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Sample records for bloch equations

  1. Squeezing corrections to the Bloch equations

    International Nuclear Information System (INIS)

    Abundo, M.; Accardi, L.

    1991-01-01

    The general analysis of quantum noise shows that a squeezing noise can produce quadratic nonlinearities in the Langevin equations leading to the Bloch equations. These quadratic nonlinearities are governed by the imaginary part of the off-diagonal terms of the covariance of the noise (the squeezing terms) and imply a correction to the usual form of the Bloch equations. Here the case of spin-one nuclei subjected to squeezing noises of particular type is studied numerically. It is shown that the corrections to the Bloch equations, suggested by the theory, to the behaviour of the macroscopic nuclear polarization in a scale of times of the order of the relaxation time can be quite substantial. In the equilibrium regime, even if the qualitative behaviour of the system is the same (exponential decay), the numerical equilibrium values predicted by the theory are consistently different from those predicted by the usual Bloch equation. It is suggested that this difference might be used to test experimentally the observable effects of squeezing noises

  2. Chaotic dynamics in the Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Holm, D.D.; Kovacic, G.

    1992-01-01

    In the slowly varying envelope approximation and the rotating wave approximation for the Maxwell-Bloch equations, we describe how the presence of a small-amplitude probe laser in an excited, two-level, resonant medium leads to homoclinic chaos in the laser-matter dynamics. We also describe a derivation of the Maxwell-Bloch equations from an action principle

  3. Chaos synchronization of nonlinear Bloch equations

    International Nuclear Information System (INIS)

    Park, Ju H.

    2006-01-01

    In this paper, the problem of chaos synchronization of Bloch equations is considered. A novel nonlinear controller is designed based on the Lyapunov stability theory. The proposed controller ensures that the states of the controlled chaotic slave system asymptotically synchronizes the states of the master system. A numerical example is given to illuminate the design procedure and advantage of the result derived

  4. Optical Bloch equations with multiply connected states

    International Nuclear Information System (INIS)

    Stacey, D N; Lucas, D M; Allcock, D T C; Szwer, D J; Webster, S C

    2008-01-01

    The optical Bloch equations, which give the time evolution of the elements of the density matrix of an atomic system subject to radiation, are generalized so that they can be applied when transitions between pairs of states can proceed by more than one stimulated route. The case considered is that for which the time scale of interest in the problem is long compared with that set by the differences in detuning of the radiation fields stimulating via the different routes. It is shown that the Bloch equations then reduce to the standard form of linear differential equations with constant coefficients. The theory is applied to a two-state system driven by two lasers with different intensities and frequencies and to a three-state Λ-system with one laser driving one transition and two driving the second. It is also shown that the theory reproduces well the observed response of a cold 40 Ca + ion when subject to a single laser frequency driving the 4S 1/2 -4P 1/2 transition and a laser with two strong sidebands driving 3D 3/2 -4P 1/2

  5. Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems

    Science.gov (United States)

    Skinner, Thomas E.

    2018-01-01

    The Bloch equation and its variants constitute the fundamental dynamical model for arbitrary two-level systems. Many important processes, including those in more complicated systems, can be modeled and understood through the two-level approximation. It is therefore of widespread relevance, especially as it relates to understanding dissipative processes in current cutting-edge applications of quantum mechanics. Although the Bloch equation has been the subject of considerable analysis in the 70 years since its inception, there is still, perhaps surprisingly, significant work that can be done. This paper extends the scope of previous analyses. It provides a framework for more fully understanding the dynamics of dissipative two-level systems. A solution is derived that is compact, tractable, and completely general, in contrast to previous results. Any solution of the Bloch equation depends on three roots of a cubic polynomial that are crucial to the time dependence of the system. The roots are typically only sketched out qualitatively, with no indication of their dependence on the physical parameters of the problem. Degenerate roots, which modify the solutions, have been ignored altogether. Here the roots are obtained explicitly in terms of a single real-valued root that is expressed as a simple function of the system parameters. For the conventional Bloch equation, a simple graphical representation of this root is presented that makes evident the explicit time dependence of the system for each point in the parameter space. Several intuitive, visual models of system dynamics are developed. A Euclidean coordinate system is identified in which any generalized Bloch equation is separable, i.e., the sum of commuting rotation and relaxation operators. The time evolution in this frame is simply a rotation followed by relaxation at modified rates that play a role similar to the standard longitudinal and transverse rates. These rates are functions of the applied field, which

  6. General PFG signal attenuation expressions for anisotropic anomalous diffusion by modified-Bloch equations

    Science.gov (United States)

    Lin, Guoxing

    2018-05-01

    Anomalous diffusion exists widely in polymer and biological systems. Pulsed-field gradient (PFG) anomalous diffusion is complicated, especially in the anisotropic case where limited research has been reported. A general PFG signal attenuation expression, including the finite gradient pulse (FGPW) effect for free general anisotropic fractional diffusion { 0 integral modified-Bloch equation, were extended to obtain general PFG signal attenuation expressions for anisotropic anomalous diffusion. Various cases of PFG anisotropic anomalous diffusion were investigated, including coupled and uncoupled anisotropic anomalous diffusion. The continuous-time random walk (CTRW) simulation was also carried out to support the theoretical results. The theory and the CTRW simulation agree with each other. The obtained signal attenuation expressions and the three-dimensional fractional modified-Bloch equations are important for analyzing PFG anisotropic anomalous diffusion in NMR and MRI.

  7. Effective Hamiltonians, two level systems, and generalized Maxwell-Bloch equations

    International Nuclear Information System (INIS)

    Sczaniecki, L.

    1981-02-01

    A new method is proposed involving a canonical transformation leading to the non-secular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating wave approximation is written anew within the framework of our formalism. (author)

  8. Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron

    CERN Document Server

    Fujita, Shigeji

    2007-01-01

    Quantum Theory of Conducting Matter: Newtonian Equations of Motion for a Bloch Electron targets scientists, researchers and graduate-level students focused on experimentation in the fields of physics, chemistry, electrical engineering, and material sciences. It is important that the reader have an understanding of dynamics, quantum mechanics, thermodynamics, statistical mechanics, electromagnetism and solid-state physics. Many worked-out problems are included in the book to aid the reader's comprehension of the subject. The Bloch electron (wave packet) moves by following the Newtonian equation of motion. Under an applied magnetic field B the electron circulates around the field B counterclockwise or clockwise depending on the curvature of the Fermi surface. The signs of the Hall coefficient and the Seebeck coefficient are known to give the sign of the major carrier charge. For alkali metals, both are negative, indicating that the carriers are "electrons." These features arise from the Fermi surface difference...

  9. Chaos synchronization in bi-axial magnets modeled by Bloch equation

    International Nuclear Information System (INIS)

    Moukam Kakmeni, F.M.; Nguenang, J.P.; Kofane, T.C.

    2005-10-01

    In this paper, we show that the bi-axial magnetic material modelled by Bloch equation admits chaotic solutions for a certain set of numerical values assigned to the system of parameters and initial conditions. Using the unidirectional linear and nonlinear feedback schemes, we demonstrate that two such systems can be synchronized together. The chaotic synchronization is discussed in the context of complete synchronization which means that the difference of the states of two relevant systems converge to zero. (author)

  10. Properties of solutions of Bloch-type equations for the paraelectric phase of KDP

    Energy Technology Data Exchange (ETDEWEB)

    Glowacki, M; Paszkiewicz, T [Wroclaw Univ. (Poland). Inst. Fyziki Teoretycznej

    1979-10-01

    Exact solutions for two sets of Bloch-like equations describing the paraelectric phase of the model of KDP were studied. The general properties of both solutions are the same. However, in numerical calculations they differ significantly. A modification of the decay law connected with the soft mode frequency fluctuations is considered.

  11. Variational principle for the Bloch unified reaction theory

    International Nuclear Information System (INIS)

    MacDonald, W.; Rapheal, R.

    1975-01-01

    The unified reaction theory formulated by Claude Bloch uses a boundary value operator to write the Schroedinger equation for a scattering state as an inhomogeneous equation over the interaction region. As suggested by Lane and Robson, this equation can be solved by using a matrix representation on any set which is complete over the interaction volume. Lane and Robson have proposed, however, that a variational form of the Bloch equation can be used to obtain a ''best'' value for the S-matrix when a finite subset of this basis is used. The variational principle suggested by Lane and Robson, which gives a many-channel S-matrix different from the matrix solution on a finite basis, is considered first, and it is shown that the difference results from the fact that their variational principle is not, in fact, equivalent to the Bloch equation. Then a variational principle is presented which is fully equivalent to the Bloch form of the Schroedinger equation, and it is shown that the resulting S-matrix is the same as that obtained from the matrix solution of this equation. (U.S.)

  12. A Bloch-Torrey Equation for Diffusion in a Deforming Media

    International Nuclear Information System (INIS)

    Rohmer, Damien; Gullberg, Grant T.

    2006-01-01

    Diffusion Tensor Magnetic Resonance Imaging (DTMRI)technique enables the measurement of diffusion parameters and therefore, informs on the structure of the biological tissue. This technique is applied with success to the static organs such as brain. However, the diffusion measurement on the dynamically deformable organs such as the in-vivo heart is a complex problem that has however a great potential in the measurement of cardiac health. In order to understand the behavior of the Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torrey equation that leads the MR behavior is expressed in general curvilinear coordinates. These coordinates enable to follow the heart geometry and deformations through time. The equation is finally discredited and presented in a numerical formulation using implicit methods, in order to get a stable scheme that can be applied to any smooth deformations. Diffusion process enables the link between the macroscopic behavior of molecules and the microscopic structure in which they evolve. The measurement of diffusion in biological tissues is therefore of major importance in understanding the complex underlying structure that cannot be studied directly. The Diffusion Tensor Magnetic Resonance Imaging(DTMRI) technique enables the measurement of diffusion parameters and therefore provides information on the structure of the biological tissue. This technique has been applied with success to static organs such as the brain. However, diffusion measurement of dynamically deformable organs such as the in-vivo heart remains a complex problem, which holds great potential in determining cardiac health. In order to understand the behavior of the magnetic resonance (MR) signal in a deforming media, the Bloch-Torrey equation that defines the MR behavior is expressed in general curvilinear coordinates. These coordinates enable us to follow the heart geometry and deformations through time. The equation is finally discredited and presented in a

  13. Simulation of NMR signals through the Bloch equations; Simulação de sinais de RMN através das equações de Bloch

    Energy Technology Data Exchange (ETDEWEB)

    Moraes, Tiago Bueno, E-mail: tiagobuemoraes@gmail.com [Universidade de Sao Paulo (USP), Sao Carlos, SP (Brazil). Inst. de Física; Colnago, Luiz Alberto, E-mail: tiagobuemoraes@gmail.com [Embrapa Instrumentação, São Carlos, SP (Brazil)

    2014-07-01

    The aim of this paper was to present a simple and fast way of simulating Nuclear Magnetic Resonance signals using the Bloch equations. These phenomenological equations describe the classical behavior of macroscopic magnetization and are easily simulated using rotation matrices. Many NMR pulse sequences can be simulated with this formalism, allowing a quantitative description of the influence of many experimental parameters. Finally, the paper presents simulations of conventional sequences such as Single Pulse, Inversion Recovery, Spin Echo and CPMG. (author)

  14. A Bloch-Torrey Equation for Diffusion in a Deforming Media

    Energy Technology Data Exchange (ETDEWEB)

    Rohmer, Damien; Gullberg, Grant T.

    2006-12-29

    Diffusion Tensor Magnetic Resonance Imaging (DTMRI)technique enables the measurement of diffusion parameters and therefore,informs on the structure of the biological tissue. This technique isapplied with success to the static organs such as brain. However, thediffusion measurement on the dynamically deformable organs such as thein-vivo heart is a complex problem that has however a great potential inthe measurement of cardiac health. In order to understand the behavior ofthe Magnetic Resonance (MR)signal in a deforming media, the Bloch-Torreyequation that leads the MR behavior is expressed in general curvilinearcoordinates. These coordinates enable to follow the heart geometry anddeformations through time. The equation is finally discretized andpresented in a numerical formulation using implicit methods, in order toget a stable scheme that can be applied to any smooth deformations.Diffusion process enables the link between the macroscopic behavior ofmolecules and themicroscopic structure in which they evolve. Themeasurement of diffusion in biological tissues is therefore of majorimportance in understanding the complex underlying structure that cannotbe studied directly. The Diffusion Tensor Magnetic ResonanceImaging(DTMRI) technique enables the measurement of diffusion parametersand therefore provides information on the structure of the biologicaltissue. This technique has been applied with success to static organssuch as the brain. However, diffusion measurement of dynamicallydeformable organs such as the in-vivo heart remains a complex problem,which holds great potential in determining cardiac health. In order tounderstand the behavior of the magnetic resonance (MR) signal in adeforming media, the Bloch-Torrey equation that defines the MR behavioris expressed in general curvilinear coordinates. These coordinates enableus to follow the heart geometry and deformations through time. Theequation is finally discretized and presented in a numerical formulationusing

  15. Quantum anomalous Bloch-Siegert shift in Weyl semimetal

    Science.gov (United States)

    Kumar, Upendra; Kumar, Vipin; Enamullah, Setlur, Girish S.

    2018-05-01

    A periodic exchange of energy between the light field and two level system is known as Rabi oscillations. The Bloch-Siegert shift (BSS) is a shift in Rabi oscillation resonance condition, when the driving field is sufficiently strong. There are new type of oscillations exhibit in Weyl semimetal at far from resonance, known as anomalous Rabi oscillation. In this work, we study the phenomenon of the Bloch-Siegert shift in Weyl semimetal at far from resonance called anomalous Bloch-Siegert shift (ABSS) by purely quantum mechanical treatment and describe it's anisotropic nature. A fully numerical solution of the Floquet-Bloch equations unequivocally establishes the presence of not only anomalous Rabi oscillations in these systems but also their massless character.

  16. Computational Diffusion Magnetic Resonance Imaging Based on Time-Dependent Bloch NMR Flow Equation and Bessel Functions.

    Science.gov (United States)

    Awojoyogbe, Bamidele O; Dada, Michael O; Onwu, Samuel O; Ige, Taofeeq A; Akinwande, Ninuola I

    2016-04-01

    Magnetic resonance imaging (MRI) uses a powerful magnetic field along with radio waves and a computer to produce highly detailed "slice-by-slice" pictures of virtually all internal structures of matter. The results enable physicians to examine parts of the body in minute detail and identify diseases in ways that are not possible with other techniques. For example, MRI is one of the few imaging tools that can see through bones, making it an excellent tool for examining the brain and other soft tissues. Pulsed-field gradient experiments provide a straightforward means of obtaining information on the translational motion of nuclear spins. However, the interpretation of the data is complicated by the effects of restricting geometries as in the case of most cancerous tissues and the mathematical concept required to account for this becomes very difficult. Most diffusion magnetic resonance techniques are based on the Stejskal-Tanner formulation usually derived from the Bloch-Torrey partial differential equation by including additional terms to accommodate the diffusion effect. Despite the early success of this technique, it has been shown that it has important limitations, the most of which occurs when there is orientation heterogeneity of the fibers in the voxel of interest (VOI). Overcoming this difficulty requires the specification of diffusion coefficients as function of spatial coordinate(s) and such a phenomenon is an indication of non-uniform compartmental conditions which can be analyzed accurately by solving the time-dependent Bloch NMR flow equation analytically. In this study, a mathematical formulation of magnetic resonance flow sequence in restricted geometry is developed based on a general second order partial differential equation derived directly from the fundamental Bloch NMR flow equations. The NMR signal is obtained completely in terms of NMR experimental parameters. The process is described based on Bessel functions and properties that can make it

  17. Bloch electrons in 2D periodic electric and magnetic fields; Bloch-Elektronen in 2D periodischen elektrischen und magnetischen Feldern

    Energy Technology Data Exchange (ETDEWEB)

    Naundorf, B.

    2001-06-01

    The following topics were dealt with: electrons in periodic potentials, Bloch states, Landau states, wave packets, Harper equation, uncoupled Landau band states, matrix elements and matrix equations, periodic electric and magnetic fields (WL)

  18. Extended rate equations

    International Nuclear Information System (INIS)

    Shore, B.W.

    1981-01-01

    The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence

  19. Self-consistent Maxwell-Bloch theory of quantum-dot-population switching in photonic crystals

    International Nuclear Information System (INIS)

    Takeda, Hiroyuki; John, Sajeev

    2011-01-01

    We theoretically demonstrate the population switching of quantum dots (QD's), modeled as two-level atoms in idealized one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) by self-consistent solution of the Maxwell-Bloch equations. In our semiclassical theory, energy states of the electron are quantized, and electron dynamics is described by the atomic Bloch equation, while electromagnetic waves satisfy the classical Maxwell equations. Near a waveguide cutoff in a photonic band gap, the local electromagnetic density of states (LDOS) and spontaneous emission rates exhibit abrupt changes with frequency, enabling large QD population inversion driven by both continuous and pulsed optical fields. We recapture and generalize this ultrafast population switching using the Maxwell-Bloch equations. Radiative emission from the QD is obtained directly from the surrounding PC geometry using finite-difference time-domain simulation of the electromagnetic field. The atomic Bloch equations provide a source term for the electromagnetic field. The total electromagnetic field, consisting of the external input and radiated field, drives the polarization components of the atomic Bloch vector. We also include a microscopic model for phonon dephasing of the atomic polarization and nonradiative decay caused by damped phonons. Our self-consistent theory captures stimulated emission and coherent feedback effects of the atomic Mollow sidebands, neglected in earlier treatments. This leads to remarkable high-contrast QD-population switching with relatively modest (factor of 10) jump discontinuities in the electromagnetic LDOS. Switching is demonstrated in three separate models of QD's placed (i) in the vicinity of a band edge of a 1D PC, (ii) near a cutoff frequency in a bimodal waveguide channel of a 2D PC, and (iii) in the vicinity of a localized defect mode side coupled to a single-mode waveguide channel in a 2D PC.

  20. A 2D multi-term time and space fractional Bloch-Torrey model based on bilinear rectangular finite elements

    Science.gov (United States)

    Qin, Shanlin; Liu, Fawang; Turner, Ian W.

    2018-03-01

    The consideration of diffusion processes in magnetic resonance imaging (MRI) signal attenuation is classically described by the Bloch-Torrey equation. However, many recent works highlight the distinct deviation in MRI signal decay due to anomalous diffusion, which motivates the fractional order generalization of the Bloch-Torrey equation. In this work, we study the two-dimensional multi-term time and space fractional diffusion equation generalized from the time and space fractional Bloch-Torrey equation. By using the Galerkin finite element method with a structured mesh consisting of rectangular elements to discretize in space and the L1 approximation of the Caputo fractional derivative in time, a fully discrete numerical scheme is derived. A rigorous analysis of stability and error estimation is provided. Numerical experiments in the square and L-shaped domains are performed to give an insight into the efficiency and reliability of our method. Then the scheme is applied to solve the multi-term time and space fractional Bloch-Torrey equation, which shows that the extra time derivative terms impact the relaxation process.

  1. A theory of generalized Bloch oscillations

    International Nuclear Information System (INIS)

    Duggen, Lars; Lassen, Benny; Lew Yan Voon, L C; Willatzen, Morten

    2016-01-01

    Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact calculation is given to confirm this phenomenon. Our results allow for a greater freedom of design for experimentally observing Bloch oscillations. For strongly coupled oscillator systems displaying Bloch oscillations, it is further demonstrated that reordering of oscillators leads to destruction of Bloch oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics. (paper)

  2. Vacuum Bloch-Siegert shift in Landau polaritons with ultra-high cooperativity

    Science.gov (United States)

    Li, Xinwei; Bamba, Motoaki; Zhang, Qi; Fallahi, Saeed; Gardner, Geoff C.; Gao, Weilu; Lou, Minhan; Yoshioka, Katsumasa; Manfra, Michael J.; Kono, Junichiro

    2018-06-01

    A two-level system resonantly interacting with an a.c. magnetic or electric field constitutes the physical basis of diverse phenomena and technologies. However, Schrödinger's equation for this seemingly simple system can be solved exactly only under the rotating-wave approximation, which neglects the counter-rotating field component. When the a.c. field is sufficiently strong, this approximation fails, leading to a resonance-frequency shift known as the Bloch-Siegert shift. Here, we report the vacuum Bloch-Siegert shift, which is induced by the ultra-strong coupling of matter with the counter-rotating component of the vacuum fluctuation field in a cavity. Specifically, an ultra-high-mobility two-dimensional electron gas inside a high-Q terahertz cavity in a quantizing magnetic field revealed ultra-narrow Landau polaritons, which exhibited a vacuum Bloch-Siegert shift up to 40 GHz. This shift, clearly distinguishable from the photon-field self-interaction effect, represents a unique manifestation of a strong-field phenomenon without a strong field.

  3. Behaviour of neutrons passing through the Bloch wall

    International Nuclear Information System (INIS)

    Schaerpf, O.

    1976-01-01

    In part I of the present paper the pertinent knowledge about Bloch walls is presented and developed insofar as it appears necessary for the experiments with neutrons, that is to say the direction of magnetization within the domains, the calculation of the variation of magnetization in the wall, the wall thickness, and the zigzag structure of the Bloch wall. In part II it is first clarified why the Bloch wall can be treated as a continuum problem. It shows that this is possible far away from Laue reflexes. For angles far away from Laure-reflex angles the interaction of the periodic structure of the magnetization can be described with the aid of an averaged magnetic flux density. The consequence of it is the possibility of treating the problem by means of a Schroedinger equation with continous interaction. This leads to a law of refraction. The question of the possibilities for explaining the intensity behavior is treated in part III. This part, from different aspects, describes the fact, which already was pointed out in Schaerpf, O., Vehoff, H., Schwink, Ch. 1973, that the spin of the neutrons in passing through the wall is partly taken along by the magnetization gradually rotating in the wall. (orig./WBU) [de

  4. A theory of generalized Bloch oscillations

    DEFF Research Database (Denmark)

    Duggen, Lars; Lew Yan Voon, L. C.; Lassen, Benny

    2016-01-01

    Bloch oscillations of electrons are shown to occur for cases when the energy spectrum does not consist of the traditional evenly-spaced ladders and the potential gradient does not result from an external electric field. A theory of such generalized Bloch oscillations is presented and an exact...... oscillations. We stipulate that the presented theory of generalized Bloch oscillations can be extended to other systems such as acoustics and photonics....

  5. Designing non-Hermitian dynamics for conservative state evolution on the Bloch sphere

    Science.gov (United States)

    Yu, Sunkyu; Piao, Xianji; Park, Namkyoo

    2018-03-01

    An evolution on the Bloch sphere is the fundamental state transition, including optical polarization controls and qubit operations. Conventional evolution of a polarization state or qubit is implemented within a closed system that automatically satisfies energy conservation from the Hermitian formalism. Although particular forms of static non-Hermitian Hamiltonians, such as parity-time-symmetric Hamiltonians, allow conservative states in an open system, the criteria for the energy conservation in a dynamical open system have not been fully explored. Here, we derive the condition of conservative state evolution in open-system dynamics and its inverse design method, by developing the non-Hermitian modification of the Larmor precession equation. We show that the geometrically designed locus on the Bloch sphere can be realized by different forms of dynamics, leading to the isolocus family of non-Hermitian dynamics. This increased degree of freedom allows the complementary phenomena of error-robust and highly sensitive evolutions on the Bloch sphere, which could be applicable to stable polarizers, quantum gates, and optimized sensors in dynamical open systems.

  6. Self-consistent Maxwell-Bloch model of quantum-dot photonic-crystal-cavity lasers

    Science.gov (United States)

    Cartar, William; Mørk, Jesper; Hughes, Stephen

    2017-08-01

    We present a powerful computational approach to simulate the threshold behavior of photonic-crystal quantum-dot (QD) lasers. Using a finite-difference time-domain (FDTD) technique, Maxwell-Bloch equations representing a system of thousands of statistically independent and randomly positioned two-level emitters are solved numerically. Phenomenological pure dephasing and incoherent pumping is added to the optical Bloch equations to allow for a dynamical lasing regime, but the cavity-mediated radiative dynamics and gain coupling of each QD dipole (artificial atom) is contained self-consistently within the model. These Maxwell-Bloch equations are implemented by using Lumerical's flexible material plug-in tool, which allows a user to define additional equations of motion for the nonlinear polarization. We implement the gain ensemble within triangular-lattice photonic-crystal cavities of various length N (where N refers to the number of missing holes), and investigate the cavity mode characteristics and the threshold regime as a function of cavity length. We develop effective two-dimensional model simulations which are derived after studying the full three-dimensional passive material structures by matching the cavity quality factors and resonance properties. We also demonstrate how to obtain the correct point-dipole radiative decay rate from Fermi's golden rule, which is captured naturally by the FDTD method. Our numerical simulations predict that the pump threshold plateaus around cavity lengths greater than N =9 , which we identify as a consequence of the complex spatial dynamics and gain coupling from the inhomogeneous QD ensemble. This behavior is not expected from simple rate-equation analysis commonly adopted in the literature, but is in qualitative agreement with recent experiments. Single-mode to multimode lasing is also observed, depending on the spectral peak frequency of the QD ensemble. Using a statistical modal analysis of the average decay rates, we also

  7. Electric dipoles on the Bloch sphere

    OpenAIRE

    Vutha, Amar C.

    2014-01-01

    The time evolution of a two-level quantum mechanical system can be geometrically described using the Bloch sphere. By mapping the Bloch sphere evolution onto the dynamics of oscillating electric dipoles, we provide a physically intuitive link between classical electromagnetism and the electric dipole transitions of atomic & molecular physics.

  8. Electric dipoles on the Bloch sphere

    International Nuclear Information System (INIS)

    Vutha, Amar C

    2015-01-01

    The time evolution of a two-level quantum mechanical system can be geometrically described using the Bloch sphere. By mapping the Bloch sphere evolution onto the dynamics of oscillating electric dipoles, we provide a physically intuitive link between classical electromagnetism and the electric dipole transitions of atomic and molecular physics. (paper)

  9. The transmission factor of a bloch wall for spin waves whose wave vector is perpendicular to the wall (1961); Facteur de transmission d'une paroi de bloch pour des ondes de spin de vecteur d'onde normal a la paroi (1961)

    Energy Technology Data Exchange (ETDEWEB)

    Boutron, F [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires

    1961-07-01

    When, for a ferromagnetic, the anisotropic energy takes the form E= K sin{sup 2} {alpha}, the study of the propagation of spin waves of low energy across a Bloch wall leads to a one-dimensional Schrodinger equation in which is found a potential well which has the remarkable property of being completely transparent for all values of the incident wave energy. (author) [French] Dans un ferromagnetique, lorsque la densite d'energie d'anisotropie est de la forme E= K sin{sup 2} {alpha}, l'etude de la propagation des ondes de spin de faible energie a travers une paroi de Bloch, conduit a une equation de Schrodinger a une dimension, dans laquelle figure un puits de potentiel qui a la propriete remarquable d'etre completement transparent quelle que soit l'energie de l'onde incidente. (auteur)

  10. On history and salvation in Emmanuel Levinas and Ernst Bloch

    African Journals Online (AJOL)

    p1243322

    “Chronos” who devours his own children.13 In addition to this, one would invert ... death” against Bloch, one could argue that Bloch, in effect, is glorifying death .... fantasy or wishful thinking) to Bloch's belief that in a humanised world the.

  11. Composition operators between Bloch type spaces and Zygmund ...

    Indian Academy of Sciences (India)

    MS received 1 September 2009; revised 31 March 2011. Abstract. The boundedness and compactness of composition operators between. Bloch type spaces and Zygmund spaces of holomorphic functions in the unit ball are characterized in the paper. Keywords. Composition operator; Bloch type space; Zygmund space. 1.

  12. Bloch-Siegert shift in Dirac-Weyl fermionic systems

    Science.gov (United States)

    Kumar, Upendra; Kumar, Vipin; Enamullah, Setlur, Girish S.

    2018-04-01

    The Bloch-Siegert shift is a phenomenon in quantum optics, typically seen in two-level systems, when the driving field is sufficiently strong. The inclusion of frequency doubling effect (counter rotating term) in the conventional rotating wave approximation (RWA) changes the resonance condition thereby producing a rather small shift in the resonance condition, which is known as the Bloch-Siegert shift (BSS). Rabi oscillations in Dirac-Weyl fermionic systems exhibit anomalous behavior far from resonance, called anomalous Rabi oscillations. Therefore, in the present work, we study the phenomenon of the Bloch-Siegert shift in Weyl semimetal and topological insulator (TI) far from resonance, called anomalous Bloch-Siegert shift (ABSS). It is seen that the change in the resonance condition of anomalous Rabi oscillations is drastic in Weyl semimetal and TI. The ABSS in Weyl semimetals is highly anisotropic, whereas it is isotropic in TI. In case of TI, it is the Chern number which plays a crucial role to produce substantial change in the ABSS.

  13. The basic properties of Bloch functions

    Directory of Open Access Journals (Sweden)

    Joseph A. Cima

    1979-01-01

    Full Text Available A Bloch function f(z is an analytic function on the unit disc whose derivative grows no faster than a constant times the reciprocal of the distance from z to ∂. We reprove here the basic analytic facts concerning Bloch functions. We establish the Banach space structure and collect facts concerning the geometry of the space. We indicate duality relationships, and known isomorphic correspondences are given. We give a rather complete list of references for further study in the case of several variables.

  14. The Bloch wave operator: generalizations and applications: Part I. The time-independent case

    CERN Document Server

    Killingbeck, J P

    2003-01-01

    This is part 1 of a two-part review on wave operator theory and methods. The basic theory of the time-independent wave operator is presented in terms of partitioned matrix theory for the benefit of general readers, with a discussion of the links between the matrix and projection operator approaches. The matrix approach is shown to lead to simple derivations of the wave operators and effective Hamiltonians of Loewdin, Bloch, Des Cloizeaux and Kato as well as to some associated variational forms. The principal approach used throughout stresses the solution of the nonlinear equation for the reduced wave operator, leading to the construction of the effective Hamiltonians of Bloch and of Des Cloizeaux. Several mathematical techniques which are useful in implementing this approach are explained, some of them being relatively little known in the area of wave operator calculations. The theoretical discussion is accompanied by several specimen numerical calculations which apply the described techniques to a selection ...

  15. Skyrmion clusters from Bloch lines in ferromagnetic films

    KAUST Repository

    Garanin, Dmitry A.

    2017-12-29

    Conditions under which various skyrmion objects emerge in experiments on thin magnetic films remain largely unexplained. We investigate numerically centrosymmetric spin lattices in films of finite thickness with ferromagnetic exchange, magnetic anisotropy, and dipole-dipole interaction. Evolution of labyrinth domains into compact topological structures on application of the magnetic field is found to be governed by the configuration of Bloch lines inside domain walls. Depending on the combination of Bloch lines, the magnetic domains evolve into individual skyrmions, biskyrmions, or more complex topological objects. While the geometry of such objects is sensitive to the parameters, their topological charge is uniquely determined by the topological charge of Bloch lines inside the magnetic domain from which the object emerges.

  16. Bloch-mode analysis for retrieving effective parameters of metamaterials

    DEFF Research Database (Denmark)

    Andryieuski, Andrei; Ha, Sangwoo; Sukhorukov, Andrey A.

    2012-01-01

    by our method with a high accuracy. We employ both surface and volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes to determine the Bloch and wave impedances, respectively. We discuss how this method works for several characteristic examples, and demonstrate...

  17. Bloch walls in a nickel single crystal

    International Nuclear Information System (INIS)

    Peters, J.; Treimer, W.

    2001-01-01

    We present a consistent theory for the dependence of the magnetic structure in bulk samples on external static magnetic fields and corresponding experimental results. We applied the theory of micromagnetism to this crystal and calculated the Bloch wall thickness as a function of external magnetic fields. The theoretical results agree well with the experimental data, so that the Bloch wall thickness of a 71 deg. nickel single crystal was definitely determined with some hundred of nanometer

  18. Non-Bloch decay of Rabi oscillations in liquid state NMR

    Science.gov (United States)

    Chakrabarti, Arnab; Bhattacharyya, Rangeet

    2018-03-01

    Rabi oscillations are known to exhibit non-Bloch behaviour in anisotropic media. In this letter, we report an experimental observation of non-Bloch decay of Rabi oscillations in isotropic liquid state NMR. To avoid the dephasing due to the radio-frequency inhomogeneities, we develop a modified version of the rotary echo protocol and use it to determine the decay rates of Rabi oscillations. We find that the measured decay rates are proportional to the square of the Rabi frequencies and the proportionality constant is of the order of tens of picoseconds. Further, we show that this non-Bloch nature of the decay rates becomes less prominent with increasing temperature. The implications of the presence of non-Bloch decay rates in liquid state NMR in the context of ensemble quantum computing are also discussed.

  19. Modeling Bloch oscillations in nanoscale Josephson junctions

    Science.gov (United States)

    Vora, Heli; Kautz, R. L.; Nam, S. W.; Aumentado, J.

    2018-01-01

    Bloch oscillations in nanoscale Josephson junctions with a Coulomb charging energy comparable to the Josephson coupling energy are explored within the context of a model previously considered by Geigenmüller and Schön that includes Zener tunneling and treats quasiparticle tunneling as an explicit shot-noise process. The dynamics of the junction quasicharge are investigated numerically using both Monte Carlo and ensemble approaches to calculate voltage-current characteristics in the presence of microwaves. We examine in detail the origin of harmonic and subharmonic Bloch steps at dc biases I = (n/m)2ef induced by microwaves of frequency f and consider the optimum parameters for the observation of harmonic (m = 1) steps. We also demonstrate that the GS model allows a detailed semiquantitative fit to experimental voltage-current characteristics previously obtained at the Chalmers University of Technology, confirming and strengthening the interpretation of the observed microwave-induced steps in terms of Bloch oscillations. PMID:29577106

  20. Quantum qubit measurement by a quantum point contact with a quantum Langevin equation approach

    International Nuclear Information System (INIS)

    Dong, Bing; Lei, X.L.; Horing, N.J.M.; Cui, H.L.

    2007-01-01

    We employ a microscopic quantum Heisenberg-Langevin equation approach to establish a set of quantum Bloch equations for a two-level system (coupled quantum dots) capacitively coupled to a quantum point contact (QPC). The resulting Bloch equations facilitate our analysis of qubit relaxation and decoherence in coupled quantum dots induced by measurement processes at arbitrary bias-voltage and temperature. We also examine the noise spectrum of the meter output current for a symmetric qubit. These results help resolve a recent debate about a quantum oscillation peak in the noise spectrum. (copyright 2007 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

  1. Bloch spaces of holomorphic functions in the polydisk

    Directory of Open Access Journals (Sweden)

    Anahit Harutyunyan

    2007-01-01

    Full Text Available This work is an introduction to anisotropic spaces of holomorphic functions, which have ω-weight and are generalizations of Bloch spaces to a polydisc. We prove that these classes form an algebra and are invariant with respect to monomial multiplication. Some theorems on projection and diagonal mapping are proved. We establish a description of (Ap(ω* (or (Hp(ω* via the Bloch classes for all 0

  2. Quasi-periodic Schroedinger operators in one dimension, absolutely continuous spectra, Bloch waves, and integrable Hamiltonian systems

    International Nuclear Information System (INIS)

    Chierchia, L.

    1986-01-01

    In the first chapter, the eigenvalue problem for a periodic Schroedinger operator, Lf = (-d 2 /dx 2 + v)f = Ef, is viewed as a two-dimensional Hamiltonian system which is integrable in the sense of Arnold and Liouville. With the aid of the Floquet-BLoch theory, it is shown that such a system is conjugate to two harmonic oscillators with frequencies α and omega, being the rotation number for L and 2π/omega the period of the potential v. This picture is generalized in the second chapter, to quasi periodic Schroedinger operators, L/sub epsilon/, with highly irrational frequencies (omega 1 , ..., omega/sub d/), which are a small perturbation of periodic operators. In the last chapter, the absolutely continuous spectrum σ/sub ac/ of a general quasi-periodic Schroedinger operators is considered. The Radon-Nikodym derivatives (with respect to Lebesgue measure) of the spectral measures are computed in terms of special independent eigensolutions existing for almost ever E in σ/sub ac/. Finally, it is shown that weak Bloch waves always exist for almost ever E in σ/sub ac/ and the question of the existence of genuine Bloch waves is turned into a regularity problem for a certain nonlinear partial differential equation on a d-dimensional torus

  3. Spin wave vortex from the scattering on Bloch point solitons

    Energy Technology Data Exchange (ETDEWEB)

    Carvalho-Santos, V.L., E-mail: vagson.carvalho@usach.cl [Instituto Federal de Educação, Ciência e Tecnologia Baiano - Campus Senhor do Bonfim, Km 04 Estrada da Igara, 48970-000 Senhor do Bonfim, Bahia (Brazil); Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Elías, R.G., E-mail: gabriel.elias@usach.cl [Departamento de Física, Universidad de Santiago de Chile and CEDENNA, Avda. Ecuador 3493, Santiago (Chile); Nunez, A.S., E-mail: alnunez@dfi.uchile.cl [Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago (Chile)

    2015-12-15

    The interaction of a spin wave with a stationary Bloch point is studied. The topological non-trivial structure of the Bloch point manifests in the propagation of spin waves endowing them with a gauge potential that resembles the one associated with the interaction of a magnetic monopole and an electron. By pursuing this analogy, we are led to the conclusion that the scattering of spin waves and Bloch points is accompanied by the creation of a magnon vortex. Interference between such a vortex and a plane wave leads to dislocations in the interference pattern that can be measurable by means of magnon holography.

  4. Modeling Bloch oscillations in ultra-small Josephson junctions

    Science.gov (United States)

    Vora, Heli; Kautz, Richard; Nam, Sae Woo; Aumentado, Jose

    In a seminal paper, Likharev et al. developed a theory for ultra-small Josephson junctions with Josephson coupling energy (Ej) less than the charging energy (Ec) and showed that such junctions demonstrate Bloch oscillations which could be used to make a fundamental current standard that is a dual of the Josephson volt standard. Here, based on the model of Geigenmüller and Schön, we numerically calculate the current-voltage relationship of such an ultra-small junction which includes various error processes present in a nanoscale Josephson junction such as random quasiparticle tunneling events and Zener tunneling between bands. This model allows us to explore the parameter space to see the effect of each process on the width and height of the Bloch step and serves as a guide to determine whether it is possible to build a quantum current standard of a metrological precision using Bloch oscillations.

  5. Nonlinear Bloch waves in metallic photonic band-gap filaments

    International Nuclear Information System (INIS)

    Kaso, Artan; John, Sajeev

    2007-01-01

    We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament

  6. Nonlinear Bloch waves in metallic photonic band-gap filaments

    Science.gov (United States)

    Kaso, Artan; John, Sajeev

    2007-11-01

    We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.

  7. Self-consistent Maxwell-Bloch model of quantum-dot photonic-crystal-cavity lasers

    DEFF Research Database (Denmark)

    Cartar, William; Mørk, Jesper; Hughes, Stephen

    2017-01-01

    -level emitters are solved numerically. Phenomenological pure dephasing and incoherent pumping is added to the optical Bloch equations to allow for a dynamical lasing regime, but the cavity-mediated radiative dynamics and gain coupling of each QD dipole (artificial atom) is contained self-consistently within......-mode to multimode lasing is also observed, depending on the spectral peak frequency of the QD ensemble. Using a statistical modal analysis of the average decay rates, we also show how the average radiative decay rate decreases as a function of cavity size. In addition, we investigate the role of structural disorder...

  8. Orbital magnetism of Bloch electrons I. General formula

    International Nuclear Information System (INIS)

    Ogata, Masao; Fukuyama, Hidetoshi

    2015-01-01

    We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time. (author)

  9. A formula for the Bloch vector of some Lindblad quantum systems

    International Nuclear Information System (INIS)

    Salgado, D.; Sanchez-Gomez, J.L.

    2004-01-01

    Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators

  10. From Bloch to random lasing in ZnO self-assembled nanostructures

    DEFF Research Database (Denmark)

    Garcia-Fernandez, Pedro David; Cefe, López

    2013-01-01

    In this paper, we present measurements on UV lasing in ZnO ordered and disordered nanostructures. Bloch lasing is achieved in the ordered structures by exploiting very low group-velocity Bloch modes in ZnO photonic crystals. In the second case, random lasing is observed in ZnO photonic glasses. We...... study the lasing threshold in both cases and its dependence on the structural parameters. Finally, we present the transition from Bloch to random lasing by deliberately doping a ZnO inverse photonic crystal with a controlled amount of lattice vacancies effectively converting it into a translationally...

  11. Felix Bloch (1905–1983)

    Indian Academy of Sciences (India)

    IAS Admin

    1905, to Jewish parents, Gustav and Agnes Bloch. The year he ... Both the student and the supervisor were in their 20's, separated by 5– ... up on the West Coast, in the University of Stanford, where he stayed for the rest of his academic life.

  12. Properties of Floquet-Bloch space harmonics in 1D periodic magneto-dielectric structures

    DEFF Research Database (Denmark)

    Breinbjerg, O.

    2012-01-01

    Recent years have witnessed a significant research interest in Floquet-Bloch analysis for determining the homogenized permittivity and permeability of metamaterials consisting of periodic structures. This work investigates fundamental properties of the Floquet-Bloch space harmonics in a 1......-dimensional magneto-dielectric lossless structure supporting a transverse-electric-magnetic Floquet-Bloch wave; in particular, the space harmonic permittivity and permeability, as well as the space harmonic Poynting vector....

  13. Computational Modeling of Bloch Surface Waves in One-Dimensional Periodic and Aperiodic Multilayer Structures

    Science.gov (United States)

    Koju, Vijay

    Photonic crystals and their use in exciting Bloch surface waves have received immense attention over the past few decades. This interest is mainly due to their applications in bio-sensing, wave-guiding, and other optical phenomena such as surface field enhanced Raman spectroscopy. Improvement in numerical modeling techniques, state of the art computing resources, and advances in fabrication techniques have also assisted in growing interest in this field. The ability to model photonic crystals computationally has benefited both the theoretical as well as experimental communities. It helps the theoretical physicists in solving complex problems which cannot be solved analytically and helps to acquire useful insights that cannot be obtained otherwise. Experimentalists, on the other hand, can test different variants of their devices by changing device parameters to optimize performance before fabrication. In this dissertation, we develop two commonly used numerical techniques, namely transfer matrix method, and rigorous coupled wave analysis, in C++ and MATLAB, and use two additional software packages, one open-source and another commercial, to model one-dimensional photonic crystals. Different variants of one-dimensional multilayered structures such as perfectly periodic dielectric multilayers, quasicrystals, aperiodic multilayer are modeled, along with one-dimensional photonic crystals with gratings on the top layer. Applications of Bloch surface waves, along with new and novel aperiodic dielectric multilayer structures that support Bloch surface waves are explored in this dissertation. We demonstrate a slow light configuration that makes use of Bloch Surface Waves as an intermediate excitation in a double-prism tunneling configuration. This method is simple compared to the more usual techniques for slowing light using the phenomenon of electromagnetically induced transparency in atomic gases or doped ionic crystals operated at temperatures below 4K. Using a semi

  14. Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

    Directory of Open Access Journals (Sweden)

    Flavia Colonna

    2012-01-01

    Full Text Available The logarithmic Bloch space Blog⁡ is the Banach space of analytic functions on the open unit disk 𝔻 whose elements f satisfy the condition ∥f∥=sup⁡z∈𝔻(1-|z|2log⁡  (2/(1-|z|2|f'(z|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy space Hp (with 1≤p≤∞ into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mapping Hp into the little logarithmic Bloch space defined as the subspace of Blog⁡ consisting of the functions f such that lim⁡|z|→1(1-|z|2log⁡  (2/(1-|z|2|f'(z|=0.

  15. Bloch wave deafness and modal conversion at a phononic crystal boundary

    Directory of Open Access Journals (Sweden)

    Vincent Laude

    2011-12-01

    Full Text Available We investigate modal conversion at the boundary between a homogeneous incident medium and a phononic crystal, with consideration of the impact of symmetry on the excitation of Bloch waves. We give a quantitative criterion for the appearance of deaf Bloch waves, which are antisymmetric with respect to a symmetry axis of the phononic crystal, in the frame of generalized Fresnel formulas for reflection and transmission at the phononic crystal boundary. This criterion is used to index Bloch waves in the complex band structure of the phononic crystal, for directions of incidence along a symmetry axis. We argue that within deaf frequency ranges transmission is multi-exponential, as it is within frequency band gaps.

  16. Nonlinear tunneling of bright and dark rogue waves in combined nonlinear Schrödinger and Maxwell-Bloch systems

    Science.gov (United States)

    Raju, Thokala Soloman; Pal, Ritu

    2018-05-01

    We derive the analytical rogue wave solutions for the generalized inhomogeneous nonlinear Schrödinger-Maxwell-Bloch (GINLS-MB) equation describing the pulse propagation in erbium-doped fibre system. Then by suitably choosing the inhomogeneous parameters, we delineate the tunneling properties of rogue waves through dispersion and nonlinearity barriers or wells. Finally, we demonstrate the propagating characteristics of optical solitons by considering their tunneling through periodic barriers by the proper choice of external potential.

  17. Electroweak evolution equations

    International Nuclear Information System (INIS)

    Ciafaloni, Paolo; Comelli, Denis

    2005-01-01

    Enlarging a previous analysis, where only fermions and transverse gauge bosons were taken into account, we write down infrared-collinear evolution equations for the Standard Model of electroweak interactions computing the full set of splitting functions. Due to the presence of double logs which are characteristic of electroweak interactions (Bloch-Nordsieck violation), new infrared singular splitting functions have to be introduced. We also include corrections related to the third generation Yukawa couplings

  18. Mechanical Properties of Laminate Materials: From Surface Waves to Bloch Oscillations

    DEFF Research Database (Denmark)

    Liang, Z.; Willatzen, Morten; Christensen, Johan

    2015-01-01

    for designing Bloch oscillations in classical plate structures and show how mechanical Bloch oscillations can be generated in arrays of solid plates when the modal wavelength is gradually reduced. The design recipe describes how Bloch oscillations in classical structures of arbitrary dimensions can be generated......We propose hitherto unexplored and fully analytical insights into laminate elastic materials in a true condensed-matter-physics spirit. Pure mechanical surface waves that decay as evanescent waves from the interface are discussed, and we demonstrate how these designer Scholte waves are controlled......, and we demonstrate this numerically for structures with millimeter and centimeter dimensions in the kilohertz to megahertz range. Analytical predictions agree entirely with full wave simulations showing how elastodynamics can mimic quantum-mechanical condensed-matter phenomena....

  19. The Bloch Approximation in Periodically Perforated Media

    International Nuclear Information System (INIS)

    Conca, C.; Gomez, D.; Lobo, M.; Perez, E.

    2005-01-01

    We consider a periodically heterogeneous and perforated medium filling an open domain Ω of R N . Assuming that the size of the periodicity of the structure and of the holes is O(ε),we study the asymptotic behavior, as ε → 0, of the solution of an elliptic boundary value problem with strongly oscillating coefficients posed in Ω ε (Ω ε being Ω minus the holes) with a Neumann condition on the boundary of the holes. We use Bloch wave decomposition to introduce an approximation of the solution in the energy norm which can be computed from the homogenized solution and the first Bloch eigenfunction. We first consider the case where Ωis R N and then localize the problem for abounded domain Ω, considering a homogeneous Dirichlet condition on the boundary of Ω

  20. Bloch-Surface-Polariton-Based Hybrid Nanowire Structure for Subwavelength, Low-Loss Waveguiding

    Directory of Open Access Journals (Sweden)

    Weijing Kong

    2018-03-01

    Full Text Available Surface plasmon polaritons (SPPs have been thoroughly studied in the past decades for not only sensing but also waveguiding applications. Various plasmonic device structures have been explored due to their ability to confine their optical mode to the subwavelength level. However, with the existence of metal, the large ohmic loss limits the propagation distance of the SPP and thus the scalability of such devices. Therefore, different hybrid waveguides have been proposed to overcome this shortcoming. Through fine tuning of the coupling between the SPP and a conventional waveguide mode, a hybrid mode could be excited with decent mode confinement and extended propagation distance. As an effective alternative of SPP, Bloch surface waves have been re-investigated more recently for their unique advantages. As is supported in all-dielectric structures, the optical loss for the Bloch surface wave is much lower, which stands for a much longer propagating distance. Yet, the confinement of the Bloch surface wave due to the reflections and refractions in the multilayer structure is not as tight as that of the SPP. In this work, by integrating a periodic multilayer structure that supports the Bloch surface wave with a metallic nanowire structure, a hybrid Bloch surface wave polariton could be excited. With the proposed hybrid nanowire structure, a hybrid mode is demonstrated with the deep subwavelength mode confinement and a propagation distance of tens of microns.

  1. Terahertz emission of Bloch oscillators excited by electromagnetic field in lateral semiconductor superlattices

    International Nuclear Information System (INIS)

    Dodin, E.P.; Zharov, A.A.

    2003-01-01

    The effect of the strong high-frequency electromagnetic field on the lateral semiconductor superlattice is considered on the basis of the quasi-classical theory on the electron transport in the self-consistent wave arrangement. It is theoretically identified, that the lateral superlattice in the strong feed-up wave field may emit the terahertz radiation wave trains, which are associated with the periodical excitation of the Bloch oscillations in the superlattice. The conditions, required for the Bloch oscillators radiation observation, are determined. The spectral composition of the radiation, passing through the superlattice, and energy efficiency of multiplying the frequency, related to the Bloch oscillator excitation, are calculated [ru

  2. Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7 T.

    Science.gov (United States)

    Qin, Shanlin; Liu, Fawang; Turner, Ian W; Yu, Qiang; Yang, Qianqian; Vegh, Viktor

    2017-04-01

    To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain. Magn Reson Med 77:1485-1494, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

  3. Optical Effects Induced by Bloch Surface Waves in One-Dimensional Photonic Crystals

    Directory of Open Access Journals (Sweden)

    Irina V. Soboleva

    2018-01-01

    Full Text Available The review considers the influence of Bloch surface waves on the optical and magneto-optical effects observed in photonic crystals; for example, the Goos–Hänchen effect, the Faraday effect, optical trapping and so on. Prospects for using Bloch surface waves for spatial light modulation, for controlling the polarization of light, for optical trapping and control of micro-objects are discussed.

  4. Bloch oscillations and accelerated Bose–Einstein condensates in an optical lattice

    Energy Technology Data Exchange (ETDEWEB)

    Sacchetti, Andrea, E-mail: andrea.sacchetti@unimore.it

    2017-01-30

    Highlights: • Discrete nonlinear Schrödinger model for accelerated BECs in optical lattices. • Numerical computation of wavefunction BECs dynamics. • Correlation between nonlinearity and the oscillating period of the BEC's center of mass. • Discussion of the validity of the Bloch Theorem for accelerated BECs in an optical lattice. - Abstract: We discuss the method for the measurement of the gravity acceleration g by means of Bloch oscillations of an accelerated BEC in an optical lattice. This method has a theoretical critical point due to the fact that the period of the Bloch oscillations depends, in principle, on the initial shape of the BEC wavepacket. Here, by making use of the nearest-neighbor model for the numerical analysis of the BEC wavefunction, we show that in real experiments the period of the Bloch oscillations does not really depend on the shape of the initial wavepacket and that the relative uncertainty, due to the fact that the initial shape of the wavepacket may be asymmetrical, is smaller than the one due to experimental errors. Furthermore, we also show that the relation between the oscillation period and the scattering length of the BEC's atoms is linear; this fact suggests us a new experimental procedure for the measurement of the scattering length of atoms.

  5. Skyrmion clusters from Bloch lines in ferromagnetic films

    KAUST Repository

    Garanin, Dmitry A.; Chudnovsky, Eugene M.; Zhang, Xixiang

    2017-01-01

    anisotropy, and dipole-dipole interaction. Evolution of labyrinth domains into compact topological structures on application of the magnetic field is found to be governed by the configuration of Bloch lines inside domain walls. Depending on the combination

  6. Observation of Bloch oscillations in complex PT-symmetric photonic lattices

    Science.gov (United States)

    Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf

    2015-01-01

    Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations. PMID:26639941

  7. Integral type operators from normal weighted Bloch spaces to QT,S spaces

    Directory of Open Access Journals (Sweden)

    Yongyi GU

    2016-08-01

    Full Text Available Operator theory is an important research content of the analytic function space theory. The discussion of simultaneous operator and function space is an effective way to study operator and function space. Assuming that  is an analytic self map on the unit disk Δ, and the normal weighted bloch space μ-B is a Banach space on the unit disk Δ, defining a composition operator C∶C(f=f on μ-B for all f∈μ-B, integral type operator JhC and CJh are generalized by integral operator and composition operator. The boundeness and compactness of the integral type operator JhC acting from normal weighted Bloch spaces to QT,S spaces are discussed, as well as the boundeness of the integral type operators CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.

  8. Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

    Directory of Open Access Journals (Sweden)

    Matthias Saba

    2015-01-01

    Full Text Available We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell’s equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and μ and coupling matrices ς. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction.

  9. Reve et action: Bloch, Heidegger et Levinas

    Czech Academy of Sciences Publication Activity Database

    Bierhanzl, Jan

    2016-01-01

    Roč. 12, č. 3 (2016), s. 1-6 ISSN 1336-6556 R&D Projects: GA ČR(CZ) GA16-23046S Institutional support: RVO:67985955 Keywords : possibility * wishing * decision * action * dream * utopia Subject RIV: AA - Philosophy ; Religion http://www.ostium.sk/sk/r%C8%87ve-er-action-bloch-heidegger-et-levinas/

  10. Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes-Cummings model

    Science.gov (United States)

    Azuma, Hiroo; Ban, Masashi

    2014-07-01

    We study a quasiperiodic structure in the time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, motion of the Bloch vector seems to be in disorder. Because of the thermal photon distribution, both a norm and a direction of the Bloch vector change hard at random. In this paper, taking a different viewpoint compared with ones that we have been used to, we investigate quasiperiodicity of the Bloch vector’s trajectories. Introducing the concept of the quasiperiodic motion, we can explain the confused behaviour of the system as an intermediate state between periodic and chaotic motions. More specifically, we discuss the following two facts: (1) If we adjust the time interval Δt properly, figures consisting of plotted dots at the constant time interval acquire scale invariance under replacement of Δt by sΔt, where s(>1) is an arbitrary real but not transcendental number. (2) We can compute values of the time variable t, which let |Sz(t)| (the absolute value of the z-component of the Bloch vector) be very small, with the Diophantine approximation (a rational approximation of an irrational number).

  11. Taking a peek at Bloch oscillations

    Science.gov (United States)

    Morsch, Oliver

    2016-11-01

    Bloch oscillations arise when matter waves inside a periodic potential, such as a crystal lattice, are accelerated by a constant force. Keßler et al (2016 New J. Phys. 18 102001) have now experimentally tested a method that allows one to observe those oscillations continuously, without a destructive measurement on the matter wave. Their approach could help to make cold atom-based accelerometers and gravimeters more precise.

  12. Incorporating excitation-induced dephasing into the Maxwell-Bloch numerical modeling of photon echoes

    International Nuclear Information System (INIS)

    Burr, G.W.; Harris, Todd L.; Babbitt, Wm. Randall; Jefferson, C. Michael

    2004-01-01

    We describe the incorporation of excitation-induced dephasing (EID) into the Maxwell-Bloch numerical simulation of photon echoes. At each time step of the usual numerical integration, stochastic frequency jumps of ions--caused by excitation of neighboring ions--is modeled by convolving each Bloch vector with the Bloch vectors of nearby frequency detunings. The width of this convolution kernel follows the instantaneous change in overall population, integrated over the simulated bandwidth. This approach is validated by extensive comparison against published and original experimental results. The enhanced numerical model is then used to investigate the accuracy of experiments designed to extrapolate to the intrinsic dephasing time T 2 from data taken in the presence of EID. Such a modeling capability offers improved understanding of experimental results, and should allow quantitative analysis of engineering tradeoffs in realistic optical coherent transient applications

  13. A note on the Königs domain of compact composition operators on the Bloch space

    Directory of Open Access Journals (Sweden)

    Jones Matthew

    2011-01-01

    Full Text Available Abstract Let be the unit disk in the complex plane. We define to be the little Bloch space of functions f analytic in which satisfy lim|z|→1 (1 - |z|2|f'(z| = 0. If is analytic then the composition operator Cφ : f ↦ f ∘ φ is a continuous operator that maps into itself. In this paper, we show that the compactness of Cφ , as an operator on , can be modelled geometrically by its principal eigenfunction. In particular, under certain necessary conditions, we relate the compactness of Cφ to the geometry of , where σ satisfies Schöder's functional equation σ ∘ φ = φ'(0σ. 2000 Mathematics Subject Classification: Primary 30D05; 47B33 Secondary 30D45.

  14. Improved Reading Gate For Vertical-Bloch-Line Memory

    Science.gov (United States)

    Wu, Jiin-Chuan; Stadler, Henry L.; Katti, Romney R.

    1994-01-01

    Improved design for reading gate of vertical-Bloch-line magnetic-bubble memory increases reliability of discrimination between binary ones and zeros. Magnetic bubbles that signify binary "1" and "0" produced by applying sufficiently large chopping currents to memory stripes. Bubbles then propagated differentially in bubble sorter. Method of discriminating between ones and zeros more reliable.

  15. On averaging the Kubo-Hall conductivity of magnetic Bloch bands leading to Chern numbers

    International Nuclear Information System (INIS)

    Riess, J.

    1997-01-01

    The authors re-examine the topological approach to the integer quantum Hall effect in its original form where an average of the Kubo-Hall conductivity of a magnetic Bloch band has been considered. For the precise definition of this average it is crucial to make a sharp distinction between the discrete Bloch wave numbers k 1 , k 2 and the two continuous integration parameters α 1 , α 2 . The average over the parameter domain 0 ≤ α j 1 , k 2 . They show how this can be transformed into a single integral over the continuous magnetic Brillouin zone 0 ≤ α j j , j = 1, 2, n j = number of unit cells in j-direction, keeping k 1 , k 2 fixed. This average prescription for the Hall conductivity of a magnetic Bloch band is exactly the same as the one used for a many-body system in the presence of disorder

  16. Quantum Transport in Solids: Bloch Dynamics and Role of Oscillating Fields

    National Research Council Canada - National Science Library

    Kim, Ki

    1997-01-01

    .... The specific areas of research are those of Bloch electron dynamics, quantum transport in oscillating electric fields or in periodic potentials, and the capacitive nature of atomic size structures...

  17. Bloch-wave engineered submicron-diameter quantum-dot micropillars for cavity QED experiments

    DEFF Research Database (Denmark)

    Gregersen, Niels; Lermer, Matthias; Reitzenstein, Stephan

    2013-01-01

    The semiconductor micropillar is attractive for cavity QED experiments. For strong coupling, the figure of merit is proportional to Q/√V, and a design combining a high Q and a low mode volume V is thus desired. However, for the standard submicron diameter design, poor mode matching between the ca...... the cavity and the DBR Bloch mode limits the Q. We present a novel adiabatic design where Bloch-wave engineering is employed to improve the mode matching, allowing the demonstration of a record-high vacuum Rabi splitting of 85 μeV and a Q of 13600 for a 850 nm diameter micropillar....

  18. On the equilibrium configuration of the Kittel type domain structure with Bloch walls, l80deg

    International Nuclear Information System (INIS)

    Gavrila, H.

    1975-01-01

    Using a phenomenologic method for appreciating different components of the free energy, the equilibrium configuration of the Kittel-type domain structure with Bloch walls is obtained. By improving the known methods, more accurate magnetostatic energy calculations are reported. In order to determine the equilibrium structure, the total free energy is minimized with respect to two system parameters: the Bloch wall width and the structure half-period. (author)

  19. Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).

    Science.gov (United States)

    Murase, Kenya

    2016-01-01

    In this issue, simultaneous differential equations were introduced. These differential equations are often used in the field of medical physics. The methods for solving them were also introduced, which include Laplace transform and matrix methods. Some examples were also introduced, in which Laplace transform and matrix methods were applied to solving simultaneous differential equations derived from a three-compartment kinetic model for analyzing the glucose metabolism in tissues and Bloch equations for describing the behavior of the macroscopic magnetization in magnetic resonance imaging.In the next (final) issue, partial differential equations and various methods for solving them will be introduced together with some examples in medical physics.

  20. A Greenian approach to the solution of the Schroedinger equation for periodic lattice potentials

    International Nuclear Information System (INIS)

    Minelli, T.A.

    1976-01-01

    A modified structural Green's function (MSGF), exploiting all the information contained in the previously solved Schroedinger equation for the electron interacting with a single lattice site, has been introduced and used in order to obtain, from a Dyson-type equation, a kernel whose poles and residues give the E-vs.-k relation and, respectively, the Bloch functions. Such a formulation suggests an alternative technique for the approximate solution of the KKR equations. The MSGF formalism has been also used in order to determine the structure constants of a one-dimensional lattice in a general representation

  1. News Focus: NSF Director Erich Bloch Discusses Foundation's Problems, Outlook.

    Science.gov (United States)

    Chemical and Engineering News, 1987

    1987-01-01

    Relates the comments offered in an interview with Erich Bloch, the National Science Foundation (NSF) Director. Discusses issues related to NSF and its funding, engineering research centers, involvement with industry, concern for science education, computer centers, and its affiliation with the social sciences. (ML)

  2. Resonant absorption in semiconductor nanowires and nanowire arrays: Relating leaky waveguide modes to Bloch photonic crystal modes

    Energy Technology Data Exchange (ETDEWEB)

    Fountaine, Katherine T., E-mail: kfountai@caltech.edu [Department of Chemistry and Chemical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Whitney, William S. [Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Department of Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Atwater, Harry A. [Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States); Department of Applied Physics and Materials Science, California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125 (United States)

    2014-10-21

    We present a unified framework for resonant absorption in periodic arrays of high index semiconductor nanowires that combines a leaky waveguide theory perspective and that of photonic crystals supporting Bloch modes, as array density transitions from sparse to dense. Full dispersion relations are calculated for each mode at varying illumination angles using the eigenvalue equation for leaky waveguide modes of an infinite dielectric cylinder. The dispersion relations along with symmetry arguments explain the selectivity of mode excitation and spectral red-shifting of absorption for illumination parallel to the nanowire axis in comparison to perpendicular illumination. Analysis of photonic crystal band dispersion for varying array density illustrates that the modes responsible for resonant nanowire absorption emerge from the leaky waveguide modes.

  3. Influence of relaxation times on the Bloch-Siegert shift

    International Nuclear Information System (INIS)

    Cao Long Van

    1981-01-01

    A new method for calculations of Bloch-Siegert shifts in resonances between excited states with the inclusion of relaxation times is given. It will be shown that in this case the definition of the resonance given by I. Bialynicka-Birula is in agreement with the criterion defining the resonance used by D.A. Andrews and G. Newton. (author)

  4. Prolongation Loop Algebras for a Solitonic System of Equations

    Directory of Open Access Journals (Sweden)

    Maria A. Agrotis

    2006-11-01

    Full Text Available We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.

  5. Surface Acoustic Bloch Oscillations, the Wannier-Stark Ladder, and Landau-Zener Tunneling in a Solid

    Science.gov (United States)

    de Lima, M. M., Jr.; Kosevich, Yu. A.; Santos, P. V.; Cantarero, A.

    2010-04-01

    We present the experimental observation of Bloch oscillations, the Wannier-Stark ladder, and Landau-Zener tunneling of surface acoustic waves in perturbed grating structures on a solid substrate. A model providing a quantitative description of our experimental observations, including multiple Landau-Zener transitions of the anticrossed surface acoustic Wannier-Stark states, is developed. The use of a planar geometry for the realization of the Bloch oscillations and Landau-Zener tunneling allows a direct access to the elastic field distribution. The vertical surface displacement has been measured by interferometry.

  6. Bloch Oscillations in the Chains of Artificial Atoms Dressed with Photons

    Directory of Open Access Journals (Sweden)

    Ilay Levie

    2018-06-01

    Full Text Available We present a model of one-dimensional chain of two-level artificial atoms driven with DC field and quantum light simultaneously in a strong coupling regime. The interaction of atoms with light leads to electron-photon entanglement (dressing of the atoms with light. The driving via dc field leads to the Bloch oscillations (BO in the chain of dressed atoms. We consider the mutual influence of dressing and BO and show that scenario of oscillations dramatically differs from predicted by the Jaynes-Cummings and Bloch-Zener models. We study the evolution of the population inversion, tunneling current, photon probability distribution, mean number of photons, and photon number variance, and show the influence of BO on the quantum-statistical characteristics of light. For example, the collapse-revivals picture and vacuum Rabi-oscillations are strongly modulated with Bloch frequency. As a result, quantum properties of light and degree of electron-photon entanglement become controllable via adiabatic dc field turning. On the other hand, the low-frequency tunneling current depends on the quantum light statistics (in particular, for coherent initial state it is modulated accordingly the collapse-revivals picture. The developed model is universal with respect to the physical origin of artificial atom and frequency range of atom-light interaction. The model is adapted to the 2D-heterostructures (THz frequencies, semiconductor quantum dots (optical range, and Josephson junctions (microwaves. The data for numerical simulations are taken from recently published experiments. The obtained results open a new way in quantum state engineering and nano-photonic spectroscopy.

  7. An Optomechanical Elevator: Transport of a Bloch Oscillating Bose–Einstein Condensate up and down an Optical Lattice by Cavity Sideband Amplification and Cooling

    Directory of Open Access Journals (Sweden)

    B. Prasanna Venkatesh

    2015-12-01

    Full Text Available In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose–Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force, such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a high-finesse optical cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice depth at the Bloch frequency which can in turn transport the atoms up or down the lattice. In the optomechanical picture, the transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the Bloch oscillator. Depending on the sign of the pump-cavity detuning, atoms are transported either with or against the bias force accompanied by an up- or down-conversion of the frequency of the pump laser light. We also evaluate the prospects for using the optomechanical Bloch oscillator to make continuous measurements of forces by reading out the Bloch frequency. In this context, we establish the significant result that the optical spring effect is absent and the Bloch frequency is not modified by the backaction.

  8. New algorithm for efficient Bloch-waves calculations of orientation-sensitive ELNES

    Czech Academy of Sciences Publication Activity Database

    Rusz, Ján; Muto, S.; Tatsumi, K.

    2013-01-01

    Roč. 125, Feb (2013), s. 81-88 ISSN 0304-3991 Institutional support: RVO:68378271 Keywords : transmission electron microscopy * density functional theory * dynamical diffraction theory * Bloch waves * electron magnetic circular dichroism Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 2.745, year: 2013

  9. Integral-Type Operators from Bloch-Type Spaces to QK Spaces

    Directory of Open Access Journals (Sweden)

    Stevo Stević

    2011-01-01

    Full Text Available The boundedness and compactness of the integral-type operator Iφ,g(nf(z=∫0zf(n(φ(ζg(ζdζ, where n∈N0, φ is a holomorphic self-map of the unit disk D, and g is a holomorphic function on D, from α-Bloch spaces to QK spaces are characterized.

  10. Surface Acoustic Analog of Bloch Oscillations, Wannier-Stark Ladders and Landau-Zener Tunneling

    Science.gov (United States)

    de Lima, M. M.; Kosevich, Yu. A.; Santos, P. V.; Cantarero, A.

    2011-12-01

    In this contribution, we discuss the recent experimental demonstration of Wannier-Stark ladders, Bloch Oscillations and Landau Zener tunneling in a solid by means of surface acoustic waves propagating through perturbed grating structures.

  11. Exact solutions of a nonpolynomially nonlinear Schrodinger equation

    International Nuclear Information System (INIS)

    Parwani, R.; Tan, H.S.

    2007-01-01

    A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurrence of higher-derivative nonlinear terms at all orders. Here we construct some exact solutions to that equation in 1+1 dimensions. On the half-line, the solutions resemble (exponentially damped) Bloch waves even though no external periodic potential is included. The solutions are nonperturbative as they do not reduce to solutions of the linear theory in the limit that the nonlinearity parameter vanishes. An intriguing feature of the solutions is their infinite degeneracy: for a given energy, there exists a very large arbitrariness in the normalisable wavefunctions. We also consider solutions to a q-deformed version of the nonlinear equation and discuss a natural discretisation implied by the nonpolynomiality. Finally, we contrast the properties of our solutions with other solutions of nonlinear Schrodinger equations in the literature and suggest some possible applications of our results in the domains of low-energy and high-energy physics

  12. Bloch-Kohn and Wannier-Kohn functions in one dimension

    International Nuclear Information System (INIS)

    Bruno-Alfonso, Alexys; Guo-Qiang, Hai

    2003-01-01

    Bloch and Wannier functions of the Kohn type for a quite general one-dimensional Hamiltonian with inversion symmetry are studied. Important clarifications on null minigaps and the symmetry of those functions are given, with emphasis on the Kronig-Penney model. The lack of a general selection rule on the miniband index for optical transitions between edge states in semiconductor superlattices is discussed. A direct method for the calculation of Wannier-Kohn functions is presented

  13. A new characterization of Bloch function in the unit ball of Cn

    International Nuclear Information System (INIS)

    Shi Jihuai.

    1989-07-01

    Bloch function in the unit disc v has many different but equivalent characterizations. Recently, a new characterization has been obtained by the study of Hankel operators. The purpose of this note is to generalize this characterization to the unit ball of C n . 7 refs

  14. The quantum group, Harper equation and structure of Bloch eigenstates on a honeycomb lattice

    International Nuclear Information System (INIS)

    Eliashvili, M; Tsitsishvili, G; Japaridze, G I

    2012-01-01

    The tight-binding model of quantum particles on a honeycomb lattice is investigated in the presence of a homogeneous magnetic field. Provided the magnetic flux per unit hexagon is a rational of the elementary flux, the one-particle Hamiltonian is expressed in terms of the generators of the quantum group U q (sl 2 ). Employing the functional representation of the quantum group U q (sl 2 ), the Harper equation is rewritten as a system of two coupled functional equations in the complex plane. For the special values of quasi-momentum, the entangled system admits solutions in terms of polynomials. The system is shown to exhibit a certain symmetry allowing us to resolve the entanglement, and a basic single equation determining the eigenvalues and eigenstates (polynomials) is obtained. Equations specifying the locations of the roots of polynomials in the complex plane are found. Employing numerical analysis, the roots of polynomials corresponding to different eigenstates are solved and diagrams exhibiting the ordered structure of one-particle eigenstates are depicted. (paper)

  15. Traffic restrictions on Routes Bloch, Maxwell and Bohr

    CERN Multimedia

    IT Department

    2008-01-01

    Excavation and pipework is being carried out in the framework of the transfer of the waste water treatment plant for the effluents from the surface treatment workshops from Building 254 to Building 676, currently under construction. This work may encroach onto Routes Bloch, Maxwell and Bohr and disrupt the flow of traffic. Users are requested to comply with the road signs that will be erected. The work is expected to last until the beginning of December 2008. Thank you for your understanding. TS/CE and TS/FM Groups Tel.7 4188 or 16 4314

  16. Diagrammatical display of the counter-example to non-Abelian Bloch-Nordsieck conjecture

    International Nuclear Information System (INIS)

    Yoshida, Nobuo

    1981-01-01

    The reason why the Bloch-Nordsieck theorem breaks down in the Drell-Yan process is shown through a simple diagrammatical calculation. The uncancelled contribution is from the retarded soft gluons, and the colour weight different for each ''double cut diagram'' interrupts the cancellation analogous to QED. (author)

  17. Bloch Surface Waves Using Graphene Layers: An Approach toward In-Plane Photodetectors

    Directory of Open Access Journals (Sweden)

    Richa Dubey

    2018-03-01

    Full Text Available A dielectric multilayer platform was investigated as a foundation for two-dimensional optics. In this paper, we present, to the best of our knowledge, the first experimental demonstration of absorption of Bloch surface waves in the presence of graphene layers. Graphene is initially grown on a Cu foil via Chemical Vapor Deposition and transferred layer by layer by a wet-transfer method using poly(methyl methacrylate, (PMMA. We exploit total internal reflection configuration and multi-heterodyne scanning near-field optical microscopy as a far-field coupling method and near-field characterization tool, respectively. The absorption is quantified in terms of propagation lengths of Bloch surface waves. A significant drop in the propagation length of the BSWs is observed in the presence of graphene layers. The propagation length of BSWs in bare multilayer is reduced to 17 times shorter in presence of graphene monolayer, and 23 times shorter for graphene bilayer.

  18. Stochastic wave-function unravelling of the generalized Lindblad equation using correlated states

    International Nuclear Information System (INIS)

    Moodley, Mervlyn; Nsio Nzundu, T; Paul, S

    2012-01-01

    We perform a stochastic wave-function unravelling of the generalized Lindblad master equation using correlated states, a combination of the system state vectors and the environment population. The time-convolutionless projection operator method using correlated projection superoperators is applied to a two-state system, a qubit, that is coupled to an environment consisting of two energy bands which are both populated. These results are compared to the data obtained from Monte Carlo wave-function simulations based on the unravelling of the master equation. We also show a typical quantum trajectory and the average time evolution of the state vector on the Bloch sphere. (paper)

  19. On an Integral-Type Operator Acting between Bloch-Type Spaces on the Unit Ball

    Directory of Open Access Journals (Sweden)

    Stevo Stević

    2010-01-01

    Full Text Available Let 𝔹 denote the open unit ball of ℂn. For a holomorphic self-map φ of 𝔹 and a holomorphic function g in 𝔹 with g(0=0, we define the following integral-type operator: Iφgf(z=∫01ℜf(φ(tzg(tz(dt/t, z∈𝔹. Here ℜf denotes the radial derivative of a holomorphic function f in 𝔹. We study the boundedness and compactness of the operator between Bloch-type spaces ℬω and ℬμ, where ω is a normal weight function and μ is a weight function. Also we consider the operator between the little Bloch-type spaces ℬω,0 and ℬμ,0.

  20. Optimal cloning of qubits given by an arbitrary axisymmetric distribution on the Bloch sphere

    International Nuclear Information System (INIS)

    Bartkiewicz, Karol; Miranowicz, Adam

    2010-01-01

    We find an optimal quantum cloning machine, which clones qubits of arbitrary symmetrical distribution around the Bloch vector with the highest fidelity. The process is referred to as phase-independent cloning in contrast to the standard phase-covariant cloning for which an input qubit state is a priori better known. We assume that the information about the input state is encoded in an arbitrary axisymmetric distribution (phase function) on the Bloch sphere of the cloned qubits. We find analytical expressions describing the optimal cloning transformation and fidelity of the clones. As an illustration, we analyze cloning of qubit state described by the von Mises-Fisher and Brosseau distributions. Moreover, we show that the optimal phase-independent cloning machine can be implemented by modifying the mirror phase-covariant cloning machine for which quantum circuits are known.

  1. Bipolaron assisted Bloch-like oscillations in organic lattices

    International Nuclear Information System (INIS)

    Ribeiro, Luiz Antonio; Ferreira da Cunha, Wiliam; Magela e Silva, Geraldo

    2017-01-01

    The transport of a dissociated bipolaron in organic one-dimensional lattices is theoretically investigated in the scope of a tight-binding model that includes electron-lattice interactions and an external electric field. Remarkably, the results point to a physical picture in which the dissociated bipolaron propagates as a combined state of two free-like electrons that coherently perform spatial Bloch oscillations (BO) above a critical field strength. It was also obtained that the BO's trajectory presents a net forward motion in the direction of the applied electric field. The impact of dynamical disorder in the formation of electronic BOs is determined.

  2. Bipolaron assisted Bloch-like oscillations in organic lattices

    Science.gov (United States)

    Ribeiro, Luiz Antonio; Ferreira da Cunha, Wiliam; Magela e Silva, Geraldo

    2017-06-01

    The transport of a dissociated bipolaron in organic one-dimensional lattices is theoretically investigated in the scope of a tight-binding model that includes electron-lattice interactions and an external electric field. Remarkably, the results point to a physical picture in which the dissociated bipolaron propagates as a combined state of two free-like electrons that coherently perform spatial Bloch oscillations (BO) above a critical field strength. It was also obtained that the BO's trajectory presents a net forward motion in the direction of the applied electric field. The impact of dynamical disorder in the formation of electronic BOs is determined.

  3. Bipolaron assisted Bloch-like oscillations in organic lattices

    Energy Technology Data Exchange (ETDEWEB)

    Ribeiro, Luiz Antonio, E-mail: ribeirojr@unb.br [International Center for Condensed Matter Physics, University of Brasília, P.O. Box 04531, 70.919-970, Brasília, DF (Brazil); University of Brasília, UnB Faculty of Planaltina, 73.345-010, Planaltina, DF (Brazil); Ferreira da Cunha, Wiliam; Magela e Silva, Geraldo [Institute of Physics, University of Brasília, 70.919-970, Brasília (Brazil)

    2017-06-15

    The transport of a dissociated bipolaron in organic one-dimensional lattices is theoretically investigated in the scope of a tight-binding model that includes electron-lattice interactions and an external electric field. Remarkably, the results point to a physical picture in which the dissociated bipolaron propagates as a combined state of two free-like electrons that coherently perform spatial Bloch oscillations (BO) above a critical field strength. It was also obtained that the BO's trajectory presents a net forward motion in the direction of the applied electric field. The impact of dynamical disorder in the formation of electronic BOs is determined.

  4. Direct Observation of Bloch Harmonics and Negative Phase Velocity in Photonic Crystal Waveguides

    NARCIS (Netherlands)

    Gersen, H.; Karle, T.J.; Engelen, R.J.P.; Engelen, R.J.P.; Bogaerts, W.; Korterik, Jeroen P.; van Hulst, N.F.; Krauss, T.F.; Kuipers, L.

    2005-01-01

    The eigenfield distribution and the band structure of a photonic crystal waveguide have been measured with a phase-sensitive near-field scanning optical microscope. Bloch modes, which consist of more than one spatial frequency, are visualized in the waveguide. In the band structure, multiple

  5. Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

    Science.gov (United States)

    Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.

    2010-09-01

    We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

  6. Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with spatially modulated nonlinearity

    International Nuclear Information System (INIS)

    Zhang Jiefang; Meng Jianping; Wu Lei; Li Yishen; Malomed, Boris A.

    2010-01-01

    We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices (OLs). By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite set of exact soliton solutions in terms of Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite gap of the OL-induced spectrum. Starting from the particular exact solutions, we employ the relaxation method to construct generic families of soliton solutions in a numerical form. The stability of the solitons is investigated through the computation of the eigenvalues for small perturbations, and also by direct simulations. Finally, we demonstrate a virtually exact (in the numerical sense) composition relation between nonlinear Bloch waves and solitons.

  7. Modeling Dzyaloshinskii-Moriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem

    KAUST Repository

    Dong, Yao-Jun

    2017-10-29

    Dzyaloshinskii-Moriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that long-range magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

  8. Modeling Dzyaloshinskii-Moriya Interaction at Transition Metal Interfaces: Constrained Moment versus Generalized Bloch Theorem

    KAUST Repository

    Dong, Yao-Jun; Belabbes, Abderrezak; Manchon, Aurelien

    2017-01-01

    Dzyaloshinskii-Moriya interaction (DMI) at Pt/Co interfaces is investigated theoretically using two different first principles methods. The first one uses the constrained moment method to build a spin spiral in real space, while the second method uses the generalized Bloch theorem approach to construct a spin spiral in reciprocal space. We show that although the two methods produce an overall similar total DMI energy, the dependence of DMI as a function of the spin spiral wavelength is dramatically different. We suggest that long-range magnetic interactions, that determine itinerant magnetism in transition metals, are responsible for this discrepancy. We conclude that the generalized Bloch theorem approach is more adapted to model DMI in transition metal systems, where magnetism is delocalized, while the constrained moment approach is mostly applicable to weak or insulating magnets, where magnetism is localized.

  9. Magnetic resonance described in the excitation dependent rotating frame of reference.

    Science.gov (United States)

    Tahayori, Bahman; Johnston, Leigh A; Mareels, Iven M Y; Farrell, Peter M

    2008-01-01

    An excitation dependent rotating frame of reference to observe the magnetic resonance phenomenon is introduced in this paper that, to the best of our knowledge, has not been used previously in the nuclear magnetic resonance context. The mathematical framework for this new rotating frame of reference is presented based on time scaling the Bloch equation after transformation to the classical rotating frame of reference whose transverse plane is rotating at the Larmor frequency. To this end, the Bloch equation is rewritten in terms of a magnetisation vector observed from the excitation dependent rotating frame of reference. The resultant Bloch equation is referred to as the time scaled Bloch equation. In the excitation dependent rotating frame of reference whose coordinates are rotating at the instantaneous Rabi frequency the observed magnetisation vector is a much slower signal than the true magnetisation in the rotating frame of reference. As a result the ordinary differential equation solvers have the ability to solve the time scaled version of the Bloch equation with a larger step size resulting in a smaller number of samples for solving the equation to a desired level of accuracy. The simulation results for different types of excitation are presented in this paper. This method may be used in true Bloch simulators in order to reduce the simulation time or increase the accuracy of the numerical solution. Moreover, the time scaled Bloch equation may be employed to determine the optimal excitation pattern in magnetic resonance imaging as well as designing pulses with better slice selectivity which is an active area of research in this field.

  10. Magnon localization and Bloch oscillations in finite Heisenberg spin chains in an inhomogeneous magnetic field.

    Science.gov (United States)

    Kosevich, Yuriy A; Gann, Vladimir V

    2013-06-19

    We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.

  11. Magnon localization and Bloch oscillations in finite Heisenberg spin chains in an inhomogeneous magnetic field

    International Nuclear Information System (INIS)

    Kosevich, Yuriy A; Gann, Vladimir V

    2013-01-01

    We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier–Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier–Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier–Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier–Zeeman states. (paper)

  12. The annihilation of vertical-Bloch lines in the walls of hard domains to which bias fields and in-plane fields are alternately applied

    International Nuclear Information System (INIS)

    Sun, H.Y.; Hu, H.N.; Nie, X.F.

    2001-01-01

    The annihilation of vertical-Bloch lines in magnetic domain walls of the ordinary hard bubbles, to which both bias fields and in-plane fields are alternately applied, is investigated experimentally. The influence of an in-plane magnetic field on ordinary hard bubbles (OHB), dumbbell domains of the first kind (ID), and dumbbell domains of the second kind (IID) was analyzed, and a critical in-plane field range [H ip 0 ,H ip 2 ] for vertical Bloch line (VBL) annihilation was found. For the three types of hard domains (H ip 0 is the minimum critical in-plane field of VBLs which begin to be unstable, H ip 2 is the minimum critical in-plane field which only needs to be applied one time for collapse of all OHBs), the critical field range is the same with H ip 0 ≅8πM s . We hypothesize that there exists a direction along which the vertical-Bloch lines in the domain walls are annihilated most easily. It is also observed that the stability of vertical-Bloch lines in the domain walls does not depend on the initial state. This provides a more detailed description of the minimum critical in-plane field than previously known

  13. Weighted Differentiation Composition Operator from Logarithmic Bloch Spaces to Zygmund-Type Spaces

    Directory of Open Access Journals (Sweden)

    Huiying Qu

    2014-01-01

    Full Text Available Let H( denote the space of all holomorphic functions on the unit disk of ℂ, u∈H( and let  n be a positive integer, φ a holomorphic self-map of , and μ a weight. In this paper, we investigate the boundedness and compactness of a weighted differentiation composition operator φ,unf(z=u(zf(n(φ(z,f∈H(, from the logarithmic Bloch spaces to the Zygmund-type spaces.

  14. Introduction to spintronics

    CERN Document Server

    Bandyopadhyay, Supriyo

    2008-01-01

    The Early History of Spin Spin The Bohr Planetary Model and Space Quantization The Birth of "Spin" The Stern-Gerlach Experiment The Advent of Spintronics The Quantum Mechanics of Spin Pauli Spin Matrices The Pauli Equation and Spinors More on the Pauli Equation Extending the Pauli Equation - the Dirac Equation The Time Independent Dirac Equation Appendix The Bloch Sphere The Spinor and the "Qubit" The Bloch Sphere Concept Evolution of a Spinor Spin-1/2 Particle in a Constant Magnetic Field: Larmor Precession Preparing to Derive the Rabi Formula The Rabi Formula The Density Matrix The Density Matrix Concept: Case of a Pure State Properties of the Density Matrix Pure Versus Mixed State Concept of the Bloch Ball Time Evolution of the Density Matrix: Case of Mixed State The Relaxation Times T1 and T2 and the Bloch Equations Spin Orbit Interaction Spin Orbit Interaction in a Solid Magneto-Electric Sub-Bands in Quantum Confined Structures in the Presence of Spin-Orbit Interaction Dispersion Relations of Spin Resolv...

  15. Several Growth Characteristics of an Invasive Cyprinid Fish (Carassius gibelio Bloch, 1782

    Directory of Open Access Journals (Sweden)

    Sait BULUT

    2013-05-01

    Full Text Available Age composition, length-weight relationships, growth, and condition factors of the gibel carp (Carassius gibelio Bloch, 1782 were determined using specimens collected from Seyitler Reservoir between July 2005 to June 2006. A total of 149 gibel carp were observed and examined. The age composition of the samples ranged between I and VII years of age. It has been determined than 82.55% of the obtained samples are comprised of females, 16.11% is comprised of males and 1.34% is comprised of immature. The population is dominated by females able to reproduce gynogenetically. The mean fork lengths and mean weights of the population were 14.8-32.5 cm and 43.1-807.3 g respectively. The length-weight relation were calculated as W = 0.0696 L2.132, r=0.838 for females, for males W = 0.2942 L2.6417 r=0.784 and W = 0.0274 L2.9382, r=0.813 for all samples. The mean Fulton Condition Factor was calculated as 2.342 for females, 2.064 for males and 2.276 for all samples. Age-length and age-weight relations were determined according to von Bertalanffy growth equation formula. Growth parameters of the population were Lt = 48.09 [1-e-0.093(t+0.29], and Wt=2323.62 [1-e-0.093(t+0.29]2.9382. The growth performance index value (Ø´ was computed as 5.37 for all specimens.

  16. Permittivity and Permeability for Floquet-Bloch Space Harmonics in Infinite 1D Magneto-Dielectric Periodic Structures

    DEFF Research Database (Denmark)

    Breinbjerg, Olav; Yaghjian, Arthur D.

    2014-01-01

    -Bloch space harmonics. We discuss how space harmonic permittivity and permeability can be expressed in seemingly different though equivalent forms, and we investigate these parameters of the zeroeth order space harmonic for a particular 1D periodic structure that is based on a previously reported 3D periodic...

  17. Entanglement and the three-dimensionality of the Bloch ball

    Energy Technology Data Exchange (ETDEWEB)

    Masanes, Ll., E-mail: ll.masanes@gmail.com [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Müller, M. P. [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany); Pérez-García, D. [Departamento de Analisis Matematico and IMI, Universidad Complutense de Madrid, 28040 Madrid (Spain); Augusiak, R. [ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona (Spain)

    2014-12-15

    We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.

  18. Coherent excitation of vibrational levels using ultra short pulses

    CSIR Research Space (South Africa)

    De Clercq, LE

    2009-07-01

    Full Text Available population in a specific vibrational level. We used two approaches to do this, in the one model we used Von Neumann’s equations and the other the Optical Bloch equations (OBE’s). In this poster presentation the Optical Bloch model was used to do...

  19. Projectile-z3 and -z4 corrections to basic Bethe-Bloch stopping power theory and mean excitation energies of Al, Si, Ni, Ge, Se, Y, Ag and Au

    International Nuclear Information System (INIS)

    Porter, L.E.; Bryan, S.R.

    1980-01-01

    Three independent sets of measurements of the stopping power of solid elemental targets for alpha particles were previously analyzed in terms of basic Bethe-Bloch theory with the low velocity projectile-z 3 correction term included. These data for Al, Si, Ni, Ge, Se, Y, Ag and Au have now been analyzed with the Bloch projectile-z 4 term and a revised projectile-z 3 term incorporated in the Bethe-Bloch formula, the projectile-z 3 revision having been effected by variation of the single free parameter of the projectile-z 3 effect formalism. The value of this parameter, fixed at 1.8 in previous studies, which counteracts inclusion of the projectile-z 4 term is 1.3 +- 0.1 for all target elements except Si. (orig.)

  20. A new distributional record of alligator pipefish, Syngnathoides biaculeatus (Bloch, 1785) along Goa, central west coast of India

    Digital Repository Service at National Institute of Oceanography (India)

    Sanaye, S.V.; Rivonker, C.U.; Ansari, Z.A; Sreepada, R.A

    Present study is based on a single male specimen of alligator pipefish, Syngnathoides biaculeatus (Bloch, 1785) collected from the bay-estuarine system of, Goa (central west coast of India) which is the new distributional record for this species. A...

  1. Identification of Bloch-modes in hollow-core Photonic Crystal Fiber cladding

    DEFF Research Database (Denmark)

    Couny, F.; Benabid, F.; Roberts, John

    2007-01-01

    We report on the experimental visualization of the cladding Bloch-modes of a hollow-core photonic crystal fiber. Both spectral and spatial field information is extracted using the approach, which is based on measurement of the near-field and Fresnel-zone that results after propagation over a short...... length of fiber. A detailed study of the modes near the edges of the band gap shows that it is formed by the influence of three types of resonator: the glass interstitial apex, the silica strut which joins the neighboring apexes, and the air hole. The cladding electromagnetic field which survives...

  2. Notes on the genus Amphiprion Bloch & Schneider, 1801 (Teleostei: Pomacentridae) and its host sea anemones in the Seychelles

    NARCIS (Netherlands)

    Hartog, den J.C.

    1997-01-01

    The genus Amphiprion Bloch & Schneider, 1801, is represented in the Seychelles by two species, A. akallopisos Bleeker, 1853, and the endemic A. fuscocaudatus Allen, 1972. Throughout its distributional range Amphiprion akallopisos has exclusively been recorded to associate with the clownfish anemones

  3. Full-angle Negative Reflection with An Ultrathin Acoustic Gradient Metasurface: Floquet-Bloch Modes Perspective and Experimental Verification

    KAUST Repository

    Liu, Bingyi

    2017-07-01

    Metasurface with gradient phase response offers new alternative for steering the propagation of waves. Conventional Snell\\'s law has been revised by taking the contribution of local phase gradient into account. However, the requirement of momentum matching along the metasurface sets its nontrivial beam manipulation functionality within a limited-angle incidence. In this work, we theoretically and experimentally demonstrate that the acoustic gradient metasurface supports the negative reflection for full-angle incidence. The mode expansion theory is developed to help understand how the gradient metasurface tailors the incident beams, and the full-angle negative reflection occurs when the first negative order Floquet-Bloch mode dominates. The coiling-up space structures are utilized to build desired acoustic gradient metasurface and the full-angle negative reflections have been perfectly verified by experimental measurements. Our work offers the Floquet-Bloch modes perspective for qualitatively understanding the reflection behaviors of the acoustic gradient metasurface and enables a new degree of the acoustic wave manipulating.

  4. Fast-forward scaling theory for phase imprinting on a BEC: creation of a wave packet with uniform momentum density and loading to Bloch states without disturbance

    Science.gov (United States)

    Masuda, Shumpei; Nakamura, Katsuhiro; Nakahara, Mikio

    2018-02-01

    We study phase imprinting on Bose-Einstein condensates (BECs) with the fast-forward scaling theory revealing a nontrivial scaling property in quantum dynamics. We introduce a wave packet with uniform momentum density (WPUM) which has peculiar properties but is short-lived. The fast-forward scaling theory is applied to derive the driving potential for creation of the WPUMs in a predetermined time. Fast manipulation is essential for the creation of WPUMs because of the instability of the state. We also study loading of a BEC into a predetermined Bloch state in the lowest band from the ground state of a periodic potential. Controlled linear potential is not sufficient for creation of the Bloch state with large wavenumber because the change in the amplitude of the order parameter is not negligible. We derive the exact driving potential for creation of predetermined Bloch states using the obtained theory.

  5. Myocardial T1 mapping at 3.0 tesla using an inversion recovery spoiled gradient echo readout and bloch equation simulation with slice profile correction (BLESSPC) T1 estimation algorithm.

    Science.gov (United States)

    Shao, Jiaxin; Rapacchi, Stanislas; Nguyen, Kim-Lien; Hu, Peng

    2016-02-01

    To develop an accurate and precise myocardial T1 mapping technique using an inversion recovery spoiled gradient echo readout at 3.0 Tesla (T). The modified Look-Locker inversion-recovery (MOLLI) sequence was modified to use fast low angle shot (FLASH) readout, incorporating a BLESSPC (Bloch Equation Simulation with Slice Profile Correction) T1 estimation algorithm, for accurate myocardial T1 mapping. The FLASH-MOLLI with BLESSPC fitting was compared with different approaches and sequences with regards to T1 estimation accuracy, precision and image artifact based on simulation, phantom studies, and in vivo studies of 10 healthy volunteers and three patients at 3.0 Tesla. The FLASH-MOLLI with BLESSPC fitting yields accurate T1 estimation (average error = -5.4 ± 15.1 ms, percentage error = -0.5% ± 1.2%) for T1 from 236-1852 ms and heart rate from 40-100 bpm in phantom studies. The FLASH-MOLLI sequence prevented off-resonance artifacts in all 10 healthy volunteers at 3.0T. In vivo, there was no significant difference between FLASH-MOLLI-derived myocardial T1 values and "ShMOLLI+IE" derived values (1458.9 ± 20.9 ms versus 1464.1 ± 6.8 ms, P = 0.50); However, the average precision by FLASH-MOLLI was significantly better than that generated by "ShMOLLI+IE" (1.84 ± 0.36% variance versus 3.57 ± 0.94%, P < 0.001). The FLASH-MOLLI with BLESSPC fitting yields accurate and precise T1 estimation, and eliminates banding artifacts associated with bSSFP at 3.0T. © 2015 Wiley Periodicals, Inc.

  6. Bloch-Nordsieck estimates of high-temperature QED

    International Nuclear Information System (INIS)

    Fried, H. M.; Sheu, Y.-M.; Grandou, T.

    2008-01-01

    In anticipation of a subsequent application to QCD, we consider the case of QED at high temperature. We introduce a Fradkin representation into the exact, Schwingerian, functional expression of a fermion propagator, as well as a new and relevant version of the Bloch-Nordsieck model, which extracts the soft contributions of every perturbative graph, in contradistinction to the assumed separation of energy scales of previous semiperturbative treatments. Our results are applicable to the absorption of a fast particle which enters a heat bath, as well as to the propagation of a symmetric pulse within the thermal medium due to the appearance of an instantaneous, shockwave-like source acting in the medium. An exponentially decreasing time dependence of the incident particle's initial momentum combines with a stronger decrease in the particle's energy, estimated by a sum over all Matsubara frequencies, to model an initial 'fireball', which subsequently decays in a Gaussian fashion. When extended to QCD, qualitative applications could be made to RHIC scattering, in which a fireball appears, expands, and is damped away

  7. Manipulation of Bloch surface waves: from subwavelength focusing to nondiffracting beam

    Science.gov (United States)

    Kim, Myun-Sik; Herzig, Hans Peter

    2018-01-01

    We present a different type of electromagnetic surface wave than a surface plasmon polariton (SPP), called Bloch surface wave (BSW). BSWs are sustained by dielectric multilayers, and therefore they do not suffer from dissipation. Their propagation length is unbeatably long, e.g., over several millimeters. Thanks to this feature, larger integrations of 2D photonic chips are realizable. To do this, 2D optical components and corresponding techniques are necessary to manipulate in-plane propagation of surface waves. We overview recent progresses of the BSW research on manipulation techniques and developed components. Our study will provide a good guideline of the BSW components for users.

  8. Third harmonic generation by Bloch-oscillating electrons in a quasioptical array

    International Nuclear Information System (INIS)

    Ghosh, A.W.; Wanke, M.C.; Allen, S.J.; Wilkins, J.W.

    1999-01-01

    We compute the third harmonic field generated by Bloch-oscillating electrons in a quasioptical array of superlattices under THz irradiation. The third harmonic power transmitted oscillates with the internal electric field, with nodes associated with Bessel functions in eEd/ℎω. The nonlinear response of the array causes the output power to be a multivalued function of the incident laser power. The output can be optimized by adjusting the frequency of the incident pulse to match one of the Fabry-Pacute erot resonances in the substrate. Within the transmission-line model of the array, the maximum conversion efficiency is 0.1%. copyright 1999 American Institute of Physics

  9. Philippe Bloch: Reducing distance between experiments and CERN

    CERN Multimedia

    2009-01-01

    With its unique combination of several hundred staff members and thousands of users from around the world sharing offices and physics data and profiting from mutually beneficial exchanges of know-how and expertise, the PH Department is a good example of a successful worldwide collaboration, set up as it was to construct and run the Laboratory’s physics experiments. The PH Depart-ment has always played host to thousands of users that contribute to CERN experiments and work on them, and whose numbers are set to grow in the years to come. With his long-standing experience as a user and then as the head of the CERN group within the CMS collaboration, Philippe Bloch, the new PH Department Head, is in favour of closer links between the Department and the experiments. "I think that the PH management should have a direct link to the experiments, and to do so we are holding regular management team meetings comprising members of the Department’s management and the e...

  10. Boundedness and compactness of a new product-type operator from a general space to Bloch-type spaces

    Directory of Open Access Journals (Sweden)

    Stevo Stević

    2016-09-01

    Full Text Available Abstract We characterize the boundedness and compactness of a product-type operator, which, among others, includes all the products of the single composition, multiplication, and differentiation operators, from a general space to Bloch-type spaces. We also give some upper and lower bounds for the norm of the operator.

  11. Schroedinger equation from 0 (h/2π) to o(h/2πinfinity)

    International Nuclear Information System (INIS)

    Voros, A.

    1985-08-01

    The Balian and Bloch idea, that the semiclassical treatment of the Schroedinger equation can be carried out exactly to all orders, o(h/2πinfinity), has been explicitly confirmed upon the time-independent equation with a polynomial potential V(q) in one degree of freedom. The global analytic structure of certain functions, which encode the full eigenvalue distribution, has indeed been computed in great detail with the complex WKB method, yielding a structure called a resurgence algebra. In the special case V(q) = q 2 sub(M), this leads to sum rules for the eigenvalues, which have been verified numerically. Inasmuch as the leading order 0(h/2π) of the WKB expansion amounts to the stationary phase evaluation of the Feynman path integral, it is a yet unsolved challenge to reproduce our results by an exact analysis of this path integral using a generalized saddle-point treatment

  12. Motives and algebraic cycles a celebration in honour of Spencer J. Bloch

    CERN Document Server

    Jeu, Rob de; Lewis, James D

    2009-01-01

    Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic K-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to res

  13. Integrable motion of curves in self-consistent potentials: Relation to spin systems and soliton equations

    Energy Technology Data Exchange (ETDEWEB)

    Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)

    2014-06-13

    Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.

  14. High-order-harmonic generation from solids: The contributions of the Bloch wave packets moving at the group and phase velocities

    Science.gov (United States)

    Du, Tao-Yuan; Huang, Xiao-Huan; Bian, Xue-Bin

    2018-01-01

    We study numerically the Bloch electron wave-packet dynamics in periodic potentials to simulate laser-solid interactions. We introduce an alternative perspective in the coordinate space combined with the motion of the Bloch electron wave packets moving at group and phase velocities under the laser fields. This model interprets the origins of the two contributions (intra- and interband transitions) in the high-order harmonic generation (HHG) processes by investigating the local and global behaviours of the wave packets. It also elucidates the underlying physical picture of the HHG intensity enhancement by means of carrier-envelope phase, chirp, and inhomogeneous fields. It provides a deep insight into the emission of high-order harmonics from solids. This model is instructive for experimental measurements and provides an alternative avenue to distinguish mechanisms of the HHG from solids in different laser fields.

  15. Design of Slow and Fast Light Photonic Crystal Waveguides for Single-photon Emission Using a Bloch Mode Expansion Technique

    DEFF Research Database (Denmark)

    de Lasson, Jakob Rosenkrantz; Rigal, B.; Kapon, E.

    We design slow and fast light photonic crystal waveguides for single-photon emission using a Bloch mode expansion and scattering matrix technique. We propose slow light designs that increase the group index-waveguide mode volume ratio for larger Purcell enhancement, and address efficient slow-to-...

  16. Effects of gamma radiations on certain tissues of heteropneustes fossils bloch

    International Nuclear Information System (INIS)

    Purohit, R.K.; Rathore, N.; Ahluwalia, P.; Srivastava, M.; Gupta, M.L.

    1992-01-01

    In the present investigation effect of gamma radiation on certain tissues (kidney, stomach and gills) of Heteropneustes fossilis Bloch, an Indian Cat fish, were studied. The fish were irradiated with 10 Gy of gamma radiations at the dose rate of 1.60 Gy/minute from a 60 Co source. Five fish were autopsied at each post-irradiation time of 1,2,3,7,15 and 30 days. Radiation induced histopathology was observed in all the tissues studied. The radio lesions appeared on day-1 after exposure which became exaggerated on day-2 and 3. Signs of recovery were noticed on day-7 which progressed on day-15 and normal histology was observed on day-30. (author). 18 refs

  17. Multiple Bloch surface waves in visible region of light at the interfaces between rugate filter/rugate filter and rugate filter/dielectric slab/rugate filter

    Science.gov (United States)

    Ullah Manzoor, Habib; Manzoor, Tareq; Hussain, Masroor; Manzoor, Sanaullah; Nazar, Kashif

    2018-04-01

    Surface electromagnetic waves are the solution of Maxwell’s frequency domain equations at the interface of two dissimilar materials. In this article, two canonical boundary-value problems have been formulated to analyze the multiplicity of electromagnetic surface waves at the interface between two dissimilar materials in the visible region of light. In the first problem, the interface between two semi-infinite rugate filters having symmetric refractive index profiles is considered and in the second problem, to enhance the multiplicity of surface electromagnetic waves, a homogeneous dielectric slab of 400 nm is included between two semi-infinite symmetric rugate filters. Numerical results show that multiple Bloch surface waves of different phase speeds, different polarization states, different degrees of localization and different field profiles are propagated at the interface between two semi-infinite rugate filters. Having two interfaces when a homogeneous dielectric layer is placed between two semi-infinite rugate filters has increased the multiplicity of electromagnetic surface waves.

  18. Dilation of non-quasifree dissipative evolution

    Energy Technology Data Exchange (ETDEWEB)

    Varilly, J C [Costa Rica Univ., San Jose. Escuela de Matematica

    1981-03-01

    A semigroup evolution for the 1/2-spin which admits a conservative dilation is known to be governed by a Bloch equation in a standard form. Here we construct a conservative dilation directly from the Bloch equation, thus yielding an example of a dilation scheme for an evolution which is not quasifree. Moreover, we show that this conservative evolution is never ergodic in the non-quasifree case.

  19. Matter-wave solitons and finite-amplitude Bloch waves in optical lattices with a spatially modulated nonlinearity

    OpenAIRE

    Zhang, Jie-Fang; Li, Yi-Shen; Meng, Jianping; Wu, Lei; Malomed, Boris A.

    2010-01-01

    We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an infinite number of exact soliton solutions in terms of the Mathieu and elliptic functions, with the chemical potential belonging to the semi-infinite bandgap of the optical-lattice-induced spectrum. Starting from the exact solutions, we employ the relaxation met...

  20. Plasmonic Photonic-Crystal Slabs: Visualization of the Bloch Surface Wave Resonance for an Ultrasensitive, Robust and Reusable Optical Biosensor

    Directory of Open Access Journals (Sweden)

    Alexander V. Baryshev

    2014-12-01

    Full Text Available A one-dimensional photonic crystal (PhC with termination by a metal film—a plasmonic photonic-crystal slab—has been theoretically analyzed for its optical response at a variation of the dielectric permittivity of an analyte and at a condition simulating the molecular binding event. Visualization of the Bloch surface wave resonance (SWR was done with the aid of plasmon absorption in a dielectric/metal/dielectric sandwich terminating a PhC. An SWR peak in spectra of such a plasmonic photonic crystal (PPhC slab comprising a noble or base metal layer was shown to be sensitive to a negligible variation of refractive index of a medium adjoining to the slab. As a consequence, the considered PPhC-based optical sensors exhibited an enhanced sensitivity and a good robustness in comparison with the conventional surface-plasmon and Bloch surface wave sensors. The PPhC biosensors can be of practical importance because the metal layer is protected by a capping dielectric layer from contact with analytes and, consequently, from deterioration.

  1. Near-field imaging of light propagation in photonic crystal waveguides: Explicit role of Bloch harmonics

    DEFF Research Database (Denmark)

    Bozhevolnyi, Sergey I.; Volkov, V.S.; Søndergaard, Thomas

    2002-01-01

    We employ a collection scanning near-field optical microscope (SNOM) to image the propagation of light at telecommunication wavelengths along straight and bent regions of silicon-on-insulator photonic crystal waveguides (PCWs) formed by removing a single row of holes in the triangular 410-nm...... the interference between a quasihomogeneous background field and Bloch harmonics of the PCW mode, we account for spatial frequency spectra of the intensity variations and determine the propagation constant of the PCW mode at 1520 nm. The possibilities and limitations of SNOM imaging for the characterization...

  2. Exact solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED

    International Nuclear Information System (INIS)

    Kernemann, A.; Stefanis, N.G.

    1989-01-01

    A set of new closed-form solutions for fermionic Green's functions in the Bloch-Nordsieck approximation of QED is presented. A manifestly covariant phase-space path-integral method is applied for calculating the n-fermion Green's function in a classical external field. In the case of one and two fermions, explicit expressions for the full Green's functions are analytically obtained, with renormalization carried out in the modified minimal subtraction scheme. The renormalization constants and the corresponding anomalous dimensions are determined. The mass-shell behavior of the two-fermion Green's function is investigated in detail. No assumptions are made concerning the structure of asymptotic states and no IR cutoff is used in the calculations

  3. Influence of rotating in-plane field on vertical Bloch lines in the walls of second kind of dumbbell domains

    International Nuclear Information System (INIS)

    Sun, H.Y.; Hu, H.N.; Sun, Y.P.; Nie, X.F.

    2004-01-01

    Influence of rotating in-plane field on vertical Bloch lines in the walls of second kind of dumbbell domains (IIDs) was investigated, and a critical in-plane field range [H ip 1 ,H ip 2 ] of which vertical-Bloch lines (VBLs) annihilated in IIDs is found under rotating in-plane field (H ip 1 is the maximal critical in-plane-field of which hard domains remain stable, H ip 2 is the minimal critical in-plane-field of which all of the hard domains convert to soft bubbles (SBs, without VBLs)). It shows that the in-plane field range [H ip 1 , H ip 2 ] changes with the change of the rotating angle Δφ H ip 1 maintains stable, while H ip 2 decreases with the decreasing of rotating angle Δφ. Comparing it with the spontaneous shrinking experiment of IIDs under both bias field and in-plane field, we presume that under the application of in-plane field there exists a direction along which the VBLs in the domain walls annihilate most easily, and it is in the direction that domain walls are perpendicular to the in-plane field

  4. Perturbation theory for the bloch electrons on strongly coupled chains in both uniform electric and magnetic fields

    International Nuclear Information System (INIS)

    Zhao, X.G.; Chen, S.G.

    1992-01-01

    In this paper, the energy spectrum and the wave functions for a tight-binding Bloch electron on coupled chains under the action of both uniform electric and magnetic fields are studied in detail. Exact results are obtained for the case when the coupling between chains is large by using the perturbation theory, from which it is found that the spectrum is that of two interspaced Stark ladders. The magnetic field dependence of the energy spectrum is also discussed

  5. Influence of in-plane field on vertical Bloch line in the walls of the second kind of dumbbell domains at various temperatures

    International Nuclear Information System (INIS)

    Xu, J.P.; Liu, S.P.; Guo, G.X.; Zhen, C.M.; Tang, G.D.; Sun, H.Y.; Nie, X.F.

    2004-01-01

    The stability of vertical Bloch lines (VBLs) in the second kind of dumbbell domain (IIDs) walls in liquid phase epitaxy garnet bubble films subjected to an in-plane field at various temperatures is studied experimentally. It is found that there exists a critical in-plane field range depending on temperature, in which vertical Bloch lines (VBLs) in the second kind of IIDs walls are unstable, i.e., [Hip(1)(T),Hip(2)(T)]. Here, Hip(1)(T) is the initial critical in-plane field at which VBLs in the walls of IIDs annihilate; while Hip(2)(T) is the lowest in-plane field at which all VBLs in the walls of IIDs have annihilated completely. Also, the critical in-plane field range [Hip(1)(T),Hip(2)(T)],Hip(1)(T) and Hip(2)(T) all decrease with the temperature increasing. Hip(1)(T) and Hip(2)(T) reach zero at T0' and T0, respectively

  6. Bloch oscillations of quasispin polaritons in a magneto-optically controlled atomic ensemble

    International Nuclear Information System (INIS)

    Jiang, Chang; Lu, Jing; Zhou, Lan

    2012-01-01

    We consider the propagation of quantized polarized light in a magneto-optically-manipulated atomic ensemble with a tripod configuration. A polariton formalism is applied when the medium is subjected to a washboard magnetic field under electromagnetically-induced transparency. The dark-state polariton with multiple components is achieved. We analyze the quantum dynamics of the dark-state polariton using experimental data from the rubidium D1-line. It is found that one component propagates freely, however the wave packet trajectory of the other component performs Bloch oscillations. -- Highlights: ► We study the wave–particle dualism of quasiparticles in a magneto-optical medium. ► We generate a “spin”-component dark-state polariton. ► Magnetic fields lead to oscillation and free propagation of a dark-state polariton. ► Our approach shows the role of entanglement of degrees of freedom of photons.

  7. Bloch oscillations of quasispin polaritons in a magneto-optically controlled atomic ensemble

    Energy Technology Data Exchange (ETDEWEB)

    Jiang, Chang [Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of Physics, Hunan Normal University, Changsha 410081 (China); Lu, Jing, E-mail: lujing@hunnu.edu.cn [Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of Physics, Hunan Normal University, Changsha 410081 (China); Zhou, Lan [Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, and Department of Physics, Hunan Normal University, Changsha 410081 (China)

    2012-10-01

    We consider the propagation of quantized polarized light in a magneto-optically-manipulated atomic ensemble with a tripod configuration. A polariton formalism is applied when the medium is subjected to a washboard magnetic field under electromagnetically-induced transparency. The dark-state polariton with multiple components is achieved. We analyze the quantum dynamics of the dark-state polariton using experimental data from the rubidium D1-line. It is found that one component propagates freely, however the wave packet trajectory of the other component performs Bloch oscillations. -- Highlights: ► We study the wave–particle dualism of quasiparticles in a magneto-optical medium. ► We generate a “spin”-component dark-state polariton. ► Magnetic fields lead to oscillation and free propagation of a dark-state polariton. ► Our approach shows the role of entanglement of degrees of freedom of photons.

  8. Bloch surface waves confined in one dimension with a single polymeric nanofibre

    Science.gov (United States)

    Wang, Ruxue; Xia, Hongyan; Zhang, Douguo; Chen, Junxue; Zhu, Liangfu; Wang, Yong; Yang, Erchan; Zang, Tianyang; Wen, Xiaolei; Zou, Gang; Wang, Pei; Ming, Hai; Badugu, Ramachandram; Lakowicz, Joseph R.

    2017-02-01

    Polymeric fibres with small radii (such as ≤125 nm) are delicate to handle and should be laid down on a solid substrate to obtain practical devices. However, placing these nanofibres on commonly used glass substrates prevents them from guiding light. In this study, we numerically and experimentally demonstrate that when the nanofibre is placed on a suitable dielectric multilayer, it supports a guided mode, a Bloch surface wave (BSW) confined in one dimension. The physical origin of this new mode is discussed in comparison with the typical two-dimensional BSW mode. Polymeric nanofibres are easily fabricated to contain fluorophores, which make the dielectric nanofibre and multilayer configuration suitable for developing a large range of new nanometric scale devices, such as processor-memory interconnections, devices with sensitivity to target analytes, incident polarization and multi-colour BSW modes.

  9. Bloch surface wave structures for high sensitivity detection and compact waveguiding

    Science.gov (United States)

    Khan, Muhammad Umar; Corbett, Brian

    2016-01-01

    Resonant propagating waves created on the surface of a dielectric multilayer stack, called Bloch surface waves (BSW), can be designed for high sensitivity monitoring of the adjacent refractive index as an alternative platform to the metal-based surface plasmon resonance (SPR) sensing. The resonant wavelength and polarization can be designed by engineering of the dielectric layers unlike the fixed resonance of SPR, while the wide bandwidth low loss of dielectrics permits sharper resonances, longer propagation lengths and thus their use in waveguiding devices. The transparency of the dielectrics allows the excitation and monitoring of surface-bound fluorescent molecules. We review the recent developments in this technology. We show the advantages that can be obtained by using high index contrast layered structures. Operating at 1550 nm wavelengths will allow the BSW sensors to be implemented in the silicon photonics platform where active waveguiding can be used in the realization of compact planar integrated circuits for multi-parameter sensing.

  10. THE ACTION OF CORAGEN INSECTICIDE ON CERTAIN PHYSIOLOGICAL BIOMARKERS ON CARASSIUS AURATUS GIBELIO BLOCH L. 1758

    Directory of Open Access Journals (Sweden)

    Claudiu Alexandru Baciu

    2015-12-01

    Full Text Available In our researches we have determined the variation of certain physiological indexes, such as the oxygen consume, the breathing rhythm, the glycaemia and the number of red blood cells under the action of Coragen insecticide on Carassius auratus gibelio Bloch. Under the action of Coragen, we have registered significant changes in the oxygen consume, the breathing rhythm, the number of red blood cells and glycemia at the Carassius auratus gibelio Bloch items, considered as answers to the stress provoked by emissions. The highest variations of the physiological indexes, from the perspective of the percentage, were noticed at the glycemia, which at the mark was 28 mg/dl, and in the treated sample, with 0.1 ml/l Coragen is 42 mg/dl, representing a 50% growth and at the breathing rhythm in 24 hours, where values significantly decreased with 41.18% at the concentration of 0.07 ml/l and with 39.33% at the concentrations of 0.05 and 0.1 ml/l Coragen. The slightest variations of the physiological indexes, from the perspective of percentage, were noticed at the oxygen consumption, which, at the mark is of 55.302 ml oxygen/kg/hour, and for the treated sample, with 0.1 ml/l Coragen is 34.81 ml oxygen/kg/hour, representing a decrease of 37.06% in 24 hours and the number of red blood cells, where the values have significantly decrease with 9.58%, 13.48%, respectively 18.44% for the concentrations of 0.05, 0.07 and 0.1 ml/l Coragen.

  11. Bloch oscillations of ultracold atoms and measurement of the fine structure constant; Oscillations de Bloch d'atomes ultrafroids et mesure de la constante de structure fine

    Energy Technology Data Exchange (ETDEWEB)

    Clade, P

    2005-10-15

    From a measurement of the recoil velocity of an atom absorbing a photon, it is possible to deduce a determination of the ratio h/m between the Planck constant and the mass of the atoms and then to deduce a value of the fine structure constant alpha. To do this measurement, we use the technique of Bloch oscillations, which allows us to transfer a large number of recoils to atoms. A velocity sensor, based on velocity selective Raman transition, enables us to measure the momentum transferred to the atoms. A measurement with a statistical uncertainty of 4.4 10{sup -9}, in conjunction with a careful study of systematic effects (5 10{sup -9}), has led us to a determination of alpha with an uncertainty of 6.7 10{sup -9}: {alpha}{sup -1}(Rb) = 137.03599878 (91). This uncertainty is similar to the uncertainty of the best determinations of alpha based on atom interferometry. (author)

  12. High-frequency homogenization for travelling waves in periodic media.

    Science.gov (United States)

    Harutyunyan, Davit; Milton, Graeme W; Craster, Richard V

    2016-07-01

    We consider high-frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wave equation for vector-valued waves such as electromagnetism and elasticity; and a system that encompasses the Schrödinger equation. This homogenization applies when the wavelength is of the order of the size of the medium periodicity cell. The travelling wave is assumed to be the sum of two waves: a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 1 plus a modulated Bloch carrier wave having crystal wavevector [Formula: see text] and frequency ω 2 . We derive effective equations for the modulating functions, and then prove that there is no coupling in the effective equations between the two different waves both in the scalar and the system cases. To be precise, we prove that there is no coupling unless ω 1 = ω 2 and [Formula: see text] where Λ =(λ 1 λ 2 …λ d ) is the periodicity cell of the medium and for any two vectors [Formula: see text] the product a ⊙ b is defined to be the vector ( a 1 b 1 , a 2 b 2 ,…, a d b d ). This last condition forces the carrier waves to be equivalent Bloch waves meaning that the coupling constants in the system of effective equations vanish. We use two-scale analysis and some new weak-convergence type lemmas. The analysis is not at the same level of rigour as that of Allaire and co-workers who use two-scale convergence theory to treat the problem, but has the advantage of simplicity which will allow it to be easily extended to the case where there is degeneracy of the Bloch eigenvalue.

  13. Y spaces and global smooth solution of fractional Navier-Stokes equations with initial value in the critical oscillation spaces

    Science.gov (United States)

    Yang, Qixiang; Yang, Haibo

    2018-04-01

    For fractional Navier-Stokes equations and critical initial spaces X, one used to establish the well-posedness in the solution space which is contained in C (R+ , X). In this paper, for heat flow, we apply parameter Meyer wavelets to introduce Y spaces Y m , β where Y m , β is not contained in C (R+, B˙∞ 1 - 2 β , ∞). Consequently, for 1/2 global well-posedness of fractional Navier-Stokes equations with small initial data in all the critical oscillation spaces. The critical oscillation spaces may be any Besov-Morrey spaces (B˙p,q γ1 ,γ2 (Rn)) n or any Triebel-Lizorkin-Morrey spaces (F˙p,q γ1 ,γ2 (Rn)) n where 1 ≤ p , q ≤ ∞ , 0 ≤γ2 ≤ n/p, γ1 -γ2 = 1 - 2 β. These critical spaces include many known spaces. For example, Besov spaces, Sobolev spaces, Bloch spaces, Q-spaces, Morrey spaces and Triebel-Lizorkin spaces etc.

  14. Web-based description of the space radiation environment using the Bethe-Bloch model

    Science.gov (United States)

    Cazzola, Emanuele; Calders, Stijn; Lapenta, Giovanni

    2016-01-01

    Space weather is a rapidly growing area of research not only in scientific and engineering applications but also in physics education and in the interest of the public. We focus especially on space radiation and its impact on space exploration. The topic is highly interdisciplinary, bringing together fundamental concepts of nuclear physics with aspects of radiation protection and space science. We give a new approach to presenting the topic by developing a web-based application that combines some of the fundamental concepts from these two fields into a single tool that can be used in the context of advanced secondary or undergraduate university education. We present DREADCode, an outreach or teaching tool to rapidly assess the current conditions of the radiation field in space. DREADCode uses the available data feeds from a number of ongoing space missions (ACE, GOES-13, GOES-15) to produce a first order approximation of the radiation dose an astronaut would receive during a mission of exploration in deep space (i.e. far from the Earth’s shielding magnetic field and from the radiation belts). DREADCode is based on an easy-to-use GUI interface available online from the European Space Weather Portal (www.spaceweather.eu/dreadcode). The core of the radiation transport computation to produce the radiation dose from the observed fluence of radiation observed by the spacecraft fleet considered is based on a relatively simple approximation: the Bethe-Bloch equation. DREADCode also assumes a simplified geometry and material configuration for the shields used to compute the dose. The approach is approximate and sacrifices some important physics on the altar of rapid execution time, which allows a real-time operation scenario. There is no intention here to produce an operational tool for use in space science and engineering. Rather, we present an educational tool at undergraduate level that uses modern web-based and programming methods to learn some of the most important

  15. Web-based description of the space radiation environment using the Bethe–Bloch model

    International Nuclear Information System (INIS)

    Cazzola, Emanuele; Lapenta, Giovanni; Calders, Stijn

    2016-01-01

    Space weather is a rapidly growing area of research not only in scientific and engineering applications but also in physics education and in the interest of the public. We focus especially on space radiation and its impact on space exploration. The topic is highly interdisciplinary, bringing together fundamental concepts of nuclear physics with aspects of radiation protection and space science. We give a new approach to presenting the topic by developing a web-based application that combines some of the fundamental concepts from these two fields into a single tool that can be used in the context of advanced secondary or undergraduate university education. We present DREADCode, an outreach or teaching tool to rapidly assess the current conditions of the radiation field in space. DREADCode uses the available data feeds from a number of ongoing space missions (ACE, GOES-13, GOES-15) to produce a first order approximation of the radiation dose an astronaut would receive during a mission of exploration in deep space (i.e. far from the Earth’s shielding magnetic field and from the radiation belts). DREADCode is based on an easy-to-use GUI interface available online from the European Space Weather Portal (www.spaceweather.eu/dreadcode). The core of the radiation transport computation to produce the radiation dose from the observed fluence of radiation observed by the spacecraft fleet considered is based on a relatively simple approximation: the Bethe–Bloch equation. DREADCode also assumes a simplified geometry and material configuration for the shields used to compute the dose. The approach is approximate and sacrifices some important physics on the altar of rapid execution time, which allows a real-time operation scenario. There is no intention here to produce an operational tool for use in space science and engineering. Rather, we present an educational tool at undergraduate level that uses modern web-based and programming methods to learn some of the most

  16. Illuminating "spin-polarized" Bloch wave-function projection from degenerate bands in decomposable centrosymmetric lattices

    Science.gov (United States)

    Li, Pengke; Appelbaum, Ian

    2018-03-01

    The combination of space inversion and time-reversal symmetries results in doubly degenerate Bloch states with opposite spin. Many lattices with these symmetries can be constructed by combining a noncentrosymmetric potential (lacking this degeneracy) with its inverted copy. Using simple models, we unravel the evolution of local spin splitting during this process of inversion symmetry restoration, in the presence of spin-orbit interaction and sublattice coupling. Importantly, through an analysis of quantum mechanical commutativity, we examine the difficulty of identifying states that are simultaneously spatially segregated and spin polarized. We also explain how surface-sensitive experimental probes (such as angle-resolved photoemission spectroscopy, or ARPES) of "hidden spin polarization" in layered materials are susceptible to unrelated spin splitting intrinsically induced by broken inversion symmetry at the surface.

  17. Asymmetric rogue waves, breather-to-soliton conversion, and nonlinear wave interactions in the Hirota–Maxwell–Bloch system

    International Nuclear Information System (INIS)

    Wang Lei; Zhu Yujie; Wang Ziqi; Xu Tao; Qi Fenghua; Xue Yushan

    2016-01-01

    We study the nonlinear localized waves on constant backgrounds of the Hirota–Maxwell–Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons. (author)

  18. Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

    Science.gov (United States)

    Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

    2016-02-01

    We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

  19. Emergence of quasiparticle Bloch states in artificial crystals crafted atom-by-atom

    Directory of Open Access Journals (Sweden)

    Jan Girovsky, Jose L. Lado, Floris E. Kalff, Eleonora Fahrenfort, Lucas J. J. M. Peters, Joaquín Fernández-Rossier, Alexander F. Otte

    2017-06-01

    Full Text Available The interaction of electrons with a periodic potential of atoms in crystalline solids gives rise to band structure. The band structure of existing materials can be measured by photoemission spectroscopy and accurately understood in terms of the tight-binding model, however not many experimental approaches exist that allow to tailor artificial crystal lattices using a bottom-up approach. The ability to engineer and study atomically crafted designer materials by scanning tunnelling microscopy and spectroscopy (STM/STS helps to understand the emergence of material properties. Here, we use atom manipulation of individual vacancies in a chlorine monolayer on Cu(100 to construct one- and two-dimensional structures of various densities and sizes. Local STS measurements reveal the emergence of quasiparticle bands, evidenced by standing Bloch waves, with tuneable dispersion. The experimental data are understood in terms of a tight-binding model combined with an additional broadening term that allows an estimation of the coupling to the underlying substrate.

  20. Bloch oscillations of ultracold atoms and measurement of the fine structure constant

    International Nuclear Information System (INIS)

    Clade, P.

    2005-10-01

    From a measurement of the recoil velocity of an atom absorbing a photon, it is possible to deduce a determination of the ratio h/m between the Planck constant and the mass of the atoms and then to deduce a value of the fine structure constant alpha. To do this measurement, we use the technique of Bloch oscillations, which allows us to transfer a large number of recoils to atoms. A velocity sensor, based on velocity selective Raman transition, enables us to measure the momentum transferred to the atoms. A measurement with a statistical uncertainty of 4.4 10 -9 , in conjunction with a careful study of systematic effects (5 10 -9 ), has led us to a determination of alpha with an uncertainty of 6.7 10 -9 : α -1 (Rb) = 137.03599878 (91). This uncertainty is similar to the uncertainty of the best determinations of alpha based on atom interferometry. (author)

  1. Corrections to Newton’s law of gravitation - application to hybrid Bloch brane

    Science.gov (United States)

    Almeida, C. A. S.; Veras, D. F. S.; Dantas, D. M.

    2018-02-01

    We present in this work, the calculations of corrections in the Newton’s law of gravitation due to Kaluza-Klein gravitons in five-dimensional warped thick braneworld scenarios. We consider here a recently proposed model, namely, the hybrid Bloch brane. This model couples two scalar fields to gravity and is engendered from a domain wall-like defect. Also, two other models the so-called asymmetric hybrid brane and compact brane are considered. Such models are deformations of the ϕ 4 and sine-Gordon topological defects, respectively. Therefore we consider the branes engendered by such defects and we also compute the corrections in their cases. In order to attain the mass spectrum and its corresponding eigenfunctions which are the essential quantities for computing the correction to the Newtonian potential, we develop a suitable numerical technique. The calculation of slight deviations in the gravitational potential may be used as a selection tool for braneworld scenarios matching with future experimental measurements in high energy collisions

  2. Dark and bright solitons for the two-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch system with time-dependent coefficient

    Science.gov (United States)

    Shaikhova, G.; Ozat, N.; Yesmakhanova, K.; Bekova, G.

    2018-02-01

    In this work, we present Lax pair for two-dimensional complex modified Korteweg-de Vries and Maxwell-Bloch (cmKdV-MB) system with the time-dependent coefficient. Dark and bright soliton solutions for the cmKdV-MB system with variable coefficient are received by Darboux transformation. Moreover, the determinant representation of the one-fold and two-fold Darboux transformation for the cmKdV-MB system with time-dependent coefficient is presented.

  3. Generalized Bloch Theorem for Complex Periodic Potentials - A Powerful Application to Quantum Transport Calculations

    International Nuclear Information System (INIS)

    Zhang, Xiaoguang; Varga, Kalman; Pantelides, Sokrates T

    2007-01-01

    Band-theoretic methods with periodically repeated supercells have been a powerful approach for ground-state electronic structure calculations, but have not so far been adapted for quantum transport problems with open boundary conditions. Here we introduce a generalized Bloch theorem for complex periodic potentials and use a transfer-matrix formulation to cast the transmission probability in a scattering problem with open boundary conditions in terms of the complex wave vectors of a periodic system with absorbing layers, allowing a band technique for quantum transport calculations. The accuracy and utility of the method is demonstrated by the model problems of the transmission of an electron over a square barrier and the scattering of a phonon in an inhomogeneous nanowire. Application to the resistance of a twin boundary in nanocrystalline copper yields excellent agreement with recent experimental data

  4. Energy spectrum, the spin polarization, and the optical selection rules of the Kronig-Penney superlattice model with spin-orbit coupling

    Science.gov (United States)

    Li, Rui

    2018-02-01

    The Kronig-Penney model, an exactly solvable one-dimensional model of crystal in solid physics, shows how the allowed and forbidden bands are formed in solids. In this paper, we study this model in the presence of both strong spin-orbit coupling and the Zeeman field. We analytically obtain four transcendental equations that represent an implicit relation between the energy and the Bloch wave vector. Solving these four transcendental equations, we obtain the spin-orbital bands exactly. In addition to the usual band gap opened at the boundary of the Brillouin zone, a much larger spin-orbital band gap is also opened at some special sites inside the Brillouin zone. The x component of the spin-polarization vector is an even function of the Bloch wave vector, while the z component of the spin-polarization vector is an odd function of the Bloch wave vector. At the band edges, the optical transition rates between adjacent bands are nonzero.

  5. Establishment of a cell line from kidney of seabass, Lates calcarifer (Bloch

    Directory of Open Access Journals (Sweden)

    Phromkunthong, W.

    2003-01-01

    Full Text Available Primary cell culture from caudal fin and kidney of seabass (Lates calcarifer Bloch using tissue explant method were cultured in three different medias with various salt concentrations. Only seabass kidney (SK cells grew well in Leibovitze's-15 medium containing 8 g/l of NaCl supplemented with 10 % fetal bovine serum at an optimum temperature of 25 oC. Over a period of 24 months, SK cells were subcultured over than 75 passages and exhibited epithelial-like cells. The chromosome number of SK cells was 42. The cells were found to be free from bacterial, fungal and mycoplasma contamination. Seabass cells can be kept at -80 oC and/or in liquid nitrogen (-196 oC for at least 24 months with a survival rate of 83.20 and 74.50 %, respectively. Nine fish viruses were tested for their infectivity and this SK cells were susceptible to sand goby virus (SGV, chub reovirus (CRV, snake-head rhabdovirus (SHRV, red seabream iridovirus (RSIV, seabass iridovirus (SIV and grouper iridovirus-2 (GIV-2.

  6. Matter-wave dark solitons in optical lattices

    International Nuclear Information System (INIS)

    Louis, Pearl J Y; Ostrovskaya, Elena A; Kivshar, Yuri S

    2004-01-01

    We analyse the Floquet-Bloch spectrum of matter waves in Bose-Einstein condensates loaded into single-periodic optical lattices and double-periodic superlattices. In the framework of the Gross-Pitaevskii equation, we describe the structure and analyse the mobility properties of matter-wave dark solitons residing on backgrounds of extended nonlinear Bloch-type states. We demonstrate that interactions between dark solitons can be effectively controlled in optical superlattices

  7. A new phase coding method using a slice selection gradient for high speed flow velocity meaurements in NMR tomography

    International Nuclear Information System (INIS)

    Oh, C.H.; Cho, Z.H.; California Univ., Irvine

    1986-01-01

    A new phase coding method using a selection gradient for high speed NMR flow velocity measurements is introduced and discussed. To establish a phase-velocity relationship of flow under the slice selection gradient and spin-echo RF pulse, the Bloch equation was numerically solved under the assumption that only one directional flow exists, i.e. in the direction of slice selection. Details of the numerical solution of the Bloch equation and techniques related to the numerical computations are also given. Finally, using the numerical calculation, high speed flow velocity measurement was attempted and found to be in good agreement with other complementary controlled measurements. (author)

  8. Self-similar solutions of certain coupled integrable systems

    CERN Document Server

    Chakravarty, S; Kent, S L

    2003-01-01

    Similarity reductions of the coupled nonlinear Schroedinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painleve transcendents, leading to new exact self-similar solutions for these integrable equations.

  9. Self-similar solutions of certain coupled integrable systems

    International Nuclear Information System (INIS)

    Chakravarty, S; Halburd, R G; Kent, S L

    2003-01-01

    Similarity reductions of the coupled nonlinear Schroedinger equation and an integrable version of the coupled Maxwell-Bloch system are obtained by applying non-translational symmetries. The reduced system of coupled ordinary differential equations are solved in terms of Painleve transcendents, leading to new exact self-similar solutions for these integrable equations

  10. High-Q contacted ring microcavities with scatterer-avoiding “wiggler” Bloch wave supermode fields

    Energy Technology Data Exchange (ETDEWEB)

    Liu, Yangyang, E-mail: yangyang.liu@colorado.edu; Popović, Miloš A., E-mail: milos.popovic@colorado.edu [Nanophotonic Systems Laboratory, Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309 (United States)

    2014-05-19

    High-Q ring resonators with contacts to the waveguide core provide a versatile platform for various applications in chip-scale optomechanics, thermo-, and electro-optics. We propose and demonstrate azimuthally periodic contacted ring resonators based on multi-mode Bloch matching that support contacts on both the inner and outer radius edges with small degradation to the optical quality factor (Q). Radiative coupling between degenerate modes of adjacent radial spatial order leads to imaginary frequency (Q) splitting and a scatterer avoiding high-Q “wiggler” supermode field. We experimentally measure Qs up to 258 000 in devices fabricated in a silicon device layer on buried oxide undercladding and up to 139 000 in devices fully suspended in air using an undercut step. Wiggler supermodes are true modes of the microphotonic system that offer additional degrees of freedom in electrical, thermal, and mechanical design.

  11. Dynamics of Peregrine combs and Peregrine walls in an inhomogeneous Hirota and Maxwell-Bloch system

    Science.gov (United States)

    Wang, Lei; Wang, Zi-Qi; Sun, Wen-Rong; Shi, Yu-Ying; Li, Min; Xu, Min

    2017-06-01

    Under investigation in this paper is an inhomogeneous Hirota-Maxwell-Bloch (IHMB) system which can describe the propagation of optical solitons in an erbium-doped optical fiber. The breather multiple births (BMBs) are derived with periodically varying group velocity dispersion (GVD) coefficients. Under large periodic modulations in the GVD coefficient of IHMB system, the Peregrine comb (PC) solution is produced, which can be viewed as the limiting case of the BMBs. When the amplitude of the modulation satisfies a special condition, the Peregrine wall (PW) that can be regarded as an intermediate state between rogue wave and PC is obtained. The effects of the third-order dispersion on the spatiotemporal characteristics of PCs and PWs are studied. Our results may be useful for the experimental control and manipulation of the formation of generalized Peregrine rogue waves in inhomogeneous erbium-doped optical fiber.

  12. Narrow Bloch walls and intrinsic characteristics of the pseudoternary Nd14Fe78-xMnxC8 systems

    International Nuclear Information System (INIS)

    Xing, F.; Ho, W.W.

    1990-01-01

    The lattice constants of Nd 14 Fe 78-x Mn x C 8 compounds decrease with the increase of Mn context x and have a minimum at about x=14. The Curie temperature T c decreases linearly and falls off below room temperature beyond x=14. The strong reduction of the saturation magnetization and T c are attributed to the antiparallel alignment of the Mn and Fe atoms moments. The behavior of magnetization and magnetization reversal in the high-Mn-containing samples at low temperature can be interpreted by the narrow domain wall effect. The relationship of the intrinsic coercive force i H c on temperature agrees well with the exponential formula of the narrow Bloch wall

  13. The Bergman spaces, the Bloch space and the pluriharmonic conjugates in the unit ball of Cn

    International Nuclear Information System (INIS)

    Shi Jihuai.

    1989-06-01

    It has been proved that if f is holomorphic in the unit ball B of C m , then f is an element of L p (B,dν) if all the functions (1 - |z| 2 ) m (D n f)(z) with |α| = m are in L p (B,dν). This method can only deal with the case of p ≥ 1. In this paper, we give a new approach to prove that the above result holds for all p is an element of (0, ∞). A simple proof about the characterization of the Bloch space will be given. As a by-product of our approach, we generalize a theorem to the unit ball of C m , and use this result to generalize some theorems about the pluriharmonic conjugates to the case 0 < p < 1. 9 refs

  14. The Bloch self-consistently renormalized spin wave approximation and behaviour of some thermodynamic quantities of a Heisenberg ferromagnet in the critical region

    International Nuclear Information System (INIS)

    Jezewski, W.

    1979-01-01

    Properties of the Bloch self-consistently renormalized spin wave approximation are analyzed near the zero-field transition temperature Tsub(m). The analysis is carried out on the basis of the application of this approximation to the Heisenberg ferromagnet involving nearest neighbour interaction. Series expansions for the resulting Helmholtz free energy, magnetization, and specific heat in the reduced temperature t=(Tsub(m)-T)/Tsub(m) are derived and the critical exponents β and α' are obtained. The limiting case of infinite spin (the classical limit) is also investigated. (author)

  15. Computational Modeling of Ultrafast Pulse Propagation in Nonlinear Optical Materials

    Science.gov (United States)

    Goorjian, Peter M.; Agrawal, Govind P.; Kwak, Dochan (Technical Monitor)

    1996-01-01

    There is an emerging technology of photonic (or optoelectronic) integrated circuits (PICs or OEICs). In PICs, optical and electronic components are grown together on the same chip. rib build such devices and subsystems, one needs to model the entire chip. Accurate computer modeling of electromagnetic wave propagation in semiconductors is necessary for the successful development of PICs. More specifically, these computer codes would enable the modeling of such devices, including their subsystems, such as semiconductor lasers and semiconductor amplifiers in which there is femtosecond pulse propagation. Here, the computer simulations are made by solving the full vector, nonlinear, Maxwell's equations, coupled with the semiconductor Bloch equations, without any approximations. The carrier is retained in the description of the optical pulse, (i.e. the envelope approximation is not made in the Maxwell's equations), and the rotating wave approximation is not made in the Bloch equations. These coupled equations are solved to simulate the propagation of femtosecond optical pulses in semiconductor materials. The simulations describe the dynamics of the optical pulses, as well as the interband and intraband.

  16. Ultrafast dynamic optical prop erties of graphene%石墨烯超快动态光学性质∗

    Institute of Scientific and Technical Information of China (English)

    金芹; 董海明; 韩奎; 王雪峰

    2015-01-01

    Graphene exhibits excellent ultrafast optical properties due to its unique electronic structure. In this paper we investigate theoretically the ultrafast dynamic optical properties of graphene based on the Bloch-equations, and introduce the theoretical model of graphene. First, we give the energy which has a linear relationship with the wave vector k. The behavior of electrons in the vicinity of the two Dirac points can be described by the massless Dirac-equation, thus we have the Dirac equation of graphene. Second, we discuss the interaction between graphene and light field. The Bloch-equations of graphene are obtained through the Heisenberg equation and then we discuss the photon carriers ,electric polarization and optical current change over time by analyzing the Bloch-equations. It is found that the nonequilibrium carriers in graphene induced by a terahertz field can be built in 20–200 fs due to the Pauli blocking and the conservation of energy principle. The photon carrier density will increase with the frequency of enhanced light field. Thus an optical current can be created rapidly within 1 ps. A graphene system responds linearly to the external optical field for √2evFE0t≪~ω, while the graphene systems respond nonlinearly to the external optical field, where E0 andωare respectively the intensity and the frequency of the light, t is the time and vF the Dirac velocity in graphene. The electric polarization and optical current increase with increasing photon energies. These theoretical results are in agreement with recent experimental findings and indicate that graphene exhibits important features and has practical applications in the ultrafast optic filed, especially in terahertz field.

  17. Violation of Bloch's Law That Specifies Reciprocity of Intensity and Duration with Brief Light Flashes

    Directory of Open Access Journals (Sweden)

    Ernest Greene

    2013-12-01

    Full Text Available For more than a century researchers have been reporting that the visual impact of a very brief flash is determined by the quantity of photons that the flash delivers. This has been variously described as the Bunsen-Roscoe Law or Bloch's Law, often specified as reciprocity of intensity × duration. Prior research found no evidence for such reciprocity when microsecond-duration flashes from a light-emitting diode array were used to display the major contours of nameable shapes. The present work tested with flash durations ranging up to 100 ms and also found no reciprocity. This departure from classic principles might be due to the specific range of wavelengths of the light-emitting diodes and to a mesopic level of ambient light, which together would preclude activation of rods. The reciprocity of intensity and duration may only be valid with full dark adaptation and very dim flashes that activate rods.

  18. A size selective porous silicon grating-coupled Bloch surface and sub-surface wave biosensor.

    Science.gov (United States)

    Rodriguez, Gilberto A; Ryckman, Judson D; Jiao, Yang; Weiss, Sharon M

    2014-03-15

    A porous silicon (PSi) grating-coupled Bloch surface and sub-surface wave (BSW/BSSW) biosensor is demonstrated to size selectively detect the presence of both large and small molecules. The BSW is used to sense large immobilized analytes at the surface of the structure while the BSSW that is confined inside but near the top of the structure is used to sensitively detect small molecules. Functionality of the BSW and BSSW modes is theoretically described by dispersion relations, field confinements, and simulated refractive index shifts within the structure. The theoretical results are experimentally verified by detecting two different small chemical molecules and one large 40 base DNA oligonucleotide. The PSi-BSW/BSSW structure is benchmarked against current porous silicon technology and is shown to have a 6-fold higher sensitivity in detecting large molecules and a 33% improvement in detecting small molecules. This is the first report of a grating-coupled BSW biosensor and the first report of a BSSW propagating mode. © 2013 Published by Elsevier B.V.

  19. Differential geometric invariants for time-reversal symmetric Bloch-bundles: The “Real” case

    International Nuclear Information System (INIS)

    De Nittis, Giuseppe; Gomi, Kiyonori

    2016-01-01

    Topological quantum systems subjected to an even (resp. odd) time-reversal symmetry can be classified by looking at the related “Real” (resp. “Quaternionic”) Bloch-bundles. If from one side the topological classification of these time-reversal vector bundle theories has been completely described in De Nittis and Gomi [J. Geom. Phys. 86, 303–338 (2014)] for the “Real” case and in De Nittis and Gomi [Commun. Math. Phys. 339, 1–55 (2015)] for the “Quaternionic” case, from the other side it seems that a classification in terms of differential geometric invariants is still missing in the literature. With this article and its companion [G. De Nittis and K. Gomi (unpublished)] we want to cover this gap. More precisely, we extend in an equivariant way the theory of connections on principal bundles and vector bundles endowed with a time-reversal symmetry. In the “Real” case we generalize the Chern-Weil theory and we show that the assignment of a “Real” connection, along with the related differential Chern class and its holonomy, suffices for the classification of “Real” vector bundles in low dimensions.

  20. A quick and easy test for deciding entanglement status of an N-qubit pure quantum state

    International Nuclear Information System (INIS)

    Mehendale, D.P.; Joag, P.S.

    2018-01-01

    We develop a simple criterion in terms of a necessary-sufficient condition (NS condition) for deciding separability of an arbitrary n-qubit pure quantum state. This NS condition provides a quick and easy test procedure to determine the entanglement status of a pure quantum state. We normalize the given quantum state and using this normalized state we can easily build a simplest system of equations containing trigonometric functions by making use of the well known Bloch Sphere representation for single qubit states and check whether or not this system of equations is consistent. According to proposed NS condition the given pure quantum state is separable (entangled) if and only if the above mentioned system of equations is consistent (inconsistent). We build this system of equations by equating the coefficients of computational basis states in the superposition representing the given pure quantum state with certain products of trigonometric functions obtained using standard Bloch Sphere representation for single qubit states. To establish separability of given state one requires to find a valid solution of the above mentioned system of equations but entanglement on the other hand follows when any two equations in this system of equations are mutually inconsistent. Thus, entanglement of the state can follow easily if one succeeds in finding any two mutually inconsistent equations in the above mentioned system of equations.

  1. Coherent dynamics in semiconductors

    DEFF Research Database (Denmark)

    Hvam, Jørn Märcher

    1998-01-01

    enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic......Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further...... and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena Ultrafast degenerate four-wave mixing is used...

  2. Energies and bounds from perturbative approximations to the Bloch-Horowitz effective Hamiltonian

    International Nuclear Information System (INIS)

    Darema-Rogers, F.; Vincent, C.M.

    1978-01-01

    Bloch-Horowitz perturbation theory is applied to the calculation of approximate energies and model-space eigenvectors, for the solvable large-matrix Hamiltonian H used by Pittel, Vincent, and Vergados. Two types of upper and lower bounds to the energies are discussed: moment-theory bounds, obtained by applying moment theory to the terms of perturbation theory, and norm bounds, derived from the expectation E-bar and variance sigma 2 of H with respect to an eigenvector approximated by nth order perturbation theory (n < or = 6). It is shown that lower bounds cannot be constructed unless some fourth-order quantity is known. The upper bounds are generally stricter than the lower bounds. All of the bounds apply even when back-door intruder states cause perturbation theory to diverge; but they lose their rigor and become ''quasibounds'' when there are physical intruders. The moment-theory and norm lower quasibounds always require estimation of a parameter. For the solvable Hamiltonians, it is shown that this can be done quite reliably, and that the resulting quasibounds are tight enough to have some practical utility. The energy-independent effective interaction V is constructed and its errors are displayed and discussed. Finally, a certain [1/2] pseudo-Pade approximant is empirically shown to give energies with a mean absolute error of less than 0.3 MeV in all cases

  3. Cytotoxic and genotoxic affects of acid mine drainage on fish Channa punctata (Bloch).

    Science.gov (United States)

    Talukdar, B; Kalita, H K; Basumatary, S; Saikia, D J; Sarma, D

    2017-10-01

    The investigation deals with the effects of Acid Mine Drainage (AMD) of coal mine on fish Channa punctata (Bloch) by examining the incidence of haematological, morphological, histological changes and DNA fragmentation in tissues of C. punctata in laboratory condition. For this study fishes were exposed to 10% of AMD for a period of 30 days. The fusion of the primary and secondary gill lamellae, distortion, loss of alignment, deposition of worn out tissues and mucous on the surface of the lamella in the gills; degeneration of morphological architecture, loss of alignment of tubules, mucous deposition in the kidney; cellular damage, cellular necrosis, extraneous deposition on the surface, pore formation in the liver are some important changes detected by scanning electron microscopy. Fishes of AMD treated group showed gradual significant decrease in TEC, Hb and, increase in TLC and DLC as compared to that of the control. DNA fragmentation observed in kidney of fishes from treated group indicates an intricate pollutant present in the AMD. The high incidence of morphological and histological alterations, haematological changes along with DNA breakage in C. punctata is an evidence of the cytotoxic and genotoxic potential of AMD of coal mines. Copyright © 2017 Elsevier Inc. All rights reserved.

  4. Anisotropy and multi-band effects in weak-coupling superconductors

    International Nuclear Information System (INIS)

    Berger, T.L.

    1977-01-01

    The techniques of second quantization and thermodynamic Green functions are used to investigate energy gap anisotropy and multi-band effects in pure, single-crystal, weak-coupling superconductors. A generalized version of the standard Gorkov factorization is used to linearize the Green functions equations of motion. The effects of lattice periodicity and band structure are taken into account by means of Bloch wave expansions and Bloch transforms. A pairing selection rule is derived which indicates the possibility of pairing between single particle states belonging to different bands, as well as the usual Cooper pairing. It is shown that the interband gap parameter, which is coupled to the usual gap parameter by the Green functions equations of motion, can only contribute indirectly to the tunneling electric current and the thermodynamic potential. In the absence of interband pairing, the equations of motion lead to the usual BCS gap equation. Also, in the absence of interband pairing, the gap parameter is found to be equal to the diagonal matrix element of the superconductor pair potential between electronic Bloch states. An essentially temperature independent anisotropy function which contains all angular dependence of the gap is shown to evolve naturally from this formalism. The overall temperature dependence of the gap is investigated and it is found that with a change of temperature, the magnitude of the gap in different directions changes in the same ration. The ordinary Markowitz-Kadanoff model is shown to be inappropriate for the case of a multi-band superconductor and a generalized version of this model is introduced and discussed. A special case of this model is considered which leads to gap discontinuities at Brillouin zone boundaries

  5. Nonlinear emission from dark anapole modes and route to all-dielectric metamaterial near-field lasers

    KAUST Repository

    Gongora, J. S. Totero; Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Fratalocchi, Andrea

    2016-01-01

    By employing ab-initio simulations of Maxwell-Bloch equations with a source of quantum noise, we study a new laser concept based on photonic dark-matter nanostructures that emit only in the near-field, with no far-field radiation pattern

  6. Near-Field Nanolasers based on Nonradiating Anapole Modes

    KAUST Repository

    Gongora, J. S. Totero; Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Fratalocchi, Andrea

    2016-01-01

    By employing ab-initio simulations of Maxwell-Bloch equations with a source of quantum noise, we study a new laser concept based on photonic dark-matter nanostructures that emit only in the near-field, with no far-field radiation pattern.

  7. Near-Field Nanolasers based on Nonradiating Anapole Modes

    KAUST Repository

    Gongora, J. S. Totero

    2016-05-31

    By employing ab-initio simulations of Maxwell-Bloch equations with a source of quantum noise, we study a new laser concept based on photonic dark-matter nanostructures that emit only in the near-field, with no far-field radiation pattern.

  8. Nonlinear emission from dark anapole modes and route to all-dielectric metamaterial near-field lasers

    KAUST Repository

    Gongora, J. S. Totero

    2016-08-29

    By employing ab-initio simulations of Maxwell-Bloch equations with a source of quantum noise, we study a new laser concept based on photonic dark-matter nanostructures that emit only in the near-field, with no far-field radiation pattern

  9. Some models of spin coherence and decoherence in storage rings

    International Nuclear Information System (INIS)

    Heinemann, K.

    1997-09-01

    I present some simple exactly solvable models of spin diffusion caused by synchrotron radiation noise in storage rings. I am able to use standard stochastic differential equation and Fokker-Planck methods and I thereby introduce, and exploit, the polarization density. This quantity obeys a linear evolution equation of the Bloch type, which is, like the Fokker-Planck equation, universal in the sense that it is independent of the state of the system. I also briefly consider Bloch equations for other local polarization quantities derived from the polarization density. One of the models chosen is of relevance for some existing and proposed low energy electron (positron) storage rings which need polarization. I present numerical results for a ring with parameters typical of HERA and show that, where applicable, the results of my approach are in satisfactory agreement with calculations using SLIM. These calculations provide a numerical check of a basic tenet of the conventional method of calculating depolarization using the n-vector-axis. I also investigate the equilibrium behaviour of the spin ensemble when there is no synchrotron radiation. Finally, I summarize other results which I have obtained using the polarization density and which will be published separately. (orig.)

  10. The taxonomic status of Japanese threadfin bream Nemipterus japonicus (Bloch, 1791) (Perciformes: Nemipteridae) with a redescription of this species from the south china sea based on morphology and DNA barcodes

    Science.gov (United States)

    Ning, Ping; Sha, Zhongli; Hebert, Paul D. N.; Russell, Barry

    2015-02-01

    Because of its importance as a food source, Nemipterus japonicus (Bloch, 1791) (Nemipteridae) or Japanese threadfin bream is the best studied of these taxa, and numerous investigations have examined its fisheries, its biology and biochemistry. Despite such intensive work, the taxonomic status of N. japonicus has never been seriously questioned and it is regarded as a common species, widely distributed throughout the Indo-Western Pacific Ocean. In fact, Bloch's description of the type specimen of N. japonicus has ambiguous collection data and lacks a designation for the type locality, though it is probably Java. In this paper, DNA barcode results based on COI gene support the existence of two geographically separated lineages of the Japanese threadfin bream, both being an Indian Ocean and western Pacific lineage, with 2.7% sequence divergence, and the results indicate a possible existing of some cryptic species. The two lineages also possess a diagnostic difference in their belly color, with specimens in the South China Sea having a silver belly, while those from the Indian Ocean isolate specimen have a yellow coloration. Based upon new collections from the South China Sea, this species from the western Pacific is morphologically redescribed and its details of DNA barcode diversity are shown for the future investigations.

  11. Development of immune functionality in larval and juvenile crimson snapper Lutjanus erythropterus (Bloch 1790

    Directory of Open Access Journals (Sweden)

    Ke Cui

    2018-05-01

    Full Text Available Ontogenetic development of the immune system in crimson snapper (Lutjanus erythropterus Bloch 1790 larvae was histologically and enzymatically studied from hatch to 36 days post-hatch (DPH. Primitive hepatopancreas appeared on 2 DPH and renal tubules started hematopoiesis on 4 DPH. The spleen anlage appeared on 6 DPH and the thymus formed on 14 DPH. Total activities of superoxide dismutase (SOD, catalase (CAT, glutathione peroxidase (GPX and sodium-potassium adenosine triphosphatase (Na+ K+-ATPase gradually increased after hatch, and showed a sharp increase after 29 DPH during the transitional feeding period from Artemia to inert feed. The specific activities of SOD, CAT, and GPX showed a trend of sharp increase and reached the maximum level on 4 DPH when exogenous feeding started, except for Na+ K+-ATPase where the peak occurred on10 DPH. The specific activities of these five enzymes reached the peak during the food transition from rotifers to Artemia, but the total activity of enzymes showed an increasing trend as fish grew. The present study provides new knowledge of the development of functional enzymes relevant to fish larvae immunity, sheds light on the understanding of the change of larval health, and improves hatchery management of crimson snapper. Keywords: Immune system, Enzyme activity, Ontogenetic development, Crimson snapper Lutjanus erythropterus

  12. Electric- and magnetic-dipole contributions to a theory of radiation reaction field and atom self-energy: An operator reaction field

    International Nuclear Information System (INIS)

    Obada, A.S.F.; Mahran, M.H.

    1982-08-01

    The consequences of including magnetic-dipole contributions, besides the electric-dipole, are considered in the operators for the radiation field. The Bloch equations which describe the two-level atom operators are modified. These equations together with the field operators are discussed, and the contributions are manifested. The spectrum for spontaneous emission and a generalized dynamical Stark effect are obtained. Rabi frequency is modified. (author)

  13. The semi classical laser theory and some applications of laser

    International Nuclear Information System (INIS)

    Abdalla, Abbaker Ali

    1995-04-01

    The semi classical laser theory is concerned with the interaction between light and matter in such a way that the matter is treated quantum-mechanically whereas light is treated in terms of the classical electromagnetic equations. In this work the Maxwell-Bloch equations are employed to describe the interaction between light and matter. Applications of the theory as well as different types of lasers are reviewed. (Author)

  14. Morphometric evaluation of the spermatogenesis in trahira Hoplias malabaricus (Bloch (Characiformes, Erythrinidae Avaliação morfométrica da espermatogênese da traíra Hoplias malabaricus (Bloch (Characiformes, Erythrinidae

    Directory of Open Access Journals (Sweden)

    Paula M. Bizzott

    2007-01-01

    Full Text Available The Erythrinidae trahira, Hoplias malabaricus (Bloch, 1794, is widespread throughout South America river basins. We determined Sertoli cell supporting capacity (ratio of primary spermatocytes: Sertoli cells and spermatids: Sertoli cells, meiotic index (ratio of spermatids: primary spermatocytes and the number of spermatogonial mitotic generations of this fish. The fish were captured in the Igarapava reservoir, Grande River, Alto Paraná River basin, Brazil. Testis fragments of three sexually mature trahiras were fixed in 5% buffered glutaraldehyde solution and embedded in glycol methacrylate. Serial sections of 2 and 3 µm in thickness were stained with 0.5% toluidine blue. Histological counts from cysts of primary spermatocytes and spermatids revealed, respectively, 326 ± 99 and 468 ± 73 nuclei of these cells. Sertoli cell supporting capacity was considerably higher for spermatids (113.3 ± 16:1 when compared to primary spermatocytes (71 ± 5:1. Between eight and ten spermatogonial generations were formed to give rise to primary spermatocytes. These values were within the generation range of those already found in freshwater teleosts of external fertilization. Correlation between the number of Sertoli cells and primary spermatocytes per cyst, and Sertoli cells and spermatids per cyst were statistically significant (p A traíra, Hoplias malabaricus (Bloch, 1794, da família Erythrinidae, encontra-se espalhada pelas bacias fluviais da América do Sul. Determinou-se a capacidade de suporte das células de Sertoli (espermatócitos primários: células de Sertoli e espermátides: células de Sertoli, índice meiótico (espermátides: espermatócitos primário e o número de gerações mitóticas de espermatogônias desse peixe. Os indivíduos foram capturados no reservatório de Igarapava, rio Grande, bacia do Alto Paraná, Brasil. Fragmentos dos testículos de três traíras sexualmente maduras foram fixados em glutaraldeído a 5%, e inclu

  15. Discontinuous Galerkin Approximations for Computing Electromagnetic Bloch Modes in Photonic Crystals

    NARCIS (Netherlands)

    Lu, Zhongjie; Cesmelioglu, A.; van der Vegt, Jacobus J.W.; Xu, Yan

    We analyze discontinuous Galerkin finite element discretizations of the Maxwell equations with periodic coefficients. These equations are used to model the behavior of light in photonic crystals, which are materials containing a spatially periodic variation of the refractive index commensurate with

  16. Carrier-carrier relaxation kinetics in quantum well semiconductor structures with nonparabolic energy bands

    DEFF Research Database (Denmark)

    Dery, H.; Tromborg, Bjarne; Eisenstein, G.

    2003-01-01

    We describe carrier-carrier scattering dynamics in an inverted quantum well structure including the nonparabolic nature of the valance band. A solution of the semiconductor Bloch equations yields strong evidence to a large change in the temporal evolution of the carrier distributions compared to ...

  17. Differential Equations Compatible with KZ Equations

    International Nuclear Information System (INIS)

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions

  18. Suppression of error in qubit rotations due to Bloch-Siegert oscillation via the use of off-resonant Raman excitation

    International Nuclear Information System (INIS)

    Pradhan, Prabhakar; Cardoso, George C; Shahriar, M S

    2009-01-01

    The rotation of a quantum bit (qubit) is an important step in quantum computation. The rotation is generally performed using a Rabi oscillation. In a direct two-level qubit system, if the Rabi frequency is comparable to its resonance frequency, the rotating wave approximation is not valid, and the Rabi oscillation is accompanied by the so-called Bloch-Siegert oscillation (BSO) that occurs at twice the frequency of the driving field. One implication of the BSO is that for a given interaction time and Rabi frequency, the degree of rotation experienced by the qubit depends explicitly on the initial phase of the driving field. If this effect is not controlled, it leads to an apparent fluctuation in the rotation of the qubit. Here we show that when an off-resonant lambda system is used to realize a two-level qubit, the BSO is inherently negligible, thus eliminating this source of potential error.

  19. Architecture and Bloch-Maxwell modelling of multi-mJ 100 fs fully-coherent soft X-ray laser based on X-ray CPA

    International Nuclear Information System (INIS)

    Zeitoun, Ph.; Oliva, E.; Fajardo, M.; Cheriaux, G.; Le, T. T. T.; Li, L.; Pitman, M.; Ros, D.; Sebban, S.; Velarde, P.

    2012-01-01

    By seeding amplifying plasmas pumped with the so-called Transient collisionnal excitation scheme, the amplified pulse seems to be limited to an energy of several 10's of μJ. Aiming to attain several mJ, we study the seeding of plasma pumped by long laser pulse. Thanks to our time-dependent Maxwell-Bloch code, we demonstrate that direct seeding with femtosecond pulse is inefficient. We also study the amplification of pulse train with the drawback of re-synchronizing the pulses. We proposed and studied the amplification of high harmonic seed stretched by a grating pair, amplified finally compressed. We consider off-axis diffraction on the gratings for maximizing their efficiency. Considering the phase deformation induced by the amplification and the spectral narrowing the final pulse is 230 fs in duration and 5 mJ.

  20. Azimuthal spin-wave excitations in magnetic nanodots over the soliton background: Vortex, Bloch, and Néel-like skyrmions

    Science.gov (United States)

    Mruczkiewicz, M.; Gruszecki, P.; Krawczyk, M.; Guslienko, K. Y.

    2018-02-01

    We study azimuthal spin-wave (SW) excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically nontrivial magnetization states, specifically, vortex, Bloch-type skyrmion, and Néel-type skyrmion states. A continuous transition between these states is realized by gradually changing the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction (DMI), and the corresponding SW spectra are calculated for each state. We observe the lifting of degeneracy of SW mode frequencies and a change in the systematics of frequency levels. The latter effect is induced by the geometric Berry phase, which occurs in SWs localized at the edge of the dot in the vortex state, and vanishes in the skyrmion states. Furthermore, channeling of edge-localized azimuthal SWs and a related large frequency splitting are observed in the skyrmion states. This is attributed to DMI-induced nonreciprocity, while the coupling of the breathing and gyrotropic modes is related to the skyrmion motion. Finally, we demonstrate efficient coupling of the dynamic magnetization to a uniform magnetic field in nanodots of noncircular symmetry in the skyrmion states.

  1. Bloch Surface Waves Biosensors for High Sensitivity Detection of Soluble ERBB2 in a Complex Biological Environment.

    Science.gov (United States)

    Sinibaldi, Alberto; Sampaoli, Camilla; Danz, Norbert; Munzert, Peter; Sonntag, Frank; Centola, Fabio; Occhicone, Agostino; Tremante, Elisa; Giacomini, Patrizio; Michelotti, Francesco

    2017-08-17

    We report on the use of one-dimensional photonic crystals to detect clinically relevant concentrations of the cancer biomarker ERBB2 in cell lysates. Overexpression of the ERBB2 protein is associated with aggressive breast cancer subtypes. To detect soluble ERBB2, we developed an optical set-up which operates in both label-free and fluorescence modes. The detection approach makes use of a sandwich assay, in which the one-dimensional photonic crystals sustaining Bloch surface waves are modified with monoclonal antibodies, in order to guarantee high specificity during the biological recognition. We present the results of exemplary protein G based label-free assays in complex biological matrices, reaching an estimated limit of detection of 0.5 ng/mL. On-chip and chip-to-chip variability of the results is addressed too, providing repeatability rates. Moreover, results on fluorescence operation demonstrate the capability to perform high sensitive cancer biomarker assays reaching a resolution of 0.6 ng/mL, without protein G assistance. The resolution obtained in both modes meets international guidelines and recommendations (15 ng/mL) for ERBB2 quantification assays, providing an alternative tool to phenotype and diagnose molecular cancer subtypes.

  2. Microbiological and biochemical changes in pearl spot (Etroplus suratensis Bloch) stored under modified atmospheres.

    Science.gov (United States)

    Lalitha, K V; Sonaji, E R; Manju, S; Jose, L; Gopal, T K S; Ravisankar, C N

    2005-01-01

    This study aimed to determine the effect of packaging [air, modified atmosphere (MA)] on microbial growth, sensory and chemical parameters and also on shelf life of fresh pearl spot (Etroplus suratensis Bloch) and on the selection of microbial association. Fresh pearl spot (whole, gutted) were packaged under both 100% air and MAs (40%CO(2)/60% O(2), 50%CO(2)/50%O(2), 60% CO(2)/40%O(2), 70% CO(2)/30% O(2) and 40% CO(2)/30% O(2)/30% N(2)) and stored at 0 degrees C. Microbial growth (counts of total aerobic bacteria, H(2)S-producing bacteria, Lactic acid bacteria, Brochothrix thermosphacta, yeast and mould), chemical spoilage indicators (pH, total volatile basic nitrogen) and sensory characteristics were monitored. Microbial changes in Pearl spot packed under 100% air and 40% CO(2)/30%O(2)/30% N(2) were similar. The total volatile basic nitrogen values increased, but the values never exceeded the acceptability limit of 25 mg 100 g(-1). MA 60% CO(2) : 40%O(2) was found to be better with a shelf life of 21 days whereas air stored samples had a shelf-life of 12-14 days only. Storage of pearl spot under MAs 60% CO(2) : 40%O(2) is a promising method to extend shelf-life. Longer shelf life expands the market potential of pearl spot and reduces waste during distribution and retail display.

  3. QuTiP 2: A Python framework for the dynamics of open quantum systems

    Science.gov (United States)

    Johansson, J. R.; Nation, P. D.; Nori, Franco

    2013-04-01

    We present version 2 of QuTiP, the Quantum Toolbox in Python. Compared to the preceding version [J.R. Johansson, P.D. Nation, F. Nori, Comput. Phys. Commun. 183 (2012) 1760.], we have introduced numerous new features, enhanced performance, and made changes in the Application Programming Interface (API) for improved functionality and consistency within the package, as well as increased compatibility with existing conventions used in other scientific software packages for Python. The most significant new features include efficient solvers for arbitrary time-dependent Hamiltonians and collapse operators, support for the Floquet formalism, and new solvers for Bloch-Redfield and Floquet-Markov master equations. Here we introduce these new features, demonstrate their use, and give a summary of the important backward-incompatible API changes introduced in this version. Catalog identifier: AEMB_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEMB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 33625 No. of bytes in distributed program, including test data, etc.: 410064 Distribution format: tar.gz Programming language: Python. Computer: i386, x86-64. Operating system: Linux, Mac OSX. RAM: 2+ Gigabytes Classification: 7. External routines: NumPy, SciPy, Matplotlib, Cython Catalog identifier of previous version: AEMB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 183 (2012) 1760 Does the new version supercede the previous version?: Yes Nature of problem: Dynamics of open quantum systems Solution method: Numerical solutions to Lindblad, Floquet-Markov, and Bloch-Redfield master equations, as well as the Monte Carlo wave function method. Reasons for new version: Compared to the preceding version we have introduced numerous new features, enhanced performance, and made changes in

  4. Geometric interpretation of four-wave mixing

    DEFF Research Database (Denmark)

    Ott, Johan Raunkjær; Steffensen, Henrik; Rottwitt, Karsten

    2013-01-01

    -like coordinates of the electric fields, which reduce the FWM dynamics to a closed two-dimensional surface, similar to the Bloch sphere of quantum electrodynamics or the Pointcare´ sphere in polarization dynamics. The coordinates are chosen so as to use the gauge invariance symmetries of the FWM equations which...

  5. Anachronism in the writing of History: ¿Error or Possibility? Some reflections about the concept of time in Carlo Ginzburg, Marc Bloch and Georges Didi-Huberman

    Directory of Open Access Journals (Sweden)

    Maria Eugenia Chaves Maldonado

    2016-01-01

    Full Text Available In his unfinished and posthumously published book Apologie pour l’histoire, Marc Bloch bestowed on future historians a seminal legacy of critical reflections on the concept of time as the object of historical analysis. During the last decades, the concept of time in History has experienced a renewed interest by professional historians, in particular in reference to the category of anachronism. The Italian historian Carlo Ginzburg and the French art historian Georges Didi-Huberman are among those engaged in this debate. This article offers a reading of two works by these historians with the purpose of underlying the fundamental influence that Marc Bloch’s ideas on time had in Ginzburg and Didi-Hubermans’ critical interventions.

  6. Effective-mass analysis of Bose-Einstein condensates in optical lattices: Stabilization and levitation

    International Nuclear Information System (INIS)

    Pu, H.; Zhang, W.; Meystre, P.; Baksmaty, L.O.; Bigelow, N.P.

    2003-01-01

    We investigate the time evolution of a Bose-Einstein condensate in a periodic optical potential. Using an effective mass formalism, we study the equation of motion for the envelope function modulating the Bloch states of the lattice potential. In particular, we show how the negative effective-mass affects the dynamics of the condensate

  7. Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses.

    Science.gov (United States)

    Guo, Xiao; Wei, Peijun

    2016-03-01

    The dispersion relations of elastic waves in a one-dimensional phononic crystal formed by periodically repeating of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are studied in this paper. The influences of initial stress on the dispersive relation are considered based on the incremental stress theory. First, the incremental stress theory of elastic solid is extended to the magneto-electro-elasto solid. The governing equations, constitutive equations, and boundary conditions of the incremental stresses in a magneto-electro-elasto solid are derived with consideration of the existence of initial stresses. Then, the transfer matrices of a pre-stressed piezoelectric slab and a pre-stressed piezomagnetic slab are formulated, respectively. The total transfer matrix of a single cell in the phononic crystal is obtained by the multiplication of two transfer matrixes related with two adjacent slabs. Furthermore, the Bloch theorem is used to obtain the dispersive equations of in-plane and anti-plane Bloch waves. The dispersive equations are solved numerically and the numerical results are shown graphically. The oblique propagation and the normal propagation situations are both considered. In the case of normal propagation of elastic waves, the analytical expressions of the dispersion equation are derived and compared with other literatures. The influences of initial stresses, including the normal initial stresses and shear initial stresses, on the dispersive relations are both discussed based on the numerical results. Copyright © 2015 Elsevier B.V. All rights reserved.

  8. The peripheral olfactory organ in the Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801

    Directory of Open Access Journals (Sweden)

    Laura Ghigliotti

    2015-11-01

    Full Text Available The Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801 is the largest predatory fish in Arctic waters. The socio-economic significance of Greenland shark is demonstrated by its impact on the fishing cultures in Greenland, Scandinavia and Iceland for centuries. The fundamental biology and ecological role of Greenland shark, on the other hand, is virtually unknown. Although knowledge of its life history is limited, increasing evidence indicates that the Greenland shark may undertake long-distance migrations and perform vertical movements from the surface to the deep sea. It is an omnivorous species feeding on carrion and a wide variety of pelagic and bottom-dwelling organisms ranging from invertebrates to mammals, and including active species such as fishes and seals. Accordingly, Greenland shark should be recognized as a top predator, with a strong potential to influence the trophic dynamics of the Arctic marine ecosystem. The sensory biology of Greenland shark is scarcely studied, and considering the importance of olfaction in chemoreception, feeding and other behavioral traits, we examined the architecture of the peripheral olfactory organ where olfactory cues are received from the environment – the olfactory rosette. The structural organization of the olfactory rosette, in terms of histological features of the sensory epithelium, number of primary lamellae and total sensory surface area, provides a first proxy of the olfactory capability of Greenland shark. Based on own results and published studies, the overall morphology of the olfactory rosette is viewed in context of the functional and trophic ecology among other elasmobranch species.

  9. Theory of the nuclear self-oscillator used to measure the earth's magnetic field; Theorie de l'auto-oscillateur nucleaire utilise pour la mesure du champ magnetique terrestre

    Energy Technology Data Exchange (ETDEWEB)

    Solomon, Ionel

    1961-07-01

    After an energy assessment of the device, this note reports the development of theoretical formulations describing its operation. The author uses Bloch equations, addresses the rotating field produced by nuclear magnetisation, and discusses a steady solution. The next part discusses the field measurement precision, notably while assessing various noises. The sample is then presented.

  10. Magnetic susceptibility of Dirac fermions, Bi-Sb alloys, interacting Bloch fermions, dilute nonmagnetic alloys, and Kondo alloys

    Energy Technology Data Exchange (ETDEWEB)

    Buot, Felix A., E-mail: fbuot@gmu.edu [Computational Materials Science Center, George Mason University, Fairfax, VA 22030 (United States); TCSE Center, Spintronics Group, Physics Department, University of San Carlos, Talamban, Cebu 6000 (Philippines); C& LB Research Institute, Carmen, Cebu 6005 (Philippines); Otadoy, Roland E.S.; Rivero, Karla B. [TCSE Center, Spintronics Group, Physics Department, University of San Carlos, Talamban, Cebu 6000 (Philippines)

    2017-03-01

    Wide ranging interest in Dirac Hamiltonian is due to the emergence of novel materials, namely, graphene, topological insulators and superconductors, the newly-discovered Weyl semimetals, and still actively-sought after Majorana fermions in real materials. We give a brief review of the relativistic Dirac quantum mechanics and its impact in the developments of modern physics. The quantum band dynamics of Dirac Hamiltonian is crucial in resolving the giant diamagnetism of bismuth and Bi-Sb alloys. Quantitative agreement of the theory with the experiments on Bi-Sb alloys has been achieved, and physically meaningful contributions to the diamagnetism has been identified. We also treat relativistic Dirac fermion as an interband dynamics in uniform magnetic fields. For the interacting Bloch electrons, the role of translation symmetry for calculating the magnetic susceptibility avoids any approximation to second order in the field. The expressions for magnetic susceptibility of dilute nonmagnetic alloys give a firm theoretical foundation of the empirical formulas used in fitting experimental results. The unified treatment of all the above calculations is based on the lattice Weyl-Wigner formulation of discrete phase-space quantum mechanics. For completeness, the magnetic susceptibility of Kondo alloys is also given since Dirac fermions in conduction band and magnetic impurities exhibit Kondo effect.

  11. Approximate representations of propagators in an external field

    International Nuclear Information System (INIS)

    Fried, H.M.

    1979-01-01

    A method of forming approximate representations for propagators with external field dependence is suggested and discussed in the context of potential scattering. An integro-differential equation in D+1 variables, where D represents the dimensionality of Euclidian space-time, is replaced by a Volterra equation in one variable. Approximate solutions to the latter provide a generalization of the Bloch-Nordsieck representation, containing the effects of all powers of hard-potential interactions, each modified by a characteristic soft-potential dependence [fr

  12. Transients of the electromagnetically-induced-transparency-enhanced refractive Kerr nonlinearity: Theory

    International Nuclear Information System (INIS)

    Pack, M. V.; Camacho, R. M.; Howell, J. C.

    2006-01-01

    We present a theory describing the transients and rise times of the refractive Kerr nonlinearity which is enhanced using electromagnetically induced transparency (EIT). We restrict our analysis to the case of a pulsed signal field with continuous-wave EIT fields, and all fields are well below saturation. These restrictions enable the reduction of an EIT Kerr, four-level, density-matrix equation to a two-level Bloch-vector equation which has a simple and physically intuitive algebraic solution. The physically intuitive picture of a two-level Bloch vector provides insights that are easily generalized to more complex and experimentally realistic models. We consider generalization to the cases of Doppler broadening, many-level EIT systems (we consider the D1 line of 87 Rb), and optically thick media. For the case of optically thick media we find that the rise time of the refractive EIT Kerr effect is proportional to the optical thickness. The rise time of the refractive EIT Kerr effect sets important limitations for potential few-photon applications

  13. Time-dependent Bloch-Maxwell modelling of 1 mJ, 200 fs seeded soft x-ray laser

    International Nuclear Information System (INIS)

    Zeitoun, Ph.; Oliva, E.; Fajardo, M.; Velarde, P.; Ros, D.; Sebban, S.

    2010-01-01

    Complete text of publication follows. Seeding of high harmonic generation in a soft x-ray plasma amplifier has been first proposed and tested by T. Ditmire and collaborators. The experiment demonstrated low amplification (*2), with a very strong background coming from the soft x-ray laser ASE. Later seeding experiments reached very high amplification factors (up to 600) in both gas (Ph. Zeitoun et al.) and solid amplifiers (Wang et at.). Surprisingly, solid amplifiers extracted less energy (90 nJ) than gas amplifier (∼ 1 μJ) with equivalent pump energy. We recently demonstrated that 50-100 μJ is achievable with adequate plasma tailoring. However, this energy is still low as compared to the 10 mJ per pulse demonstrated on the ASE soft x-ray laser running at PALS facility (Czech Republic). In order to model the seeding process of PALS soft x-ray laser, we developed a time-dependent Bloch-Maxwell model that solves coherently the pumping, amplification and saturation processes. We demonstrated that direct seeding, with femtosecond pulse, a soft x-ray plasma amplifier having gain duration of several 100s of picosecond cannot extract the stored energy keeping the output beam energy in the 100 μJ range. We proposed and fully modelled a new seeding scheme that allows to achieve 10 mJ, 200 fs soft x-ray laser.

  14. p-Euler equations and p-Navier-Stokes equations

    Science.gov (United States)

    Li, Lei; Liu, Jian-Guo

    2018-04-01

    We propose in this work new systems of equations which we call p-Euler equations and p-Navier-Stokes equations. p-Euler equations are derived as the Euler-Lagrange equations for the action represented by the Benamou-Brenier characterization of Wasserstein-p distances, with incompressibility constraint. p-Euler equations have similar structures with the usual Euler equations but the 'momentum' is the signed (p - 1)-th power of the velocity. In the 2D case, the p-Euler equations have streamfunction-vorticity formulation, where the vorticity is given by the p-Laplacian of the streamfunction. By adding diffusion presented by γ-Laplacian of the velocity, we obtain what we call p-Navier-Stokes equations. If γ = p, the a priori energy estimates for the velocity and momentum have dual symmetries. Using these energy estimates and a time-shift estimate, we show the global existence of weak solutions for the p-Navier-Stokes equations in Rd for γ = p and p ≥ d ≥ 2 through a compactness criterion.

  15. Optical pulse dynamics for quantum-dot logic operations in a photonic-crystal waveguide

    Energy Technology Data Exchange (ETDEWEB)

    Ma, Xun; John, Sajeev [Department of Physics, University of Toronto, Toronto, Ontario, M5S 1A7 Canada (Canada)

    2011-11-15

    We numerically demonstrate all-optical logic operations with quantum dots (QDs) embedded in a bimodal photonic-crystal waveguide using Maxwell-Bloch equations in a slowly varying envelope approximation (SVEA). The two-level QD excitation level is controlled by one or more femtojoule optical driving pulses passing through the waveguide. Specific logic operations depend on the relative pulse strengths and their detunings from an inhomogeneouslly broadened (about 1% for QD transitions centered at 1.5 {mu}m) QD transition. This excitation controlled two-level medium then determines passage of subsequent probe optical pulses. Envelope equations for electromagnetic waves in the linear dispersion and cutoff waveguide modes are derived to simplify solution of the coupled Maxwell-Bloch equations in the waveguide. These determine the quantum mechanical evolution of the QD excitation and its polarization, driven by classical electromagnetic (EM) pulses near a sharp discontinuity in the EM density of states of the bimodal waveguide. Different configurations of the driving pulses lead to distinctive relations between driving pulse strength and probe pulse passage, representing all-optical logic and, or, and not operations. Simulation results demonstrate that such operations can be done on picosecond time scales and within a waveguide length of about 10 {mu}m in a photonic-band-gap (PBG) optical microchip.

  16. Equating error in observed-score equating

    NARCIS (Netherlands)

    van der Linden, Willem J.

    2006-01-01

    Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of

  17. Optical bistability without the rotating wave approximation

    Energy Technology Data Exchange (ETDEWEB)

    Sharaby, Yasser A., E-mail: Yasser_Sharaby@hotmail.co [Physics Department, Faculty of Applied Sciences, Suez Canal University, Suez (Egypt); Joshi, Amitabh, E-mail: ajoshi@eiu.ed [Department of Physics, Eastern Illinois University, Charleston, IL 61920 (United States); Hassan, Shoukry S., E-mail: Shoukryhassan@hotmail.co [Mathematics Department, College of Science, University of Bahrain, P.O. Box 32038 (Bahrain)

    2010-04-26

    Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.

  18. Optical bistability without the rotating wave approximation

    International Nuclear Information System (INIS)

    Sharaby, Yasser A.; Joshi, Amitabh; Hassan, Shoukry S.

    2010-01-01

    Optical bistability for two-level atomic system in a ring cavity is investigated outside the rotating wave approximation (RWA) using non-autonomous Maxwell-Bloch equations with Fourier decomposition up to first harmonic. The first harmonic output field component exhibits reversed or closed loop bistability simultaneously with the usual (anti-clockwise) bistability in the fundamental field component.

  19. Non-equilibrium reversible dynamics of work production in four-spin system in a magnetic field

    Directory of Open Access Journals (Sweden)

    E.A. Ivanchenko

    2011-06-01

    Full Text Available A closed system of the equations for the local Bloch vectors and spin correlation functions is obtained by decomplexification of the Liouville-von Neumann equation for 4 magnetic particles with the exchange interaction that takes place in an arbitrary time-dependent external magnetic field. The analytical and numerical analysis of the quantum thermodynamic variables is carried out depending on separable mixed initial state and the magnetic field modulation. Under unitary evolution, non-equilibrium reversible dynamics of power production in the finite environment is investigated.

  20. Inverse problem for in vivo NMR spatial localization

    International Nuclear Information System (INIS)

    Hasenfeld, A.C.

    1985-11-01

    The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs

  1. Inverse problem for in vivo NMR spatial localization

    Energy Technology Data Exchange (ETDEWEB)

    Hasenfeld, A.C.

    1985-11-01

    The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs.

  2. Artifacts in magnetic spirals retrieved by transport of intensity equation (TIE)

    Science.gov (United States)

    Cui, J.; Yao, Y.; Shen, X.; Wang, Y. G.; Yu, R. C.

    2018-05-01

    The artifacts in the magnetic structures reconstructed from Lorentz transmission electron microscopy (LTEM) images with TIE method have been analyzed in detail. The processing for the simulated images of Bloch and Neel spirals indicated that the improper parameters in TIE may overestimate the high frequency information and induce some false features in the retrieved images. The specimen tilting will further complicate the analysis of the images because the LTEM image contrast is not the result of the magnetization distribution within the specimen but the integral projection pattern of the magnetic induction filling the entire space including the specimen.

  3. Influence of ammonia on forming the toxicity of waters from the surface sources of water supply determined on Carassius auratus gibelio (Bloch, 1782

    Directory of Open Access Journals (Sweden)

    Е. Arystarkhova

    2018-03-01

    Full Text Available Purpose. Determination of the influence of ammonia in waters from surface sources of water supply of Zhytomyr city on forming the toxicity of these waters determined by test-reactions of atypical motor activity of Carassius auratus gibelio (Bloch, 1782 with the use of the «time sampling» method during 2012–2014. Methodology. Biotesting was performed at the Municipal Enterprise "Zhytomyrvodokanal". Water samples were taken once a month time from the Teteriv river reservoirs and tap water network and then placed into aquaria (8 dm3 on a group. Control and experimental groups of fish were formed according to the following scheme: control group — samples of settled (24 hours tap water; experimental group D-1 — water samples from the Denyshivske reservoir; experimental group D-2 — water samples from the Vidsichne water intake. Test specimens were females of C. auratus gibelio. Biotesting was conducted using the «time sampling» method by keeping fish (n=30 in water for 12 hours. The toxicity indexes of waters were calculated on the basis of the following test-reactions: spiral-like and vector movements, jumping out from water, immobilization and death of fish. Statistical processing of study results were performed using cross-correlation and regression analysis in MS Excel 2007 and Statistica-6. Findings. The study showed an effect of ammonia on the toxicity of waters from reservoirs of the Teteriv river that was determined by atypical motor activity with the use of the «time sampling» method, which consisted in the instantaneous fixation of the number of individuals that favored one or another act of behavior. It was shown that females not adapted to the action of ammonia reacted to its concentration in water of more than 0.55 mg/dm3 by disorders in movements. Unlike fish of experience groups, only single pathological acts were observed in the control group. A positive moderate relationship, which had a tendency to an increase, was

  4. equateIRT: An R Package for IRT Test Equating

    Directory of Open Access Journals (Sweden)

    Michela Battauz

    2015-12-01

    Full Text Available The R package equateIRT implements item response theory (IRT methods for equating different forms composed of dichotomous items. In particular, the IRT models included are the three-parameter logistic model, the two-parameter logistic model, the one-parameter logistic model and the Rasch model. Forms can be equated when they present common items (direct equating or when they can be linked through a chain of forms that present common items in pairs (indirect or chain equating. When two forms can be equated through different paths, a single conversion can be obtained by averaging the equating coefficients. The package calculates direct and chain equating coefficients. The averaging of direct and chain coefficients that link the same two forms is performed through the bisector method. Furthermore, the package provides analytic standard errors of direct, chain and average equating coefficients.

  5. Impact of slow-light enhancement on optical propagation in active semiconductor photonic crystal waveguides

    DEFF Research Database (Denmark)

    Chen, Yaohui; de Lasson, Jakob Rosenkrantz; Gregersen, Niels

    2015-01-01

    We derive and validate a set of coupled Bloch wave equations for analyzing the reflection and transmission properties of active semiconductor photonic crystal waveguides. In such devices, slow-light propagation can be used to enhance the material gain per unit length, enabling, for example......, the realization of short optical amplifiers compatible with photonic integration. The coupled wave analysis is compared to numerical approaches based on the Fourier modal method and a frequency domain finite element technique. The presence of material gain leads to the build-up of a backscattered field, which...... is interpreted as distributed feedback effects or reflection at passive-active interfaces, depending on the approach taken. For very large material gain values, the band structure of the waveguide is perturbed, and deviations from the simple coupled Bloch wave model are found....

  6. Fish condensate as effective replacer of fish meal protein in diet for striped snakehead, Channa striata (Bloch).

    Science.gov (United States)

    Wattanakul, Wattana; Wattanakul, Uraiwan; Thongprajukaew, Karun; Muenpo, Chutchawan

    2017-02-01

    The optimal protein replacement of fish meal (FM) by fish condensate (FC) was investigated in striped snakehead, Channa striata (Bloch) (1.78 ± 0.02 g initial weight). The FM-based diet (0FC) was replaced by substituting protein from FC for 100 (100FC), 200 (200FC), 300 (300FC), 400 (400FC), 500 (500FC) or 600 (600FC) g kg -1 of the FM, and a commercial diet (CD) for carnivorous fish was included for comparison. The experiment was conducted indoors under completely randomized design (8 treatments × 3 replications × 60 fish per pond) over a 6-month trial. There were no significant differences in water quality during the experiment. The fish fed with 500FC had superior growth performance and feed utilization. This dietary treatment gave similar levels to all observed specific activities of digestive enzymes as did baseline 0FC. Survival, carcass composition, hematological parameters and liver histopathology were not negatively impacted by this protein replacement level. Economic analysis also supports the use of this by-product as a potent protein replacer in striped snakehead diet. Findings from the current study indicate that a 500 g kg -1 protein replacement of FM by FC is near optimal for striped snakehead, and similar use of it in the aquafeed of other species appears worth further studies.

  7. Dynamics of Bloch oscillating transistor near bifurcation threshold and its applicability for common mode rejection capability of a differential pair BOT

    Science.gov (United States)

    Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti

    2014-03-01

    Bloch oscillating transistor (BOT) is mesoscopic current amplier based on a combination of a Josephson junction or a squid connected with a large resistor and a NIS junction. We have studied the dynamics of BOT near the bifurcation threshold. This is an important feature for an amplifier as this can be utilized to improve its performance characteristics. We have measured the I - V characteristics of the BOT with different base currents (IB) over a wide range of Josephson coupling energies (EJ) . The current gain (β) is found to be increasing with increasing IB and eventually diverging. We have found a record large β = 50 in our experiment. In order to determine the common mode rejection ratio (CMRR) of a differential pair BOT we have used two BOTs fabricated on the same chip. The common mode port is connected to the bases of the two BOTs and fed with varying voltages; simultaneously emitter currents of the two BOTs are recorded. In our experiment we found a 20dB of CMRR.

  8. Influence of in-plane field on the stability of vertical Bloch lines in the walls of OHB at various bias fields

    International Nuclear Information System (INIS)

    Guo, G.X.; Wang, L.N.; Zhen, C.M.; Nie, X.F.

    2006-01-01

    The stability of vertical Bloch line (VBL) chains subjected to in-plane field (H ip ) was statistically studied for the ordinary hard bubbles (OHB) in garnet bubble films at various bias fields (H b ). The dumbbell domains were also investigated. We found that (H ip (1) ) IID ip (1) ) ID ip (1) ) OHB and (H ip (2) ) IID =(H ip (2) ) ID =(H ip (2) ) OHB when keeping H b unchanged. With the increasing of H b , the in-plane field H ip (1) , H ip * and H ip (2) all decrease, while the in-plane field range [H ip (1) , H ip * ] and [H ip (1) , H ip (2) ] become narrower. Here, H ip (1) is the initial critical in-plane field where VBLs in the walls of three types of hard domains are annihilated, H ip * stands for the in-plane field where the retention rate of three types of hard domains R reduces to zero, and H ip (2) is the lowest in-plane field where VBLs in their corresponding hard domains are annihilated completely

  9. Computing generalized Langevin equations and generalized Fokker-Planck equations.

    Science.gov (United States)

    Darve, Eric; Solomon, Jose; Kia, Amirali

    2009-07-07

    The Mori-Zwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized non-Markovian Fokker-Planck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the Mori-Zwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.

  10. Selection of planes in nuclear magnetic resonance tomography

    International Nuclear Information System (INIS)

    Bonagamba, T.J.

    1986-01-01

    A prototype aiming to obtain images in nuclear magnetic resonance tomography was developed, by adjusting NMR spectrometer in the IFQSC Laboratory. The techniques for selecting planes were analysed by a set of computer codes, which were elaborated from Bloch equation solutions to simulate the spin system behaviour. Images were obtained using planes with thickness inferior to 1 cm. (M.C.K.)

  11. Development of kinetics equations from the Boltzmann equation; Etablissement des equations de la cinetique a partir de l'equation de Boltzmann

    Energy Technology Data Exchange (ETDEWEB)

    Plas, R.

    1962-07-01

    The author reports a study on kinetics equations for a reactor. He uses the conventional form of these equations but by using a dynamic multiplication factor. Thus, constants related to delayed neutrons are not modified by efficiency factors. The author first describes the theoretic kinetic operation of a reactor and develops the associated equations. He reports the development of equations for multiplication factors.

  12. Simple equation method for nonlinear partial differential equations and its applications

    Directory of Open Access Journals (Sweden)

    Taher A. Nofal

    2016-04-01

    Full Text Available In this article, we focus on the exact solution of the some nonlinear partial differential equations (NLPDEs such as, Kodomtsev–Petviashvili (KP equation, the (2 + 1-dimensional breaking soliton equation and the modified generalized Vakhnenko equation by using the simple equation method. In the simple equation method the trial condition is the Bernoulli equation or the Riccati equation. It has been shown that the method provides a powerful mathematical tool for solving nonlinear wave equations in mathematical physics and engineering problems.

  13. Diploposthe laevis (Bloch Jacobi (Eucestoda, Hymenolepididae from Netta peposaca (Vieillot (Aves: Anatidae: first record for the Neotropical Region and a new host Diploposthe laevis (Bloch Jacobi (Eucestoda: Hymenolepididae em Netta peposaca (Vieillot (Aves, Anatidae: primeiro registro para Região Neotropical e novo hospedeiro

    Directory of Open Access Journals (Sweden)

    Eliane F. da Silveira

    2008-03-01

    Full Text Available One hundred eight rosy-billed pochards, Netta peposaca (Vieillot, 1816, collected in Brazil and Argentina were examined for endoparasites. Collection sites included the municipalities of Santa Vitória do Palmar and Jaguarão, Rio Grande do Sul State, Brazil (wintering site and Alvear, Corrientes Province, northern Argentina (nesting site. Birds were frozen in dry ice after collection. During necropsy they were categorized according to sex and maturation, either adult or juvenile. The cestode Diploposthe laevis (Bloch Jacobi, 1896 was found (prevalence 68.5%, mean infection was 2. The mean prevalence of D. laevis in Alvear (25.9% was higher than found in Jaguarão and Santa Vitória do Palmar, Rio Grande do Sul (19%, and could be related to the nesting site and to the period when the birds may ingest a higher amount of food. This is the first record of a species of the genus Diploposthe in anatideans from South America, and the first record of the species in N. peposaca. Details of the cirrus pouch and vagina were described based on histological sections.Com o objetivo de conhecer a helmintofauna do marrecão, Netta peposaca (Vieillot, 1816, na América do Sul, 108 aves foram amostradas. Os pontos de captura foram os municípios de Santa Vitória do Palmar e Jaguarão, no Estado do Rio Grande do Sul, sul do Brasil (pólo de invernia, e em Alvear, Província de Corrientes, região norte da Argentina (pólo de nidificação, entre 2002 e 2004. As aves foram congeladas em gelo seco logo após o abate. Durante o procedimento de necropsia tiveram o sexo identificado, e foram classificadas de acordo com estado de maturação sexual, em juvenil e adulto. O cestóide Diploposthe laevis (Bloch Jacobi, 1896 foi encontrado com prevalência média de 68,5% e intensidade média de infecção de dois espécimes por hospedeiro. A prevalência média de D. laevis em Alvear (25,9% foi maior do que a encontrada em Jaguarão e Santa Vitória do Palmar, Rio Grande

  14. Histopathological alterations of the gills, liver and kidneys in Anabas Testudineus (Bloch) fish living in an unused lignite mine, Li District, Lamphun Povince, Thailand

    Energy Technology Data Exchange (ETDEWEB)

    Saenphet, S.; Thaworn, W.; Saenphet, K. [Chiang Mai University, Chiang Mai (Thailand). Faculty of Science

    2009-09-15

    The acidity of mine water generally makes it toxic to most organisms. The gills, kidneys and livers of Anabas testudineus Bloch fish inhabiting the acidic water (pH 2-4) of an unused lignite mine in Li District, Lamphun Province, Thailand were examined and compared to those of farmed fish. Tissue abnormalities were found in all investigated organs. Deterioration and telangiectasia of gill filaments were found. Liver tissue revealed hemorrhages, blood congestion and necrotic cells with mononuclear cell infiltration. In addition, hypertrophy of the epithelial cells of the renal tubules with reduced lumens, aneurisms of the renal tubules, and contractions of the glomeruli in the Bowman's capsule were observed. These histopathological findings suggest the acidic water in this habitat causes severe damage to the internal organs of fish and consequently alter their physiological status. Since the water in this pond is utilized by local people, these findings highlight the need for adequate water treatment.

  15. Numerical Solution of Heun Equation Via Linear Stochastic Differential Equation

    Directory of Open Access Journals (Sweden)

    Hamidreza Rezazadeh

    2014-05-01

    Full Text Available In this paper, we intend to solve special kind of ordinary differential equations which is called Heun equations, by converting to a corresponding stochastic differential equation(S.D.E.. So, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this S.D.E. is solved by numerically methods. Moreover, its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed. Finally, the attained solutions of these S.D.E.s compared with exact solution of corresponding differential equations.

  16. A generalization of the simplest equation method and its application to (3+1)-dimensional KP equation and generalized Fisher equation

    International Nuclear Information System (INIS)

    Zhao, Zhonglong; Zhang, Yufeng; Han, Zhong; Rui, Wenjuan

    2014-01-01

    In this paper, the simplest equation method is used to construct exact traveling solutions of the (3+1)-dimensional KP equation and generalized Fisher equation. We summarize the main steps of the simplest equation method. The Bernoulli and Riccati equation are used as simplest equations. This method is straightforward and concise, and it can be applied to other nonlinear partial differential equations

  17. Analysis of wave equation in electromagnetic field by Proca equation

    International Nuclear Information System (INIS)

    Pamungkas, Oky Rio; Soeparmi; Cari

    2017-01-01

    This research is aimed to analyze wave equation for the electric and magnetic field, vector and scalar potential, and continuity equation using Proca equation. Then, also analyze comparison of the solution on Maxwell and Proca equation for scalar potential and electric field, both as a function of distance and constant wave number. (paper)

  18. Comparison of Kernel Equating and Item Response Theory Equating Methods

    Science.gov (United States)

    Meng, Yu

    2012-01-01

    The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…

  19. Integral equations

    CERN Document Server

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  20. Partial Differential Equations

    CERN Document Server

    1988-01-01

    The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.

  1. Nonlinear evolution equations

    CERN Document Server

    Uraltseva, N N

    1995-01-01

    This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p

  2. FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...

    African Journals Online (AJOL)

    eobe

    plant made of 12mm thick steel plate was used in de steel plate ... water treatment plant. ... ameters affecting filtration processes were used to derive an equation usin ..... system. However, in deriving the equation onl terms are incorporated.

  3. Kinetic equations for an unstable plasma; Equations cinetiques d'un plasma instable

    Energy Technology Data Exchange (ETDEWEB)

    Laval, G; Pellat, R [Commissariat a l' Energie Atomique, Fontenay-aux-Roses (France). Centre d' Etudes Nucleaires

    1968-07-01

    In this work, we establish the plasma kinetic equations starting from the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy of equations. We demonstrate that relations existing between correlation functions may help to justify the truncation of the hierarchy. Then we obtain the kinetic equations of a stable or unstable plasma. They do not reduce to an equation for the one-body distribution function, but generally involve two coupled equations for the one-body distribution function and the spectral density of the fluctuating electric field. We study limiting cases where the Balescu-Lenard equation, the quasi-linear theory, the Pines-Schrieffer equations and the equations of weak turbulence in the random phase approximation are recovered. At last we generalise the H-theorem for the system of equations and we define conditions for irreversible behaviour. (authors) [French] Dans ce travail nous etablissons les equations cinetiques d'un plasma a partir des equations de la recurrence de Bogoliubov, Born, Green, Kirkwood et Yvon. Nous demontrons qu'entre les fonctions de correlation d'un plasma existent des relations qui permettent de justifier la troncature de la recurrence. Nous obtenons alors les equations cinetiques d'un plasma stable ou instable. En general elles ne se reduisent pas a une equation d'evolution pour la densite simple, mais se composent de deux equations couplees portant sur la densite simple et la densite spectrale du champ electrique fluctuant. Nous etudions le cas limites ou l'on retrouve l'equation de Balescu-Lenard, les equations de la theorie quasi-lineaire, les equations de Pines et Schrieffer et les equations de la turbulence faible dans l'approximation des phases aleatoires. Enfin, nous generalisons le theoreme H pour ce systeme d'equations et nous precisons les conditions d'evolution irreversible. (auteurs)

  4. equate: An R Package for Observed-Score Linking and Equating

    Directory of Open Access Journals (Sweden)

    Anthony D. Albano

    2016-10-01

    Full Text Available The R package equate contains functions for observed-score linking and equating under single-group, equivalent-groups, and nonequivalent-groups with anchor test(s designs. This paper introduces these designs and provides an overview of observed-score equating with details about each of the supported methods. Examples demonstrate the basic functionality of the equate package.

  5. Nonlinear nuclear magnetic resonance in ferromagnets

    International Nuclear Information System (INIS)

    Nurgaliev, T.

    1988-01-01

    The properties of nonlinear nuclear magnetic resonance (NMR) have been studied theoretically by taking into account the interaction between NMR and FMR in the ferromagnets. The Landau-Lifshitz-Bloch equations, describing the electron and nuclear magnetization behaviour in ferromagnets are presented in an integral form for a weakly excited electronic system. The stationary solution of these equations has been analysed in the case of equal NMR and FMR frequencies: the criteria for the appearance of two stable dynamic states is found and the high-frequency magnetic susceptibility for these systems is investigated. 2 figs., 8 refs

  6. A Compressed Sensing Framework for Magnetic Resonance Fingerprinting

    OpenAIRE

    Davies, Mike; Puy, Gilles; Vandergheynst, Pierre; Wiaux, Yves

    2013-01-01

    Inspired by the recently proposed Magnetic Resonance Fingerprinting (MRF) technique, we develop a principled compressed sensing framework for quantitative MRI. The three key components are: a random pulse excitation sequence following the MRF technique; a random EPI subsampling strategy and an iterative projection algorithm that imposes consistency with the Bloch equations. We show that theoretically, as long as the excitation sequence possesses an appropriate form of persistent excitation, w...

  7. Quantum memory for nonstationary light fields based on controlled reversible inhomogeneous broadening

    International Nuclear Information System (INIS)

    Kraus, B.; Tittel, W.; Gisin, N.; Nilsson, M.; Kroell, S.; Cirac, J. I.

    2006-01-01

    We propose a method for efficient storage and recall of arbitrary nonstationary light fields, such as, for instance, single photon time-bin qubits or intense fields, in optically dense atomic ensembles. Our approach to quantum memory is based on controlled, reversible, inhomogeneous broadening and relies on a hidden time-reversal symmetry of the optical Bloch equations describing the propagation of the light field. We briefly discuss experimental realizations of our proposal

  8. Chemical Equation Balancing.

    Science.gov (United States)

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  9. A new auxiliary equation and exact travelling wave solutions of nonlinear equations

    International Nuclear Information System (INIS)

    Sirendaoreji

    2006-01-01

    A new auxiliary ordinary differential equation and its solutions are used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the auxiliary equation which has more new exact solutions. More new exact travelling wave solutions are obtained for the quadratic nonlinear Klein-Gordon equation, the combined KdV and mKdV equation, the sine-Gordon equation and the Whitham-Broer-Kaup equations

  10. Optimal cloning of arbitrary mirror-symmetric distributions on the Bloch sphere: a proposal for practical photonic realization

    International Nuclear Information System (INIS)

    Bartkiewicz, Karol; Miranowicz, Adam

    2012-01-01

    We study state-dependent quantum cloning that can outperform universal cloning (UC). This is possible by using some a priori information on a given quantum state to be cloned. Specifically, we propose a generalization and optical implementation of quantum optimal mirror phase-covariant cloning, which refers to optimal cloning of sets of qubits of known modulus of the expectation value of Pauli's Z operator. Our results can be applied to cloning of an arbitrary mirror-symmetric distribution of qubits on the Bloch sphere including in special cases UC and phase-covariant cloning. We show that the cloning is optimal by adapting our former optimality proof for axisymmetric cloning (Bartkiewicz and Miranowicz 2010 Phys. Rev. A 82 042330). Moreover, we propose an optical realization of the optimal mirror phase-covariant 1→2 cloning of a qubit, for which the mean probability of successful cloning varies from 1/6 to 1/3 depending on prior information on the set of qubits to be cloned. The qubits are represented by polarization states of photons generated by the type-I spontaneous parametric down-conversion. The scheme is based on the interference of two photons on an unbalanced polarization-dependent beam splitter with different splitting ratios for vertical and horizontal polarization components and the additional application of feedforward by means of Pockels cells. The experimental feasibility of the proposed setup is carefully studied including various kinds of imperfections and losses. Moreover, we briefly describe two possible cryptographic applications of the optimal mirror phase-covariant cloning corresponding to state discrimination (or estimation) and secure quantum teleportation.

  11. Solitons and rogue waves for a higher-order nonlinear Schroedinger-Maxwell-Bloch system in an erbium-doped fiber

    International Nuclear Information System (INIS)

    Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin; Xue, Long; Aviation Univ. of Air Force, Liaoning

    2015-01-01

    Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.

  12. On a functional equation related to the intermediate long wave equation

    International Nuclear Information System (INIS)

    Hone, A N W; Novikov, V S

    2004-01-01

    We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is resolved using the perturbative symmetry approach introduced by one of us with Mikhailov. By solving a certain functional equation, we prove that the intermediate long wave equation and the Benjamin-Ono equation are the unique integrable cases within a particular class of integro-differential equations. Furthermore, we explain how the perturbative symmetry approach is naturally extended to treat equations on a periodic domain. (letter to the editor)

  13. Some New Integrable Equations from the Self-Dual Yang-Mills Equations

    International Nuclear Information System (INIS)

    Ivanova, T.A.; Popov, A.D.

    1994-01-01

    Using the symmetry reductions of the self-dual Yang-Mills (SDYM) equations in (2+2) dimensions, we introduce new integrable equations which are 'deformations' of the chiral model in (2+1) dimensions, generalized nonlinear Schroedinger, Korteweg-de Vries, Toda lattice, Garnier, Euler-Arnold, generalized Calogero-Moser and Euler-Calogero-Moser equations. The Lax pairs for all of these equations are derived by the symmetry reductions of the Lax pair for the SDYM equations. 34 refs

  14. Auxiliary equation method for solving nonlinear partial differential equations

    International Nuclear Information System (INIS)

    Sirendaoreji,; Jiong, Sun

    2003-01-01

    By using the solutions of an auxiliary ordinary differential equation, a direct algebraic method is described to construct several kinds of exact travelling wave solutions for some nonlinear partial differential equations. By this method some physically important nonlinear equations are investigated and new exact travelling wave solutions are explicitly obtained with the aid of symbolic computation

  15. The equationally-defined commutator a study in equational logic and algebra

    CERN Document Server

    Czelakowski, Janusz

    2015-01-01

    This monograph introduces and explores the notions of a commutator equation and the equationally-defined commutator from the perspective of abstract algebraic logic.  An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebras.  The author discusses the general properties of the equationally-defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally-defined commutator, and its behavior in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally-Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.

  16. A Comparison between Linear IRT Observed-Score Equating and Levine Observed-Score Equating under the Generalized Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen

    2012-01-01

    In this article, linear item response theory (IRT) observed-score equating is compared under a generalized kernel equating framework with Levine observed-score equating for nonequivalent groups with anchor test design. Interestingly, these two equating methods are closely related despite being based on different methodologies. Specifically, when…

  17. Coherent manipulation of atoms using laser light

    International Nuclear Information System (INIS)

    Shore, B.W.

    2008-01-01

    The internal structure of a particle an atom or other quantum system in which the excitation energies are discrete undergoes change when exposed to pulses of near-resonant laser light. This tutorial review presents basic concepts of quantum states, of laser radiation and of the Hilbert-space state vector that provides the theoretical portrait of probability amplitudes the tools for quantifying quantum properties not only of individual atoms and molecules but also of artificial atoms and other quantum systems. It discusses the equations of motion that describe the laser-induced changes (coherent excitation), and gives examples of laser=pulse effects, with particular emphasis on two-state and three-state adiabatic time evolution within the rotating-wave approximation. It provides pictorial descriptions of excitation based on the Bloch equations that allow visualization of two-state excitation as motion of a three-dimensional vector (the Bloch vector). Other visualization techniques allow portrayal of more elaborate systems, particularly the Hilbert-space motion of adiabatic states subject to various pulse sequences. Various more general multilevel systems receive treatment that includes degeneracies, chains and loop linkages. The concluding sections discuss techniques for creating arbitrary pre-assigned quantum states, for manipulating them into alternative coherent superpositions and for analyzing an unknown superposition. Appendices review some basic mathematical concepts and provide further details of the theoretical formalism, including photons, pulse propagation, statistical averages, analytic solutions to the equations of motion, exact solutions of periodic Hamiltonians, and population-trapping 'dark' states. (author)

  18. Five-dimensional Monopole Equation with Hedge-Hog Ansatz and Abel's Differential Equation

    OpenAIRE

    Kihara, Hironobu

    2008-01-01

    We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential equation.

  19. Differential equations a dynamical systems approach ordinary differential equations

    CERN Document Server

    Hubbard, John H

    1991-01-01

    This is a corrected third printing of the first part of the text Differential Equations: A Dynamical Systems Approach written by John Hubbard and Beverly West. The authors' main emphasis in this book is on ordinary differential equations. The book is most appropriate for upper level undergraduate and graduate students in the fields of mathematics, engineering, and applied mathematics, as well as the life sciences, physics and economics. Traditional courses on differential equations focus on techniques leading to solutions. Yet most differential equations do not admit solutions which can be written in elementary terms. The authors have taken the view that a differential equations defines functions; the object of the theory is to understand the behavior of these functions. The tools the authors use include qualitative and numerical methods besides the traditional analytic methods. The companion software, MacMath, is designed to bring these notions to life.

  20. Validity of the electrical model representation of the effects of nuclear magnetic resonance (1961); Validite de la representation par modele electrique des effets de resonance magnetique nucleaire (1961)

    Energy Technology Data Exchange (ETDEWEB)

    Bonnet, G [Commissariat a l' Energie Atomique, Grenoble (France). Centre d' Etudes Nucleaires

    1961-07-01

    When studying the behaviour of a magnetic resonance transducer formed by the association of an electrical network and of a set of nuclear spins, it is possible to bring about a representation that is analytically equivalent by means of an entirely electrical model, available for transients as well as steady-state. A detailed study of the validity conditions justifies its use in most cases. Also proposed is a linearity criterion of Bloch's equations in transient state that is simply the prolongation of the well-known condition of non-saturation in the steady-state. (author) [French] L'etude du comportement d'un transducteur a resonance magnetique forme de l'association d'un reseau electrique et d'un ensemble de noyaux dotes de spin, montre qu'il est possible d'en deduire une representation analytiquement equivalente au moyen d'un modele entierement electrique utilisable pour un regime transitoire aussi bien que pour un regime permanent. Une etude detaillee des conditions de validite permet d'en justifier l'emploi dans la majorite des cas. On propose enfin un critere de linearite des equations de Bloch en regime transitoire, qui constitue un prolongement de la condition connue de non-saturation en regime stationnaire. (auteur)

  1. The dc electrical conductivity calculation purely from the dissipative component of the ac conductivity II. formula for conductors with static scatterers

    International Nuclear Information System (INIS)

    Milinski, Nikola; Milinski, Eduard

    2001-01-01

    While the first part of this work was devoted to the conceptual and most crucial questions of the dc electrical conductivity σ, the present second part is devoted to the technical questions of the theory, to elaboration of the concept to the particular systems. The conducting system to be investigated has been defined here by five suppositions (postulates), rather general to include the systems of practical interest, like metals in solid and liquid phase are, and the amorphous conductors, like the alloys and conducting glasses are. A formula for dc conductivity calculation has been derived, which gives σ in terms of the matrix elements / k +g/F/Ψ k >/ 2 , where F is scattering force, and Ψ k +g, Ψ k , are the Bloch functions. For the case when Bloch functions are approximated by plane waves, an approximate formula for σ has been obtained in a more tractable form. Specific to our concept is the inclusion of an equation constitutive to σ calculation, which also has been elaborated for the considered system, to the stage suitable for practical application, σ calculation in conjunction with the mentioned constitutive equation is the most important innovative element of our concept, and we expect it will lead to substantial advance in research of this subject. (authors)

  2. Differential equations

    CERN Document Server

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  3. New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating Framework

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2010-01-01

    In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of…

  4. Relations between nonlinear Riccati equations and other equations in fundamental physics

    International Nuclear Information System (INIS)

    Schuch, Dieter

    2014-01-01

    Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract ''quantizations'' such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown

  5. Bridging the Knowledge Gaps between Richards' Equation and Budyko Equation

    Science.gov (United States)

    Wang, D.

    2017-12-01

    The empirical Budyko equation represents the partitioning of mean annual precipitation into evaporation and runoff. Richards' equation, based on Darcy's law, represents the movement of water in unsaturated soils. The linkage between Richards' equation and Budyko equation is presented by invoking the empirical Soil Conservation Service curve number (SCS-CN) model for computing surface runoff at the event-scale. The basis of the SCS-CN method is the proportionality relationship, i.e., the ratio of continuing abstraction to its potential is equal to the ratio of surface runoff to its potential value. The proportionality relationship can be derived from the Richards' equation for computing infiltration excess and saturation excess models at the catchment scale. Meanwhile, the generalized proportionality relationship is demonstrated as the common basis of SCS-CN method, monthly "abcd" model, and Budyko equation. Therefore, the linkage between Darcy's law and the emergent pattern of mean annual water balance at the catchment scale is presented through the proportionality relationship.

  6. Partial differential equations

    CERN Document Server

    Evans, Lawrence C

    2010-01-01

    This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...

  7. Nonlinear Dirac Equations

    Directory of Open Access Journals (Sweden)

    Wei Khim Ng

    2009-02-01

    Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.

  8. Mudança na dieta da traíra Hoplias malabaricus (Bloch (Erythrinidae, Characiformes em lagoas da bacia do rio Doce devido à introdução de peixes piscívoros Diet changes of the trahira Hoplias malabaricus (Bloch (Erythrinidae, Characiformes due to piscivorous introductions in Rio Doce valley lakes

    Directory of Open Access Journals (Sweden)

    Paulo dos Santos Pompeu

    2001-12-01

    Full Text Available Two piscivorous fishes, peacock bass (Cichla monoculus Spix & Agassiz, 1831 (Perciformes and piranha (Pygocentrus nattereri Kner, 1860 (Characiformes, were introduced in some Rio Doce valley lakes (19º50'S, 42º40'W for sport fisheries enhancement. As a consequence, small individuals and species were practically vanished in the host lakes. In this study, the effects of peacock bass and piranha introductions on the diet of a native piscivorous fish, the trahira - Hoplias malabaricus (Bloch, 1794 are presented. Trahira's diet from three lakes were was compared with the stomach contentsdiet of trahira's living in another between three lakes with and three withoutstocked with the piscivorous species peacock bass and piranha. In the lakes with introduced fishes species, the consumption of fish was significantly smaller and this food item have been this item partly replaced by aquatic invertebrates. This shift on of trahira's diet to the low abundance of its original prey, is attributed to the small fishes. This diet plasticity adaptative capacity he diet plasticity detected for trahira might be allowing its maintenance in the lakes with peacock bass and piranha.

  9. Functional equations with causal operators

    CERN Document Server

    Corduneanu, C

    2003-01-01

    Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.

  10. Mode-Locking in Broad-Area Semiconductor Lasers Enhanced by Picosecond-Pulse Injection

    OpenAIRE

    Kaiser, J; Fischer, I; Elsasser, W; Gehrig, E; Hess, O

    2004-01-01

    We present combined experimental and theoretical investigations of the picosecond emission dynamics of broad-area semiconductor lasers (BALs). We enhance the weak longitudinal self-mode-locking that is inherent to BALs by injecting a single optical 50-ps pulse, which triggers the output of a distinct regular train of 13-ps pulses. Modeling based on multimode Maxwell-Bloch equations illustrates how the dynamic interaction of the injected pulse with the internal laser field efficiently couples ...

  11. A many-particle quantum-kinetic formalism for describing properties of light emitters in frozen dielectrics

    Directory of Open Access Journals (Sweden)

    Gladush M.G.

    2017-01-01

    Full Text Available A many particle quantum-kinetic formalism is suggested to derive the Maxwell-Bloch-type equations which describe the interaction of quantum emitters with light in a frozen dielectric. It is shown that the quantum-kinetic formalism can meet the concept of local variations of dielectric properties and their influence on the emitter. The definitions of the local response and the effective refractive index in macroscopically homogeneous media are discussed.

  12. Ultrafast Gain Dynamics in Quantum Dot Amplifiers: Theoretical Analysis and Experimental Investigations

    DEFF Research Database (Denmark)

    Poel, Mike van der; Gehrig, Edeltraud; Hess, Ortwin

    2005-01-01

    Ultrafast gain dynamics in an optical amplifier with an active layer of self-organized quantum dots (QDs) emitting near 1.3$muhbox m$is characterized experimentally in a pump-probe experiment and modeled theoretically on the basis of QD Maxwell–Bloch equations. Experiment and theory are in good......$factor) is theoretically predicted and demonstrated in the experiments. The fundamental analysis reveals the underlying physical processes and indicates limitations to QD-based devices....

  13. An Update on the Invasion of Weakfish Cynoscion regalis (Bloch & Schneider, 1801 (Actinopterygii: Sciaenidae into Europe

    Directory of Open Access Journals (Sweden)

    Pedro Morais

    2017-10-01

    Full Text Available New information on weakfish introduction vectors, its invasive status, distribution, and use as a fishing resource arose after the publication of “The transatlantic introduction of weakfish Cynoscion regalis (Bloch & Schneider, 1801 (Sciaenidae, Pisces into Europe” by Morais and Teodósio (2016. Currently, the first known report of weakfish in Europe dates back to September 2009, with a specimen captured in the Schelde estuary (Belgium/The Netherlands. This fact suggests that weakfish could have been introduced into Europe via multiple and independent ballast water introduction events, and not through a point-source introduction event with subsequent dispersion as previously hypothesized. It is also unlikely that Schelde weakfish migrated southwards to colonize Iberian aquatic ecosystems. Weakfish have established a population in the Gulf of Cádiz region and have already reached an invasive status in the Sado estuary (Portugal. Weakfish were also captured in several other locations along the Portuguese coast, including the Tagus and Mira estuaries at least since 2013 or 2014, and the Ria Formosa lagoon in 2017. Tagus anglers caught weakfish specimens of ~1 kg and ~40 cm in November 2016, which corresponds to fish of 3+ years of age in the native range. The presence of weakfish in the Tagus estuary is still fairly unknown to local anglers. Sado weakfish has already been sold in local fish markets in southern Portugal for 3 to 10 € kg−1. However, we consider that the weakfish sale price is underrated in comparison with other wild species (e.g., meagre, seabass, gilthead seabream. Increasing sale price will convince fishers to use weakfish as a new fishing resource; however, it is necessary to promote the species among consumers and evaluate consumers’ preference in respect to other species. A putative biological threat might turn into a new valuable fishing resource by implementing adequate management solutions.

  14. Evaluating Equating Results: Percent Relative Error for Chained Kernel Equating

    Science.gov (United States)

    Jiang, Yanlin; von Davier, Alina A.; Chen, Haiwen

    2012-01-01

    This article presents a method for evaluating equating results. Within the kernel equating framework, the percent relative error (PRE) for chained equipercentile equating was computed under the nonequivalent groups with anchor test (NEAT) design. The method was applied to two data sets to obtain the PRE, which can be used to measure equating…

  15. Handbook of integral equations

    CERN Document Server

    Polyanin, Andrei D

    2008-01-01

    This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.

  16. Electron dynamics in solid state via time varying wavevectors

    Science.gov (United States)

    Khaneja, Navin

    2018-06-01

    In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a periodic potential. We do this by introducing time varying wavevectors k(t). In the presence of magnetic field, our wavepacket reproduces the classical cyclotron orbits once the origin of the Schröedinger equation is correctly chosen to be center of cyclotron orbit. In the presence of both electric and magnetic fields, our equations for wavepacket dynamics differ from classical Lorentz force equations. We show that in a periodic potential, on application of electric field, the electron wave function adiabatically follows the wavefunction of a time varying Bloch wavevector k(t), with its energies suitably shifted with time. We derive the effective mass equation and discuss conduction in conductors and insulators.

  17. Ordinary differential equations

    CERN Document Server

    Greenberg, Michael D

    2014-01-01

    Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps

  18. Fractional Schroedinger equation

    International Nuclear Information System (INIS)

    Laskin, Nick

    2002-01-01

    Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations

  19. Introduction to differential equations

    CERN Document Server

    Taylor, Michael E

    2011-01-01

    The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen

  20. Stochastic optimal control, forward-backward stochastic differential equations and the Schroedinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Paul, Wolfgang; Koeppe, Jeanette [Institut fuer Physik, Martin Luther Universitaet, 06099 Halle (Germany); Grecksch, Wilfried [Institut fuer Mathematik, Martin Luther Universitaet, 06099 Halle (Germany)

    2016-07-01

    The standard approach to solve a non-relativistic quantum problem is through analytical or numerical solution of the Schroedinger equation. We show a way to go around it. This way is based on the derivation of the Schroedinger equation from conservative diffusion processes and the establishment of (several) stochastic variational principles leading to the Schroedinger equation under the assumption of a kinematics described by Nelson's diffusion processes. Mathematically, the variational principle can be considered as a stochastic optimal control problem linked to the forward-backward stochastic differential equations of Nelson's stochastic mechanics. The Hamilton-Jacobi-Bellmann equation of this control problem is the Schroedinger equation. We present the mathematical background and how to turn it into a numerical scheme for analyzing a quantum system without using the Schroedinger equation and exemplify the approach for a simple 1d problem.

  1. Averaged RMHD equations

    International Nuclear Information System (INIS)

    Ichiguchi, Katsuji

    1998-01-01

    A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)

  2. Differential equations

    CERN Document Server

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  3. How to obtain the covariant form of Maxwell's equations from the continuity equation

    International Nuclear Information System (INIS)

    Heras, Jose A

    2009-01-01

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations

  4. A generalized simplest equation method and its application to the Boussinesq-Burgers equation.

    Science.gov (United States)

    Sudao, Bilige; Wang, Xiaomin

    2015-01-01

    In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund transformation between NLEEs and a related constraint equation. By dealing with the constraint equation, we can derive infinite number of exact solutions for NLEEs. These solutions include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. As applications, we obtained wide classes of exact solutions for the Boussinesq-Burgers equation by using the generalized simplest equation method.

  5. On separable Pauli equations

    International Nuclear Information System (INIS)

    Zhalij, Alexander

    2002-01-01

    We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field

  6. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    Science.gov (United States)

    Vitanov, Nikolay K.; Dimitrova, Zlatinka I.

    2018-03-01

    We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  7. Elliptic and solitary wave solutions for Bogoyavlenskii equations system, couple Boiti-Leon-Pempinelli equations system and Time-fractional Cahn-Allen equation

    Directory of Open Access Journals (Sweden)

    Mostafa M.A. Khater

    Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions

  8. Modified Method of Simplest Equation Applied to the Nonlinear Schrödinger Equation

    Directory of Open Access Journals (Sweden)

    Vitanov Nikolay K.

    2018-03-01

    Full Text Available We consider an extension of the methodology of the modified method of simplest equation to the case of use of two simplest equations. The extended methodology is applied for obtaining exact solutions of model nonlinear partial differential equations for deep water waves: the nonlinear Schrödinger equation. It is shown that the methodology works also for other equations of the nonlinear Schrödinger kind.

  9. Integrable dissipative nonlinear second order differential equations via factorizations and Abel equations

    Energy Technology Data Exchange (ETDEWEB)

    Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)

    2013-09-02

    We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.

  10. KONSERVASI GENETIK IKAN BETOK (Anabas testudineus Bloch 1792 DI PERAIRAN RAWA, KALIMANTAN SELATAN

    Directory of Open Access Journals (Sweden)

    Slamat Slamat

    2016-05-01

    Full Text Available Penelitian ini dilakukan dengan menggunakan sample ikan betok (Anabas testudineus Bloch 1972 yang berasal dari perairan rawa Kalimantan Selatan, dengan tujuan untuk mendeskripsikan keragaman  genetik dan aspek konservasinya dengan metode amplifikasi mtDNA. Proses amplifikasi mtDNA ikan betok terjadi di daerah D Loop.  Hasil analisis mt-DNA D Loop ikan betok menunjukkan bahwa, analisis keseimbangan populasi Hardy-Weinberg  berkisar antara 0,02 - 0,09, sedangkan haplotipe tertinggi terdapat pada rawa monoton (0,9384, kemudian tadah hujan (0,7111 dan pasang surut (0,6.  Heterozigositas ditemukan unik pada populasi rawa monoton (BAAAA dan rawa pasang surut (BAACA dan umum di temukan di ketiga ekosistem rawa (AAABA.  Ikan betok di bagi menjadi dua stok populasi yaitu populasi rawa monoton dan pasang surut serta stok tadah hujan.  Konsep utama dalam konservasi genetik adalah fitness population dimana populasi dipertahankan minimal 500 ekor/kawasan. Untuk meningkatkan keragaman genetik ikan betok, dilakukan dengan cara introduksi individu-individu baru yang memiliki keragaman genetik yang lebih tinggi kedalam populasi lokal, restocking dan membuat kawasan suaka yang dilindungi oleh Dinas Perikanan setempat bersama-sama dengan masyarakat di sekitar perairan rawa tersebut.   The research was conducted using climbing perch samples originated from the swampy waters of the southern Borneo, and the objektive of this study to investigate the genetic diversity and the conservation aspect using mtDNA amplification method.  mtDNA amplification process occurs in the D Loop region.  The results of the analysis of D-Loop mtDNA of climbing perch showed that, the analysis of Hardy-Weinberg equilibrium population ranged from 0.02 to 0.09, while the highest haplotypes found in swamp bogs (monotonic (0.9384 then rainfed (0.7111 and tides (0.6. Heterozygosity was found uniquely in the swamp monotonic population (BAAAA and marsh tides (BAACA and common in all

  11. Phase-space quantum mechanics study of two identical particles in an external oscillatory potential

    Science.gov (United States)

    Nieto, Luis M.; Gadella, Manuel

    1993-01-01

    This simple example is used to show how the formalism of Moyal works when it is applied to systems of identical particles. The symmetric and antisymmetric Moyal propagators are evaluated for this case; from them, the correct energy levels of energy are obtained, as well as the Wigner functions for the symmetric and antisymmetric states of the two identical particle system. Finally, the solution of the Bloch equation is straightforwardly obtained from the expressions of the Moyal propagators.

  12. Magnetization Transfer Effects on the Efficiency of Flow-driven Adiabatic Fast Passage Inversion of Arterial Blood

    OpenAIRE

    Hernandez-Garcia, Luis; Lewis, David P.; Moffat, Bradford; Branch, Craig A.

    2007-01-01

    Continuous arterial spin labeling experiments typically use flow-driven adiabatic fast passage (AFP) inversion of the arterial blood water protons. In this article, we measure the effect of magnetization transfer in blood and how it affects the inversion label. We use modified Bloch equations to model flow-driven adiabatic inversion in the presence of magnetization transfer in blood flowing at velocities from 1 to 30 cm/s in order to explain our findings. Magnetization transfer results in a r...

  13. Experimental and theoretical investigations of photocurrents in non-centrosymmetric semiconductor quantum wells

    Energy Technology Data Exchange (ETDEWEB)

    Duc, Huynh Thanh; Foerstner, Jens; Meier, Torsten [Department of Physics and CeOPP, University Paderborn (Germany); Priyadarshi, Shekar; Racu, Ana Maria; Pierz, Klaus; Siegner, Uwe; Bieler, Mark [Physikalisch-Technische Bundesanstalt, Braunschweig (Germany)

    2010-07-01

    We compute photocurrents generated by femtosecond single-color laser pulses in non-centrosymmetric semiconductor quantum wells by combining a 14 x 14 k.p band structure theory with multi-band semiconductor Bloch equations. The transient photocurrents are investigated experimentally by measuring the associated Terahertz emission. The dependencies of the photocurrent and the Terahertz emission on the excitation conditions are discussed for (110)-oriented GaAs quantum wells. The comparison between theory and experiment shows a good agreement.

  14. Propagation of complex shaped ultrafast pulses in highly optically dense samples

    International Nuclear Information System (INIS)

    Davis, J. C.; Fetterman, M. R.; Warren, W. S.; Goswami, D.

    2008-01-01

    We examine the propagation of shaped (amplitude- and frequency-modulated) ultrafast laser pulses through optically dense rubidium vapor. Pulse reshaping, stimulated emission dynamics, and residual electronic excitation all strongly depend on the laser pulse shape. For example, frequency swept pulses, which produce adiabatic passage in the optically thin limit (independent of the sign of the frequency sweep), behave unexpectedly in optically dense samples. Paraxial Maxwell optical Bloch equations can model our ultrafast pulse propagation results well and provide insight

  15. On the Existence and the Applications of Modified Equations for Stochastic Differential Equations

    KAUST Repository

    Zygalakis, K. C.

    2011-01-01

    In this paper we describe a general framework for deriving modified equations for stochastic differential equations (SDEs) with respect to weak convergence. Modified equations are derived for a variety of numerical methods, such as the Euler or the Milstein method. Existence of higher order modified equations is also discussed. In the case of linear SDEs, using the Gaussianity of the underlying solutions, we derive an SDE which the numerical method solves exactly in the weak sense. Applications of modified equations in the numerical study of Langevin equations is also discussed. © 2011 Society for Industrial and Applied Mathematics.

  16. An Auxiliary Equation for the Bellman Equation in a One-Dimensional Ergodic Control

    International Nuclear Information System (INIS)

    Fujita, Y.

    2001-01-01

    In this paper we consider the Bellman equation in a one-dimensional ergodic control. Our aim is to show the existence and the uniqueness of its solution under general assumptions. For this purpose we introduce an auxiliary equation whose solution gives the invariant measure of the diffusion corresponding to an optimal control. Using this solution, we construct a solution to the Bellman equation. Our method of using this auxiliary equation has two advantages in the one-dimensional case. First, we can solve the Bellman equation under general assumptions. Second, this auxiliary equation gives an optimal Markov control explicitly in many examples

  17. Covariant field equations in supergravity

    Energy Technology Data Exchange (ETDEWEB)

    Vanhecke, Bram [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium); Ghent University, Faculty of Physics, Gent (Belgium); Proeyen, Antoine van [KU Leuven, Institute for Theoretical Physics, Leuven (Belgium)

    2017-12-15

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  18. Covariant field equations in supergravity

    International Nuclear Information System (INIS)

    Vanhecke, Bram; Proeyen, Antoine van

    2017-01-01

    Covariance is a useful property for handling supergravity theories. In this paper, we prove a covariance property of supergravity field equations: under reasonable conditions, field equations of supergravity are covariant modulo other field equations. We prove that for any supergravity there exist such covariant equations of motion, other than the regular equations of motion, that are equivalent to the latter. The relations that we find between field equations and their covariant form can be used to obtain multiplets of field equations. In practice, the covariant field equations are easily found by simply covariantizing the ordinary field equations. (copyright 2017 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

  19. Reduction of lattice equations to the Painlevé equations: PIV and PV

    Science.gov (United States)

    Nakazono, Nobutaka

    2018-02-01

    In this paper, we construct a new relation between Adler-Bobenko-Suris equations and Painlevé equations. Moreover, using this connection we construct the difference-differential Lax representations of the fourth and fifth Painlevé equations.

  20. Test equating methods and practices

    CERN Document Server

    Kolen, Michael J

    1995-01-01

    In recent years, many researchers in the psychology and statistical communities have paid increasing attention to test equating as issues of using multiple test forms have arisen and in response to criticisms of traditional testing techniques This book provides a practically oriented introduction to test equating which both discusses the most frequently used equating methodologies and covers many of the practical issues involved The main themes are - the purpose of equating - distinguishing between equating and related methodologies - the importance of test equating to test development and quality control - the differences between equating properties, equating designs, and equating methods - equating error, and the underlying statistical assumptions for equating The authors are acknowledged experts in the field, and the book is based on numerous courses and seminars they have presented As a result, educators, psychometricians, professionals in measurement, statisticians, and students coming to the subject for...

  1. On generalized fractional vibration equation

    International Nuclear Information System (INIS)

    Dai, Hongzhe; Zheng, Zhibao; Wang, Wei

    2017-01-01

    Highlights: • The paper presents a generalized fractional vibration equation for arbitrary viscoelastically damped system. • Some classical vibration equations can be derived from the developed equation. • The analytic solution of developed equation is derived under some special cases. • The generalized equation is particularly useful for developing new fractional equivalent linearization method. - Abstract: In this paper, a generalized fractional vibration equation with multi-terms of fractional dissipation is developed to describe the dynamical response of an arbitrary viscoelastically damped system. It is shown that many classical equations of motion, e.g., the Bagley–Torvik equation, can be derived from the developed equation. The Laplace transform is utilized to solve the generalized equation and the analytic solution under some special cases is derived. Example demonstrates the generalized transfer function of an arbitrary viscoelastic system.

  2. Differential equations for dummies

    CERN Document Server

    Holzner, Steven

    2008-01-01

    The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.

  3. Every Equation Tells a Story: Using Equation Dictionaries in Introductory Geophysics

    Science.gov (United States)

    Caplan-Auerbach, Jacqueline

    2009-01-01

    Many students view equations as a series of variables and operators into which numbers should be plugged rather than as representative of a physical process. To solve a problem they may simply look for an equation with the correct variables and assume it meets their needs, rather than selecting an equation that represents the appropriate physical…

  4. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J M [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  5. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks; Equations fondamentales des ecoulements diphasiques. Premiere partie: equations generales de conservation. Deuxieme partie: complements et remarques

    Energy Technology Data Exchange (ETDEWEB)

    Delhaye, J.M. [Commissariat a l' Energie Atomique, 38 - Grenoble (France). Centre d' Etudes Nucleaires

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  6. Equating TIMSS Mathematics Subtests with Nonlinear Equating Methods Using NEAT Design: Circle-Arc Equating Approaches

    Science.gov (United States)

    Ozdemir, Burhanettin

    2017-01-01

    The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test…

  7. Solving polynomial differential equations by transforming them to linear functional-differential equations

    OpenAIRE

    Nahay, John Michael

    2008-01-01

    We present a new approach to solving polynomial ordinary differential equations by transforming them to linear functional equations and then solving the linear functional equations. We will focus most of our attention upon the first-order Abel differential equation with two nonlinear terms in order to demonstrate in as much detail as possible the computations necessary for a complete solution. We mention in our section on further developments that the basic transformation idea can be generali...

  8. Lorentz-force equations as Heisenberg equations for a quantum system in the euclidean space

    International Nuclear Information System (INIS)

    Rodriguez D, R.

    2007-01-01

    In an earlier work, the dynamic equations for a relativistic charged particle under the action of electromagnetic fields were formulated by R. Yamaleev in terms of external, as well as internal momenta. Evolution equations for external momenta, the Lorentz-force equations, were derived from the evolution equations for internal momenta. The mapping between the observables of external and internal momenta are related by Viete formulae for a quadratic polynomial, the characteristic polynomial of the relativistic dynamics. In this paper we show that the system of dynamic equations, can be cast into the Heisenberg scheme for a four-dimensional quantum system. Within this scheme the equations in terms of internal momenta play the role of evolution equations for a state vector, whereas the external momenta obey the Heisenberg equation for an operator evolution. The solutions of the Lorentz-force equation for the motion inside constant electromagnetic fields are presented via pentagonometric functions. (Author)

  9. Differential Equation over Banach Algebra

    OpenAIRE

    Kleyn, Aleks

    2018-01-01

    In the book, I considered differential equations of order $1$ over Banach $D$-algebra: differential equation solved with respect to the derivative; exact differential equation; linear homogeneous equation. In noncommutative Banach algebra, initial value problem for linear homogeneous equation has infinitely many solutions.

  10. Elements of partial differential equations

    CERN Document Server

    Sneddon, Ian Naismith

    1957-01-01

    Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information on systems of surfaces, and solutions to the odd-numbered problems appear at the end of the book. Readers pursuing independent st

  11. New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method

    International Nuclear Information System (INIS)

    Kong Cuicui; Wang Dan; Song Lina; Zhang Hongqing

    2009-01-01

    In this paper, with the aid of symbolic computation and a general ansaetz, we presented a new extended rational expansion method to construct new rational formal exact solutions to nonlinear partial differential equations. In order to illustrate the effectiveness of this method, we apply it to the MKDV-Burgers equation and the (2 + 1)-dimensional dispersive long wave equation, then several new kinds of exact solutions are successfully obtained by using the new ansaetz. The method can also be applied to other nonlinear partial differential equations.

  12. Introduction to partial differential equations

    CERN Document Server

    Greenspan, Donald

    2000-01-01

    Designed for use in a one-semester course by seniors and beginning graduate students, this rigorous presentation explores practical methods of solving differential equations, plus the unifying theory underlying the mathematical superstructure. Topics include basic concepts, Fourier series, second-order partial differential equations, wave equation, potential equation, heat equation, approximate solution of partial differential equations, and more. Exercises appear at the ends of most chapters. 1961 edition.

  13. Improving the time efficiency of the Fourier synthesis method for slice selection in magnetic resonance imaging.

    Science.gov (United States)

    Tahayori, B; Khaneja, N; Johnston, L A; Farrell, P M; Mareels, I M Y

    2016-01-01

    The design of slice selective pulses for magnetic resonance imaging can be cast as an optimal control problem. The Fourier synthesis method is an existing approach to solve these optimal control problems. In this method the gradient field as well as the excitation field are switched rapidly and their amplitudes are calculated based on a Fourier series expansion. Here, we provide a novel insight into the Fourier synthesis method via representing the Bloch equation in spherical coordinates. Based on the spherical Bloch equation, we propose an alternative sequence of pulses that can be used for slice selection which is more time efficient compared to the original method. Simulation results demonstrate that while the performance of both methods is approximately the same, the required time for the proposed sequence of pulses is half of the original sequence of pulses. Furthermore, the slice selectivity of both sequences of pulses changes with radio frequency field inhomogeneities in a similar way. We also introduce a measure, referred to as gradient complexity, to compare the performance of both sequences of pulses. This measure indicates that for a desired level of uniformity in the excited slice, the gradient complexity for the proposed sequence of pulses is less than the original sequence. Copyright © 2015 Associazione Italiana di Fisica Medica. Published by Elsevier Ltd. All rights reserved.

  14. A New Fractional Projective Riccati Equation Method for Solving Fractional Partial Differential Equations

    International Nuclear Information System (INIS)

    Feng Qing-Hua

    2014-01-01

    In this paper, a new fractional projective Riccati equation method is proposed to establish exact solutions for fractional partial differential equations in the sense of modified Riemann—Liouville derivative. This method can be seen as the fractional version of the known projective Riccati equation method. For illustrating the validity of this method, we apply this method to solve the space-time fractional Whitham—Broer—Kaup (WBK) equations and the nonlinear fractional Sharma—Tasso—Olever (STO) equation, and as a result, some new exact solutions for them are obtained. (general)

  15. A new sine-Gordon equation expansion algorithm to investigate some special nonlinear differential equations

    International Nuclear Information System (INIS)

    Yan Zhenya

    2005-01-01

    A new transformation method is developed using the general sine-Gordon travelling wave reduction equation and a generalized transformation. With the aid of symbolic computation, this method can be used to seek more types of solutions of nonlinear differential equations, which include not only the known solutions derived by some known methods but new solutions. Here we choose the double sine-Gordon equation, the Magma equation and the generalized Pochhammer-Chree (PC) equation to illustrate the method. As a result, many types of new doubly periodic solutions are obtained. Moreover when using the method to these special nonlinear differential equations, some transformations are firstly needed. The method can be also extended to other nonlinear differential equations

  16. Singular stochastic differential equations

    CERN Document Server

    Cherny, Alexander S

    2005-01-01

    The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.

  17. Reactimeter dispersion equation

    OpenAIRE

    A.G. Yuferov

    2016-01-01

    The aim of this work is to derive and analyze a reactimeter metrological model in the form of the dispersion equation which connects reactimeter input/output signal dispersions with superimposed random noise at the inlet. It is proposed to standardize the reactimeter equation form, presenting the main reactimeter computing unit by a convolution equation. Hence, the reactimeter metrological characteristics are completely determined by this unit hardware function which represents a transient re...

  18. Symmetries and Invariants of the Time-dependent Oscillator Equation and the Envelope Equation

    CERN Document Server

    Qin, Hong

    2005-01-01

    Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

  19. A generalized fractional sub-equation method for fractional differential equations with variable coefficients

    International Nuclear Information System (INIS)

    Tang, Bo; He, Yinnian; Wei, Leilei; Zhang, Xindong

    2012-01-01

    In this Letter, a generalized fractional sub-equation method is proposed for solving fractional differential equations with variable coefficients. Being concise and straightforward, this method is applied to the space–time fractional Gardner equation with variable coefficients. As a result, many exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the considered method provides a very effective, convenient and powerful mathematical tool for solving many other fractional differential equations in mathematical physics. -- Highlights: ► Study of fractional differential equations with variable coefficients plays a role in applied physical sciences. ► It is shown that the proposed algorithm is effective for solving fractional differential equations with variable coefficients. ► The obtained solutions may give insight into many considerable physical processes.

  20. True amplitude wave equation migration arising from true amplitude one-way wave equations

    Science.gov (United States)

    Zhang, Yu; Zhang, Guanquan; Bleistein, Norman

    2003-10-01

    One-way wave operators are powerful tools for use in forward modelling and inversion. Their implementation, however, involves introduction of the square root of an operator as a pseudo-differential operator. Furthermore, a simple factoring of the wave operator produces one-way wave equations that yield the same travel times as the full wave equation, but do not yield accurate amplitudes except for homogeneous media and for almost all points in heterogeneous media. Here, we present augmented one-way wave equations. We show that these equations yield solutions for which the leading order asymptotic amplitude as well as the travel time satisfy the same differential equations as the corresponding functions for the full wave equation. Exact representations of the square-root operator appearing in these differential equations are elusive, except in cases in which the heterogeneity of the medium is independent of the transverse spatial variables. Here, we address the fully heterogeneous case. Singling out depth as the preferred direction of propagation, we introduce a representation of the square-root operator as an integral in which a rational function of the transverse Laplacian appears in the integrand. This allows us to carry out explicit asymptotic analysis of the resulting one-way wave equations. To do this, we introduce an auxiliary function that satisfies a lower dimensional wave equation in transverse spatial variables only. We prove that ray theory for these one-way wave equations leads to one-way eikonal equations and the correct leading order transport equation for the full wave equation. We then introduce appropriate boundary conditions at z = 0 to generate waves at depth whose quotient leads to a reflector map and an estimate of the ray theoretical reflection coefficient on the reflector. Thus, these true amplitude one-way wave equations lead to a 'true amplitude wave equation migration' (WEM) method. In fact, we prove that applying the WEM imaging condition

  1. Bose-Einstein condensates in optical lattices: Band-gap structure and solitons

    International Nuclear Information System (INIS)

    Louis, Pearl J. Y.; Kivshar, Yuri S.; Ostrovskaya, Elena A.; Savage, Craig M.

    2003-01-01

    We analyze the existence and stability of spatially extended (Bloch-type) and localized states of a Bose-Einstein condensate loaded into an optical lattice. In the framework of the Gross-Pitaevskii equation with a periodic potential, we study the band-gap structure of the matter-wave spectrum in both the linear and nonlinear regimes. We demonstrate the existence of families of spatially localized matter-wave gap solitons, and analyze their stability in different band gaps, for both repulsive and attractive atomic interactions

  2. First-order partial differential equations

    CERN Document Server

    Rhee, Hyun-Ku; Amundson, Neal R

    2001-01-01

    This first volume of a highly regarded two-volume text is fully usable on its own. After going over some of the preliminaries, the authors discuss mathematical models that yield first-order partial differential equations; motivations, classifications, and some methods of solution; linear and semilinear equations; chromatographic equations with finite rate expressions; homogeneous and nonhomogeneous quasilinear equations; formation and propagation of shocks; conservation equations, weak solutions, and shock layers; nonlinear equations; and variational problems. Exercises appear at the end of mo

  3. Equating Multidimensional Tests under a Random Groups Design: A Comparison of Various Equating Procedures

    Science.gov (United States)

    Lee, Eunjung

    2013-01-01

    The purpose of this research was to compare the equating performance of various equating procedures for the multidimensional tests. To examine the various equating procedures, simulated data sets were used that were generated based on a multidimensional item response theory (MIRT) framework. Various equating procedures were examined, including…

  4. Comparing the IRT Pre-equating and Section Pre-equating: A Simulation Study.

    Science.gov (United States)

    Hwang, Chi-en; Cleary, T. Anne

    The results obtained from two basic types of pre-equatings of tests were compared: the item response theory (IRT) pre-equating and section pre-equating (SPE). The simulated data were generated from a modified three-parameter logistic model with a constant guessing parameter. Responses of two replication samples of 3000 examinees on two 72-item…

  5. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2014-01-01

    A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or

  6. A new formulation of equations of compressible fluids by analogy with Maxwell's equations

    International Nuclear Information System (INIS)

    Kambe, Tsutomu

    2010-01-01

    A compressible ideal fluid is governed by Euler's equation of motion and equations of continuity, entropy and vorticity. This system can be reformulated in a form analogous to that of electromagnetism governed by Maxwell's equations with source terms. The vorticity plays the role of magnetic field, while the velocity field plays the part of a vector potential and the enthalpy (of isentropic flows) plays the part of a scalar potential in electromagnetism. The evolution of source terms of fluid Maxwell equations is determined by solving the equations of motion and continuity. The equation of sound waves can be derived from this formulation, where time evolution of the sound source is determined by the equation of motion. The theory of vortex sound of aeroacoustics is included in this formulation. It is remarkable that the forces acting on a point mass moving in a velocity field of an inviscid fluid are analogous in their form to the electric force and Lorentz force in electromagnetism. The significance of the reformulation is interpreted by examples taken from fluid mechanics. This formulation can be extended to viscous fluids without difficulty. The Maxwell-type equations are unchanged by the viscosity effect, although the source terms have additional terms due to viscosities.

  7. Degenerate nonlinear diffusion equations

    CERN Document Server

    Favini, Angelo

    2012-01-01

    The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...

  8. Computational partial differential equations using Matlab

    CERN Document Server

    Li, Jichun

    2008-01-01

    Brief Overview of Partial Differential Equations The parabolic equations The wave equations The elliptic equations Differential equations in broader areasA quick review of numerical methods for PDEsFinite Difference Methods for Parabolic Equations Introduction Theoretical issues: stability, consistence, and convergence 1-D parabolic equations2-D and 3-D parabolic equationsNumerical examples with MATLAB codesFinite Difference Methods for Hyperbolic Equations IntroductionSome basic difference schemes Dissipation and dispersion errors Extensions to conservation lawsThe second-order hyperbolic PDE

  9. Integrable systems of partial differential equations determined by structure equations and Lax pair

    International Nuclear Information System (INIS)

    Bracken, Paul

    2010-01-01

    It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a constraint equation is selected and imposed on the system of equations. This allows for the possibility of selecting the coefficients in the second fundamental form in a general way.

  10. Drift-Diffusion Equation

    Directory of Open Access Journals (Sweden)

    K. Banoo

    1998-01-01

    equation in the discrete momentum space. This is shown to be similar to the conventional drift-diffusion equation except that it is a more rigorous solution to the Boltzmann equation because the current and carrier densities are resolved into M×1 vectors, where M is the number of modes in the discrete momentum space. The mobility and diffusion coefficient become M×M matrices which connect the M momentum space modes. This approach is demonstrated by simulating electron transport in bulk silicon.

  11. Symmetries of the Euler compressible flow equations for general equation of state

    Energy Technology Data Exchange (ETDEWEB)

    Boyd, Zachary M. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Ramsey, Scott D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Baty, Roy S. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

    2015-10-15

    The Euler compressible flow equations exhibit different Lie symmetries depending on the equation of state (EOS) of the medium in which the flow occurs. This means that, in general, different types of similarity solution will be available in different flow media. We present a comprehensive classification of all EOS’s to which the Euler equations apply, based on the Lie symmetries admitted by the corresponding flow equations, restricting to the case of 1-D planar, cylindrical, or spherical geometry. The results are conveniently summarized in tables. This analysis also clarifies past work by Axford and Ovsiannikov on symmetry classification.

  12. Alternatives to the Dirac equation

    International Nuclear Information System (INIS)

    Girvin, S.M.; Brownstein, K.R.

    1975-01-01

    Recent work by Biedenharn, Han, and van Dam (BHvD) has questioned the uniqueness of the Dirac equation. BHvD have obtained a two-component equation as an alternate to the Dirac equation. Although they later show their alternative to be unitarily equivalent to the Dirac equation, certain physical differences were claimed. BHvD attribute the existence of this alternate equation to the fact that their factorizing matrices were position-dependent. To investigate this, we factor the Klein-Gordon equation in spherical coordinates allowing the factorizing matrices to depend arbitrarily upon theta and phi. It is shown that despite this additional freedom, and without involving any relativistic covariance, the conventional four-component Dirac equation is the only possibility

  13. Nonlinear differential equations

    Energy Technology Data Exchange (ETDEWEB)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics.

  14. Nonlinear differential equations

    International Nuclear Information System (INIS)

    Dresner, L.

    1988-01-01

    This report is the text of a graduate course on nonlinear differential equations given by the author at the University of Wisconsin-Madison during the summer of 1987. The topics covered are: direction fields of first-order differential equations; the Lie (group) theory of ordinary differential equations; similarity solutions of second-order partial differential equations; maximum principles and differential inequalities; monotone operators and iteration; complementary variational principles; and stability of numerical methods. The report should be of interest to graduate students, faculty, and practicing scientists and engineers. No prior knowledge is required beyond a good working knowledge of the calculus. The emphasis is on practical results. Most of the illustrative examples are taken from the fields of nonlinear diffusion, heat and mass transfer, applied superconductivity, and helium cryogenics

  15. Semilinear Schrödinger equations

    CERN Document Server

    Cazenave, Thierry

    2003-01-01

    The nonlinear Schrödinger equation has received a great deal of attention from mathematicians, in particular because of its applications to nonlinear optics. It is also a good model dispersive equation, since it is often technically simpler than other dispersive equations, such as the wave or Korteweg-de Vries equation. Particularly useful tools in studying the nonlinear Schrödinger equation are energy and Strichartz's estimates. This book presents various mathematical aspects of the nonlinear Schrödinger equation. It examines both problems of local nature (local existence of solutions, unique

  16. Quantum linear Boltzmann equation

    International Nuclear Information System (INIS)

    Vacchini, Bassano; Hornberger, Klaus

    2009-01-01

    We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.

  17. Exact Solutions to Nonlinear Schroedinger Equation and Higher-Order Nonlinear Schroedinger Equation

    International Nuclear Information System (INIS)

    Ren Ji; Ruan Hangyu

    2008-01-01

    We study solutions of the nonlinear Schroedinger equation (NLSE) and higher-order nonlinear Schroedinger equation (HONLSE) with variable coefficients. By considering all the higher-order effect of HONLSE as a new dependent variable, the NLSE and HONLSE can be changed into one equation. Using the generalized Lie group reduction method (GLGRM), the abundant solutions of NLSE and HONLSE are obtained

  18. Nonlinear diffusion equations

    CERN Document Server

    Wu Zhuo Qun; Li Hui Lai; Zhao Jun Ning

    2001-01-01

    Nonlinear diffusion equations, an important class of parabolic equations, come from a variety of diffusion phenomena which appear widely in nature. They are suggested as mathematical models of physical problems in many fields, such as filtration, phase transition, biochemistry and dynamics of biological groups. In many cases, the equations possess degeneracy or singularity. The appearance of degeneracy or singularity makes the study more involved and challenging. Many new ideas and methods have been developed to overcome the special difficulties caused by the degeneracy and singularity, which

  19. On the F-equation

    International Nuclear Information System (INIS)

    Kalinowski, M.W.; Szymanowski, L.

    1982-03-01

    A generalization of the Truesdell F-equations is proposed and some solutions to them - generalized Fox F-functions - are found. It is also shown that a non-linear difference-differential equation, which does not belong to the Truesdell class, nevertheless may be transformed into the standard F-equation. (author)

  20. How to obtain the covariant form of Maxwell's equations from the continuity equation

    Energy Technology Data Exchange (ETDEWEB)

    Heras, Jose A [Departamento de Ciencias Basicas, Universidad Autonoma Metropolitana, Unidad Azcapotzalco, Av. San Pablo No. 180, Col. Reynosa, 02200, Mexico D. F. (Mexico); Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prolongacion Paseo de la Reforma 880, Mexico D. F. 01210 (Mexico)

    2009-07-15

    The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom underlying these equations.

  1. Linear integral equations and soliton systems

    International Nuclear Information System (INIS)

    Quispel, G.R.W.

    1983-01-01

    A study is presented of classical integrable dynamical systems in one temporal and one spatial dimension. The direct linearizations are given of several nonlinear partial differential equations, for example the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the sine-Gordon equation, the nonlinear Schroedinger equation, and the equation of motion for the isotropic Heisenberg spin chain; the author also discusses several relations between these equations. The Baecklund transformations of these partial differential equations are treated on the basis of a singular transformation of the measure (or equivalently of the plane-wave factor) occurring in the corresponding linear integral equations, and the Baecklund transformations are used to derive the direct linearization of a chain of so-called modified partial differential equations. Finally it is shown that the singular linear integral equations lead in a natural way to the direct linearizations of various nonlinear difference-difference equations. (Auth.)

  2. Lectures on partial differential equations

    CERN Document Server

    Petrovsky, I G

    1992-01-01

    Graduate-level exposition by noted Russian mathematician offers rigorous, transparent, highly readable coverage of classification of equations, hyperbolic equations, elliptic equations and parabolic equations. Wealth of commentary and insight invaluable for deepening understanding of problems considered in text. Translated from the Russian by A. Shenitzer.

  3. Reduction operators of Burgers equation.

    Science.gov (United States)

    Pocheketa, Oleksandr A; Popovych, Roman O

    2013-02-01

    The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is presented, and the representation of the coefficients of operators in terms of solutions of the initial equation is constructed for this case. All possible nonclassical reductions of the Burgers equation to single ordinary differential equations are exhaustively described. Any Lie reduction of the Burgers equation proves to be equivalent via the Hopf-Cole transformation to a parameterized family of Lie reductions of the linear heat equation.

  4. The magnetic field experiment onboard Equator-S and its scientific possibilities

    Directory of Open Access Journals (Sweden)

    K.-H. Fornacon

    1999-12-01

    Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

  5. The magnetic field experiment onboard Equator-S and its scientific possibilities

    Directory of Open Access Journals (Sweden)

    K.-H. Fornacon

    Full Text Available The special feature of the ringcore fluxgate magnetometer on Equator-S is the high time and field resolution. The scientific aim of the experiment is the investigation of waves in the 10–100 picotesla range with a time resolution up to 64 Hz. The instrument characteristics and the influence of the spacecraft on the magnetic field measurement will be discussed. The work shows that the applied pre- and inflight calibration techniques are sufficient to suppress spacecraft interferences. The offset in spin axis direction was determined for the first time with an independent field measurement by the Equator-S Electron Drift Instrument. The data presented gives an impression of the accuracy of the measurement.

    Key words. Magnetospheric physics (instruments and techniques · Space plasma physics (instruments and techniques

  6. Methods for Equating Mental Tests.

    Science.gov (United States)

    1984-11-01

    1983) compared conventional and IRT methods for equating the Test of English as a Foreign Language ( TOEFL ) after chaining. Three conventional and...three IRT equating methods were examined in this study; two sections of TOEFL were each (separately) equated. The IRT methods included the following: (a...group. A separate base form was established for each of the six equating methods. Instead of equating the base-form TOEFL to itself, the last (eighth

  7. Supersymmetric quasipotential equations

    International Nuclear Information System (INIS)

    Zaikov, R.P.

    1981-01-01

    A supersymmetric extension of the Logunov-Tavkhelidze quasipotential approach is suggested. The supersymmetric Bethe- Salpeter equation is an initial equation. The transition from the four-time to the two-time Green function is made in the super- center-of-mass system. The two-time Green function has no inverse function in the whole spinor space. The resolvent operator if found using the Majorana character of the spinor wave function. The supersymmetric quasipotential equation is written. The consideration is carried out in the framework of the theory of chiral scalar superfields [ru

  8. Ordinary differential equations

    CERN Document Server

    Miller, Richard K

    1982-01-01

    Ordinary Differential Equations is an outgrowth of courses taught for a number of years at Iowa State University in the mathematics and the electrical engineering departments. It is intended as a text for a first graduate course in differential equations for students in mathematics, engineering, and the sciences. Although differential equations is an old, traditional, and well-established subject, the diverse backgrounds and interests of the students in a typical modern-day course cause problems in the selection and method of presentation of material. In order to compensate for this diversity,

  9. Uncertain differential equations

    CERN Document Server

    Yao, Kai

    2016-01-01

    This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors. It covers the analytic method and numerical method for solving uncertain differential equations, as well as their applications in the field of finance. Furthermore, the book provides a number of new potential research directions for uncertain differential equation. It will be of interest to researchers, engineers and students in the fields of mathematics, information science, operations research, industrial engineering, computer science, artificial intelligence, automation, economics, and management science.

  10. Introduction to nonlinear dispersive equations

    CERN Document Server

    Linares, Felipe

    2015-01-01

    This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...

  11. Generalized Lorentz-Force equations

    International Nuclear Information System (INIS)

    Yamaleev, R.M.

    2001-01-01

    Guided by Nambu (n+1)-dimensional phase space formalism we build a new system of dynamic equations. These equations describe a dynamic state of the corporeal system composed of n subsystems. The dynamic equations are formulated in terms of dynamic variables of the subsystems as well as in terms of dynamic variables of the corporeal system. These two sets of variables are related respectively as roots and coefficients of the n-degree polynomial equation. In the special n=2 case, this formalism reproduces relativistic dynamics for the charged spinning particles

  12. A new evolution equation

    International Nuclear Information System (INIS)

    Laenen, E.

    1995-01-01

    We propose a new evolution equation for the gluon density relevant for the region of small x B . It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multigluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed α s . We find that the effects of multigluon correlations on the deep-inelastic structure function are small. (orig.)

  13. Morphological, histological and molecular characterization of Myxobolus kingchowensis and Thelohanellus cf. sinensis infecting gibel carp Carassius auratus gibelio (Bloch, 1782).

    Science.gov (United States)

    Zhang, Bo; Zhai, Yanhua; Gu, Zemao; Liu, Yang

    2018-06-26

    A Myxobolus species and a Thelohanellus species infecting Carassius auratus gibelio (Bloch, 1782) were redescribed by their morphological, histological and molecular characterization. In the present study, the Myxobolus species infecting the muscle was identified as Myxobolus kingchowensis Chen et Ma, 1998 by the morphological and molecular data. Histologically, mature spores of M. kingchowensis were observed in the intercellular and connective tissue of muscle, though the plasmodia were not found. In addition, scattered spores also occurred in the intercellular of haematopoietic cells, intraepithelial of the renal tubules and interior of the melano-macrophage centres. Phylogenetic analysis showed that M. kingchowensis clustered in the clade of muscle-infecting Myxobolus species, further supporting muscle as the infection site of M. kingchowensis. The present Thelohanellus species infecting the gills was identified conspecific as Thelohanellus sinensis reported in Sun (2006) (mark it as T. sinensis-Sun)based on spore morphology, biological traits (host specificity and organ specificity), and molecular data. However, compared with the original description of T. sinensis Chen et Hsieh, 1960, the present Thelohanellus species and T. sinensis-Sun both infecting the gills of gibel carp are distinguishable from the original description in the host and infection site, which made the validity of T. sinensis-Sun dubious. Due to the absence of molecular data in the original description of T. sinensis, we suggest marking the present species and T. sinensis-Sun as T. cf. sinensis to avoid the confusion until T. sinensis is obtained from the type host and type infection site.

  14. Thermoviscous Model Equations in Nonlinear Acoustics

    DEFF Research Database (Denmark)

    Rasmussen, Anders Rønne

    Four nonlinear acoustical wave equations that apply to both perfect gasses and arbitrary fluids with a quadratic equation of state are studied. Shock and rarefaction wave solutions to the equations are studied. In order to assess the accuracy of the wave equations, their solutions are compared...... to solutions of the basic equations from which the wave equations are derived. A straightforward weakly nonlinear equation is the most accurate for shock modeling. A higher order wave equation is the most accurate for modeling of smooth disturbances. Investigations of the linear stability properties...... of solutions to the wave equations, reveal that the solutions may become unstable. Such instabilities are not found in the basic equations. Interacting shocks and standing shocks are investigated....

  15. Invalidity of the spectral Fokker-Planck equation forCauchy noise driven Langevin equation

    DEFF Research Database (Denmark)

    Ditlevsen, Ove Dalager

    2004-01-01

    -called alpha-stable noise (or Levy noise) the Fokker-Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. In stead it has been attempted to formulate an equation for the characteristic function (the Fourier transform...

  16. Difference equations theory, applications and advanced topics

    CERN Document Server

    Mickens, Ronald E

    2015-01-01

    THE DIFFERENCE CALCULUS GENESIS OF DIFFERENCE EQUATIONS DEFINITIONS DERIVATION OF DIFFERENCE EQUATIONS EXISTENCE AND UNIQUENESS THEOREM OPERATORS ∆ AND E ELEMENTARY DIFFERENCE OPERATORS FACTORIAL POLYNOMIALS OPERATOR ∆−1 AND THE SUM CALCULUS FIRST-ORDER DIFFERENCE EQUATIONS INTRODUCTION GENERAL LINEAR EQUATION CONTINUED FRACTIONS A GENERAL FIRST-ORDER EQUATION: GEOMETRICAL METHODS A GENERAL FIRST-ORDER EQUATION: EXPANSION TECHNIQUES LINEAR DIFFERENCE EQUATIONSINTRODUCTION LINEARLY INDEPENDENT FUNCTIONS FUNDAMENTAL THEOREMS FOR HOMOGENEOUS EQUATIONSINHOMOGENEOUS EQUATIONS SECOND-ORDER EQUATIONS STURM-LIOUVILLE DIFFERENCE EQUATIONS LINEAR DIFFERENCE EQUATIONS INTRODUCTION HOMOGENEOUS EQUATIONS CONSTRUCTION OF A DIFFERENCE EQUATION HAVING SPECIFIED SOLUTIONS RELATIONSHIP BETWEEN LINEAR DIFFERENCE AND DIFFERENTIAL EQUATIONS INHOMOGENEOUS EQUATIONS: METHOD OF UNDETERMINED COEFFICIENTS INHOMOGENEOUS EQUATIONS: OPERATOR METHODS z-TRANSFORM METHOD SYSTEMS OF DIFFERENCE EQUATIONS LINEAR PARTIAL DIFFERENCE EQUATI...

  17. Weak self-adjoint differential equations

    International Nuclear Information System (INIS)

    Gandarias, M L

    2011-01-01

    The concepts of self-adjoint and quasi self-adjoint equations were introduced by Ibragimov (2006 J. Math. Anal. Appl. 318 742-57; 2007 Arch. ALGA 4 55-60). In Ibragimov (2007 J. Math. Anal. Appl. 333 311-28), a general theorem on conservation laws was proved. In this paper, we generalize the concept of self-adjoint and quasi self-adjoint equations by introducing the definition of weak self-adjoint equations. We find a class of weak self-adjoint quasi-linear parabolic equations. The property of a differential equation to be weak self-adjoint is important for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)

  18. Modeling the diffusion magnetic resonance imaging signal inside neurons

    International Nuclear Information System (INIS)

    Nguyen, D V; Li, J R; Grebenkov, D S; Le Bihan, D

    2014-01-01

    The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times

  19. Solutions of system of P1 equations without use of auxiliary differential equations coupled

    International Nuclear Information System (INIS)

    Martinez, Aquilino Senra; Silva, Fernando Carvalho da; Cardoso, Carlos Eduardo Santos

    2000-01-01

    The system of P1 equations is composed by two equations coupled itself one for the neutron flux and other for the current. Usually this system is solved by definitions of two integrals parameters, which are named slowing down densities of the flux and the current. Hence, the system P1 can be change from integral to only two differential equations. However, there are two new differentials equations that may be solved with the initial system. The present work analyzes this procedure and studies a method, which solve the P1 equations directly, without definitions of slowing down densities. (author)

  20. The DD Cold Fusion-Transmutation Connection

    Science.gov (United States)

    Chubb, Talbot A.

    2005-12-01

    LENR theory must explain dd fusion, alpha-addition transmutations, radiationless nuclear reactions, and three-body nuclear particle reactions. Reaction without radiation requires many-body D Bloch+ periodicity in both location and internal structure dependencies. Electron scattering leads to mixed quantum states. The radiationless dd fusion reaction is 2-D Bloch+ -> {}4 He Bloch2+. Overlap between {}4 He Bloch2+ and surface Cs leads to alpha absorption. In the Iwamura et al. studies active deuterium is created by scattering at diffusion barriers.

  1. Equations of radiation hydrodynamics

    International Nuclear Information System (INIS)

    Mihalas, D.

    1982-01-01

    The purpose of this paper is to give an overview of the role of radiation in the transport of energy and momentum in a combined matter-radiation fluid. The transport equation for a moving radiating fluid is presented in both a fully Eulerian and a fully Lagrangian formulation, along with conservation equations describing the dynamics of the fluid. Special attention is paid to the problem of deriving equations that are mutually consistent in each frame, and between frames, to 0(v/c). A detailed analysis is made to show that in situations of broad interest, terms that are formally of 0(v/c) actually dominate the solution, demonstrating that it is esential (1) to pay scrupulous attention to the question of the frame dependence in formulating the equations; and (2) to solve the equations to 0(v/c) in quite general circumstances. These points are illustrated in the context of the nonequilibrium radiation diffusion limit, and a sketch of how the Lagrangian equations are to be solved will be presented

  2. The numerical solution of linear multi-term fractional differential equations: systems of equations

    Science.gov (United States)

    Edwards, John T.; Ford, Neville J.; Simpson, A. Charles

    2002-11-01

    In this paper, we show how the numerical approximation of the solution of a linear multi-term fractional differential equation can be calculated by reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity. We begin by showing how our method applies to a simple class of problems and we give a convergence result. We solve the Bagley Torvik equation as an example. We show how the method can be applied to a general linear multi-term equation and give two further examples.

  3. A Comparison of Kernel Equating and Traditional Equipercentile Equating Methods and the Parametric Bootstrap Methods for Estimating Standard Errors in Equipercentile Equating

    Science.gov (United States)

    Choi, Sae Il

    2009-01-01

    This study used simulation (a) to compare the kernel equating method to traditional equipercentile equating methods under the equivalent-groups (EG) design and the nonequivalent-groups with anchor test (NEAT) design and (b) to apply the parametric bootstrap method for estimating standard errors of equating. A two-parameter logistic item response…

  4. Weighted composition operators from Bergman-type spaces into ...

    Indian Academy of Sciences (India)

    Weighted composition operators from Bergman-type spaces into Bloch spaces and little. Bloch spaces are characterized by function theoretic properties of their inducing maps. Keywords. Weighted composition operator; Bergman-type space; Bloch space. 1. Introduction. Let D be the open unit disk in the complex plane C.

  5. Monge-Ampere equations and tensorial functors

    International Nuclear Information System (INIS)

    Tunitsky, Dmitry V

    2009-01-01

    We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

  6. Nonlinear integrodifferential equations as discrete systems

    Science.gov (United States)

    Tamizhmani, K. M.; Satsuma, J.; Grammaticos, B.; Ramani, A.

    1999-06-01

    We analyse a class of integrodifferential equations of the `intermediate long wave' (ILW) type. We show that these equations can be formally interpreted as discrete, differential-difference systems. This allows us to link equations of this type with previous results of ours involving differential-delay equations and, on the basis of this, propose new integrable equations of ILW type. Finally, we extend this approach to pure difference equations and propose ILW forms for the discrete lattice KdV equation.

  7. Trichromatic Open Digraphs for Understanding Qubits

    Directory of Open Access Journals (Sweden)

    Alex Lang

    2012-10-01

    Full Text Available We introduce a trichromatic graphical calculus for quantum computing. The generators represent three complementary observables that are treated on equal footing, hence reflecting the symmetries of the Bloch sphere. We derive the Euler angle decomposition of the Hadamard gate within it as well as the so-called supplementary relationships, which are valid equations for qubits that were not derivable within Z/X-calculus of Coecke and Duncan. More specifically, we have: dichromatic Z/X-calculus + Euler angle decomposition of the Hadamard gate = trichromatic calculus.

  8. Analytic solutions of hydrodynamics equations

    International Nuclear Information System (INIS)

    Coggeshall, S.V.

    1991-01-01

    Many similarity solutions have been found for the equations of one-dimensional (1-D) hydrodynamics. These special combinations of variables allow the partial differential equations to be reduced to ordinary differential equations, which must then be solved to determine the physical solutions. Usually, these reduced ordinary differential equations are solved numerically. In some cases it is possible to solve these reduced equations analytically to obtain explicit solutions. In this work a collection of analytic solutions of the 1-D hydrodynamics equations is presented. These can be used for a variety of purposes, including (i) numerical benchmark problems, (ii) as a basis for analytic models, and (iii) to provide insight into more complicated solutions

  9. The modified simplest equation method to look for exact solutions of nonlinear partial differential equations

    OpenAIRE

    Efimova, Olga Yu.

    2010-01-01

    The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.

  10. Equationally Noetherian property of Ershov algebras

    OpenAIRE

    Dvorzhetskiy, Yuriy

    2014-01-01

    This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.

  11. Differential equations extended to superspace

    International Nuclear Information System (INIS)

    Torres, J.; Rosu, H.C.

    2003-01-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  12. Differential equations extended to superspace

    Energy Technology Data Exchange (ETDEWEB)

    Torres, J. [Instituto de Fisica, Universidad de Guanajuato, A.P. E-143, Leon, Guanajuato (Mexico); Rosu, H.C. [Instituto Potosino de Investigacion Cientifica y Tecnologica, A.P. 3-74, Tangamanga, San Luis Potosi (Mexico)

    2003-07-01

    We present a simple SUSY Ns = 2 superspace extension of the differential equations in which the sought solutions are considered to be real superfields but maintaining the common derivative operators and the coefficients of the differential equations unaltered. In this way, we get self consistent systems of coupled differential equations for the components of the superfield. This procedure is applied to the Riccati equation, for which we obtain in addition the system of coupled equations corresponding to the components of the general superfield solution. (Author)

  13. Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

    International Nuclear Information System (INIS)

    Angilella, G.G.N.; Pucci, R.; March, N.H.

    2004-01-01

    We give here the derivation of a Gross-Pitaevskii-type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91, 030401 (2003)]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided

  14. Iterative Splitting Methods for Differential Equations

    CERN Document Server

    Geiser, Juergen

    2011-01-01

    Iterative Splitting Methods for Differential Equations explains how to solve evolution equations via novel iterative-based splitting methods that efficiently use computational and memory resources. It focuses on systems of parabolic and hyperbolic equations, including convection-diffusion-reaction equations, heat equations, and wave equations. In the theoretical part of the book, the author discusses the main theorems and results of the stability and consistency analysis for ordinary differential equations. He then presents extensions of the iterative splitting methods to partial differential

  15. Algorithm for research of mathematical physics equations symmetries. Symmetries of the free Schroedinger equation

    International Nuclear Information System (INIS)

    Kotel'nikov, G.A.

    1994-01-01

    An algorithm id proposed for research the symmetries of mathematical physics equation. The application of this algorithm to the Schroedinger equation permitted to establish, that in addition to the known symmetry the Schroedinger equation possesses also the relativistic symmetry

  16. Generalized quantal equation of motion

    International Nuclear Information System (INIS)

    Morsy, M.W.; Embaby, M.

    1986-07-01

    In the present paper, an attempt is made for establishing a generalized equation of motion for quantal objects, in which intrinsic self adjointness is naturally built in, independently of any prescribed representation. This is accomplished by adopting Hamilton's principle of least action, after incorporating, properly, the quantal features and employing the generalized calculus of variations, without being restricted to fixed end points representation. It turns out that our proposed equation of motion is an intrinsically self-adjoint Euler-Lagrange's differential equation that ensures extremization of the quantal action as required by Hamilton's principle. Time dependence is introduced and the corresponding equation of motion is derived, in which intrinsic self adjointness is also achieved. Reducibility of the proposed equation of motion to the conventional Schroedinger equation is examined. The corresponding continuity equation is established, and both of the probability density and the probability current density are identified. (author)

  17. Higher order field equations. II

    International Nuclear Information System (INIS)

    Tolhoek, H.A.

    1977-01-01

    In a previous paper wave propagation was studied according to a sixth-order partial differential equation involving a complex mass M. The corresponding Yang-Feldman integral equations (indicated as SM-YF-equations), were formulated using modified Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x), which then incorporate the partial differential equation together with certain boundary conditions. In this paper certain limit properties of these modified Green's functions are derived: (a) It is shown that for mod(M)→infinity the Green's functions Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) approach the Green's functions Δsub(R)(x) and Δsub(A)(x) of the corresponding KG-equation (Klein-Gordon equation). (b) It is further shown that the asymptotic behaviour of Gsub(R)sup(M)(x) and Gsub(A)sup(M)(x) is the same as of Δsub(R)(x) and Δsub(A)(x)-and also the same as for Dsub(R)(x) and Dsub(A)(x) for t→+-infinity;, where Dsub(R) and Dsub(A) are the Green's functions for the KG-equation with mass zero. It is essential to take limits in the sense of distribution theory in both cases (a) and (b). The property (b) indicates that the wave propagation properties of the SM-YF-equations, the KG-equation with finite mass and the KG-equation with mass zero are closely related in an asymptotic sense. (Auth.)

  18. Bäcklund transformation of fractional Riccati equation and its applications to nonlinear fractional partial differential equations

    International Nuclear Information System (INIS)

    Lu, Bin

    2012-01-01

    In this Letter, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the Bäcklund transformation of fractional Riccati equation are employed for constructing the exact solutions of nonlinear fractional partial differential equations. The power of this manageable method is presented by applying it to several examples. This approach can also be applied to other nonlinear fractional differential equations. -- Highlights: ► Backlund transformation of fractional Riccati equation is presented. ► A new method for solving nonlinear fractional differential equations is proposed. ► Three important fractional differential equations are solved successfully. ► Some new exact solutions of the fractional differential equations are obtained.

  19. Equational type logic

    NARCIS (Netherlands)

    Manca, V.; Salibra, A.; Scollo, Giuseppe

    1990-01-01

    Equational type logic is an extension of (conditional) equational logic, that enables one to deal in a single, unified framework with diverse phenomena such as partiality, type polymorphism and dependent types. In this logic, terms may denote types as well as elements, and atomic formulae are either

  20. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1994-01-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that the perpendicular component of Ohm's law be solved to ensure ∇·j=0 for energy conservation

  1. Model Compaction Equation

    African Journals Online (AJOL)

    The currently proposed model compaction equation was derived from data sourced from the. Niger Delta and it relates porosity to depth for sandstones under hydrostatic pressure condition. The equation is useful in predicting porosity and compaction trend in hydrostatic sands of the. Niger Delta. GEOLOGICAL SETTING OF ...

  2. Reduction of infinite dimensional equations

    Directory of Open Access Journals (Sweden)

    Zhongding Li

    2006-02-01

    Full Text Available In this paper, we use the general Legendre transformation to show the infinite dimensional integrable equations can be reduced to a finite dimensional integrable Hamiltonian system on an invariant set under the flow of the integrable equations. Then we obtain the periodic or quasi-periodic solution of the equation. This generalizes the results of Lax and Novikov regarding the periodic or quasi-periodic solution of the KdV equation to the general case of isospectral Hamiltonian integrable equation. And finally, we discuss the AKNS hierarchy as a special example.

  3. Impact of Salinity on the Incubation Rate and the Performance during the Nursery Phase of Square Head Climbing Perch (Anabas testudineus Bloch, 1792

    Directory of Open Access Journals (Sweden)

    Le, DV.

    2016-01-01

    Full Text Available Square head climbing perch (Anabas testudineus Bloch, 1792 is a high quality fish without small bones. It grows in a wide range of temperatures (10-42 oC, pH (3.5-9.5 and salinity (up to 16%. As regards climate change, this species may become important for aquaculture in the Tam Giang-Cau Hai lagoon near Hue city. To optimise the quality of fingerlings, we analyzed the effect of salinity levels on hatching and nursing in three subsequent experiments. Fertilization, hatching, survival and growth rates for 30 days were determined at salinity levels 0%, 5%, 7%, 13% and 15%. Water temperature and pH varied between 22-29.5 oC and 7.3-7.8, respectively. Between 0-5%, fertilization ratio was 77% to 83% and highest at 5%, but this dropped to 0% when salinity increased; hatching ratio was larger than 90%, but decreased to 0% at 13-15%. Between 0-11%, hatching time of fertilized eggs was not affected by salinity levels. The ratio of deformation gradually increased above 5%. After hatching at either 0 or 5%, survival ratios for square head climbing perch were above 13% up to 5%, but dropped to 0% at 9%. The growth after 30 days of nursing was higher at 5 and 7% compared with that of 0 and 3%.

  4. Detection of cyprinid herpesvirus 2 in peripheral blood cells of silver crucian carp, Carassius auratus gibelio (Bloch), suggests its potential in viral diagnosis.

    Science.gov (United States)

    Wang, H; Xu, Lj; Lu, Lq

    2016-02-01

    Epidemics caused by cyprinid herpesvirus 2 (CyHV-2) in domestic cyprinid species have been reported in both European and Asian countries. Although the mechanisms remain unknown, acute CyHV-2 infections generally result in high mortality, and the surviving carps become chronic carriers displaying no external clinical signs. In this study, in situ hybridization analysis showed that CyHV-2 tended to infect peripheral blood cells during either acute or chronic infections in silver crucian carp, Carassius auratus gibelio (Bloch). Laboratory challenge experiments coupled with real-time PCR quantification assays further indicated that steady-state levels of the viral genomic copy number in fish serum exhibited a typical 'one-step' growth curve post-viral challenge. Transcriptional expression of open reading frames (ORF) 121, which was selected due to its highest transcriptional levels in almost all tested tissues, was monitored to represent the replication kinetics of CyHV-2 in peripheral blood cells. Similar kinetic curve of active viral gene transcription in blood cells was obtained as that of serum viral load, indicating that CyHV-2 replicated in peripheral blood cells as well as in other well-characterized tissues. This study should pave the way for designing non-invasive and cost-effective serum diagnostic methods for quick detection of CyHV-2 infection. © 2015 John Wiley & Sons Ltd.

  5. Natural outbreak of Streptococcus agalactiae (GBS) infection in wild giant Queensland grouper, Epinephelus lanceolatus (Bloch), and other wild fish in northern Queensland, Australia.

    Science.gov (United States)

    Bowater, R O; Forbes-Faulkner, J; Anderson, I G; Condon, K; Robinson, B; Kong, F; Gilbert, G L; Reynolds, A; Hyland, S; McPherson, G; Brien, J O'; Blyde, D

    2012-03-01

    Ninety-three giant Queensland grouper, Epinephelus lanceolatus (Bloch), were found dead in Queensland, Australia, from 2007 to 2011. Most dead fish occurred in northern Queensland, with a peak of mortalities in Cairns in June 2008. In 2009, sick wild fish including giant sea catfish, Arius thalassinus (Rüppell), and javelin grunter, Pomadasys kaakan (Cuvier), also occurred in Cairns. In 2009 and 2010, two disease epizootics involving wild stingrays occurred at Sea World marine aquarium. Necropsy, histopathology, bacteriology and PCR determined that the cause of deaths of 12 giant Queensland grouper, three wild fish, six estuary rays, Dasyatis fluviorum (Ogilby), one mangrove whipray, Himantura granulata (Macleay), and one eastern shovelnose ray, Aptychotrema rostrata (Shaw), was Streptococcus agalactiae septicaemia. Biochemical testing of 34 S. agalactiae isolates from giant Queensland grouper, wild fish and stingrays showed all had identical biochemical profiles. The 16S rRNA gene sequences of isolates confirmed all isolates were S. agalactiae; genotyping of selected S. agalactiae isolates showed the isolates from giant Queensland grouper were serotype Ib, whereas isolates from wild fish and stingrays closely resembled serotype II. This is the first report of S. agalactiae from wild giant Queensland grouper and other wild tropical fish and stingray species in Queensland, Australia. © 2012 Blackwell Publishing Ltd and State of Queensland.

  6. Construction of Chained True Score Equipercentile Equatings under the Kernel Equating (KE) Framework and Their Relationship to Levine True Score Equating. Research Report. ETS RR-09-24

    Science.gov (United States)

    Chen, Haiwen; Holland, Paul

    2009-01-01

    In this paper, we develop a new chained equipercentile equating procedure for the nonequivalent groups with anchor test (NEAT) design under the assumptions of the classical test theory model. This new equating is named chained true score equipercentile equating. We also apply the kernel equating framework to this equating design, resulting in a…

  7. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2004-01-01

    This primer on elementary partial differential equations presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs. What makes this book unique is that it is a brief treatment, yet it covers all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. Mathematical ideas are motivated from physical problems, and the exposition is presented in a concise style accessible to science and engineering students; emphasis is on motivation, concepts, methods, and interpretation, rather than formal theory. This second edition contains new and additional exercises, and it includes a new chapter on the applications of PDEs to biology: age structured models, pattern formation; epidemic wave fronts, and advection-diffusion processes. The student who reads through this book and solves many of t...

  8. Equations of motion derived from a generalization of Einstein's equation for the gravitational field

    International Nuclear Information System (INIS)

    Mociutchi, C.

    1980-01-01

    The extended Einstein's equation, combined with a vectorial theory of maxwellian type of the gravitational field, leads to: a) the equation of motion; b) the equation of the trajectory for the static case of spherical symmetry, the test particle having a rest mass other than zero, and c) the propagation of light on null geodesics. All the basic tests of the theory given by Einstein's extended equation. Thus, the new theory of gravitation suggested by us is competitive. (author)

  9. The Wouthuysen equation

    NARCIS (Netherlands)

    M. Hazewinkel (Michiel)

    1995-01-01

    textabstractDedication: I dedicate this paper to Prof. P.C. Baayen, at the occasion of his retirement on 20 December 1994. The beautiful equation which forms the subject matter of this paper was invented by Wouthuysen after he retired. The four complex variable Wouthuysen equation arises from an

  10. Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation

    Directory of Open Access Journals (Sweden)

    V. O. Vakhnenko

    2016-01-01

    Full Text Available A variety of methods for examining the properties and solutions of nonlinear evolution equations are explored by using the Vakhnenko equation (VE as an example. The VE, which arises in modelling the propagation of high-frequency waves in a relaxing medium, has periodic and solitary traveling wave solutions some of which are loop-like in nature. The VE can be written in an alternative form, known as the Vakhnenko-Parkes equation (VPE, by a change of independent variables. The VPE has an N-soliton solution which is discussed in detail. Individual solitons are hump-like in nature whereas the corresponding solution to the VE comprises N-loop-like solitons. Aspects of the inverse scattering transform (IST method, as applied originally to the KdV equation, are used to find one- and two-soliton solutions to the VPE even though the VPE’s spectral equation is third-order and not second-order. A Bäcklund transformation for the VPE is used to construct conservation laws. The standard IST method for third-order spectral problems is used to investigate solutions corresponding to bound states of the spectrum and to a continuous spectrum. This leads to N-soliton solutions and M-mode periodic solutions, respectively. Interactions between these types of solutions are investigated.

  11. Parallels between control PDE's (Partial Differential Equations) and systems of ODE's (Ordinary Differential Equations)

    Science.gov (United States)

    Hunt, L. R.; Villarreal, Ramiro

    1987-01-01

    System theorists understand that the same mathematical objects which determine controllability for nonlinear control systems of ordinary differential equations (ODEs) also determine hypoellipticity for linear partial differentail equations (PDEs). Moreover, almost any study of ODE systems begins with linear systems. It is remarkable that Hormander's paper on hypoellipticity of second order linear p.d.e.'s starts with equations due to Kolmogorov, which are shown to be analogous to the linear PDEs. Eigenvalue placement by state feedback for a controllable linear system can be paralleled for a Kolmogorov equation if an appropriate type of feedback is introduced. Results concerning transformations of nonlinear systems to linear systems are similar to results for transforming a linear PDE to a Kolmogorov equation.

  12. Exact results for the Boltzmann equation and Smoluchowski's coagulation equation

    International Nuclear Information System (INIS)

    Hendriks, E.M.

    1983-01-01

    Almost no analytical solutions have been found for realistic intermolecular forces, largely due to the complicated structure of the collision term which calls for the construction of simplified models, in which as many physical properties are maintained as possible. In the first three chapters of this thesis such model Boltzmann equations are studied. Only spatially homogeneous gases with isotropic distribution functions are considered. Chapter I considers transition kernels, chapter II persistent scattering models and chapter III very hard particles. The second part of this dissertation deals with Smoluchowski's coagulation equation for the size distribution function in a coagulating system, with chapters devoted to the following topics: kinetics of gelation and universality, coagulation equations with gelation and exactly soluble models of nucleation. (Auth./C.F.)

  13. Hybrid quantum-classical master equations

    International Nuclear Information System (INIS)

    Diósi, Lajos

    2014-01-01

    We discuss hybrid master equations of composite systems, which are hybrids of classical and quantum subsystems. A fairly general form of hybrid master equations is suggested. Its consistency is derived from the consistency of Lindblad quantum master equations. We emphasize that quantum measurement is a natural example of exact hybrid systems. We derive a heuristic hybrid master equation of time-continuous position measurement (monitoring). (paper)

  14. Quantum equations from Brownian motions

    International Nuclear Information System (INIS)

    Rajput, B.S.

    2011-01-01

    Classical Schrodinger and Dirac equations have been derived from Brownian motions of a particle, it has been shown that the classical Schrodinger equation can be transformed to usual Schrodinger Quantum equation on applying Heisenberg uncertainty principle between position and momentum while Dirac Quantum equation follows it's classical counter part on applying Heisenberg uncertainly principle between energy and time without applying any analytical continuation. (author)

  15. B-splines and Faddeev equations

    International Nuclear Information System (INIS)

    Huizing, A.J.

    1990-01-01

    Two numerical methods for solving the three-body equations describing relativistic pion deuteron scattering have been investigated. For separable two body interactions these equations form a set of coupled one-dimensional integral equations. They are plagued by singularities which occur in the kernel of the integral equations as well as in the solution. The methods to solve these equations differ in the way they treat the singularities. First the Fuda-Stuivenberg method is discussed. The basic idea of this method is an one time iteration of the set of integral equations to treat the logarithmic singularities. In the second method, the spline method, the unknown solution is approximated by splines. Cubic splines have been used with cubic B-splines as basis. If the solution is approximated by a linear combination of basis functions, an integral equation can be transformed into a set of linear equations for the expansion coefficients. This set of linear equations is solved by standard means. Splines are determined by points called knots. A proper choice of splines to approach the solution stands for a proper choice of the knots. The solution of the three-body scattering equations has a square root behaviour at a certain point. Hence it was investigated how the knots should be chosen to approximate the square root function by cubic B-splines in an optimal way. Before applying this method to solve numerically the three-body equations describing pion-deuteron scattering, an analytically solvable example has been constructed with a singularity structure of both kernel and solution comparable to those of the three-body equations. The accuracy of the numerical solution was determined to a large extent by the accuracy of the approximation of the square root part. The results for a pion laboratory energy of 47.4 MeV agree very well with those from literature. In a complete calculation for 47.7 MeV the spline method turned out to be a factor thousand faster than the Fuda

  16. Reduced Braginskii equations

    International Nuclear Information System (INIS)

    Yagi, M.; Horton, W.

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite β that we solve the perpendicular component of Ohm's law to conserve the physical energy while ensuring the relation ∇ · j = 0

  17. New multiple soliton solutions to the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

    International Nuclear Information System (INIS)

    Chen Huaitang; Zhang Hongqing

    2004-01-01

    A generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation which has more new solutions. More new multiple soliton solutions are obtained for the general Burgers-Fisher equation and the Kuramoto-Sivashinsky equation

  18. An interpolation between the wave and diffusion equations through the fractional evolution equations Dirac like

    International Nuclear Information System (INIS)

    Pierantozzi, T.; Vazquez, L.

    2005-01-01

    Through fractional calculus and following the method used by Dirac to obtain his well-known equation from the Klein-Gordon equation, we analyze a possible interpolation between the Dirac and the diffusion equations in one space dimension. We study the transition between the hyperbolic and parabolic behaviors by means of the generalization of the D'Alembert formula for the classical wave equation and the invariance under space and time inversions of the interpolating fractional evolution equations Dirac like. Such invariance depends on the values of the fractional index and is related to the nonlocal property of the time fractional differential operator. For this system of fractional evolution equations, we also find an associated conserved quantity analogous to the Hamiltonian for the classical Dirac case

  19. Equationally Compact Acts : Coproducts / Peeter Normak

    Index Scriptorium Estoniae

    Normak, Peeter

    1998-01-01

    In this article equational compactness of acts and its generalizations are discussed. As equational compactness does not carry over to coproducts a slight generalization of c-equational campactness is introduced. It is proved that a coproduct of acts is c-equationally compact if and only if all components are c-equationally campact

  20. Supersymmetric two-particle equations

    International Nuclear Information System (INIS)

    Sissakyan, A.N.; Skachkov, N.B.; Shevchenko, O.Yu.

    1986-01-01

    In the framework of the scalar superfield model, a particular case of which is the well-known Wess-Zumino model, the supersymmetric Schwinger equations are found. On their basis with the use of the second Legendre transformation the two-particle supersymmetric Edwards and Bethe-Salpeter equations are derived. A connection of the kernels and inhomogeneous terms of these equations with generating functional of the second Legendre transformation is found

  1. Solving Ordinary Differential Equations

    Science.gov (United States)

    Krogh, F. T.

    1987-01-01

    Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.

  2. Numerical resolution of Navier-Stokes equations coupled to the heat equation

    International Nuclear Information System (INIS)

    Zenouda, Jean-Claude

    1970-08-01

    The author proves a uniqueness theorem for the time dependent Navier-Stokes equations coupled with heat flow in the two-dimensional case. He studies stability and convergence of several finite - difference schemes to solve these equations. Numerical experiments are done in the case of a square domain. (author) [fr

  3. Reduced Braginskii equations

    Energy Technology Data Exchange (ETDEWEB)

    Yagi, M. [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment; Horton, W. [Texas Univ., Austin, TX (United States). Inst. for Fusion Studies

    1993-11-01

    A set of reduced Braginskii equations is derived without assuming flute ordering and the Boussinesq approximation. These model equations conserve the physical energy. It is crucial at finite {beta} that we solve the perpendicular component of Ohm`s law to conserve the physical energy while ensuring the relation {del} {center_dot} j = 0.

  4. Analytical studies on pump-induced optical resonances in an M-type six-level system

    International Nuclear Information System (INIS)

    Ghosh, Saswata; Mandal, Swapan

    2010-01-01

    In the domain of semiclassical formulation and for the Doppler-free atom-field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.

  5. Improving multilevel Monte Carlo for stochastic differential equations with application to the Langevin equation.

    Science.gov (United States)

    Müller, Eike H; Scheichl, Rob; Shardlow, Tony

    2015-04-08

    This paper applies several well-known tricks from the numerical treatment of deterministic differential equations to improve the efficiency of the multilevel Monte Carlo (MLMC) method for stochastic differential equations (SDEs) and especially the Langevin equation. We use modified equations analysis as an alternative to strong-approximation theory for the integrator, and we apply this to introduce MLMC for Langevin-type equations with integrators based on operator splitting. We combine this with extrapolation and investigate the use of discrete random variables in place of the Gaussian increments, which is a well-known technique for the weak approximation of SDEs. We show that, for small-noise problems, discrete random variables can lead to an increase in efficiency of almost two orders of magnitude for practical levels of accuracy.

  6. A new sub-equation method applied to obtain exact travelling wave solutions of some complex nonlinear equations

    International Nuclear Information System (INIS)

    Zhang Huiqun

    2009-01-01

    By using a new coupled Riccati equations, a direct algebraic method, which was applied to obtain exact travelling wave solutions of some complex nonlinear equations, is improved. And the exact travelling wave solutions of the complex KdV equation, Boussinesq equation and Klein-Gordon equation are investigated using the improved method. The method presented in this paper can also be applied to construct exact travelling wave solutions for other nonlinear complex equations.

  7. Construction and accuracy of partial differential equation approximations to the chemical master equation.

    Science.gov (United States)

    Grima, Ramon

    2011-11-01

    The mesoscopic description of chemical kinetics, the chemical master equation, can be exactly solved in only a few simple cases. The analytical intractability stems from the discrete character of the equation, and hence considerable effort has been invested in the development of Fokker-Planck equations, second-order partial differential equation approximations to the master equation. We here consider two different types of higher-order partial differential approximations, one derived from the system-size expansion and the other from the Kramers-Moyal expansion, and derive the accuracy of their predictions for chemical reactive networks composed of arbitrary numbers of unimolecular and bimolecular reactions. In particular, we show that the partial differential equation approximation of order Q from the Kramers-Moyal expansion leads to estimates of the mean number of molecules accurate to order Ω(-(2Q-3)/2), of the variance of the fluctuations in the number of molecules accurate to order Ω(-(2Q-5)/2), and of skewness accurate to order Ω(-(Q-2)). We also show that for large Q, the accuracy in the estimates can be matched only by a partial differential equation approximation from the system-size expansion of approximate order 2Q. Hence, we conclude that partial differential approximations based on the Kramers-Moyal expansion generally lead to considerably more accurate estimates in the mean, variance, and skewness than approximations of the same order derived from the system-size expansion.

  8. Linear determining equations for differential constraints

    International Nuclear Information System (INIS)

    Kaptsov, O V

    1998-01-01

    A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical determining equations used in the search for admissible Lie operators. As applications of this approach equations of an ideal incompressible fluid and non-linear heat equations are discussed

  9. Transmission problem for the Laplace equation and the integral equation method

    Czech Academy of Sciences Publication Activity Database

    Medková, Dagmar

    2012-01-01

    Roč. 387, č. 2 (2012), s. 837-843 ISSN 0022-247X Institutional research plan: CEZ:AV0Z10190503 Keywords : transmission problem * Laplace equation * boundary integral equation Subject RIV: BA - General Mathematics Impact factor: 1.050, year: 2012 http://www.sciencedirect.com/science/article/pii/S0022247X11008985

  10. Introduction to partial differential equations

    CERN Document Server

    Borthwick, David

    2016-01-01

    This modern take on partial differential equations does not require knowledge beyond vector calculus and linear algebra. The author focuses on the most important classical partial differential equations, including conservation equations and their characteristics, the wave equation, the heat equation, function spaces, and Fourier series, drawing on tools from analysis only as they arise.Within each section the author creates a narrative that answers the five questions: (1) What is the scientific problem we are trying to understand? (2) How do we model that with PDE? (3) What techniques can we use to analyze the PDE? (4) How do those techniques apply to this equation? (5) What information or insight did we obtain by developing and analyzing the PDE? The text stresses the interplay between modeling and mathematical analysis, providing a thorough source of problems and an inspiration for the development of methods.

  11. Differential equations methods and applications

    CERN Document Server

    Said-Houari, Belkacem

    2015-01-01

    This book presents a variety of techniques for solving ordinary differential equations analytically and features a wealth of examples. Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory. To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class (of all disciplines) in ordinary differential equations. .

  12. Gauge-invariant flow equation

    Science.gov (United States)

    Wetterich, C.

    2018-06-01

    We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

  13. Fundamental equations for two-phase flow. Part 1: general conservation equations. Part 2: complement and remarks

    International Nuclear Information System (INIS)

    Delhaye, J.M.

    1968-12-01

    This report deals with the general equations of mass conservation, of momentum conservation, and energy conservation in the case of a two-phase flow. These equations are presented in several forms starting from integral equations which are assumed initially a priori. 1. Equations with local instantaneous variables, and interfacial conditions; 2. Equations with mean instantaneous variables in a cross-section, and practical applications: these equations include an important experimental value which is the ratio of the cross-section of passage of one phase to the total cross-section of a flow-tube. 3. Equations with a local statistical mean, and equations averaged over a period of time: A more advanced attempt to relate theory and experiment consists in taking the statistical averages of local equations. Equations are then obtained involving variables which are averaged over a period of time with the help of an ergodic assumption. 4. Combination of statistical averages and averages over a cross-section: in this study are considered the local variables averaged statistically, then averaged over the cross-section, and also the variables averaged over the section and then averaged statistically. 5. General equations concerning emulsions: In this case a phase exists in a locally very finely divided form. This peculiarity makes it possible to define a volume concentration, and to draw up equations which have numerous applications. - Certain points arising in the first part of this report concerning general mass conservation equations for two-phase flow have been completed and clarified. The terms corresponding to the interfacial tension have been introduced into the general equations. The interfacial conditions have thus been generalized. A supplementary step has still to be carried out: it has, in effect, been impossible to take the interfacial tension into account in the case of emulsions. It was then appeared interesting to compare this large group of fundamental

  14. Partial differential equations II elements of the modern theory equations with constant coefficients

    CERN Document Server

    Shubin, M

    1994-01-01

    This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

  15. Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

    Science.gov (United States)

    Adib, Arash; Poorveis, Davood; Mehraban, Farid

    2018-03-01

    In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

  16. INVARIANTS OF GENERALIZED RAPOPORT-LEAS EQUATIONS

    Directory of Open Access Journals (Sweden)

    Elena N. Kushner

    2018-01-01

    Full Text Available For the generalized Rapoport-Leas equations, algebra of differential invariants is constructed with respect to point transformations, that is, transformations of independent and dependent variables. The finding of a general transformation of this type reduces to solving an extremely complicated functional equation. Therefore, following the approach of Sophus Lie, we restrict ourselves to the search for infinitesimal transformations which are generated by translations along the trajectories of vector fields. The problem of finding these vector fields reduces to the redefined system decision of linear differential equations with respect to their coefficients. The Rapoport-Leas equations arise in the study of nonlinear filtration processes in porous media, as well as in other areas of natural science: for example, these equations describe various physical phenomena: two-phase filtration in a porous medium, filtration of a polytropic gas, and propagation of heat at nuclear explosion. They are vital topic for research: in recent works of Bibikov, Lychagin, and others, the analysis of the symmetries of the generalized Rapoport-Leas equations has been carried out; finite-dimensional dynamics and conditions of attractors existence have been found. Since the generalized RapoportLeas equations are nonlinear partial differential equations of the second order with two independent variables; the methods of the geometric theory of differential equations are used to study them in this paper. According to this theory differential equations generate subvarieties in the space of jets. This makes it possible to use the apparatus of modern differential geometry to study differential equations. We introduce the concept of admissible transformations, that is, replacements of variables that do not derive equations outside the class of the Rapoport-Leas equations. Such transformations form a Lie group. For this Lie group there are differential invariants that separate

  17. On matrix fractional differential equations

    Directory of Open Access Journals (Sweden)

    Adem Kılıçman

    2017-01-01

    Full Text Available The aim of this article is to study the matrix fractional differential equations and to find the exact solution for system of matrix fractional differential equations in terms of Riemann–Liouville using Laplace transform method and convolution product to the Riemann–Liouville fractional of matrices. Also, we show the theorem of non-homogeneous matrix fractional partial differential equation with some illustrative examples to demonstrate the effectiveness of the new methodology. The main objective of this article is to discuss the Laplace transform method based on operational matrices of fractional derivatives for solving several kinds of linear fractional differential equations. Moreover, we present the operational matrices of fractional derivatives with Laplace transform in many applications of various engineering systems as control system. We present the analytical technique for solving fractional-order, multi-term fractional differential equation. In other words, we propose an efficient algorithm for solving fractional matrix equation.

  18. Integral equations and their applications

    CERN Document Server

    Rahman, M

    2007-01-01

    For many years, the subject of functional equations has held a prominent place in the attention of mathematicians. In more recent years this attention has been directed to a particular kind of functional equation, an integral equation, wherein the unknown function occurs under the integral sign. The study of this kind of equation is sometimes referred to as the inversion of a definite integral. While scientists and engineers can already choose from a number of books on integral equations, this new book encompasses recent developments including some preliminary backgrounds of formulations of integral equations governing the physical situation of the problems. It also contains elegant analytical and numerical methods, and an important topic of the variational principles. Primarily intended for senior undergraduate students and first year postgraduate students of engineering and science courses, students of mathematical and physical sciences will also find many sections of direct relevance. The book contains eig...

  19. Equations of motion for a (non-linear) scalar field model as derived from the field equations

    International Nuclear Information System (INIS)

    Kaniel, S.; Itin, Y.

    2006-01-01

    The problem of derivation of the equations of motion from the field equations is considered. Einstein's field equations have a specific analytical form: They are linear in the second order derivatives and quadratic in the first order derivatives of the field variables. We utilize this particular form and propose a novel algorithm for the derivation of the equations of motion from the field equations. It is based on the condition of the balance between the singular terms of the field equation. We apply the algorithm to a non-linear Lorentz invariant scalar field model. We show that it results in the Newton law of attraction between the singularities of the field moved on approximately geodesic curves. The algorithm is applicable to the N-body problem of the Lorentz invariant field equations. (Abstract Copyright [2006], Wiley Periodicals, Inc.)

  20. Numerical modeling of optical coherent transient processes with complex configurations-III: Noisy laser source

    International Nuclear Information System (INIS)

    Chang Tiejun; Tian Mingzhen

    2007-01-01

    A previously developed numerical model based on Maxwell-Bloch equations was modified to simulate optical coherent transient and spectral hole burning processes with noisy laser sources. Random walk phase noise was simulated using laser-phase sequences generated numerically according to the normal distribution of the phase shift. The noise model was tested by comparing the simulated spectral hole burning effect with the analytical solution. The noise effects on a few typical optical coherence transient processes were investigated using this numerical tool. Flicker and random walk frequency noises were considered in accumulation process

  1. Signal generation in gas detectors

    International Nuclear Information System (INIS)

    Stillman, A.

    1993-01-01

    This tutorial describes the generation of electrical signals in gas detectors. Ionization of the gas by the passage of charged particles generates these signals. Starting with the Bethe-Bloch equation, the treatment is a general introduction to the production of ion-pairs in gas devices. I continue with the characterization of the ionization as an electrical signal, and calculate the signal current in a simple example. Another example demonstrates the effect of space charge on the design of a detector. The AGS Booster ionization profile monitor is a model for this calculation

  2. Calculations of resistivity and superconducting T/sub c/ in transition metals

    International Nuclear Information System (INIS)

    Allen, P.B.; Beaulac, T.P.; Khan, F.S.; Butler, W.H.; Pinski, F.J.; Swihart, J.C.

    1985-01-01

    A survey is given of various electron-phonon effects which have been calculated for the metals Nb, Mo, Ta, Pd, and Cu. These effects include the mass enhancement λ, superconducting T/sub c/, electrical and thermal resistivity, Hall coefficient, magnetoresistance, and the successfully tested predictions of linewidths γ 0 of phonons. The calculations use local density approximations (LDA) energy bands, experimental phonons, and the rigid muffin tin (RMT) approximation. Mesh size noise is less than 1% and the Bloch-Boltzmann integral equation has been solved to unprecedented accuracy

  3. Theoretical calculation of saturated absorption for multilevel atoms

    International Nuclear Information System (INIS)

    O'Kane, T.J.; Scholten, R.E.; Farrell, P.M.

    1998-01-01

    We present the first theoretical saturated absorption spectra for general multi-level atoms, using a model based on extensions of the optical Bloch equations, and using Monte Carlo averaging of the absorption of individual atoms with random trajectories through a standing wave. We are for the first time able to accurately predict the merging of hyperfine and cross-over resonances due to intensity dependent phenomena such as power broadening. Results for 20-level sodium and 24-level rubidium models are presented and compared to experiment, demonstrating excellent agreement

  4. The relativistic electron wave equation

    International Nuclear Information System (INIS)

    Dirac, P.A.M.

    1977-08-01

    The paper was presented at the European Conference on Particle Physics held in Budapest between the 4th and 9th July of 1977. A short review is given on the birth of the relativistic electron wave equation. After Schroedinger has shown the equivalence of his wave mechanics and the matrix mechanics of Heisenberg, a general transformation theory was developed by the author. This theory required a relativistic wave equation linear in delta/delta t. As the Klein--Gordon equation available at this time did not satisfy this condition the development of a new equation became necessary. The equation which was found gave the value of the electron spin and magnetic moment automatically. (D.P.)

  5. Equation with the many fathers

    DEFF Research Database (Denmark)

    Kragh, Helge

    1984-01-01

    In this essay I discuss the origin and early development of the first relativistic wave equation, known as the Klein-Gordon equation. In 1926 several physicists, among them Klein, Fock, Schrödinger, and de Broglie, announced this equation as a candidate for a relativistic generalization of the us...... as electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....... of the usual Schrödinger equation. In most of the early versions the Klein-Gordon equation was connected with the general theory of relativity. Klein and some other physicists attempted to express quantum mechanics within a five-dimensional unified theory, embracing general relativity as well...

  6. Atomic mirrors for a Λ-type three-level atom

    International Nuclear Information System (INIS)

    Felemban, Nuha; Aldossary, Omar M; Lembessis, Vassilis E

    2014-01-01

    We propose atom mirror schemes for a three-level atom of Λ-type interacting with two evanescent fields, which are generated as a result of the total internal reflection of two coherent Gaussian laser beams at the interface of a dielectric prism with vacuum. The forces acting on the atom are derived by means of optical Bloch equations, based on the atomic density matrix elements. The theory is illustrated by setting up the equations of motion for 23 Na atom. Two types of excited schemes are examined, namely the cases in which the evanescent fields have polarization types of σ + −σ − and σ + −π. The equations are solved numerically and we get results for atomic trajectories for different parameters. The performance of the mirror for the two types of polarization schemes is quantified and discussed. The possibility of reflecting atoms at pre-determined directions is also discussed. (paper)

  7. Solving (2 + 1)-dimensional sine-Poisson equation by a modified variable separated ordinary differential equation method

    International Nuclear Information System (INIS)

    Ka-Lin, Su; Yuan-Xi, Xie

    2010-01-01

    By introducing a more general auxiliary ordinary differential equation (ODE), a modified variable separated ordinary differential equation method is presented for solving the (2 + 1)-dimensional sine-Poisson equation. As a result, many explicit and exact solutions of the (2 + 1)-dimensional sine-Poisson equation are derived in a simple manner by this technique. (general)

  8. On the Saha Ionization Equation

    Indian Academy of Sciences (India)

    Abstract. We revisit the Saha Ionization Equation in order to highlightthe rich interdisciplinary content of the equation thatstraddles distinct areas of spectroscopy, thermodynamics andchemical reactions. In a self-contained discussion, relegatedto an appendix, we delve further into the hidden message ofthe equation in terms ...

  9. Application of a Lie group admitted by a homogeneous equation for group classification of a corresponding inhomogeneous equation

    Science.gov (United States)

    Long, Feng-Shan; Karnbanjong, Adisak; Suriyawichitseranee, Amornrat; Grigoriev, Yurii N.; Meleshko, Sergey V.

    2017-07-01

    This paper proposes an algorithm for group classification of a nonhomogeneous equation using the group analysis provided for the corresponding homogeneous equation. The approach is illustrated by a partial differential equation, an integro-differential equation, and a delay partial differential equation.

  10. Neoclassical MHD equations for tokamaks

    International Nuclear Information System (INIS)

    Callen, J.D.; Shaing, K.C.

    1986-03-01

    The moment equation approach to neoclassical-type processes is used to derive the flows, currents and resistive MHD-like equations for studying equilibria and instabilities in axisymmetric tokamak plasmas operating in the banana-plateau collisionality regime (ν* approx. 1). The resultant ''neoclassical MHD'' equations differ from the usual reduced equations of resistive MHD primarily by the addition of the important viscous relaxation effects within a magnetic flux surface. The primary effects of the parallel (poloidal) viscous relaxation are: (1) Rapid (approx. ν/sub i/) damping of the poloidal ion flow so the residual flow is only toroidal; (2) addition of the bootstrap current contribution to Ohm's laws; and (3) an enhanced (by B 2 /B/sub theta/ 2 ) polarization drift type term and consequent enhancement of the perpendicular dielectric constant due to parallel flow inertia, which causes the equations to depend only on the poloidal magnetic field B/sub theta/. Gyroviscosity (or diamagnetic vfiscosity) effects are included to properly treat the diamagnetic flow effects. The nonlinear form of the neoclassical MHD equations is derived and shown to satisfy an energy conservation equation with dissipation arising from Joule and poloidal viscous heating, and transport due to classical and neoclassical diffusion

  11. The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV-MKdV, Broer-Kaup-Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs

  12. On the relation between elementary partial difference equations and partial differential equations

    NARCIS (Netherlands)

    van den Berg, I.P.

    1998-01-01

    The nonstandard stroboscopy method links discrete-time ordinary difference equations of first-order and continuous-time, ordinary differential equations of first order. We extend this method to the second order, and also to an elementary, yet general class of partial difference/differential

  13. A novel numerical flux for the 3D Euler equations with general equation of state

    KAUST Repository

    Toro, Eleuterio F.; Castro, Cristó bal E.; Bok Jik, Lee

    2015-01-01

    Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on general meshes; (ii) we use a general equation of state; and (iii) we achieve high order of accuracy in both

  14. From ordinary to partial differential equations

    CERN Document Server

    Esposito, Giampiero

    2017-01-01

    This book is addressed to mathematics and physics students who want to develop an interdisciplinary view of mathematics, from the age of Riemann, Poincaré and Darboux to basic tools of modern mathematics. It enables them to acquire the sensibility necessary for the formulation and solution of difficult problems, with an emphasis on concepts, rigour and creativity. It consists of eight self-contained parts: ordinary differential equations; linear elliptic equations; calculus of variations; linear and non-linear hyperbolic equations; parabolic equations; Fuchsian functions and non-linear equations; the functional equations of number theory; pseudo-differential operators and pseudo-differential equations. The author leads readers through the original papers and introduces new concepts, with a selection of topics and examples that are of high pedagogical value.

  15. Completely integrable operator evolutionary equations

    International Nuclear Information System (INIS)

    Chudnovsky, D.V.

    1979-01-01

    The authors present natural generalizations of classical completely integrable equations where the functions are replaced by arbitrary operators. Among these equations are the non-linear Schroedinger, the Korteweg-de Vries, and the modified KdV equations. The Lax representation and the Baecklund transformations are presented. (Auth.)

  16. On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

    International Nuclear Information System (INIS)

    Kawashima, S.; Matsumara, A.; Nishida, T.

    1979-01-01

    The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay rate tsup(-5/4)) as t → + infinitely to that of the compressible Navier-Stokes equation for the corresponding initial data. (orig.) 891 HJ/orig. 892 MKO

  17. Solution of radial spin-1 field equation in Robertson-Walker space-time via Heun's equation

    International Nuclear Information System (INIS)

    Zecca, A.

    2010-01-01

    The spin-1 field equation is considered in Robertson-Walker spacetime. The problem of the solution of the separated radial equations, previously discussed in the flat space-time case, is solved also for both the closed and open curvature case. The radial equation is reduced to Heun's differential equation that recently has been widely reconsidered. It is shown that the solution of the present Heun equation does not fall into the class of polynomial-like or hypergeometric functions. Heun's operator results also non-factorisable. The properties follow from application of general theorems and power series expansion. In the positive curvature case of the universe a discrete energy spectrum of the system is found. The result follows by requiring a polynomial-like behaviour of at least one component of the spinor field. Developments and applications of the theory suggest further study of the solution of Heun's equation.

  18. Differential equations I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Differential Equations I covers first- and second-order equations, series solutions, higher-order linear equations, and the Laplace transform.

  19. Beginning partial differential equations

    CERN Document Server

    O'Neil, Peter V

    2011-01-01

    A rigorous, yet accessible, introduction to partial differential equations-updated in a valuable new edition Beginning Partial Differential Equations, Second Edition provides a comprehensive introduction to partial differential equations (PDEs) with a special focus on the significance of characteristics, solutions by Fourier series, integrals and transforms, properties and physical interpretations of solutions, and a transition to the modern function space approach to PDEs. With its breadth of coverage, this new edition continues to present a broad introduction to the field, while also addres

  20. Modeling of optical fields in laser microcavities using a modal method

    DEFF Research Database (Denmark)

    Gregersen, Niels

    2013-01-01

    mechanism limiting the Q factor is the poor modal overlap between the cavity Bloch mode and the mirror Bloch mode. Also, the strong connement will generally lead to highly divergent far field patterns and thus low collection efficiency. In this scenario, Bloch-wave engineering [1] and the introduction...... of adiabatic transitions emerge as powerful design tools to control the optical mode. In the modal method, the eld is expanded on the eigenmodes of z-invariant layers and on the Bloch modes of periodic sections. Using mode matching at the interfaces, the method gives direct access to re ection and transmission...

  1. Banking on the equator. Are banks that adopted the equator principles different from non-adopters?

    NARCIS (Netherlands)

    Scholtens, B.; Dam, L.

    We analyze the performance of banks that adopted the Equator Principles. The Equator Principles are designed to assure sustainable development in project finance. The social, ethical, and environmental policies of the adopters differ significantly from those of banks that did not adopt the Equator

  2. Hartree--Fock density matrix equation

    International Nuclear Information System (INIS)

    Cohen, L.; Frishberg, C.

    1976-01-01

    An equation for the Hartree--Fock density matrix is discussed and the possibility of solving this equation directly for the density matrix instead of solving the Hartree--Fock equation for orbitals is considered. Toward that end the density matrix is expanded in a finite basis to obtain the matrix representative equation. The closed shell case is considered. Two numerical schemes are developed and applied to a number of examples. One example is given where the standard orbital method does not converge while the method presented here does

  3. Exact solutions to sine-Gordon-type equations

    International Nuclear Information System (INIS)

    Liu Shikuo; Fu Zuntao; Liu Shida

    2006-01-01

    In this Letter, sine-Gordon-type equations, including single sine-Gordon equation, double sine-Gordon equation and triple sine-Gordon equation, are systematically solved by Jacobi elliptic function expansion method. It is shown that different transformations for these three sine-Gordon-type equations play different roles in obtaining exact solutions, some transformations may not work for a specific sine-Gordon equation, while work for other sine-Gordon equations

  4. dimensional Jaulent–Miodek equations

    Indian Academy of Sciences (India)

    (2+1)-dimensional Jaulent–Miodek equation; the first integral method; kinks; ... and effective method for solving nonlinear partial differential equations which can ... of the method employed and exact kink and soliton solutions are constructed ...

  5. Random walk and the heat equation

    CERN Document Server

    Lawler, Gregory F

    2010-01-01

    The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation by considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equation and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. The first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For exa...

  6. On integrability of the Killing equation

    Science.gov (United States)

    Houri, Tsuyoshi; Tomoda, Kentaro; Yasui, Yukinori

    2018-04-01

    Killing tensor fields have been thought of as describing the hidden symmetry of space(-time) since they are in one-to-one correspondence with polynomial first integrals of geodesic equations. Since many problems in classical mechanics can be formulated as geodesic problems in curved space and spacetime, solving the defining equation for Killing tensor fields (the Killing equation) is a powerful way to integrate equations of motion. Thus it has been desirable to formulate the integrability conditions of the Killing equation, which serve to determine the number of linearly independent solutions and also to restrict the possible forms of solutions tightly. In this paper, we show the prolongation for the Killing equation in a manner that uses Young symmetrizers. Using the prolonged equations, we provide the integrability conditions explicitly.

  7. Algebraic entropy for differential-delay equations

    OpenAIRE

    Viallet, Claude M.

    2014-01-01

    We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations.

  8. Hyperbolic partial differential equations

    CERN Document Server

    Witten, Matthew

    1986-01-01

    Hyperbolic Partial Differential Equations III is a refereed journal issue that explores the applications, theory, and/or applied methods related to hyperbolic partial differential equations, or problems arising out of hyperbolic partial differential equations, in any area of research. This journal issue is interested in all types of articles in terms of review, mini-monograph, standard study, or short communication. Some studies presented in this journal include discretization of ideal fluid dynamics in the Eulerian representation; a Riemann problem in gas dynamics with bifurcation; periodic M

  9. Dynamical equations for the optical potential

    International Nuclear Information System (INIS)

    Kowalski, K.L.

    1981-01-01

    Dynamical equations for the optical potential are obtained starting from a wide class of N-particle equations. This is done with arbitrary multiparticle interactions to allow adaptation to few-body models of nuclear reactions and including all effects of nucleon identity. Earlier forms of the optical potential equations are obtained as special cases. Particular emphasis is placed upon obtaining dynamical equations for the optical potential from the equations of Kouri, Levin, and Tobocman including all effects of particle identity

  10. Group foliation of finite difference equations

    Science.gov (United States)

    Thompson, Robert; Valiquette, Francis

    2018-06-01

    Using the theory of equivariant moving frames, a group foliation method for invariant finite difference equations is developed. This method is analogous to the group foliation of differential equations and uses the symmetry group of the equation to decompose the solution process into two steps, called resolving and reconstruction. Our constructions are performed algorithmically and symbolically by making use of discrete recurrence relations among joint invariants. Applications to invariant finite difference equations that approximate differential equations are given.

  11. Manhattan equation for the operational amplifier

    OpenAIRE

    Mishonov, Todor M.; Danchev, Victor I.; Petkov, Emil G.; Gourev, Vassil N.; Dimitrova, Iglika M.; Varonov, Albert M.

    2018-01-01

    A differential equation relating the voltage at the output of an operational amplifier $U_0$ and the difference between the input voltages ($U_{+}$ and $U_{-}$) has been derived. The crossover frequency $f_0$ is a parameter in this operational amplifier master equation. The formulas derived as a consequence of this equation find applications in thousands of specifications for electronic devices but as far as we know, the equation has never been published. Actually, the master equation of oper...

  12. Benney's long wave equations

    International Nuclear Information System (INIS)

    Lebedev, D.R.

    1979-01-01

    Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown

  13. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  14. Solving Nonlinear Coupled Differential Equations

    Science.gov (United States)

    Mitchell, L.; David, J.

    1986-01-01

    Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.

  15. Structural Equation and Mei Conserved Quantity of Mei Symmetry for Appell Equations in Holonomic Systems with Unilateral Constraints

    International Nuclear Information System (INIS)

    Jia Liqun; Cui Jinchao; Zhang Yaoyu; Luo Shaokai

    2009-01-01

    Structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints are investigated. Appell equations and differential equations of motion for holonomic mechanic systems with unilateral constraints are established. The definition and the criterion of Mei symmetry for Appell equations in holonomic systems with unilateral constraints under the infinitesimal transformations of groups are also given. The expressions of the structural equation and Mei conserved quantity of Mei symmetry for Appell equations in holonomic systems with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results. (general)

  16. Direct 'delay' reductions of the Toda equation

    International Nuclear Information System (INIS)

    Joshi, Nalini

    2009-01-01

    A new direct method of obtaining reductions of the Toda equation is described. We find a canonical and complete class of all possible reductions under certain assumptions. The resulting equations are ordinary differential-difference equations, sometimes referred to as delay-differential equations. The representative equation of this class is hypothesized to be a new version of one of the classical Painleve equations. The Lax pair associated with this equation is obtained, also by reduction. (fast track communication)

  17. Reduction of the equation for lower hybrid waves in a plasma to a nonlinear Schroedinger equation

    Science.gov (United States)

    Karney, C. F. F.

    1977-01-01

    Equations describing the nonlinear propagation of waves in an anisotropic plasma are rarely exactly soluble. However it is often possible to make approximations that reduce the exact equations into a simpler equation. The use of MACSYMA to make such approximations, and so reduce the equation describing lower hybrid waves into the nonlinear Schrodinger equation which is soluble by the inverse scattering method is demonstrated. MACSYMA is used at several stages in the calculation only because there is a natural division between calculations that are easiest done by hand, and those that are easiest done by machine.

  18. Quadratic Diophantine equations

    CERN Document Server

    Andreescu, Titu

    2015-01-01

    This monograph treats the classical theory of quadratic Diophantine equations and guides the reader through the last two decades of computational techniques and progress in the area. These new techniques combined with the latest increases in computational power shed new light on important open problems. The authors motivate the study of quadratic Diophantine equations with excellent examples, open problems, and applications. Moreover, the exposition aptly demonstrates many applications of results and techniques from the study of Pell-type equations to other problems in number theory. The book is intended for advanced undergraduate and graduate students as well as researchers. It challenges the reader to apply not only specific techniques and strategies, but also to employ methods and tools from other areas of mathematics, such as algebra and analysis.

  19. Quantum-statistical kinetic equations

    International Nuclear Information System (INIS)

    Loss, D.; Schoeller, H.

    1989-01-01

    Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors, P q -rule, etc.) to nonequilibrium systems described by a density operator ρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived

  20. A linearizing transformation for the Korteweg-de Vries equation; generalizations to higher-dimensional nonlinear partial differential equations

    NARCIS (Netherlands)

    Dorren, H.J.S.

    1998-01-01

    It is shown that the Korteweg–de Vries (KdV) equation can be transformed into an ordinary linear partial differential equation in the wave number domain. Explicit solutions of the KdV equation can be obtained by subsequently solving this linear differential equation and by applying a cascade of

  1. PREFACE: Symmetries and integrability of difference equations Symmetries and integrability of difference equations

    Science.gov (United States)

    Levi, Decio; Olver, Peter; Thomova, Zora; Winternitz, Pavel

    2009-11-01

    The concept of integrability was introduced in classical mechanics in the 19th century for finite dimensional continuous Hamiltonian systems. It was extended to certain classes of nonlinear differential equations in the second half of the 20th century with the discovery of the inverse scattering transform and the birth of soliton theory. Also at the end of the 19th century Lie group theory was invented as a powerful tool for obtaining exact analytical solutions of large classes of differential equations. Together, Lie group theory and integrability theory in its most general sense provide the main tools for solving nonlinear differential equations. Like differential equations, difference equations play an important role in physics and other sciences. They occur very naturally in the description of phenomena that are genuinely discrete. Indeed, they may actually be more fundamental than differential equations if space-time is actually discrete at very short distances. On the other hand, even when treating continuous phenomena described by differential equations it is very often necessary to resort to numerical methods. This involves a discretization of the differential equation, i.e. a replacement of the differential equation by a difference one. Given the well developed and understood techniques of symmetry and integrability for differential equations a natural question to ask is whether it is possible to develop similar techniques for difference equations. The aim is, on one hand, to obtain powerful methods for solving `integrable' difference equations and to establish practical integrability criteria, telling us when the methods are applicable. On the other hand, Lie group methods can be adapted to solve difference equations analytically. Finally, integrability and symmetry methods can be combined with numerical methods to obtain improved numerical solutions of differential equations. The origin of the SIDE meetings goes back to the early 1990s and the first

  2. Local instant conservation equations

    International Nuclear Information System (INIS)

    Delaje, Dzh.

    1984-01-01

    Local instant conservation equations for two-phase flow are derived. Derivation of the equation starts from the recording of integral laws of conservation for a fixed reference volume, containing both phases. Transformation of the laws, using the Leibniz rule and Gauss theory permits to obtain the sum of two integrals as to the volume and integral as to the surface. Integrals as to the volume result in local instant differential equations, in particular derivatives for each phase, and integrals as to the surface reflect local instant conditions of a jump on interface surface

  3. Differential equations problem solver

    CERN Document Server

    Arterburn, David R

    2012-01-01

    REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

  4. Local Observed-Score Kernel Equating

    Science.gov (United States)

    Wiberg, Marie; van der Linden, Wim J.; von Davier, Alina A.

    2014-01-01

    Three local observed-score kernel equating methods that integrate methods from the local equating and kernel equating frameworks are proposed. The new methods were compared with their earlier counterparts with respect to such measures as bias--as defined by Lord's criterion of equity--and percent relative error. The local kernel item response…

  5. Numerical solution of Boltzmann's equation

    International Nuclear Information System (INIS)

    Sod, G.A.

    1976-04-01

    The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig

  6. The Dirac equation and its solutions

    CERN Document Server

    Bagrov, Vladislav G

    2014-01-01

    Dirac equations are of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly.In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  7. The Dirac equation and its solutions

    International Nuclear Information System (INIS)

    Bagrov, Vladislav G.; Gitman, Dmitry; P.N. Lebedev Physical Institute, Moscow; Tomsk State Univ., Tomsk

    2013-01-01

    The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  8. The modified extended Fan's sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation

    International Nuclear Information System (INIS)

    Yomba, Emmanuel

    2005-01-01

    By using a modified extended Fan's sub-equation method, we have obtained new and more general solutions including a series of non-travelling wave and coefficient function solutions namely: soliton-like solutions, triangular-like solutions, single and combined non-degenerative Jacobi elliptic wave function-like solutions for the (2 + 1)-dimensional dispersive long wave equation. The most important achievement of this method lies on the fact that, we have succeeded in one move to give all the solutions which can be previously obtained by application of at least four methods (method using Riccati equation, or first kind elliptic equation, or auxiliary ordinary equation, or generalized Riccati equation as mapping equation)

  9. Painleve test and discrete Boltzmann equations

    International Nuclear Information System (INIS)

    Euler, N.; Steeb, W.H.

    1989-01-01

    The Painleve test for various discrete Boltzmann equations is performed. The connection with integrability is discussed. Furthermore the Lie symmetry vector fields are derived and group-theoretical reduction of the discrete Boltzmann equations to ordinary differentiable equations is performed. Lie Backlund transformations are gained by performing the Painleve analysis for the ordinary differential equations. 16 refs

  10. Chew-Low equations as Cremoma transformations

    International Nuclear Information System (INIS)

    Rerikh, K.V.

    1982-01-01

    The Chew-Low equations for the p-wave pion-nucleon scattering with the crossing-symmetry matrix (3x3) are investigated in their well-known formulation as a system of nonlinear difference equations. These equations interpreted as geometrical transformations are shown to be a special case of the Cremona transformaions. Using the properties of the Cremona transformations we obtain the general 3-parametric functional equation on invariant algebraic and nonalgebraic curves in the space solutions of the Chew- Low equations. It is proved that there exists only one invariant algebraic curve, the parabola corresponding to the well-known solution. Analysis of the general functional equation on invariant nonalgebraic curves makes it possible to select in addition to this parabola 3 invariant forms defining implicitly 3 nonalgebraic curves and to concretize for them the general equation by means of fixing the parameters. From the transformational properties of the invariant forms with respect to the Cremona transformations, there follows an important result that the ration of these forms in proper powers is the general integral of the nonlinear system of the Chew-Low equations, which is an even antiperiodic function. The structure of the second general integral is given and the functional equations which determinne this integral are presented [ru

  11. General particle transport equation. Final report

    International Nuclear Information System (INIS)

    Lafi, A.Y.; Reyes, J.N. Jr.

    1994-12-01

    The general objectives of this research are as follows: (1) To develop fundamental models for fluid particle coalescence and breakage rates for incorporation into statistically based (Population Balance Approach or Monte Carlo Approach) two-phase thermal hydraulics codes. (2) To develop fundamental models for flow structure transitions based on stability theory and fluid particle interaction rates. This report details the derivation of the mass, momentum and energy conservation equations for a distribution of spherical, chemically non-reacting fluid particles of variable size and velocity. To study the effects of fluid particle interactions on interfacial transfer and flow structure requires detailed particulate flow conservation equations. The equations are derived using a particle continuity equation analogous to Boltzmann's transport equation. When coupled with the appropriate closure equations, the conservation equations can be used to model nonequilibrium, two-phase, dispersed, fluid flow behavior. Unlike the Eulerian volume and time averaged conservation equations, the statistically averaged conservation equations contain additional terms that take into account the change due to fluid particle interfacial acceleration and fluid particle dynamics. Two types of particle dynamics are considered; coalescence and breakage. Therefore, the rate of change due to particle dynamics will consider the gain and loss involved in these processes and implement phenomenological models for fluid particle breakage and coalescence

  12. Analytical solutions of time-fractional models for homogeneous Gardner equation and non-homogeneous differential equations

    Directory of Open Access Journals (Sweden)

    Olaniyi Samuel Iyiola

    2014-09-01

    Full Text Available In this paper, we obtain analytical solutions of homogeneous time-fractional Gardner equation and non-homogeneous time-fractional models (including Buck-master equation using q-Homotopy Analysis Method (q-HAM. Our work displays the elegant nature of the application of q-HAM not only to solve homogeneous non-linear fractional differential equations but also to solve the non-homogeneous fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for non-linear differential equations. Comparisons are made upon the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

  13. Electronic representation of wave equation

    Energy Technology Data Exchange (ETDEWEB)

    Veigend, Petr; Kunovský, Jiří, E-mail: kunovsky@fit.vutbr.cz; Kocina, Filip; Nečasová, Gabriela; Valenta, Václav [University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic); Šátek, Václav [IT4Innovations, VŠB Technical University of Ostrava, 17. listopadu 15/2172, 708 33 Ostrava-Poruba (Czech Republic); University of Technology, Faculty of Information Technology, Božetěchova 2, 612 66 Brno (Czech Republic)

    2016-06-08

    The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.

  14. The Dirac equation for accountants

    International Nuclear Information System (INIS)

    Ord, G.N.

    2006-01-01

    In the context of relativistic quantum mechanics, derivations of the Dirac equation usually take the form of plausibility arguments based on experience with the Schroedinger equation. The primary reason for this is that we do not know what wavefunctions physically represent, so derivations have to rely on formal arguments. There is however a context in which the Dirac equation in one dimension is directly related to a classical generating function. In that context, the derivation of the Dirac equation is an exercise in counting. We provide this derivation here and discuss its relationship to quantum mechanics

  15. Polygons of differential equations for finding exact solutions

    International Nuclear Information System (INIS)

    Kudryashov, Nikolai A.; Demina, Maria V.

    2007-01-01

    A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of polygons corresponding to nonlinear differential equations. It allows one to express exact solutions of the equation studied through solutions of another equation using properties of the basic equation itself. The ideas of power geometry are used and developed. Our approach has a pictorial interpretation, which is illustrative and effective. The method can be also applied for finding transformations between solutions of differential equations. To demonstrate the method application exact solutions of several equations are found. These equations are: the Korteveg-de Vries-Burgers equation, the generalized Kuramoto-Sivashinsky equation, the fourth-order nonlinear evolution equation, the fifth-order Korteveg-de Vries equation, the fifth-order modified Korteveg-de Vries equation and the sixth-order nonlinear evolution equation describing turbulent processes. Some new exact solutions of nonlinear evolution equations are given

  16. Unsplit complex frequency shifted perfectly matched layer for second-order wave equation using auxiliary differential equations.

    Science.gov (United States)

    Gao, Yingjie; Zhang, Jinhai; Yao, Zhenxing

    2015-12-01

    The complex frequency shifted perfectly matched layer (CFS-PML) can improve the absorbing performance of PML for nearly grazing incident waves. However, traditional PML and CFS-PML are based on first-order wave equations; thus, they are not suitable for second-order wave equation. In this paper, an implementation of CFS-PML for second-order wave equation is presented using auxiliary differential equations. This method is free of both convolution calculations and third-order temporal derivatives. As an unsplit CFS-PML, it can reduce the nearly grazing incidence. Numerical experiments show that it has better absorption than typical PML implementations based on second-order wave equation.

  17. Estimation of Tissue Distribution of mRNA Transcripts for Desaturase and Elongase Enzymes in Channa striata (Bloch, 1793 Fingerlings using PCR Technique

    Directory of Open Access Journals (Sweden)

    M. Aliyu-Paiko

    2013-06-01

    Full Text Available Fish species are varied in their capacity to biosynthesize n-3 highlyunsaturated fatty acids (HUFA such as eicosapentaenoic and docosahexaenoic acids (EPA & DHA that are crucial to the health and well-being of all higher vertebrates. Experts report that HUFA metabolism involves enzyme-mediated fatty acyl desaturation (FAD and elongation (FAE processes. In previous studies, different workers cloned, characterized, identified and reported several genes for FAD and FAE enzymes in different fish species such as Atlantic salmon, gilthead seabream, rainbow trout and zebrafish, and also demonstrated the up- and down-regulation in the activity of these enzymes in response to fluctuations in dietary HUFA. In this paper, we report on the expression of genes (mRNA transcripts for FAD and FAE enzymes in different tissues of Channa striata (Bloch, 1793 fingerling, to evaluate the tissues of the fish in which activity of both enzymes are high. To achieve this objective, we used conventional polymerase chain reaction (PCR technique to isolate and quantify the absolute copy number for each gene transcripts from 8 different tissues of the fish (reared with a commercial feed. Our estimate show that the distribution of the 2 enzyme transcripts were significantly (P < 0.05 higher in the liver and brain of C. striata than detected in the 6 other tissues evaluated (muscle, ovary, testis, intestine, kidney and skin. Subsequently, we discuss here extensively, the implication of this observation with respect to the use of vegetable oils (VO as substitute to fish oil (FO in diets for freshwater fish species.

  18. The Dirac equation and its solutions

    Energy Technology Data Exchange (ETDEWEB)

    Bagrov, Vladislav G. [Tomsk State Univ., Tomsk (Russian Federation). Dept. of Quantum Field Theroy; Gitman, Dmitry [Sao Paulo Univ. (Brazil). Inst. de Fisica; P.N. Lebedev Physical Institute, Moscow (Russian Federation); Tomsk State Univ., Tomsk (Russian Federation). Faculty of Physics

    2013-07-01

    The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In particular, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

  19. On the Inclusion of Difference Equation Problems and Z Transform Methods in Sophomore Differential Equation Classes

    Science.gov (United States)

    Savoye, Philippe

    2009-01-01

    In recent years, I started covering difference equations and z transform methods in my introductory differential equations course. This allowed my students to extend the "classical" methods for (ordinary differential equation) ODE's to discrete time problems arising in many applications.

  20. Boussinesq evolution equations

    DEFF Research Database (Denmark)

    Bredmose, Henrik; Schaffer, H.; Madsen, Per A.

    2004-01-01

    This paper deals with the possibility of using methods and ideas from time domain Boussinesq formulations in the corresponding frequency domain formulations. We term such frequency domain models "evolution equations". First, we demonstrate that the numerical efficiency of the deterministic...... Boussinesq evolution equations of Madsen and Sorensen [Madsen, P.A., Sorensen, O.R., 1993. Bound waves and triad interactions in shallow water. Ocean Eng. 20 359-388] can be improved by using Fast Fourier Transforms to evaluate the nonlinear terms. For a practical example of irregular waves propagating over...... a submerged bar, it is demonstrated that evolution equations utilising FFT can be solved around 100 times faster than the corresponding time domain model. Use of FFT provides an efficient bridge between the frequency domain and the time domain. We utilise this by adapting the surface roller model for wave...

  1. Multidimensional periodic Schrödinger operator perturbation theory and applications

    CERN Document Server

    Veliev, Oktay

    2015-01-01

    The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the ...

  2. Fractional Diffusion Equations and Anomalous Diffusion

    Science.gov (United States)

    Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin

    2018-01-01

    Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.

  3. Exact discretization of Schrödinger equation

    Energy Technology Data Exchange (ETDEWEB)

    Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

    2016-01-08

    There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

  4. Exact discretization of Schrödinger equation

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2016-01-01

    There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

  5. Abstract methods in partial differential equations

    CERN Document Server

    Carroll, Robert W

    2012-01-01

    Detailed, self-contained treatment examines modern abstract methods in partial differential equations, especially abstract evolution equations. Suitable for graduate students with some previous exposure to classical partial differential equations. 1969 edition.

  6. Generalization of Einstein's gravitational field equations

    Science.gov (United States)

    Moulin, Frédéric

    2017-12-01

    The Riemann tensor is the cornerstone of general relativity, but as is well known it does not appear explicitly in Einstein's equation of gravitation. This suggests that the latter may not be the most general equation. We propose here for the first time, following a rigorous mathematical treatment based on the variational principle, that there exists a generalized 4-index gravitational field equation containing the Riemann curvature tensor linearly, and thus the Weyl tensor as well. We show that this equation, written in n dimensions, contains the energy-momentum tensor for matter and that of the gravitational field itself. This new 4-index equation remains completely within the framework of general relativity and emerges as a natural generalization of the familiar 2-index Einstein equation. Due to the presence of the Weyl tensor, we show that this equation contains much more information, which fully justifies the use of a fourth-order theory.

  7. Extraction of dynamical equations from chaotic data

    International Nuclear Information System (INIS)

    Rowlands, G.; Sprott, J.C.

    1991-02-01

    A method is described for extracting from a chaotic time series a system of equations whose solution reproduces the general features of the original data even when these are contaminated with noise. The equations facilitate calculation of fractal dimension, Lyapunov exponents and short-term predictions. The method is applied to data derived from numerical solutions of the Logistic equation, the Henon equations, the Lorenz equations and the Roessler equations. 10 refs., 5 figs

  8. Long-time tails of correlation and memory functions

    Science.gov (United States)

    Sawada, Isao

    2002-11-01

    We review the generalized Langevin equation, which is a transformation and reformulation of equation of motion, from the two viewpoints: the projection operator method developed by Mori and the recurrence relations method developed by Lee. The fluctuating forces acting on the Bloch electrons’ current are clarified the strongly colored quantum fluctuations with the spontaneous interband transitions leading to a long-time tail of 1/ t for the envelope of the memory function. The velocity autocorrelation functions in the coupled harmonic oscillator on the Bethe lattice have a long-time tail of 1/t t. The oscillation and the form of decay found in correlation functions affect transport coefficients given by the integrated intensity up to infinity. We also study the force-force correlation functions often used as an approximation to the memory function.

  9. Self-similar decay to the marginally stable ground state in a model for film flow over inclined wavy bottoms

    Directory of Open Access Journals (Sweden)

    Tobias Hacker

    2012-04-01

    Full Text Available The integral boundary layer system (IBL with spatially periodic coefficients arises as a long wave approximation for the flow of a viscous incompressible fluid down a wavy inclined plane. The Nusselt-like stationary solution of the IBL is linearly at best marginally stable; i.e., it has essential spectrum at least up to the imaginary axis. Nevertheless, in this stable case we show that localized perturbations of the ground state decay in a self-similar way. The proof uses the renormalization group method in Bloch variables and the fact that in the stable case the Burgers equation is the amplitude equation for long waves of small amplitude in the IBL. It is the first time that such a proof is given for a quasilinear PDE with spatially periodic coefficients.

  10. The AGL equation from the dipole picture

    International Nuclear Information System (INIS)

    Gay Ducati, M.B.; Goncalves, V.P.

    1999-01-01

    The AGL equation includes all multiple pomeron exchanges in the double logarithmic approximation (DLA) limit, leading to a unitarized gluon distribution in the small x regime. This equation was originally obtained using the Glauber-Mueller approach. We demonstrate in this paper that the AGL equation and, consequently, the GLR equation, can also be obtained from the dipole picture in the double logarithmic limit, using an evolution equation, recently proposed, which includes all multiple pomeron exchanges in the leading logarithmic approximation. Our conclusion is that the AGL equation is a good candidate for a unitarized evolution equation at small x in the DLA limit

  11. Singularly perturbed Burger-Huxley equation: Analytical solution ...

    African Journals Online (AJOL)

    user

    solutions of singularly perturbed nonlinear differential equations. ... for solving generalized Burgers-Huxley equation but this equation is not singularly ...... Solitary waves solutions of the generalized Burger Huxley equations, Journal of.

  12. Baecklund transformations for integrable lattice equations

    International Nuclear Information System (INIS)

    Atkinson, James

    2008-01-01

    We give new Baecklund transformations (BTs) for some known integrable (in the sense of being multidimensionally consistent) quadrilateral lattice equations. As opposed to the natural auto-BT inherent in every such equation, these BTs are of two other kinds. Specifically, it is found that some equations admit additional auto-BTs (with Baecklund parameter), whilst some pairs of apparently distinct equations admit a BT which connects them

  13. Integrable discretizations of the short pulse equation

    International Nuclear Information System (INIS)

    Feng Baofeng; Maruno, Ken-ichi; Ohta, Yasuhiro

    2010-01-01

    In this paper, we propose integrable semi-discrete and full-discrete analogues of the short pulse (SP) equation. The key construction is the bilinear form and determinant structure of solutions of the SP equation. We also give the determinant formulas of N-soliton solutions of the semi-discrete and full-discrete analogues of the SP equations, from which the multi-loop and multi-breather solutions can be generated. In the continuous limit, the full-discrete SP equation converges to the semi-discrete SP equation, and then to the continuous SP equation. Based on the semi-discrete SP equation, an integrable numerical scheme, i.e. a self-adaptive moving mesh scheme, is proposed and used for the numerical computation of the short pulse equation.

  14. What happens to linear properties as we move from the Klein-Gordon equation to the sine-Gordon equation

    International Nuclear Information System (INIS)

    Kovalyov, Mikhail

    2010-01-01

    In this article the sets of solutions of the sine-Gordon equation and its linearization the Klein-Gordon equation are discussed and compared. It is shown that the set of solutions of the sine-Gordon equation possesses a richer structure which partly disappears during linearization. Just like the solutions of the Klein-Gordon equation satisfy the linear superposition principle, the solutions of the sine-Gordon equation satisfy a nonlinear superposition principle.

  15. Sparse dynamics for partial differential equations.

    Science.gov (United States)

    Schaeffer, Hayden; Caflisch, Russel; Hauck, Cory D; Osher, Stanley

    2013-04-23

    We investigate the approximate dynamics of several differential equations when the solutions are restricted to a sparse subset of a given basis. The restriction is enforced at every time step by simply applying soft thresholding to the coefficients of the basis approximation. By reducing or compressing the information needed to represent the solution at every step, only the essential dynamics are represented. In many cases, there are natural bases derived from the differential equations, which promote sparsity. We find that our method successfully reduces the dynamics of convection equations, diffusion equations, weak shocks, and vorticity equations with high-frequency source terms.

  16. Complex centers of polynomial differential equations

    Directory of Open Access Journals (Sweden)

    Mohamad Ali M. Alwash

    2007-07-01

    Full Text Available We present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.

  17. Numerical solutions of diffusive logistic equation

    International Nuclear Information System (INIS)

    Afrouzi, G.A.; Khademloo, S.

    2007-01-01

    In this paper we investigate numerically positive solutions of a superlinear Elliptic equation on bounded domains. The study of Diffusive logistic equation continues to be an active field of research. The subject has important applications to population migration as well as many other branches of science and engineering. In this paper the 'finite difference scheme' will be developed and compared for solving the one- and three-dimensional Diffusive logistic equation. The basis of the analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach, developed from many authors these years

  18. Applied partial differential equations

    CERN Document Server

    Logan, J David

    2015-01-01

    This text presents the standard material usually covered in a one-semester, undergraduate course on boundary value problems and PDEs.  Emphasis is placed on motivation, concepts, methods, and interpretation, rather than on formal theory. The concise treatment of the subject is maintained in this third edition covering all the major ideas: the wave equation, the diffusion equation, the Laplace equation, and the advection equation on bounded and unbounded domains. Methods include eigenfunction expansions, integral transforms, and characteristics. In this third edition, text remains intimately tied to applications in heat transfer, wave motion, biological systems, and a variety other topics in pure and applied science. The text offers flexibility to instructors who, for example, may wish to insert topics from biology or numerical methods at any time in the course. The exposition is presented in a friendly, easy-to-read, style, with mathematical ideas motivated from physical problems. Many exercises and worked e...

  19. The generalized Airy diffusion equation

    Directory of Open Access Journals (Sweden)

    Frank M. Cholewinski

    2003-08-01

    Full Text Available Solutions of a generalized Airy diffusion equation and an associated nonlinear partial differential equation are obtained. Trigonometric type functions are derived for a third order generalized radial Euler type operator. An associated complex variable theory and generalized Cauchy-Euler equations are obtained. Further, it is shown that the Airy expansions can be mapped onto the Bessel Calculus of Bochner, Cholewinski and Haimo.

  20. Exact Solutions of a Fractional-Type Differential-Difference Equation Related to Discrete MKdV Equation

    International Nuclear Information System (INIS)

    Aslan İsmail

    2014-01-01

    The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. (general)