one-gap potentials.
A simple one-dimensional model for urban canopy flows
Cheng, Wai Chi; Porté-Agel, Fernando
2016-04-01
In urban canopy parameterizations, an urban canopy is usually modelled as a drag force on the flow, and the turbulent shear stress is parametrized by various methods. One of the most common methods to parametrize the turbulent shear stress in urban canopies is to use a mixing length (lm) model. Different mixing length models have been proposed in the literature, and recent direct numerical simulation and large-eddy simulation (LES) studies have shown that these models underpredict the value of lm in urban canopies. The high value of lm in the canopies is in fact related to the turbulence generated at the high-shear region near the top of the canopy, which is similar to that in a plane mixing layer. By considering this effect, a new simple mixing length model is proposed based on physical arguments. The results of the new lm model and the previous models are compared with the LES results of flows within and above uniform cube arrays of different densities. The comparison clearly demonstrates the better performance of the new model in predicting the wind profiles especially near the top of the urban canopies. For the drag coefficient (Cd) representing an urban canopy, previous studies found that its value depends on the building density. Here, a simple model for Cd is suggested by considering the spatial distribution of mean wind within canopies of different building densities. The model prediction is found to agree reasonably well with the LES results.
Exponential Tails Near the Band Edges of a One-Dimensional Exciton System
Avgin, I.; Boukahil, A.; Zettili, N.; Huber, D. L.
2003-03-01
We report the results of studies of the tails near the band edges of a one-dimensional Frenkel exciton system in the Coherent Potential Approximation (CPA). A Gaussian distribution of the transition frequencies with rms width σ (0.1 <= σ <= 2.0) is used. We found that the tails obey two different exponential power laws depending on the value of σ. In the weak disorder limit 0.1 <= σ <= 0.5, the tails of the density of states and the absorption line shape behave like expk|E|^3/2/σ^2 and in the strong disorder limit 0.5 <= σ <= 2.0 the tails behave like exp|E|^2/2σ^2\\. Our CPA results are in excellent agreement with our simulation data for the density of states over the entire range 0.1 <= σ <= 2.0, and with previous investigations for weak disorder.
One_dimensional chains of gold clusters on the surface of highly oriented pyrolytic graphite
无
2001-01-01
We have investigated the growth of gold nanoclusters on thesurface of highly oriented pyrolytic graphite in ultrahigh vacuum. Studies of ultrahigh vacuum scanning tunneling microscopy revealed that the size distribution of gold clusters was very narrow and quasi-one-dimensional chains of gold nanoclusters of approximately 2 nm diameter were produced after being annealed at 74℃. Unlike the results obtained by previous workers, these chains of gold clusters were not formed along steps on the substrate surface, and some of them could even go across monoatomic steps. The orientation of chains of gold clusters was also dependent on the size of gold nanoclusters. These results suggest the viability of a new route to the creation of ordered nanoscale structures.
Low-lying Photoexcited States of a One-Dimensional Ionic Extended Hubbard Model
Yokoi, Kota; Maeshima, Nobuya; Hino, Ken-ichi
2017-10-01
We investigate the properties of low-lying photoexcited states of a one-dimensional (1D) ionic extended Hubbard model at half-filling. Numerical analysis by using the full and Lanczos diagonalization methods shows that, in the ionic phase, there exist low-lying photoexcited states below the charge transfer gap. As a result of comparison with numerical data for the 1D antiferromagnetic (AF) Heisenberg model, it was found that, for a small alternating potential Δ, these low-lying photoexcited states are spin excitations, which is consistent with a previous analytical study [Katsura et al., Phys. Rev. Lett. 103, 177402 (2009)]. As Δ increases, the spectral intensity of the 1D ionic extended Hubbard model rapidly deviates from that of the 1D AF Heisenberg model and it is clarified that this deviation is due to the neutral-ionic domain wall, an elementary excitation near the neutral-ionic transition point.
A detailed one-dimensional model of combustion of a woody biomass particle.
Haseli, Y; van Oijen, J A; de Goey, L P H
2011-10-01
A detailed one-dimensional model for combustion of a single biomass particle is presented. It accounts for particle heating up, pyrolysis, char gasification and oxidation and gas phase reactions within and in the vicinity of the particle. The biomass pyrolysis is assumed to take place through three competing reactions yielding char, light gas and tar. The model is validated using different sets of experiments reported in the literature. Special emphasis is placed on examination of the effects of pyrolysis kinetic constants and gas phase reactions on the combustion process which have not been thoroughly discussed in previous works. It is shown that depending on the process condition and reactor temperature, correct selection of the pyrolysis kinetic data is a necessary step for simulation of biomass particle conversion. The computer program developed for the purpose of this study enables one to get a deeper insight into the biomass particle combustion process.
Analysis and synthesis of one-dimensional magneto-photonic crystals using coupled mode theory
Saghirzadeh Darki, Behnam; Nezhad, Abolghasem Zeidaabadi; Firouzeh, Zaker Hossein
2017-03-01
We utilize our previously developed temporal coupled mode approach to investigate the performance of one-dimensional magneto-photonic crystals (MPCs). We analytically demonstrate that a double-defect MPC provides adequate degrees of freedom to design a structure for arbitrary transmittance and Faraday rotation. By using our developed analytic approach along with the numerical transfer matrix method, we present a procedure for the synthesis of an MPC to generate any desired transmittance and Faraday rotation in possible ranges. However it is seen that only discrete values of transmittance and Faraday rotation are practically obtainable. To remedy this problem along with having short structures, we introduce a class of MPC heterostructures which are combinations of stacks with high and low optical contrast ratios.
THE ONE-DIMENSIONAL HUGHES MODEL FOR PEDESTRIAN FLOW: RIEMANN-TYPE SOLUTIONS
Debora Amadori; M. Di Francesco
2012-01-01
This paper deals with a coupled system consisting of a scalar conservation law and an eikonal equation,called the Hughes model.Introduced in [24],this model attempts to describe the motion of pedestrians in a densely crowded region,in which they are seen as a 'thinking' (continuum) fluid.The main mathematical difficulty is the discontinuous gradient of the solution to the eikonal equation appearing in the flux of the conservation law.On a one dimensional interval with zero Dirichlet conditions (the two edges of the interval are interpreted as 'targets'),the model can be decoupled in a way to consider two classical conservation laws on two sub-domains separated by a turning point at which the pedestrians change their direction.We shall consider solutions with a possible jump discontinuity around the turning point.For simplicity,we shall assume they are locally constant on both sides of the discontinuity.We provide a detailed description of the localin-time behavior of the solution in terms of a 'global' qualitative property of the pedestrian density (that we call 'relative evacuation rate'),which can be interpreted as the attitude of the pedestrians to direct towards the left or the right target.We complement our result with explicitly computable examples.
Two Phase Compressible Flow Fields in One Dimensional and Eulerian Grid Framework
Lee, Sungsu; Park, Chan Wook
2008-11-01
Numerical investigation for two phase compressible flow fields of air-water in one dimensional tube are performed in the fixed Eulerian grid framework. Using an equation of states of Tait's type for a multiphase cell, the two phase compressible flow is modeled as equivalent single phase which is discretized using the Roe`s approximate Riemann solver, while the phase interface is captured via volume fractions of each phase. The most common problem found in the computational approaches in compressible multiphase flow is occurrence of the pressure oscillation at the phase interface. In order to suppress that phenomenon, tried are two approaches; a passive advection of volume fraction and a direct pressure relaxation with the compressible form of volume fraction equation. The results show that the direct pressure equalizing method suppresses pressure oscillation successfully and generates sharp discontinuities, transmitting and reflecting acoustic waves naturally at the phase interface. This work was supported by a research fund granted from Agency for Defense Development, South Korea
Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line
Sato, M.; Mukaide, T.; Nakaguchi, T.; Sievers, A. J.
2016-07-01
The experimental properties of intrinsic localized modes (ILMs) have long been compared with theoretical dynamical lattice models that make use of nonlinear onsite and/or nearest-neighbor intersite potentials. Here it is shown for a one-dimensional lumped electrical transmission line that a nonlinear inductive component in an otherwise linear parallel capacitor lattice makes possible a new kind of ILM outside the plane wave spectrum. To simplify the analysis, the nonlinear inductive current equations are transformed to flux transmission line equations with analog onsite hard potential nonlinearities. Approximate analytic results compare favorably with those obtained from a driven damped lattice model and with eigenvalue simulations. For this mono-element lattice, ILMs above the top of the plane wave spectrum are the result. We find that the current ILM is spatially compressed relative to the corresponding flux ILM. Finally, this study makes the connection between the dynamics of mass and force constant defects in the harmonic lattice and ILMs in a strongly anharmonic lattice.
Mainka, J. [Laboratorio Nacional de Computacao Cientifica (LNCC), CMC 6097, Av. Getulio Vargas 333, 25651-075 Petropolis, RJ, Caixa Postal 95113 (Brazil); Maranzana, G.; Thomas, A.; Dillet, J.; Didierjean, S.; Lottin, O. [Laboratoire d' Energetique et de Mecanique Theorique et Appliquee (LEMTA), Universite de Lorraine, 2, avenue de la Foret de Haye, 54504 Vandoeuvre-les-Nancy (France); LEMTA, CNRS, 2, avenue de la Foret de Haye, 54504 Vandoeuvre-les-Nancy (France)
2012-10-15
A one-dimensional (1D) model of oxygen transport in the diffusion media of proton exchange membrane fuel cells (PEMFC) is presented, which considers convection perpendicular to the electrode in addition to diffusion. The resulting analytical expression of the convecto-diffusive impedance is obtained using a convection-diffusion equation instead of a diffusion equation in the case of classical Warburg impedance. The main hypothesis of the model is that the convective flux is generated by the evacuation of water produced at the cathode which flows through the porous media in vapor phase. This allows the expression of the convective flux velocity as a function of the current density and of the water transport coefficient {alpha} (the fraction of water being evacuated at the cathode outlet). The resulting 1D oxygen transport impedance neglects processes occurring in the direction parallel to the electrode that could have a significant impact on the cell impedance, like gas consumption or concentration oscillations induced by the measuring signal. However, it enables us to estimate the impact of convection perpendicular to the electrode on PEMFC impedance spectra and to determine in which conditions the approximation of a purely diffusive oxygen transport is valid. Experimental observations confirm the numerical results. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
DC field response of one-dimensional flames using an ionized layer model
Xiong, Yuan
2015-11-18
We develop a simplified model to better explain electric current response when direct current (DC) is applied to a flame. In particular, different current responses have been observed by changing the polarity of the DC in a sub-saturated current regime that results from the presence of ions and electrons in the flame zone. A flame zone was modeled as a thin, ionized layer located in one-dimensional DC electric fields. We derived simplified model-governing equations from species equations by implementing mobility differences dependent on the type of charged particle, particularly between ions and electrons; we performed experiments to substantiate the model. Results showed that the sub-saturated current and local field intensity were significantly influenced by the polarity of the DC because of the combined effect of unequal mobility of charged particles and the position of the ionized layer in the gap relative to two electrodes. When an energized electrode is close to the ionized layer, applying a negative DC causes a more rapid increase in current than by applying a positive DC to the same electrode. Results from our experimental measurement of current using counterflow diffusion flames agreed qualitatively well with the model predictions. A sensitivity analysis using dimensional and non-dimensional parameters also supported the importance of the mobility difference and the relative location of the ionized layer on the electric current response.
Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas
Roy S. Baty, F. Farassat, John A. Hargreaves
2007-05-25
Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.
One-Dimensional Modelling of Marine Current Turbine Runaway Behaviour
Staffan Lundin
2016-04-01
Full Text Available If a turbine loses its electrical load, it will rotate freely and increase speed, eventually achieving that rotational speed which produces zero net torque. This is known as a runaway situation. Unlike many other types of turbine, a marine current turbine will typically overshoot the final runaway speed before slowing down and settling at the runaway speed. Since the hydrodynamic forces acting on the turbine are dependent on rotational speed and acceleration, turbine behaviour during runaway becomes important for load analyses during turbine design. In this article, we consider analytical and numerical models of marine current turbine runaway behaviour in one dimension. The analytical model is found not to capture the overshoot phenomenon, while still providing useful estimates of acceleration at the onset of runaway. The numerical model incorporates turbine wake build-up and predicts a rotational speed overshoot. The predictions of the models are compared against measurements of runaway of a marine current turbine. The models are also used to recreate previously-published results for a tidal turbine and applied to a wind turbine. It is found that both models provide reasonable estimates of maximum accelerations. The numerical model is found to capture the speed overshoot well.
Xinzhi Liu
1998-01-01
Full Text Available This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.
One-dimensional gravity in infinite point distributions.
Gabrielli, A; Joyce, M; Sicard, F
2009-10-01
The dynamics of infinite asymptotically uniform distributions of purely self-gravitating particles in one spatial dimension provides a simple and interesting toy model for the analogous three dimensional problem treated in cosmology. In this paper we focus on a limitation of such models as they have been treated so far in the literature: the force, as it has been specified, is well defined in infinite point distributions only if there is a centre of symmetry (i.e., the definition requires explicitly the breaking of statistical translational invariance). The problem arises because naive background subtraction (due to expansion, or by "Jeans swindle" for the static case), applied as in three dimensions, leaves an unregulated contribution to the force due to surface mass fluctuations. Following a discussion by Kiessling of the Jeans swindle in three dimensions, we show that the problem may be resolved by defining the force in infinite point distributions as the limit of an exponentially screened pair interaction. We show explicitly that this prescription gives a well defined (finite) force acting on particles in a class of perturbed infinite lattices, which are the point processes relevant to cosmological N -body simulations. For identical particles the dynamics of the simplest toy model (without expansion) is equivalent to that of an infinite set of points with inverted harmonic oscillator potentials which bounce elastically when they collide. We discuss and compare with previous results in the literature and present new results for the specific case of this simplest (static) model starting from "shuffled lattice" initial conditions. These show qualitative properties of the evolution (notably its "self-similarity") like those in the analogous simulations in three dimensions, which in turn resemble those in the expanding universe.
One-dimensional Array Grammars and P Systems with Array Insertion and Deletion Rules
Rudolf Freund
2013-09-01
Full Text Available We consider the (one-dimensional array counterpart of contextual as well as insertion and deletion string grammars and consider the operations of array insertion and deletion in array grammars. First we show that the emptiness problem for P systems with (one-dimensional insertion rules is undecidable. Then we show computational completeness of P systems using (one-dimensional array insertion and deletion rules even of norm one only. The main result of the paper exhibits computational completeness of one-dimensional array grammars using array insertion and deletion rules of norm at most two.
A general spectral method for the numerical simulation of one-dimensional interacting fermions
Clason, Christian; von Winckel, Gregory
2012-02-01
This work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. The approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An efficient MATLAB program for the assembly of the stiffness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. This program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e.g., for verifying the accuracy of multi-particle approximations such as Hartree-Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the time-dependent Schrödinger equation. Program summaryProgram title: assembleFermiMatrix Catalogue identifier: AEKO_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKO_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 102 No. of bytes in distributed program, including test data, etc.: 2294 Distribution format: tar.gz Programming language: MATLAB Computer: Any architecture supported by MATLAB Operating system: Any supported by MATLAB; tested under Linux (x86-64) and Mac OS X (10.6) RAM: Depends on the data Classification: 4.3, 2.2 Nature of problem: The direct numerical solution of the multi-particle one-dimensional Schrödinger equation in a quantum well is challenging due to the exponential growth in the number of degrees of freedom with increasing particles. Solution method: A nodal spectral Galerkin scheme is used where the basis functions are constructed to obey the antisymmetry relations of the fermionic wave
On the quasi-one dimensional structure of the cellular detonation in a two-dimensional duct
Uyeda, C. M.; Kurosaka, M.; Ferrante, A.
2015-11-01
We performed numerical simulations of cellular detonations in a 2D duct to establish the validity of the one-dimensional ZND model. The detonation was simulated by solving the Euler equations with a WENO-TCD numerical method using adaptive mesh refinement and a detailed chemical reaction mechanism. The results show that the properties of the ZND model of a 2H2-O2-7Ar reaction are very close to the results of the simulations initiated using three different methods for the area-averaged properties and the properties of particles tracked along their pathlines. Disagreements between the particle properties and the ZND model are greatest near the detonation front where the transverse wave and Mach stem introduce larger jumps in the flow properties than the ZND model predicts. The particle pathlines also exhibit a quasi one-dimensional motion downstream from the detonation front which is supported by the quick decay in the particles' velocity ratio of the vertical to horizontal velocity components, in the reference frame attached to the detonation front. These findings show the quasi one-dimensional nature of 2D detonations and the applicability of the ZND model.
Stationary bottom generated velocity fluctuations in one-dimensional open channel flow
Jong, de Bartele
1993-01-01
Statistical characteristics are calculated for stationary velocity fluctuations in a one-dimensional open channel flow with a given vertical velocity profile and with one-dimensional irregular bottom waves, characterized by a spectral density function. The calculations are based on an approximate ca
Synthesis and magneticproperties of one-dimensional Mn(Ⅱ) complexes linked bydithiooxalato
无
2003-01-01
Three dithiooxalato (Dto) bridging one-dimensional Mn(Ⅱ) complexes [Mn(L)Dto](L = Phen (1), Bpy (2) and en (3)) were synthesized. All of the complexes have the similar one-dimensional structure through Dto bridge. The measurement of the variable temperature magnetic susceptibility of complex 1 showed that there are weak antiferromag- netic interactions between the Mn(Ⅱ) ions.