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
The Bloch equation with terms induced by an electric field
Garbacz, Piotr
2018-01-01
The Bloch equation of the nuclear magnetization of spin-1/2 nuclei in molecules, which have permanent electric dipole moments μe that are placed simultaneously in a magnetic field B and an electric field E, is derived. It is shown that if the principal components of the nuclear magnetic shielding tensor σ and the dipole moment μe are known, then the measurement of the transverse component to the magnetic field B of the nuclear magnetization, which is induced by the application of the electric field oscillating at the half of the spin precession frequency, allows determining the orientation of the dipole moment μe with respect to the principal axis system of the symmetric part of the tensor σ. Four-component relativistic density functional theory computations, which have been performed for several molecules containing heavy nuclei, i.e., 207Pb, 205Tl, 199Hg, 195Pt, and 125Te, indicate that coefficients of the relaxation matrix perturbed by the electric field E are in favorable cases of the order of 1000 pm2 V-2 T-2. Therefore, the spin dynamics is perturbed at experimentally observable levels for the strengths of electric and magnetic fields E = 5 kV/mm and B = 10 T, respectively.
Comprehensive solutions to the Bloch equations and dynamical models for open two-level systems
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
Quantum Theory of Conducting Matter Newtonian Equations of Motion for a Bloch Electron
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...
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)
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)
Tahayori, Bahman; Johnston, Leigh A; Layton, Kelvin J; Farrell, Peter M; Mareels, Iven M Y
2015-10-01
In waveform design for magnetic resonance applications, periodic continuous-wave excitation offers potential advantages that remain largely unexplored because of a lack of understanding of the Bloch equation with periodic continuous-wave excitations. Using harmonic balancing techniques the steady state solutions of the Bloch equation with periodic excitation can be effectively solved. Moreover, the convergence speed of the proposed series approximation is such that a few terms in the series expansion suffice to obtain a very accurate description of the steady state solution. The accuracy of the proposed analytic approximate series solution is verified using both a simulation study as well as experimental data derived from a spherical phantom with doped water under continuous-wave excitation. Typically a five term series suffices to achieve a relative error of less than one percent, allowing for a very effective and efficient analytical design process. The opportunities for Rabi frequency modulated continuous-wave form excitation are then explored, based on a comparison with steady state free precession pulse sequences.
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
DEFF Research Database (Denmark)
Gaididei, Yu. B.; Christiansen, Peter Leth
2008-01-01
We study a parametrically driven Ginzburg-Landau equation model with nonlinear management. The system is made of laterally coupled long active waveguides placed along a circumference. Stationary solutions of three kinds are found: periodic Ising states and two types of Bloch states, staggered and...
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
Chai, Jun; Tian, Bo; Sun, Wen-Rong; Liu, De-Yin
2018-01-01
Under investigation in this paper is the reduced Maxwell-Bloch equations with variable coefficients, which describe the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. Hirota method and symbolic computation are applied to solve such equations. By introducing the dependent variable transformations, we give the bilinear forms, vector one-, two- and N-soliton solutions in analytic forms. The types of the vector solitons are analyzed: Only the bright-single-hump solitons can be observed in q and r1 , the soliton in r2 is the bright-double-hump soliton, and there exist three types of solitons in r3 , including the dark-single-hump soliton, dark-double-hump soliton and dark-like-bright soliton, with q as the inhomogeneous electric field, r1 and r2 as the real and imaginary parts of the polarization of the two-level medium, and r3 as the population difference between the ground and excited states. Figures are presented to show the vector soliton solutions. Different types of the interactions between the vector two solitons are presented. In each component, only the overtaking elastic interaction can be observed.
Directory of Open Access Journals (Sweden)
Gladush M.G.
2015-01-01
Full Text Available We obtained the system of Maxwell-Bloch equations (MB that describe the interaction of cw laser with optically active impurity centers (particles embedded in a dielectric material. The dielectric material is considered as a continuous medium with sufficient laser detuning from its absorption lines. The model takes into account the effects associated with both the real and the imaginary part of the dielectric constant of the material. MB equations were derived within a many-particle quantum-kinetic formalism, which is based on Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY hierarchy for reduced density matrices and correlation operators of material particles and the quantized radiation field modes. It is shown that this method is beneficial to describe the effects of individual and collective behavior of the light emitters and requires no phenomenological procedures. It automatically takes into account the characteristics associated with the presence of non-resonant and resonant particles filling the space between the optical centers.
Chai, Jun; Tian, Bo; Chai, Han-Peng
2018-02-01
Investigation in this paper is given to the reduced Maxwell-Bloch equations with variable coefficients, describing the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. We apply the Hirota method and symbolic computation to study such equations. With the help of the dependent variable transformations, we present the variable-coefficient-dependent bilinear forms. Then, we construct the one-, two- and N-soliton solutions in analytic forms for them. Supported by the National Natural Science Foundation of China under Grant Nos. 11772017, 11272023, 11471050, the Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC: 2017ZZ05), and the Fundamental Research Funds for the Central Universities of China under Grant No. 2011BUPTYB02
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
Rogue waves of the Hirota and the Maxwell-Bloch equations
Li, Chuanzhong; He, Jingsong; Porseizan, K.
2013-01-01
In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch (H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fiber and further generalize it to the matrix form of the n-fold Darboux transformation of this system. This n-fold Darboux transformation implies the determinant representation of nth solutions of (E[n],p[n],η[n]) generated from the known solution of (E,p,η). The determinant representation of (E[n],p[n],η[n]) provides soliton solutions, positon solutions, and breather solutions (both bright and dark breathers) of the H-MB system. From the breather solutions, we also construct a bright and dark rogue wave solution for the H-MB system, which is currently one of the hottest topics in mathematics and physics. Surprisingly, the rogue wave solution for p and η has two peaks because of the order of the numerator and denominator of them. Meanwhile, after fixing the time and spatial parameters and changing two other unknown parameters α and β, we generate a rogue wave shape.
Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging
Bueno-Orovio, Alfonso; Burrage, Kevin
2017-11-01
The quantification of anomalous diffusion is increasingly being recognised as an advanced modality of analysis for the evaluation of tissue microstructure in magnetic resonance imaging (MRI). One powerful framework to account for anomalous diffusion in biological and structurally heterogeneous tissues is the use of diffusion operators based on fractional calculus theory, which generalises the physical principles of standard diffusion in homogeneous media. However, their non-locality makes analytical solutions often unavailable, limiting the applicability of these modelling and analysis techniques. In this paper, we derive compact analytical signal decays for practical MRI sequences in the anisotropic fractional Bloch-Torrey setting, as described by the space fractional Laplacian and importantly the time Caputo derivative. The attained solutions convey relevant characteristics of MRI in biological tissues not replicated by standard diffusion, including super-diffusive and sub-diffusive regimes in signal decay and the diffusion-driven incomplete refocusing of spins at the end of the sequence. These results may therefore have significant implications for advancing the current interpretation of MRI, and for the estimation of tissue properties based on exact solutions to underlying diffusive processes.
Nonlinear optics using the multipolar Hamiltonian : The Bloch-Maxwell equations and local fields
Knoester, Jasper; Mukamel, Shaul
1989-01-01
A systematic method for calculating nonlinear-optical susceptibilities in condensed phases, which incorporates intermolecular forces and spontaneous emission in a consistent way, is developed, using the multipolar (µ•D) Hamiltonian. Reduced equations of motion that couple the electromagnetic field
Murase, Kenya
2012-12-01
We present a simple method for calculating the magnetization in spin-locking (SL) magnetic resonance imaging (MRI), in which a simple matrix equation was derived for solving the time-dependent Bloch equations in the 2-pool chemical exchange model. We also present a method for visualizing the trajectory of a magnetization vector in a three-dimensional (3D) space. The longitudinal relaxation time in the rotating frame (T1ρ) was calculated by fitting the z component of magnetization for a duration of SL (tSL) (Mz(tSL)) to Mz(tSL) = (M0 - Mzss)exp ( - tSL/T1ρ) + Mzss, where M0 and Mzss denote the thermal equilibrium and steady-state z component of magnetization, respectively, and was compared with that calculated from the solution given by Trott and Palmer. Our 3D plots clearly visualized the effect of SL. When the population of the two pools was highly asymmetric, there was good agreement between the T1ρ values obtained by our method and Trott and Palmer's solutions. The difference between them increased with decreasing asymmetry in the population of the two pools. Our method will be useful for better understanding and optimization of SL MRI, because it allows us to calculate the magnetization vector and to visualize its trajectory simply and quickly.
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
Directory of Open Access Journals (Sweden)
Slesarenko N.A.
2015-09-01
Full Text Available Five clinical observations in pediatric patients with Bloch — Sulzberger syndrome are presented. The observation had been performed for six months. The differential diagnosis depending on the stage of the disease was done. The article contains variants of treating patients of this category.
Indian Academy of Sciences (India)
IAS Admin
In 1933, when Hitler came to power, Felix left Germany and decided to move to USA, landing up on the West Coast, in the University of Stanford, where he stayed for the rest of his academic life. He made contacts with University of Berkeley. At the time, Robert Oppenheimer was teaching at Berkeley, and since Bloch had ...
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....
Generalized Bloch theorem and chiral transport phenomena
Yamamoto, Naoki
2015-10-01
Bloch theorem states the impossibility of persistent electric currents in the ground state of nonrelativistic fermion systems. We extend this theorem to generic systems based on the gauged particle number symmetry and study its consequences on the example of chiral transport phenomena. We show that the chiral magnetic effect can be understood as a generalization of the Bloch theorem to a nonequilibrium steady state, similarly to the integer quantum Hall effect. On the other hand, persistent axial currents are not prohibited by the Bloch theorem and they can be regarded as Pauli paramagnetism of relativistic matter. An application of the generalized Bloch theorem to quantum time crystals is also discussed.
Electric dipoles on the Bloch sphere
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.
Hybridization between Indian catfish, Heteropneustes fossilis (Bloch ...
African Journals Online (AJOL)
Hybridization between Indian catfish, ♀Heteropneustes fossilis (Bloch) and Asian catfish, Clarias batrachus ♂ (Linn.) N Jothilakshmanan, K Karal Marx. Abstract. Success has been achieved in intergeneric hybridization between two air breathing catfishes by crossing Indian catfish, Heteropneustes fossilis (Bloch) and ...
Protection of qubit-coherence on a Bloch sphere
Zong, Xiao-Lan; Chu, Wen-Jing; Yang, Ming; Yang, Qing; Cao, Zhuo-Liang
2017-07-01
Single qubit pure state is a fundamental resource in quantum information and quantum computation. Therefore, it is of great importance to protect the coherence of single qubits against decoherence. In this letter, we demonstrate that decoherence caused by spontaneous emission can be effectively suppressed by adding a universal static external field. In order to have an intuitive view to the protection effects and its physical mechanisms, we study the coherence evolution of a single qubit on a Bloch sphere. We can clearly see that different external resonant drivings can rotate the Bloch vector around different axes, and the steady-state solution of the master equation (under protection) are visualized on the Bloch sphere. Furthermore, the frequency detuning between the qubit system and the driving is taken into account, and the results show that our protection scheme still works fine in the detuned cases and the smaller the detuning is, the better the protection effect is. In addition, this protocol can protect the coherence of single qubit states with a wide range of driving parameters, and help people to design simple coherence protection schemes for qubit states. The simplicity and the abundance of the current scheme may warrant its experimental realization.
A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into -Bloch Spaces
Directory of Open Access Journals (Sweden)
René E. Castillo
2013-01-01
Full Text Available Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for , is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003.
Claude Bloch scientific works, oeuvre scientifique
Bloch, Claude; De Dominicis, Cyrano; Gillet, Vincent; Messiah, Albert
1975-01-01
Claude Bloch: Scientific Works Oeuvre Scientifique covers the collection of scientific works of Claude Bloch. The book includes topics on field theories with non-localized interaction and notes on the symmetry properties of nuclear wave functions. It also covers theory of nuclear level density; the theory of imperfect fermi gases; the structure of nuclear matter; and the canonical form of an antisymmetric tensor and its application to the theory of superconductivity.
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.
Bloch Oscillations in Complex Crystals with PT Symmetry
International Nuclear Information System (INIS)
Longhi, S.
2009-01-01
Bloch oscillations in complex lattices with PT symmetry are theoretically investigated with specific reference to optical Bloch oscillations in photonic lattices with gain or loss regions. Novel dynamical phenomena with no counterpart in ordinary lattices, such as nonreciprocal Bloch oscillations related to violation of the Friedel's law of Bragg scattering in complex potentials, are highlighted.
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/
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.
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
Taking a peek at Bloch oscillations
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.
Wave impedance retrieving via Bloch modes analysis
DEFF Research Database (Denmark)
Andryieuski, Andrei; Ha, S.; Sukhorukov, A.
2011-01-01
-ciples violation, like antiresonance behaviour with Im(ε) wave impedances by the surface and volume aver-aging of the electromagnetic field...... of the Bloch mode, respectively. Case studies prove that our ap-proach can determine material and wave effective parameters of lossy and lossless metamaterials. In some examples when the passivity is violated we made further analysis and showed that this is due to the failure of concept of impedance retrieving...
Bloch oscillations in organic and inorganic polymers
Ribeiro, Luiz Antonio; Ferreira da Cunha, Wiliam; de Almeida Fonseca, Antonio Luciano; e Silva, Geraldo Magela
2017-04-01
The transport of polarons above the mobility threshold in organic and inorganic polymers is theoretically investigated in the framework of a one-dimensional tight-binding model that includes lattice relaxation. The computational approach is based on parameters for which the model Hamiltonian suitably describes different polymer lattices in the presence of external electric fields. Our findings show that, above critical field strengths, a dissociated polaron moves through the polymer lattice as a free electron performing Bloch oscillations. These critical electric fields are considerably smaller for inorganic lattices in comparison to organic polymers. Interestingly, for inorganic lattices, the free electron propagates preserving charge and spin densities' localization which is a characteristic of a static polaron. Moreover, in the turning points of the spatial Bloch oscillations, transient polaron levels are formed inside the band gap, thus generating a fully characterized polaron structure. For the organic case, on the other hand, no polaron signature is observed: neither in the shape of the distortion—those polaron profile signatures are absent—nor in the energy levels—as no such polaron levels are formed during the simulation. These results solve controversial aspects concerning Bloch oscillations recently reported in the literature and may enlighten the understanding about the charge transport mechanism in polymers above their mobility edge.
The Bloch wave operator: generalizations and applications: Part I. The time-independent case
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 ...
Dynamics of local magnetization in the eigenbasis of the Bloch-Torrey operator
Herberthson, Magnus; Özarslan, Evren; Knutsson, Hans; Westin, Carl-Fredrik
2017-03-01
We consider diffusion within pores with general shapes in the presence of spatially linear magnetic field profiles. The evolution of local magnetization of the spin bearing particles can be described by the Bloch-Torrey equation. We study the diffusive process in the eigenbasis of the non-Hermitian Bloch-Torrey operator. It is possible to find expressions for some special temporal gradient waveforms employed to sensitize the nuclear magnetic resonance (NMR) signal to diffusion. For more general gradient waveforms, we derive an efficient numerical solution by introducing a novel matrix formalism. Compared to previous methods, this new approach requires a fewer number of eigenfunctions to achieve the same accuracy. This shows that these basis functions are better suited to the problem studied. The new framework could provide new important insights into the fundamentals of diffusion sensitization, which could further the development of the field of NMR.
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.
International Nuclear Information System (INIS)
Merkl, Franz
1999-01-01
This article describes the solution of the Kadomcev-Petviashvilli equation with C 10 real periodic initial data in terms of an asymptotic expansion of Bloch functions. The Bloch functions are parametrized by the spectral variety of a heat equation (heat curves) with an external potential. The mentioned spectral variety is a Riemann surface of in general infinite genus; the Kadomcev-Petviashvilli flow is represented by a one-parameter-subgroup in the real part of the Jacobi variety of this Riemann surface. It is shown that the KP-I flow with these initial data propagates almost periodically
Designing non-Hermitian dynamics for conservative state evolution on the Bloch sphere
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.
Stacked-Bloch-wave electron diffraction simulations using GPU acceleration
International Nuclear Information System (INIS)
Pennington, Robert S.; Wang, Feng; Koch, Christoph T.
2014-01-01
In this paper, we discuss the advantages for Bloch-wave simulations performed using graphics processing units (GPUs), based on approximating the matrix exponential directly instead of performing a matrix diagonalization. Our direct matrix-exponential algorithm yields a functionally identical electron scattering matrix to that generated with matrix diagonalization. Using the matrix-exponential scaling-and-squaring method with a Padé approximation, direct GPU-based matrix-exponential double-precision calculations are up to 20× faster than CPU-based calculations and up to approximately 70× faster than matrix diagonalization. We compare precision and runtime of scaling and squaring methods with either the Padé approximation or a Taylor expansion. We also discuss the stacked-Bloch-wave method, and show that our stacked-Bloch-wave implementation yields the same electron scattering matrix as traditional Bloch-wave matrix diagonalization. - Highlights: • Bloch-wave and stacked-Bloch-wave calculations can be accelerated with GPUs. • Direct approximation of the matrix exponential can be faster than diagonalization. • GPU-based direct approximation can be ≈70× faster than CPU diagonalization. • Larger matrices benefit more from this approach than smaller ones. • Stacked-Bloch-wave scattering results are functionally identical to diagonalization
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.
Bloch-mode analysis for effective parameters restoration
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Ha, Sangwoo
2012-01-01
We utilize the Bloch-mode analysis of periodic composite structures to introduce an approach for retrieving effective parameters of homogenized metamaterials. In the case of single-mode propagation we can restore a complex effective refractive index with a high accuracy. By further employing...... surface or volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes we are able to determine the Bloch and wave impedances, leading to wave and material effective parameters, respectively. The approach is demonstrated on several examples. We focus our discussion...
Bloch-Like Oscillations in Finite Quantum Structures
DEFF Research Database (Denmark)
Duggen, Lars; Willatzen, Morten; Lassen, Benny
of individual quantum wells and changing the coupling strength as a function of position. It is, furthermore, demonstrated that the application of a magnetic field to a structure of quantum wells may lead to the observation of Bloch oscillations (similar to Bloch oscillations stemming from the Stark effect......Inspired by several attempts to generate Bloch-like oscillations in different fields of physics [1,2], we examine a multitude of oscillator systems and interactions that lead to Bloch oscillations in finite quantum structures. A general requirement is the existence of a common period in the time...... dependence of different eigenstates which is guaranteed if eigenenergies are distributed in, e.g., a Stark ladder. We show that one possibility to create a Stark ladder is to vary the individual well widths in a chain of quantum wells. For this system we study the effect of permuting the positions...
Phase-space dynamics of semiclassical spin- 1/2 Bloch electrons.
Kerr, W C; Rave, M J; Turski, L A
2005-05-06
Following recent interest in a kinetic description of the semiclassical Bloch electron dynamics, we propose a new formulation based on the previously developed Lie-Poisson formulation of dynamics. It includes modifications required to account for the Berry curvature contribution to the electron's equation of motion as well as essential ingredients of a quantum treatment of spin- 1/2 degrees of freedom. Our theory is also manifestly gauge invariant and thus permits inclusion of the electron interactions. The scope of our formulation extends beyond its solid state physics motivation and includes recently discussed noncommutative generalizations of classical mechanics as well as historically important models from quantum gravity physics.
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
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...... on both the passive cavity and active lasers, where the latter show a general increase in the pump threshold for cavity lengths greater than N = 7, and a reduction in the nominal cavity mode volume for increasing amounts of disorder....
Mode-locked Bloch oscillations in a ring cavity
International Nuclear Information System (INIS)
Samoylova, M; Piovella, N; Hunter, D; Robb, G R M; Bachelard, R; Courteille, Ph W
2014-01-01
We present a new technique for stabilizing and monitoring Bloch oscillations of ultracold atoms in an optical lattice under the action of a constant external force. In the proposed scheme, the atoms also interact with a unidirectionally pumped optical ring cavity whose one arm is collinear with the optical lattice. For weak collective coupling, Bloch oscillations dominate over the collective atomic recoil lasing instability and develop a synchronized regime in which the atoms periodically exchange momentum with the cavity field. (letter)
Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E
2017-09-13
Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.
Rayleigh-Bloch waves in CMUT arrays.
Atalar, Abdullah; Köymen, Hayrettin; Oğuz, H Kağan
2014-12-01
Using the small-signal electrical equivalent circuit of a capacitive micromachined ultrasonic transducer (CMUT) cell, along with the self and mutual radiation impedances of such cells, we present a computationally efficient method to predict the frequency response of a large CMUT element or array. The simulations show spurious resonances, which may degrade the performance of the array. We show that these unwanted resonances are due to dispersive Rayleigh-Bloch waves excited on the CMUT surface-liquid interface. We derive the dispersion relation of these waves for the purpose of predicting the resonance frequencies. The waves form standing waves at frequencies where the reflections from the edges of the element or the array result in a Fabry-Pérot resonator. High-order resonances are eliminated by a small loss in the individual cells, but low-order resonances remain even in the presence of significant loss. These resonances are reduced to tolerable levels when CMUT cells are built from larger and thicker plates at the expense of reduced bandwidth.
Dai, Jin; Niemi, Antti J.; He, Jianfeng; Sieradzan, Adam; Ilieva, Nevena
2016-03-01
We inquire how structure emerges during the process of protein folding. For this we scrutinize collective many-atom motions during all-atom molecular dynamics simulations. We introduce, develop, and employ various topological techniques, in combination with analytic tools that we deduce from the concept of integrable models and structure of discrete nonlinear Schrödinger equation. The example we consider is an α -helical subunit of the HIV envelope glycoprotein gp41. The helical structure is stable when the subunit is part of the biological oligomer. But in isolation, the helix becomes unstable, and the monomer starts deforming. We follow the process computationally. We interpret the evolving structure both in terms of a backbone based Heisenberg spin chain and in terms of a side chain based XY spin chain. We find that in both cases the formation of protein supersecondary structure is akin the formation of a topological Bloch domain wall along a spin chain. During the process we identify three individual Bloch walls and we show that each of them can be modelled with a precision of tenths to several angstroms in terms of a soliton solution to a discrete nonlinear Schrödinger equation.
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∥=supz∈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.
Skyrmion clusters from Bloch lines in ferromagnetic films
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.
The Bloch wave operator: generalizations and applications: Part I. The time-independent case
Energy Technology Data Exchange (ETDEWEB)
Killingbeck, John P [Mathematics Department, University of Hull, Hull HU6 7RX (United Kingdom); Jolicard, Georges [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France)
2003-05-23
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 of test matrices taken from the previous literature on wave operator methods. The main emphasis throughout is on the use of numerical methods which use iterative or perturbation algorithms, with simple Pade approximant methods being found sufficient to deal with most of the cases of divergence which are encountered. The use of damping factors and relaxation parameters is found to be effective in stabilizing calculations which use the energy-dependent effective Hamiltonian of Loewdin. In general the computations suggest that the numerical applications of the nonlinear equation for the reduced wave operator are best carried out with the equation split into a pair of equations in which the Bloch effective Hamiltonian appears as a separate entity. The presentation of the theoretical and computational details throughout is accompanied by references to and discussion of many works which have used wave operator methods in physics, chemistry and engineering. Some of
Rabi-Bloch oscillations in spatially distributed systems: Temporal dynamics and frequency spectra
Levie, Ilay; Kastner, Raphael; Slepyan, Gregory
2017-10-01
We consider one-dimensional chains of two-level quantum systems coupled via tunneling. The chain is driven by the superposition of dc and ac fields in the strong coupling regime. Based on the fundamental principles of electrodynamics and quantum theory, we have developed a generalized model of quantum dynamics for such interactions, free of rotating-wave approximation. The system of equations of motion was studied numerically. We analyzed the dynamics and spectra of the inversion density, dipole current density, and tunneling current density. In the case of resonant interaction with the ac component, the particle dynamics exhibits itself in the oscillatory regime, which may be interpreted as a combination of Rabi and Bloch oscillations with their strong mutual influence. Such scenario for an obliquely incident ac field dramatically differs from the individual picture of both types of oscillations due to the interactions. This effect is counterintuitive because of the existence of markedly different frequency ranges for such two types of oscillations. These dynamics manifest themselves in multiline spectra in different combinations of Rabi and Bloch frequencies. The effect is promising as a framework of a new type of spectroscopy in nanoelectronics and electrical control of nanodevices.
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
Respiratory responses in freshwater fish Channa punctatus (Bloch ...
African Journals Online (AJOL)
Oxygen consumption plays an imperative role in the life of all organisms. The air we breathe, the food we eat, and the water we drink, are contaminated by toxic substances. In the present study, Channa punctatus (BLOCH) was used as an animal model to determine the sublethal toxicity of deltamethrin. Males weighing 10 + ...
Feeding habits of the catfish Synodontis schall (Bloch & Schneider ...
African Journals Online (AJOL)
Synodontis schall (Bloch & Schneider) is an abundant fish in Lake Chamo, but its feeding ecology is not well-known to guide its management. Diet composition and ontogenetic diet shift were investigated from stomach contents of 545 fish from August 1998 to February 2000. Volumetrically, the dominant food items were ...
Improved Reading Gate For Vertical-Bloch-Line Memory
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.
The Bloch wave operator: generalizations and applications: II. The time-dependent case
Energy Technology Data Exchange (ETDEWEB)
Jolicard, Georges [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France); Killingbeck, John P [Observatoire de Besancon (UMR-CNRS 6091), Universite de Franche-Comte, 41 bis, Avenue de l' Observatoire, 25000 Besancon (France); Mathematics Department, University of Hull, Hull HU6 7RX (United Kingdom)
2003-10-10
Part II of the review shows how the stationary Bloch wave operator of part I can be suitably modified to give a time-dependent wave operator. This operator makes it possible to use a relatively small active space in order to describe the dynamical processes which occur in quantum mechanical systems which have a time-dependent Hamiltonian. A close study is made of the links between the time-dependent and time-independent wave operators at the adiabatic limit; the analysis clarifies the way in which the wave operator formalism allows the time evolution of a system or a wave packet to be described in terms of a fast evolution inside the active space together with weak transitions out of this space which can be treated by perturbation methods. Two alternative wave operator equations of motion are derived and analysed. The first one is a non-linear differential equation in the usual Hilbert space; the second one is a differential equation in an extended Hilbert space with an extra time variable added and becomes equivalent to the usual Bloch equation when the Floquet Hamiltonian is taken in place of the ordinary Hamiltonian. A study is made of the close relationships between the time-dependent wave operator formalism, the Floquet theory and the (t, t') theory. Some original methods of solution of the two forms of wave operator equation are proposed and lead to new techniques of integration for the time-dependent Schroedinger equation (e.g., the generalized Green equation procedure). Mixed procedures involving both the time-independent and time-dependent wave operators are shown to be applicable to the internal eigenstate problem for large complex matrices. A detailed account is given of the description of inelastic and photoreactive processes by means of the time-dependent wave operator formalism, with particular attention to laser-molecule interactions. The emphasis is on projection operator techniques, with special attention being given to the method of selection
Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software
Kuprov, Ilya; Wagner-Rundell, Nicola; Hore, P. J.
2007-02-01
We describe a general method for the automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations for liquid-phase spin dynamics in the algebraically challenging case of rotationally modulated interactions. The processing typically takes no more than a few seconds (on a contemporary single-processor workstation) and yields relaxation rate expressions that are completely general with respect to the spectral density functions, relative orientations, and magnitudes of the interaction tensors, with all cross-correlations accounted for. The algorithm easily deals with fully rhombic interaction tensors, and is able, with little if any modification, to treat a large variety of the relaxation mechanisms encountered in NMR, EPR, and spin dynamics in general.
Bloch-mode analysis for retrieving effective parameters of metamaterials
DEFF Research Database (Denmark)
Andryieuski, Andrei; Ha, Sangwoo; Sukhorukov, Andrey A.
2012-01-01
We introduce an approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasiperiodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective refractive index can be assigned to the structure, being restored...... that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials....
Acoustic Bloch Wave Propagation in a Periodic Waveguide
1991-07-24
matrix (Ramo, Whinnery, and Van Duzer , 1965). Given the amplitudes of the two travelling waves in a single cell, then, we can find the amplitudes of...harmonics (Ramo, Whinnery, and Van Duzer , 1965). ; is interesting to note that because the range of the sum index n in Eq. 2.53 includ negative integers...34backwar. wave structures" (Ramo, Whinnery, and Van Duzer , 1965). 2.4.3 The Convolution Representation The apparent simplicity of the Bloch wave function
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....
Traffic restrictions on Routes Bloch, Maxwell and Bohr
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
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.
Bipolaron assisted Bloch-like oscillations in organic lattices
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.
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. W...
The Quantum Noise of Ferromagnetic π-Bloch Domain Walls
Directory of Open Access Journals (Sweden)
Peter R. Crompton
2009-09-01
Full Text Available We quantify the probability per unit Euclidean-time of reversing the magnetization of a π-Bloch vector, which describes the Ferromagnetic Domain Walls of a Ferromagnetic Nanowire at finite-temperatures. Our approach, based on Langer’s Theory, treats the double sine-Gordon model that defines the π-Bloch vectors via a procedure of nonperturbative renormalization, and uses importance sampling methods to minimise the free energy of the system and identify the saddlepoint solution corresponding to the reversal probability. We identify that whilst the general solution for the free energy minima cannot be expressed in closed form, we can obtain a closed expression for the saddlepoint by maximizing the entanglement entropy of the system as a polynomial ring. We use this approach to quantify the geometric and non-geometric contributions to the entanglement entropy of the Ferromagnetic Nanowire, defined between entangled Ferromagnetic Domain Walls, and evaluate the Euclidean-time dependence of the domain wall width and angular momentum transfer at the domain walls, which has been recently proposed as a mechanism for Quantum Memory Storage.
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.)
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
Surface Acoustic Analog of Bloch Oscillations, Wannier-Stark Ladders and Landau-Zener Tunneling
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.
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.
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)
Philippe Bloch: Reducing distance between experiments and CERN
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...
Floquet-Bloch theory for polymers in a periodic
Pablo Pedro, Ricardo; Tempel, David; Alexander-Katz, Alfredo
2014-03-01
Anderson localization in disordered systems predicts the localization of electronic wave functions and the resulting absence of diffusion. The phenomenon is much more general and has been observed in a variety of systems. In the case of the polymer, the behavior of it in a periodic potential is equivalent to the behavior of a quantum-machanicial particle in a periodic potential. According to this mapping our results for polymers in a periodic potential ara valid for localization of a quantum-mechanical particle in a periodic potential. Besides, one of our motivations for studying polymers in a periodic potential is because it reveals interesting aspects of a self-organization of the adsorbed polymers onto a surface with periodic potential. In order to describe the properties of time-periodic polymer system, we consider the potential time dependent which is periodic in time and space and we evaluate the solutions using the powerful nonperturbative Floquet-Bloch theory which is formulated for linear systems. Finally, we also consider a more interesting problem of when disorder is included in the time-periodic system, where localization of the wave function can occur.
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
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.
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.
Bloch wave deafness and modal conversion at a phononic crystal boundary
Laude, Vincent; Moiseyenko, Rayisa P.; Benchabane, Sarah; Declercq, Nico F.
2011-12-01
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.
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 CJh 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 CJh acting from normal weighted Bloch spaces to QT,S spaces. The related sufficient and necessary conditions are given.
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....
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
Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model.
Ma, Yu-Quan
2014-10-01
We study the Riemannian metric and the Euler characteristic number of the Bloch band in a one-dimensional spin model with multisite spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phase transition in zero temperature can be distinguished by the Euler number of the Bloch band.
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....
Traversa, Fabio L; Di Ventra, Massimiliano; Bonani, Fabrizio
2013-04-26
Floquet theory is a powerful tool in the analysis of many physical phenomena, and extended to spatial coordinates provides the basis for Bloch's theorem. However, in its original formulation it is limited to linear systems with periodic coefficients. Here, we extend the theory by proving a theorem for the general class of systems including linear operators commuting with the period-shift operator. The present theorem greatly expands the range of applicability of Floquet theory to a multitude of phenomena that were previously inaccessible with this type of analysis, such as dynamical systems with memory. As an important extension, we also prove Bloch's theorem for nonlocal potentials.
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
Band structure analysis of an analytically solvable Hill equation with continuous potential
Morozov, G. V.; Sprung, D. W. L.
2015-03-01
This paper concerns analytically solvable cases of Hill’s equation containing a continuously differentiable periodic potential. We outline a procedure for constructing the Floquet-Bloch fundamental system, and analyze the band structure of the system. The similarities to, and differences from, the cases of a piecewise constant periodic potential and the Mathieu potential, are illuminated.
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 shor...
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
Weak-field Hall effect and static polarizability of Bloch electrons
Czech Academy of Sciences Publication Activity Database
Středa, Pavel; Jonckheere, T.
2009-01-01
Roč. 79, č. 11 (2009), 115115/1-115115/8 ISSN 1098-0121 R&D Projects: GA ČR GA202/08/0551 Institutional research plan: CEZ:AV0Z10100521 Keywords : Hall effect * magnetization * Bloch electrons electron polarizability * electron polarizability Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.475, year: 2009
Lipschitz-Type and Bloch-Type Spaces of Pluriharmonic Mappings in a Hilbert Space
Directory of Open Access Journals (Sweden)
Yong Liu
2017-01-01
Full Text Available We investigate some properties of pluriharmonic mappings in an infinite dimensional complex Hilbert space. Several characterizations for pluriharmonic mappings to be in Lipschitz-type and Bloch-type spaces are given, which are generalizations of the corresponding known ones for holomorphic functions with several complex variables.
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)
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
Direct Observation of Bloch Harmonics and Negative Phase Velocity in Photonic Crystal Waveguides
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
DEFF Research Database (Denmark)
Bozhevolnyi, Sergey I.; Volkov, V.S.; Søndergaard, Thomas
2002-01-01
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...
Bloch oscillations of a Bose-Einstein condensate in a cavity-induced optical lattice
Georges, Ch.; Vargas, J.; Keßler, H.; Klinder, J.; Hemmerich, A.
2017-12-01
This article complements previous work on the nondestructive observation of Bloch oscillations of a Bose-Einstein condensate in an optical lattice formed inside a high-finesse optical cavity [H. Keßler et al., New J. Phys. 18, 102001 (2016), 10.1088/1367-2630/18/10/102001]. We present measurements showing that the observed Bloch frequency is independent of the atom number and hence the cooperative coupling strength, the intracavity lattice depth, and the detuning between the external pump light and the effective cavity resonance. We find that in agreement with theoretical predictions, despite the atom-cavity dynamics, the value of the Bloch frequency agrees with that expected in conventional optical lattices, where it solely depends on the sizes of the force and the lattice constant. We also show that Bloch oscillations are observed in a self-organized two-dimensional lattice, which is formed if, instead of axially pumping the cavity through one of its mirrors, the Bose-Einstein condensate is irradiated by an optical standing wave oriented perpendicularly with respect to the cavity axis. For this case, however, excessive decoherence prevents a meaningful quantitative assessment.
DEFF Research Database (Denmark)
Zhukovsky, Sergei; Babicheva, Viktoriia; Orlov, A. A.
2014-01-01
Optics of hyperbolic metamaterials is revisited in terms of large-wavevector waves, evanescent in isotropic media but propagating in presence of extreme anisotropy. Identifying the physical nature of these waves as Bloch volume plasmon polaritons, we derive their existence conditions and outline ...
Web-based description of the space radiation environment using the Bethe-Bloch model
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
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
Digital Repository Service at National Institute of Oceanography (India)
Sanaye, S.V.; Pise, N.M.; Pawar, A.P.; Parab, P.P.; Sreepada, R.A.; Pawar, H.B.; Murugan, A.
Alligator pipefish, Syngnathoides biaculeatus (Bloch, 1785) is one of the heavily traded and expensive ingredient in traditional Chinese medicines and there were no reports on its antioxidant activities Total phenolic content (TPC) and in...
Series: Utilization of Differential Equations and Methods for Solving Them in Medical Physics (3).
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.
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.
DEFF Research Database (Denmark)
Zhukovsky, Sergei; Lavrinenko, Andrei
2012-01-01
We propose proof-of-concept designs of Bragg reflectors and Fabry-Pe´rot resonators for large wave vector waves (Bloch bulk plasmon polaritons) in multilayer metal-dielectric hyperbolic metamaterials. The designs are based on hybrid multilayers having both subwavelength and wavelength-scale struc......We propose proof-of-concept designs of Bragg reflectors and Fabry-Pe´rot resonators for large wave vector waves (Bloch bulk plasmon polaritons) in multilayer metal-dielectric hyperbolic metamaterials. The designs are based on hybrid multilayers having both subwavelength and wavelength......-scale structuring. This multiscale approach is shown to be a promising platform for using bulk plasmonic waves in complex multilayer metamaterials as a new kind of information carriers....
Nanoscale switch for vortex polarization mediated by Bloch core formation in magnetic hybrid systems
Wohlhüter, Phillip; Bryan, Matthew Thomas; Warnicke, Peter; Gliga, Sebastian; Stevenson, Stephanie Elizabeth; Heldt, Georg; Saharan, Lalita; Suszka, Anna Kinga; Moutafis, Christoforos; Chopdekar, Rajesh Vilas; Raabe, Jörg; Thomson, Thomas; Hrkac, Gino; Heyderman, Laura Jane
2015-01-01
Vortices are fundamental magnetic topological structures characterized by a curling magnetization around a highly stable nanometric core. The control of the polarization of this core and its gyration is key to the utilization of vortices in technological applications. So far polarization control has been achieved in single-material structures using magnetic fields, spin-polarized currents or spin waves. Here we demonstrate local control of the vortex core orientation in hybrid structures where the vortex in an in-plane Permalloy film coexists with out-of-plane maze domains in a Co/Pd multilayer. The vortex core reverses its polarization on crossing a maze domain boundary. This reversal is mediated by a pair of magnetic singularities, known as Bloch points, and leads to the transient formation of a three-dimensional magnetization structure: a Bloch core. The interaction between vortex and domain wall thus acts as a nanoscale switch for the vortex core polarization. PMID:26238042
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.
DEFF Research Database (Denmark)
Mann, Nishan; Combrié, Sylvian; Colman, Pierre
2013-01-01
We present theory and measurements ofdisorder-induced losses for low loss 1.5 mmlong slow light photonic crystal waveguides. A recent class of dispersion engineered waveguides increases the bandwidth of slow light and shows lower propagation losses for the same group index. Our theory and experim...... and experiments explain how Bloch mode engineering can substantially reduce scattering losses for the same slow light group velocity regime....
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
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
Real-time protein aggregation monitoring with a Bloch surface wave-based approach
Santi, Sara; Barakat, Elsie; Descrovi, Emiliano; Neier, Reinhard; Herzig, Hans Peter
2014-05-01
The misfolding and aggregation of amyloid proteins has been associated with incurable diseases such as Alzheimer's or Parkinson's disease. In the specific case of Alzheimer's disease, recent studies have shown that cell toxicity is caused by soluble oligomeric forms of aggregates appearing in the early stages of aggregation, rather than by insoluble fibrils. Research on new strategies of diagnosis is imperative to detect the disease prior to the onset of clinical symptoms. Here, we propose the use of an optical method for protein aggregation dynamic studies using a Bloch surface wave based approach. A one dimension photonic crystal made of a periodic stack of silicon oxide and silicon nitride layers is used to excite a Bloch surface wave, which is sensitive to variation of the refractive index of an aqueous solution. The aim is to detect the early dynamic events of protein aggregation and fibrillogenesis of the amyloid-beta peptide Aβ42, which plays a central role in the onset of the Alzheimer's disease. The detection principle relies on the refractive index changes caused by the depletion of the Aβ42 monomer concentration during oligomerization and fibrillization. We demonstrate the efficacy of the Bloch surface wave approach by monitoring in real-time the first crucial steps of Aβ42 oligomerization.
Selective scattering between Floquet-Bloch and Volkov states in a topological insulator
Mahmood, Fahad; Chan, Ching-Kit; Alpichshev, Zhanybek; Gardner, Dillon; Lee, Young; Lee, Patrick A.; Gedik, Nuh
2016-04-01
The coherent optical manipulation of solids is emerging as a promising way to engineer novel quantum states of matter. The strong time-periodic potential of intense laser light can be used to generate hybrid photon-electron states. Interaction of light with Bloch states leads to Floquet-Bloch states, which are essential in realizing new photo-induced quantum phases. Similarly, dressing of free-electron states near the surface of a solid generates Volkov states, which are used to study nonlinear optics in atoms and semiconductors. The interaction of these two dynamic states with each other remains an open experimental problem. Here we use time- and angle-resolved photoemission spectroscopy (Tr-ARPES) to selectively study the transition between these two states on the surface of the topological insulator Bi2Se3. We find that the coupling between the two strongly depends on the electron momentum, providing a route to enhance or inhibit it. Moreover, by controlling the light polarization we can negate Volkov states to generate pure Floquet-Bloch states. This work establishes a systematic path for the coherent manipulation of solids via light-matter interaction.
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)
Bloch walls and the non-ideal bose gas spectrum
International Nuclear Information System (INIS)
Vitiello, S.A.S.
1986-05-01
The quasi-particle spectrum of non-ideal Bose gas with domain walls in the condensate is investigated. The existence of such a system is determined from solutions of Gross-Pitaevskii equation which represent many-soliton systems. The walls which make the condensate non-uniform are responsible for density and velocity fields ρ(x) and υ(x) repectively. In the laboratory, the Bogoliubov spectrum, supposed to be true for an uniform condensate at rest, is changed due to the velocity field to which the quasi-particles are submited. The spectrum in the laboratory frame is obtained by considering the Galileu invariance principle and the interaction energy between the quasi-particle and its medium. The importance in considering the last two facts is illustrated by the analyse of a constant density condensate which moves uniformly in the laboratory. The many-soliton spectrum configuration and structure function are studied by the Monte Carlo method. In an approximation that assumes the quasi-particle to be point like, the condensate can be treated as locally uniform. For each event the position x of a quasi-particle and its momentum in a frame with velocity υ(x) are determined. Thus, by a convenient Galileu transformation the energy spectrum in the laboratory an be obtained. The results show a phonon spectrum which splits in two branches in the high momenta region. In this region the lower energy branch exibiths a point of minimum. Analogies with the He II are explored. (author) [pt
Motives and algebraic cycles a celebration in honour of Spencer J. Bloch
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
Surface Acoustic Bloch Oscillations, the Wannier-Stark Ladder, and Landau-Zener Tunneling in a Solid
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.
Transport of Photonic Bloch Wave in Arrayed Two-Level Atoms.
Chang, Chih-Chun; Lin, Lee; Chen, Guang-Yin
2018-01-24
In a quantum system of arrayed two-level atoms interacting with light, the interacted (dressed) photon is propagating in a periodic medium and its eigenstate ought to be of Bloch type with lattice symmetry. As the energy of photon is around the spacing between the two atomic energy levels, the photon will be absorbed and is not in the propagating mode but the attenuated mode. Therefore an energy gap exists in the dispersion relation of the photonic Bloch wave of dressed photon in addition to the nonlinear behaviors due to atom-light interactions. There follows several interesting results which are distinct from those obtained through a linear dispersion relation of free photon. For example, slow light can exist, the density of state of dressed photon is non-Lorentzian and is very large around the energy gap; the Rabi oscillations become monotonically decreasing in some cases; and besides the superradiance occurs at long wavelengths, the spontaneous emission is also very strong near the energy gap because of the high density of state.
Bloch Waves in Minimal Landau Gauge and the Infinite-Volume Limit of Lattice Gauge Theory.
Cucchieri, Attilio; Mendes, Tereza
2017-05-12
By exploiting the similarity between Bloch's theorem for electrons in crystalline solids and the problem of Landau gauge fixing in Yang-Mills theory on a "replicated" lattice, we show that large-volume results can be reproduced by simulations performed on much smaller lattices. This approach, proposed by Zwanziger [Nucl. Phys. B412, 657 (1994)NUPBBO0550-321310.1016/0550-3213(94)90396-4], corresponds to taking the infinite-volume limit for Landau-gauge field configurations in two steps: first for the gauge transformation alone, while keeping the lattice volume finite, and second for the gauge-field configuration itself. The solutions to the gauge-fixing condition are then given in terms of Bloch waves. Applying the method to data from Monte Carlo simulations of pure SU(2) gauge theory in two and three space-time dimensions, we are able to evaluate the Landau-gauge gluon propagator for lattices of linear extent up to 16 times larger than that of the simulated lattice. This approach is reminiscent of the Fisher-Ruelle construction of the thermodynamic limit in classical statistical mechanics.
Singularity of the time-energy uncertainty in adiabatic perturbation and cycloids on a Bloch sphere
Oh, Sangchul; Hu, Xuedong; Nori, Franco; Kais, Sabre
2016-02-01
Adiabatic perturbation is shown to be singular from the exact solution of a spin-1/2 particle in a uniformly rotating magnetic field. Due to a non-adiabatic effect, its quantum trajectory on a Bloch sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic path traced by the instantaneous eigenstate. However, the non-adiabatic Aharonov- Anandan geometric phase, measured by the area enclosed by the exact path, approaches smoothly the adiabatic Berry phase, proportional to the area enclosed by the adiabatic path. The singular limit of the time-energy uncertainty and the regular limit of the geometric phase are associated with the arc length and arc area of the cycloid on a Bloch sphere, respectively. Prolate and curtate cycloids are also traced by different initial states outside and inside of the rolling circle, respectively. The axis trajectory of the rolling circle, parallel to the adiabatic path, is shown to be an example of transitionless driving. The non-adiabatic resonance is visualized by the number of cycloid arcs.
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Caroline Terra de Oliveira
2014-08-01
Full Text Available In this article we propose to discuss the concept of hope and daydream from the writings of Ernst Bloch and Paulo Freire. Based on the production of Ernst Bloch explored the philosophy of hope, as an expression of affection expectant positive, from the imperative to understand how the act related to a political commitment by the constitution from seeking concrete utopias. The problematization of the term from Paulo Freire, in turn, enters the discussion about the importance of Pedagogy of Hope as a political learning process and committed to a utopia. In this debate, we rescued the concept of hope, unpublished and unfinished viable in Freire. Therefore, it is claimed the need for a critical reflection about the importance of this subject today in the face of neoliberal discourses fatalists, and the imperative to orient ourselves with the objective of building dreams subjects that challenge the established and they see meaning in the struggle for a pedagogy of hope that both reach the school, as other educational spaces training of human beings.
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
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Eleni Bisognin
2008-03-01
Full Text Available In this work we study the asymptotic behavior of solutions of a dissipative plate equation in $mathbb{R}^N$ with periodic coefficients. We use the Bloch waves decomposition and a convenient Lyapunov function to derive a complete asymptotic expansion of solutions as $to infty$. In a first approximation, we prove that the solutions for the linear model behave as the homogenized heat kernel.
Boundedness and compactness of a new product-type operator from a general space to Bloch-type spaces
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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.
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...
Dynamics of Peregrine combs and Peregrine walls in an inhomogeneous Hirota and Maxwell-Bloch system
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.
Bloch surface waves confined in one dimension with a single polymeric nanofibre
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.
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)
The Harmonic Bloch and Besov Spaces on the Real Unit Ball by an Oscillation
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Xi Fu
2016-01-01
Full Text Available Let B be the real unit ball in Rn and f∈CN(B. Given a multi-index m=(m1,…,mn of nonnegative integers with |m|=N, we set the quantity supx∈B,y∈E(x,r,x≠y(1-|x|2α(1-|y|2β|∂mf(x-∂mf(y|/|x-y|γ[x,y]1-γ, x≠y, where 0≤γ≤1 and α+β=N+1. In terms of it, we characterize harmonic Bloch and Besov spaces on the real unit ball. This generalizes the main results of Yoneda, 2002, into real harmonic setting.
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.
de Lasson, Jakob R.; Kristensen, Philip Trøst; Mørk, Jesper; Gregersen, Niels
2013-05-01
In open nanophotonic structures, the natural modes are so-called quasi-normal modes satisfying an outgoing wave boundary condition. We present a new scheme based on a modal expansion technique, a scattering matrix approach and Bloch modes of periodic structures for determining these quasi-normal modes. As opposed to spatial discretization methods like the finite-difference time-domain method and the finite element method, the present approach satisfies automatically the outgoing wave boundary condition in the propagation direction which represents a significant advantage of our new method. The scheme uses no external excitation and determines the quasi-normal modes as unity eigenvalues of the cavity roundtrip matrix. We demonstrate the method and the quasi-normal modes for two types of two-dimensional photonic crystal structures, and discuss the quasi-normal mode field distributions and Q-factors in relation to the transmission spectra of these structures.
Nondestructive cavity QED probe of Bloch oscillations in a gas of ultracold atoms
International Nuclear Information System (INIS)
Peden, B. M.; Meiser, D.; Holland, M. J.; Chiofalo, M. L.
2009-01-01
We describe a scheme for probing a gas of ultracold atoms trapped in an optical lattice and moving in the presence of an external potential. The probe is nondestructive and uses the existing lattice fields as the measurement device. Two counterpropagating cavity fields simultaneously set up a conservative lattice potential and a weak quantum probe of the atomic motion. Balanced heterodyne detection of the probe field at the cavity output along with integration in time and across the atomic cloud yield information about the atomic dynamics in a single run. The scheme is applied to a measurement of the Bloch oscillation frequency for atoms moving in the presence of the local gravitational potential. Signal-to-noise ratios are estimated to be as high as 10 4 .
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.
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.
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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.
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Edilson Matos
2000-09-01
Full Text Available Spermatozoa of amazon fish, Acestrorhynchus falcatus Bloch, 1794 were investigated by optical microscopy (DIC and electron microscopy (TEM. Spermatozoa have no acrosome, the head is ovoid, and the midpiece region cylindrical, contains spherical mitochondria. The centriolar complex is located at the lateral side of the nucleus, formed by nine peripheral pairs of microtubules and arranged in a right angle to each other. The flagellum consists of nine pairs of peripheral and two central microtubules.
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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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
Young, C.W. [Applied Research Associates, Inc., Albuquerque, NM (United States)
1997-10-01
In 1967, Sandia National Laboratories published empirical equations to predict penetration into natural earth materials and concrete. Since that time there have been several small changes to the basic equations, and several more additions to the overall technique for predicting penetration into soil, rock, concrete, ice, and frozen soil. The most recent update to the equations was published in 1988, and since that time there have been changes in the equations to better match the expanding data base, especially in concrete penetration. This is a standalone report documenting the latest version of the Young/Sandia penetration equations and related analytical techniques to predict penetration into natural earth materials and concrete. 11 refs., 6 tabs.
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...
International Nuclear Information System (INIS)
Longhi, S.
2009-01-01
The onset of Bloch oscillations in an exactly solvable one-dimensional tight-binding lattice model with increasing hopping rates between adjacent sites is theoretically investigated. In particular, it is shown that Wannier-Stark localization is attained at a finite value of the applied dc field. An optical realization of the lattice model, based on light transport in engineered waveguide arrays, is also proposed.
Weiner, J.
2007-01-01
The purpose of this comment is first to correct a misapprehension of the role played by composite wave diffraction on surface-wave generation at subwavelength structures and second to point out that periodic Bloch structures are unnecessary for the efficient production of the surface plasmon polariton (SPP) guided mode either as traveling or standing waves. Guided surface waves originate from simple slit or groove edges illuminated under normal incidence, and one-dimensional (1-D) surface cav...
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
Establishment of a cell line from kidney of seabass, Lates calcarifer (Bloch
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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.
Bloch Surface Waves for MoS2 Emission Coupling and Polariton Systems
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Giovanni Lerario
2017-11-01
Full Text Available Due to their extraordinary quality factor and extreme sensitivity to surface perturbations, Bloch surface waves (BSW have been widely investigated for sensing applications so far. Over the last few years, on-chip control of optical signals through BSW has experienced a rapidly-expanding interest in the scientific community, attesting to BSW’s position at the forefront towards on-chip optical operations. The backbone of on-chip optical devices requires the choice of integrated optical sources with peculiar optic/optoelectronic properties, the efficient in-plane propagation of the optical signal and the possibility to dynamic manipulate the signal through optical or electrical driving. In this paper, we discuss our approach in addressing these requirements. Regarding the optical source integration, we demonstrate the possibility to couple the MoS2 mono- and bi-layers emission—when integrated on top of a 1D photonic crystal—to a BSW. Afterward, we review our results on BSW-based polariton systems (BSWP. We show that the BSWPs combine long-range propagation with energy tuning of their dispersion through polariton–polariton interactions, paving the way for logic operations.
Abner Doubleday, Marc Bloch, and the cultural significance of baseball in rural America.
Vaught, David
2011-01-01
In 1907 baseball's promoters decreed that Civil War hero Abner Doubleday created the game in the village of Cooperstown, New York, in 1839. Baseball thus acquired a distinctly rural American origin and a romantic pastoral appeal. Skeptics have since presented irrefutable evidence that America's pastime was neither born in the United States nor was a product of rural life. But in their zeal to debunk the myth of baseball's rural beginnings, historians have fallen prey to what Annales School founder Marc Bloch famously called the "idol of origins," and all but neglected the very real phenomenon of rural baseball itself. The claim that baseball has always been "a city game for city men" does not stand up to empirical scrutiny anymore than the Doubleday myth itself, as this address demonstrates with three case studies -- Cooperstown in the 1830s, Davisville, California, in the 1880s, and Milroy, Minnesota, in the 1950s. Baseball may have been a source of rural nostalgia for city people, but it was the sport of choice for farmers and a powerful cultural agent.
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.
Cytotoxic and genotoxic affects of acid mine drainage on fish Channa punctata (Bloch).
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.
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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.
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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
Baghbadorani, H Kaviani; Barvestani, J; Entezar, S Roshan
2017-01-20
In biosensors research, much effort has been made to achieve high sensitivity to detect lower concentrations of analyte in a solution by testing different kinds of materials. In this paper, we present a biosensor based on Bloch surface waves made of photonic crystal (PhC) including graphene nanolayers under the Kretschmann configuration. The band structures, surface modes, reflectivity, and sensitivity of the PhC biosensor are calculated by the transfer matrix method and results are compared with those of the structure without graphene layers. Our investigations show that the angular sensitivity of the biosensor considerably increases in the presence of the graphene layers. Moreover, we study the effect of the number of the graphene layers placed on the surface of the biosensor on the performance of our proposed biosensor. The results reveal that the sensitivity of the biosensor is enhanced by increasing the number of graphene layers on the surface due to the π-stacking interactions between graphene's honeycomb cells and the carbon rings in biomolecules. Furthermore, our results show that the phase sensitivity is higher than the angular sensitivity, which can promote the accuracy of the calculations.
Anomalous breakdown of Bloch's rule in the Mott-Hubbard insulator MnTe2
Chatterji, Tapan; dos Santos, Antonio M.; Molaison, Jamie J.; Hansen, Thomas C.; Klotz, Stefan; Tucker, Mathew; Samanta, Kartik; Saha-Dasgupta, Tanusri
2015-03-01
We reinvestigate the pressure dependence of the crystal structure and antiferromagnetic phase transition in MnTe2 using the rigorous and reliable tool of high-pressure neutron powder diffraction. First-principles density functional theory calculations are carried out in order to gain microscopic insight. The measured Néel temperature of MnTe2 is found to show unusually large pressure dependence of 12 KGPa-1 . This gives rise to a large violation of Bloch's rule given by α =d/logTN d logV =-10/3 ≈-3.3 , to an α value of -6.0 ±0.1 for MnTe2. The ab initio calculation of the electronic structure and the magnetic exchange interactions in MnTe2 for the measured crystal structures at different pressures indicates the pressure dependence of the Neél temperature α is -5.61 , in close agreement with experimental findings. The microscopic origin of this behavior turns out to be dictated by the distance dependence of the cation-anion hopping interaction strength.
Jones, Kyle M.; Randtke, Edward A.; Howison, Christine M.; Pagel, Mark D.
2016-03-01
We have developed a MRI method that can measure extracellular pH in tumor tissues, known as acidoCEST MRI. This method relies on the detection of Chemical Exchange Saturation Transfer (CEST) of iopamidol, an FDA-approved CT contrast agent that has two CEST signals. A log10 ratio of the two CEST signals is linearly correlated with pH, but independent of agent concentration, endogenous T1 relaxation time, and B1 inhomogeneity. Therefore, detecting both CEST effects of iopamidol during in vivo studies can be used to accurately measure the extracellular pH in tumor tissues. Past in vivo studies using acidoCEST MRI have suffered from respiration artifacts in orthotopic and lung tumor models that have corrupted pH measurements. In addition, the non-linear fitting method used to analyze results is unreliable as it is subject to over-fitting especially with noisy CEST spectra. To improve the technique, we have recently developed a respiration gated CEST MRI pulse sequence that has greatly reduced motion artifacts, and we have included both a prescan and post scan to remove endogenous CEST effects. In addition, we fit the results by parameterizing the contrast of the exogenous agent with respect to pH via the Bloch equations modified for chemical exchange, which is less subject to over-fitting than the non-linear method. These advances in the acidoCEST MRI technique and analysis methods have made pH measurements more reliable, especially in areas of the body subject to respiratory motion.
Directory of Open Access Journals (Sweden)
Palanivel Bharadhirajan
2014-01-01
Full Text Available Objective: To assess the nutritions in Mene maculata (Bloch & Schneider, 1801 (M. maculata. Methods: Fishes (14-16 cm were obtained from the landings at Parangipettai for the evaluation of biochemical composition. The present study deals with biochemical composition such as protein, carbohydrate, lipid, amino acids fatty acids, vitamins and minerals which were evaluated in the moonfish. Results: The results of proximate composition in M. maculata showed that the percentage of protein was high in the tissue (23.16%, followed by the carbohydrate (1.3% and lipid (2.62%. Totally 20 essential and nonessential amino acids were present at the rate of 46.72% and 43.91%. In the analysis, the fatty acid profile by gas chromatography revealed the presence of higher amount of saturated fatty acid (palmitic acid 22.17% than monounsaturated fatty acid (oleic acid 14.51% and polyunsaturated fatty acid (alpha linolenic acid 16.07%. Vitamins were detected in M. maculata. Among them, vitamin A was found in higher levels (124.5 mg/g, whereas vitamin B6 was noticed as lower levels (0.34 mg/g. In the present study, totally 5 macro minerals and 2 trace minerals were reported. The macro mineral calcium (156.7 mg/g was found at the highest level and other minerals such as sodium (31.98 mg/g, potassium (21.33 mg/g, copper (1.43 mg/g and magnesium (0.341 mg/g were also detected in the moonfish. Conclusions: The result showed that the moonfish M. maculata tissue is a valuable food recipe for human consumption, due to its high quality protein and well-balanced amino acids.
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.
Antes, desde y para el exilio. Herencia de esta época (1935/1962 de Ernst Bloch
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Salmerón Infante, Miguel
2009-10-01
Full Text Available The first edition of Erbschaft dieser Zeit was published in Zurich in 1935, during Ernst Bloch’s five-year period of emigration from Nazi-Germany in various European capitals before his final emigration to America for ten years in 1938. In this book Bloch made a courageous stand in defence of the artistic avant-garde against the dogmatic advocates of socialist realism. His particularly adversary was Georg Lukács. But of course one of the most fascinating aspects of the book is that is also reads as a contemporary observation of the rise of the Nazis. Erbschaft is undoubtedly the major work of Weimar Germany Exile.La primera edición de Erbschaft dieser Zeit fue publicada en 1935 en Zurich, durante la emigración de Ernst Bloch de la Alemania nazi por un período de cinco años en el que residió en varias capitales europeas antes de su marcha definitiva a América en 1938, donde vivió diez años. En este libro Bloch hace una encorajinada defensa de la vanguardia artística contra los abogados del realismo socialista. Su adversario específico era Georg Lukács. Pero sin duda alguna uno de los aspectos más fascinantes de este libro es que puede leerse como una observación contemporánea de la ascensión al poder de los nazis. Erbschaft es indudablemente la obra clave del exilio de la Alemania de Weimar.
Digital Repository Service at National Institute of Oceanography (India)
Sanaye, S.V.; Rivonker, C.U.; Ansari, Z.A.; Sreepada, R.A.
along the coastal waters of Goa, central west coast of India, a single male alligator pipefish, S. biaculeatus (Bloch, 1785), accidentally caught in gill net with shredded branches of seaweed Sargassum sp., at depth of 20 m on 15 January 2012 formed... coast of India Results A single male specimen of alligator pipefish (Fig. 2) accidentally caught in one of the gill net (25 mm mesh size) operated in the bay estuarine system of Zuari River at a depth of 20 m. The collected specimen was observed...
Resonant crossover of terahertz loss to the gain of a Bloch oscillating InAs/AlSb superlattice.
Savvidis, P G; Kolasa, B; Lee, G; Allen, S J
2004-05-14
Terahertz absorption in waveguides loaded with InAs/AlSb super-superlattice mesas reveals a frequency dependent crossover from loss to gain that is related to the Stark ladder produced by an applied dc electric field. Electric field domains appear to be suppressed in the super-superlattice composed of many very short segments of superlattice, interrupted by heavily doped InAs regions. Resonant crossover is indicated by an increase in terahertz transmission as the Stark splitting or Bloch frequency determined by the applied dc electric field exceeds the measurement frequency.
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.
Discontinuous Galerkin Approximations for Computing Electromagnetic Bloch Modes in Photonic Crystals
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
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.
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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.
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
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Master equation for open two-band systems and its applications to Hall conductance
Shen, H. Z.; Zhang, S. S.; Dai, C. M.; Yi, X. X.
2018-02-01
Hall conductivity in the presence of a dephasing environment has recently been investigated with a dissipative term introduced phenomenologically. In this paper, we study the dissipative topological insulator (TI) and its topological transition in the presence of quantized electromagnetic environments. A Lindblad-type equation is derived to determine the dynamics of a two-band system. When the two-band model describes TIs, the environment may be the fluctuations of radiation that surround the TIs. We find the dependence of decay rates in the master equation on Bloch vectors in the two-band system, which leads to a mixing of the band occupations. Hence the environment-induced current is in general not perfectly topological in the presence of coupling to the environment, although deviations are small in the weak limit. As an illustration, we apply the Bloch-vector-dependent master equation to TIs and calculate the Hall conductance of tight-binding electrons in a two-dimensional lattice. The influence of environments on the Hall conductance is presented and discussed. The calculations show that the phase transition points of the TIs are robust against the quantized electromagnetic environment. The results might bridge the gap between quantum optics and topological photonic materials.
Gradhand, M; Fedorov, D V; Pientka, F; Zahn, P; Mertig, I; Györffy, B L
2012-05-30
Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.
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.
Partial Differential Equations
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.
van As, Liesl L; van As, Jo G
2007-05-01
During surveys of the biodiversity of fish parasites in the Okavango River and Delta, Botswana, specimens of Lamproglena von Nordmann, 1832 were found associated with the African pike Hepsetus odoe (Bloch). This Lamproglena species distinctly differs from all known species based on morphological features, in particular the cephalothorax and the maxilliped; it is described as L. hepseti n. sp. and is specific to its host, the African pike.
Czech Academy of Sciences Publication Activity Database
Pittner, Jiří
2003-01-01
Roč. 118, č. 24 (2003), s. 10876-10889 ISSN 0021-9606 R&D Projects: GA MŠk OC D23.001; GA ČR GA203/99/D009; GA AV ČR IAA4040108 Institutional research plan: CEZ:AV0Z4040901 Keywords : continuous transition * Brillouin-Wigner * Rayleigh-Schrödinger Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.950, year: 2003
International Nuclear Information System (INIS)
Barber, D.P.
2015-10-01
I extend and update earlier work, summarised in an earlier paper (D.P. Barber, M. Voigt, AIP Conference Proceedings 1149 (28)), whereby the invariant polarisation-tensor field (ITF) for deuterons in storage rings was introduced to complement the invariant spin field (ISF). Taken together, the ITF and the ISF provide a definition of the equilibrium spin density-matrix field which, in turn, offers a clean framework for describing equilibrium spin-1 ensembles in storage rings. I show how to construct the ITF by stroboscopic averaging, I give examples, I discuss adiabatic invariance and I introduce a formalism for describing the effect of noise and damping.
Electronic states in crystals of finite size quantum confinement of bloch waves
Ren, Shang Yuan
2017-01-01
This book presents an analytical theory of the electronic states in ideal low dimensional systems and finite crystals based on a differential equation theory approach. It provides precise and fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and offers new insights into some of the basic problems in low-dimensional systems, such as the surface states and quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Many previous predictions have been confirmed in subsequent investigations by other authors on various relevant problems. In this new edition, the theory is further extended to one-dimensional photonic crystals and phononic crystals, and a general theoretical formalism for investigating the existence and properties of surface states/modes in semi-infinite one-dimensional crystals is developed. In addition, there are various revisions and improvements, including us...
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Javier Barrera-Chica
2009-12-01
Full Text Available Objetivo. Estudiar los hábitos alimentarios de la Mayupa (Sternopygus macrurus Bloch & Schneider, 1801 en el río Sinú, Colombia. Materiales y métodos. El contenido estomacal se evaluó con el coeficiente de vacuidad, grado de llenado, grado de digestión, frecuencia de ocurrencia, frecuencia numérica, gravimetría, indice de importancia relativa (IIR y la relación longitud intestinal (LI-longitud total (LT. Resultados. Solo pocos estómagos se encontraron vacíos (CV =6.9% y el 60.0% de las presas se encontraron frescas. Se identificaron cuatro ítems alimentarios: peces, crustáceos, material vegetal y otros. Peces fue el ítem más frecuente (76.9%, abundante (48.3%, con mayor composición por peso (81.9% y con mayor importancia relativa (63.2%. Conclusiones. Los resultados obtenidos permiten inferir que la Mayupa es un pez de hábitos alimentarios carnívoros, con preferencia por los peces.
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.
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.
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.
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.
Difference equations by differential equation methods
Hydon, Peter E
2014-01-01
Most well-known solution techniques for differential equations exploit symmetry in some form. Systematic methods have been developed for finding and using symmetries, first integrals and conservation laws of a given differential equation. Here the author explains how to extend these powerful methods to difference equations, greatly increasing the range of solvable problems. Beginning with an introduction to elementary solution methods, the book gives readers a clear explanation of exact techniques for ordinary and partial difference equations. The informal presentation is suitable for anyone who is familiar with standard differential equation methods. No prior knowledge of difference equations or symmetry is assumed. The author uses worked examples to help readers grasp new concepts easily. There are 120 exercises of varying difficulty and suggestions for further reading. The book goes to the cutting edge of research; its many new ideas and methods make it a valuable reference for researchers in the field.
Handbook of integral equations
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.
Controlled Population of Floquet-Bloch States via Coupling to Bose and Fermi Baths
Directory of Open Access Journals (Sweden)
Karthik I. Seetharam
2015-12-01
Full Text Available External driving is emerging as a promising tool for exploring new phases in quantum systems. The intrinsically nonequilibrium states that result, however, are challenging to describe and control. We study the steady states of a periodically driven one-dimensional electronic system, including the effects of radiative recombination, electron-phonon interactions, and the coupling to an external fermionic reservoir. Using a kinetic equation for the populations of the Floquet eigenstates, we show that the steady-state distribution can be controlled using the momentum and energy relaxation pathways provided by the coupling to phonon and Fermi reservoirs. In order to utilize the latter, we propose to couple the system and reservoir via an energy filter which suppresses photon-assisted tunneling. Importantly, coupling to these reservoirs yields a steady state resembling a band insulator in the Floquet basis. The system exhibits incompressible behavior, while hosting a small density of excitations. We discuss transport signatures and describe the regimes where insulating behavior is obtained. Our results give promise for realizing Floquet topological insulators.
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.
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
Introduction to differential equations
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
Particle methods for Boltzmann equation
International Nuclear Information System (INIS)
Hermeline, F.
1985-05-01
This work is aimed at showing how to discretize an equation such as Boltzmann equation in its most general form, by particle methods. Then method is applied to some equations of plasma physics which appear as peculiar cases of Boltzmann equation, such as Vlasov equation, Bhatnager-Gross-Krook equation, Fokker-Planck equation and neutron transport equation [fr
Bloch, Gramsci e Paulo Freire: referências fundamentais para os atos da denúncia e do anúncio
Directory of Open Access Journals (Sweden)
Maria Ceci Araujo Misoczky
Full Text Available A apropriação e aproximação das formulações de Ernst Bloch, Antonio Gramsci e Paulo Freire constituem parte importante das reflexões que compartilhamos em nosso coletivo de trabalho, que tem como tema de estudo organização e práxis libertadora. Neste artigo fazemos uma apresentação de nossas leituras situadas destes autores, seguida de um exercício de aproximação entre suas formulações. A realidade como processo histórico e a libertação do ser humano das condições de opressão (materiais e intelectuais estão presentes nas obras dos três autores. Para Freire a libertação do oprimido é também a libertação do opressor; para Gramsci os subalternos devem tornar-se hegemônicos pela concepção de uma nova direção intelectual e moral que seja comprometida com o mais alto valor do ser humano: a própria existência; para Bloch a libertação é imanente à existência humana. Por conseguinte, a libertação também é concebida pelos três autores como um processo, da mesma forma que a hegemonia, que nunca é total, fixa ou definitiva, ou a realidade que está sendo o tempo todo. Bloch, Gramsci e Freire autorizam posições que vinculam a crítica ao sistema com a utopia presente e concreta, em nossa aprendizagem na interação com os movimentos e lutadores sociais.
La conciencia de la libertad (La filosofía moral como filosofía de la historia en Ernst Bloch)
Gimbernat, José Antonio
1991-01-01
Not available.
A partir del concepto hegeliano de «progreso en la conciencia de la libertad », se puede hacer una lectura de la filosofía moral de Bloch como filosofía de la historia. Ello conduce a una reino reinterpretación libre y materialista de Hegel y a una recuperación de la moral en el marxismo. En diálogo con Kant se hace posible descubrir el potencial utópico del énfasis subjetivo de la moral. El objetivo del reino de la libertad marxiano es la clave de una histor...
Directory of Open Access Journals (Sweden)
Munawar Khalil
2013-12-01
Full Text Available Tujuan penelitian ini adalah untuk mempelajari pengaruh logam berat merkuri nitrat (Hg(NO32 pada struktur histologis hati benih ikan kakap putih (Lates calcarifer Bloch yang dipelihara di air laut. Analisis struktur jaringan hati dilakukan melalui teknik histologi. Hasil penelitian menunjukkan bahwa Hg(NO32 memberikan efek negatif pada hati benih ikan. Pada jaringan hati, (Hg(NO32 menyebabkan kerusakan atrophy, necrosis, lapisan antar sel hati berpisah, perlemakan hati, pembengkakan sel yang tidak beraturan, degenerasi pada vacuola, terbentuknya ruang antar sel, hepatitis, sirrhosis dan terdapatnya akumulasi logam berat Hg(NO32 dalam jaringan hati.
Beginning partial differential equations
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
Ordinary differential equations
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
Fay, Temple H.
2002-01-01
We investigate the pendulum equation [theta] + [lambda][squared] sin [theta] = 0 and two approximations for it. On the one hand, we suggest that the third and fifth-order Taylor series approximations for sin [theta] do not yield very good differential equations to approximate the solution of the pendulum equation unless the initial conditions are…
A Comparison of IRT Equating and Beta 4 Equating
Kim, Dong-In; Brennan, Robert; Kolen, Michael
2005-01-01
Four equating methods (3PL true score equating, 3PL observed score equating, beta 4 true score equating, and beta 4 observed score equating) were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional-mean-squared-error (CMSE) difference, and the equi-percentile equating property. True score…
RELACIONES TALLA-PESO DEL BARBUL (Pimelodus clarias f.c. Bloch, 1785 EN LA CUENCA DEL RIO SINU,
Directory of Open Access Journals (Sweden)
Iliana Santos-Sanes,
2006-12-01
Full Text Available Objetivo. Establecer las relaciones de talla y peso del barbul (Pimelodus clarias en la cuenca del río Sinú. Materiales y Métodos. Se estimaron las relaciones talla-peso de 4324 individuos de Barbul (Pimelodus clarias f.c. Bloch, 1785 colectados entre enero 2000 y diciembre 2002. Resultados. La longitud total (LT osciló entre 13.0-30.0 cm, promedio de 19.5 (±1.6 cm y el peso total (WT entre 20.0 y 248.1 g, promedio de 65.8 (±23.2 g. Las relaciones lineales estimadas fueron: LT = 1.92 (�� 0.16 + 1.20 (± 0.01 LS, r = 0.96; LT = 1.21 (± 0.16 + 1.15 (± 0.01 LH; r = 0.97 y LH = 0.91 (± 0.10 + 1.02 (± 0.01 LS, r = 0.97; con diferencias significativas entre las pendientes de la relación longitud estándar (LS-longitud horquilla (LH. La relación longitud-peso fue: WT = 0.005 (± 0.09 LT 3.16 (± 0.07, n = 4324, r = 0.81, con diferencias estadísticas significativas entre los diferentes coeficientes de crecimiento y factores de condición. Se encontró correlación entre el factor de condición, los niveles del Río Sinú y la época de desove del Barbul, la cual se extiende de marzo a octubre. Conclusión. Los resultados alcanzados en este estudio sugieren que las nuevas condiciones del río no han afectado la dinámica poblacional de la especie en lo que al crecimiento en talla y peso se refiere, y que el Barbul se ha adaptado a estas nuevas condiciones.
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
Functional equations with causal operators
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.
Elliptic partial differential equations
Volpert, Vitaly
If we had to formulate in one sentence what this book is about it might be "How partial differential equations can help to understand heat explosion, tumor growth or evolution of biological species". These and many other applications are described by reaction-diffusion equations. The theory of reaction-diffusion equations appeared in the first half of the last century. In the present time, it is widely used in population dynamics, chemical physics, biomedical modelling. The purpose of this book is to present the mathematical theory of reaction-diffusion equations in the context of their numerous applications. We will go from the general mathematical theory to specific equations and then to their applications. Mathematical anaylsis of reaction-diffusion equations will be based on the theory of Fredholm operators presented in the first volume. Existence, stability and bifurcations of solutions will be studied for bounded domains and in the case of travelling waves. The classical theory of reaction-diffusion equ...
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.
Partial differential equations
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...
Differential equations for dummies
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.
Degenerate nonlinear diffusion equations
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...
Reactimeter dispersion equation
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...
Differential equations I essentials
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.
The 'golden' algebraic equations
International Nuclear Information System (INIS)
Stakhov, A.; Rozin, B.
2006-01-01
The special case of the (p + 1)th degree algebraic equations of the kind x p+1 = x p + 1 (p = 1, 2, 3, ?) is researched in the present article. For the case p = 1, the given equation is reduced to the well-known Golden Proportion equation x 2 = x + 1. These equations are called the golden algebraic equations because the golden p-proportions τ p , special irrational numbers that follow from Pascal's triangle, are their roots. A research on the general properties of the roots of the golden algebraic equations is carried out in this article. In particular, formulas are derived for the golden algebraic equations that have degree greater than p + 1. There is reason to suppose that algebraic equations derived by the authors in the present article will interest theoretical physicists. For example, these algebraic equations could be found in the research of the energy relationships within the structures of many compounds and physical particles. For the case of butadiene (C 4 H 6 ), this fact is proved by the famous physicist Richard Feynman
Ordinary differential equations
Pontryagin, Lev Semenovich
1962-01-01
Ordinary Differential Equations presents the study of the system of ordinary differential equations and its applications to engineering. The book is designed to serve as a first course in differential equations. Importance is given to the linear equation with constant coefficients; stability theory; use of matrices and linear algebra; and the introduction to the Lyapunov theory. Engineering problems such as the Watt regulator for a steam engine and the vacuum-tube circuit are also presented. Engineers, mathematicians, and engineering students will find the book invaluable.
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Lima, Elisama E.M.; Losano, L. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil)
2017-02-15
This work reports on models described by two real scalar fields coupled with gravity in the five-dimensional spacetime, with a warped geometry involving one infinite extra dimension. Through a mechanism that smoothly changes a thick brane into a hybrid brane, one investigates the appearance of hybrid branes hosting internal structure, characterized by the splitting on the energy density and the volcano potential, induced by the parameter which controls interactions between the two scalar fields. In particular, we investigate distinct symmetric and asymmetric hybrid brane scenarios. (orig.)
fractional differential equations
Indian Academy of Sciences (India)
We apply this method for solving space–time fractional Cahn--Allen equation and space--time fractional Klein–Gordon equation. The fractional derivatives are described in the sense of modified Riemann--Lioville. As a result of some exact solution in the form of hyperbolic, trigonometric and rational solutions are deduced.
Directory of Open Access Journals (Sweden)
Hannelore Breckner
2000-01-01
Full Text Available We consider a stochastic equation of Navier-Stokes type containing a noise part given by a stochastic integral with respect to a Wiener process. The purpose of this paper is to approximate the solution of this nonlinear equation by the Galerkin method. We prove the convergence in mean square.
Indian Academy of Sciences (India)
role in converting the Fokas equation into Hirota's bilinear form. Keywords. Bilinearization; multisoliton solution; Fokas equation; Hirota's bilinear method. PACS Nos 05.45.Yv; 04.20.Jb; 02.30.Jr. 1. Introduction. As pointed out by Drazin and Johnson [1], it is not easy to give a comprehensive and precise definition of a soliton.
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
Elliptic Quadratic Operator Equations
Ganikhodjaev, Rasul; Mukhamedov, Farrukh; Saburov, Mansoor
2017-01-01
In the present paper is devoted to the study of elliptic quadratic operator equations over the finite dimensional Euclidean space. We provide necessary and sufficient conditions for the existence of solutions of elliptic quadratic operator equations. The iterative Newton-Kantorovich method is also presented for stable solutions.
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the ... tedious and more time saving than the classical method in the solution of the aforementioned differential equation. ... silos, pipelines, bridge arches or wind turbine towers [3]. The objective of this ...
Partial differential equations
Indian Academy of Sciences (India)
been a regular stream of high quality work done in these areas. Talking of elliptic partial differen- tial equations, important contributions have been made in the ...... [6] Evans L C 1992 Periodic homogenisation of certain fully nonlinear partial differential equations; Proc. Roy. Soc. Edinburgh Sect. A 120 No. 3–4, 245–265.
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.
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
Alternative equations of gravitation
International Nuclear Information System (INIS)
Pinto Neto, N.
1983-01-01
It is shown, trough a new formalism, that the quantum fluctuation effects of the gravitational field in Einstein's equations are analogs to the effects of a continuum medium in Maxwell's Electrodynamics. Following, a real example of the applications of these equations is studied. Qunatum fluctuations effects as perturbation sources in Minkowski and Friedmann Universes are examined. (L.C.) [pt
Applied partial differential equations
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...
Directory of Open Access Journals (Sweden)
К. Heina
2017-09-01
Full Text Available Purpose. To provide the biological assessment of the silver Prussian carp (Carassius auratus gibelio (Bloch, 1782 commercial stock of the Dnieper-Bug estuary in the conditions of the transformed Dnieper river flow. Methodology. During the analysis of the biological state of the Prussian carp commercial stock, the main attention was given to the dynamics of age and sexual structure, length-weight growth rate, absolute fecundity and condition factor. The basic data were collected during the work of control-observation stations of the Institute of Fisheries in the Dnieper-Bug estuary during the current century. The collection and processing of ichthyological materials were performed in accordance with the generally accepted methodologies. Findings. The analysis showed that during the current century, the age structure of the Prussian carp of the Dnieper-Bug estuary was the most labile among other commercial cyprinids. It was found that as a result of an increase in the right wing of the age series, there was a gradual increase of the mean weighted age of its commercial stock. At the beginning of studies (2001-2002, the core of the stock was formed by age-3-6 fish (up ; however in subsequent years, a displacement of dominant groups toward the dominance of age-4-7 fish (more than 80% of the total stock was observed. At the same time, the relative number of age-3 fish (recruits was at a relatively high level – up to 10.6%. The linear growth varied more intensively until the age-5, but it reduced with ageing and did not show high variability. The body weight most variable was in age-4 fish (Cv=9.62%. The noted insignificant deviations in the body weight growth rate of the right wing of the age series was due to stable predominance of females in the stock structure, which were characterized by a variability of the mean weight as a result of different development of gonads. The dynamics of the age-related changes in the condition factor indicated on a
O expressionismo na estética marxista de Ernst Bloch : diálogo com György Lukás e Bertolt Brecht
Tomé, João Miguel Banito
2017-01-01
A presente dissertação assume o objectivo de lançar um estudo acerca da estética marxista de Ernst Bloch, centrando a sua análise na questão do expressionismo. A componente histórica a que a reflexão filosófica não poderá escapar lança-nos na demanda de estabelecer uma leitura tão ampla quanto possível, evitando uma exposição de conteúdos meramente circunscrita ao pensamento do autor. Projecta-se, nessa medida, um olhar plural sobre os debates que, de forma mais significativa, marcaram a cons...
Marmodoro, Alberto; Ernst, Arthur; Ostanin, Sergei; Sandratskii, Leonid; Trevisanutto, Paolo E.; Lathiotakis, Nektarios N.; Staunton, Julie B.
2016-12-01
The nonlocal coherent-potential approximation provides a systematic technique for the study of short-range ordering effects in a variety of disordered systems. In its original formulation the technique, however, shows an unwanted dependence on details in the coarse-grained effective medium construction. This is particularly evident in the study of k ⃗-resolved quantities, such as the Bloch spectral function and other non-site-diagonal observables. We remove the issue and recover fully physical results in first principles studies of real materials, by means of a resampling procedure first proposed for model tight-binding Hamiltonians. The prescription is further generalized to the case of complex unit cell compounds, with more than a single sublattice, and illustrated through examples from metallic alloys and disordered local moment simulations of paramagnetism in the prototype iron-based superconductor FeSe.
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.
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.
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.
Ordinary differential equations
Ince, Edward Lindsay
1956-01-01
The theory of ordinary differential equations in real and complex domains is here clearly explained and analyzed. Not only classical theory, but also the main developments of modern times are covered. Exhaustive sections on the existence and nature of solutions, continuous transformation groups, the algebraic theory of linear differential systems, and the solution of differential equations by contour integration are as valuable to the pure mathematician as the fine treatment of the equations of Legendre, Bessel, and Mathieu, the conditions for the oscillatory character of solutions of a diffe
Uncertain differential equations
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.
Hyperbolic partial differential equations
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
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
Ordinary differential equations
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,
Differential equations problem solver
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
Fully nonlinear elliptic equations
Caffarelli, Luis A
1995-01-01
The goal of the book is to extend classical regularity theorems for solutions of linear elliptic partial differential equations to the context of fully nonlinear elliptic equations. This class of equations often arises in control theory, optimization, and other applications. The authors give a detailed presentation of all the necessary techniques. Instead of treating these techniques in their greatest generality, they outline the key ideas and prove the results needed for developing the subsequent theory. Topics discussed in the book include the theory of viscosity solutions for nonlinear equa
Partial differential equations
Friedman, Avner
2008-01-01
This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists.Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of we
Beginning partial differential equations
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
Saaty, Thomas L
1981-01-01
Covers major types of classical equations: operator, functional, difference, integro-differential, and more. Suitable for graduate students as well as scientists, technologists, and mathematicians. "A welcome contribution." - Math Reviews. 1964 edition.
Equations For Rotary Transformers
Salomon, Phil M.; Wiktor, Peter J.; Marchetto, Carl A.
1988-01-01
Equations derived for input impedance, input power, and ratio of secondary current to primary current of rotary transformer. Used for quick analysis of transformer designs. Circuit model commonly used in textbooks on theory of ac circuits.
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.
Applied partial differential equations
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...
Applied partial differential equations
DuChateau, Paul
2012-01-01
Book focuses mainly on boundary-value and initial-boundary-value problems on spatially bounded and on unbounded domains; integral transforms; uniqueness and continuous dependence on data, first-order equations, and more. Numerous exercises included.
dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
–. (4)) by applying the exp-function method. The computer symbolic systems such as. Maple and Mathematica allow us to perform complicated and tedious calculations. 2. Solutions of (N + 1)-dimensional generalized Boussinesq equation.
Problems in differential equations
Brenner, J L
2013-01-01
More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.
Regularized Structural Equation Modeling
Jacobucci, Ross; Grimm, Kevin J.; McArdle, John J.
2016-01-01
A new method is proposed that extends the use of regularization in both lasso and ridge regression to structural equation models. The method is termed regularized structural equation modeling (RegSEM). RegSEM penalizes specific parameters in structural equation models, with the goal of creating easier to understand and simpler models. Although regularization has gained wide adoption in regression, very little has transferred to models with latent variables. By adding penalties to specific parameters in a structural equation model, researchers have a high level of flexibility in reducing model complexity, overcoming poor fitting models, and the creation of models that are more likely to generalize to new samples. The proposed method was evaluated through a simulation study, two illustrative examples involving a measurement model, and one empirical example involving the structural part of the model to demonstrate RegSEM’s utility. PMID:27398019
Ordinary differential equations.
Lebl, Jiří
2013-01-01
In this chapter we provide an overview of the basic theory of ordinary differential equations (ODE). We give the basics of analytical methods for their solutions and also review numerical methods. The chapter should serve as a primer for the basic application of ODEs and systems of ODEs in practice. As an example, we work out the equations arising in Michaelis-Menten kinetics and give a short introduction to using Matlab for their numerical solution.
Indian Academy of Sciences (India)
continuous medium is μgrav ≡ μ + 3p/c2. Particular versions of this equation had been obtained earlier, at centers of symmetry by Tolman and Synge (see Raychaud- .... (8) by l ˙l and integrate to find. 3( ˙l)2 − κμl2 − Λl2 = const. (10). This is just the Friedmann equation which governs the time evolution of FLRW universe ...
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
Energy Technology Data Exchange (ETDEWEB)
Cadoret, M
2008-01-15
It is possible to determine the h/m{sub Rb} ratio between the Planck constant and the mass of the atoms, and then to deduce a value of the fine structure constant alpha, from the accurate measurement of the recoil velocity of an atom absorbing a photon. To perform this measurement we combine the high efficiency of Bloch oscillations with the high sensitivity of a Ramsey-Borde interferometer. The Bloch oscillations technic allows us to transfer a large number of recoils to the atoms (up to 1600 recoil momenta). An interferometric Ramsey-Borde velocity sensor, based on velocity selective Raman transitions, allows us to measure the momentum transferred to the atoms. A measurement with a statistical uncertainty of 3 ppb (3*10{sup -9}), in conjunction with a careful study of systematic effects (3.4 ppb), lead us to a determination of alpha with a relative uncertainty of 4.8 ppb. The value of {alpha}{sup -1} is 137.03599887(65). It is the best determination of alpha, independent from quantum electrodynamics.
The Bernoulli-Poiseuille Equation.
Badeer, Henry S.; Synolakis, Costas E.
1989-01-01
Describes Bernoulli's equation and Poiseuille's equation for fluid dynamics. Discusses the application of the combined Bernoulli-Poiseuille equation in real flows, such as viscous flows under gravity and acceleration. (YP)
Soliton multidimensional equations and integrable evolutions preserving Laplace's equation
International Nuclear Information System (INIS)
Fokas, A.S.
2008-01-01
The KP equation, which is an integrable nonlinear evolution equation in 2+1, i.e., two spatial and one temporal dimensions, is a physically significant generalization of the KdV equation. The question of constructing an integrable generalization of the KP equation in 3+1, has been one of the central open problems in the field of integrability. By complexifying the independent variables of the KP equation, I obtain an integrable nonlinear evolution equation in 4+2. The requirement that real initial conditions remain real under this evolution, implies that the dependent variable satisfies a nonlinear evolution equation in 3+1 coupled with Laplace's equation. A reduction of this system of equations to a single equation in 2+1 contains as particular cases certain singular integro-differential equations which appear in the theory of water waves
Introduction to partial differential equations
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.
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...
Quadratic Diophantine equations
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.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Equations of mathematical physics
Tikhonov, A N
2011-01-01
Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced-undergraduate or graduate-level text considers only those problems leading to partial differential equations. The authors - two well-known Russian mathematicians - have focused on typical physical processes and the principal types of equations deailing with them. Special attention is paid throughout to mathematical formulation, ri
Partial differential equations
Agranovich, M S
2002-01-01
Mark Vishik's Partial Differential Equations seminar held at Moscow State University was one of the world's leading seminars in PDEs for over 40 years. This book celebrates Vishik's eightieth birthday. It comprises new results and survey papers written by many renowned specialists who actively participated over the years in Vishik's seminars. Contributions include original developments and methods in PDEs and related fields, such as mathematical physics, tomography, and symplectic geometry. Papers discuss linear and nonlinear equations, particularly linear elliptic problems in angles and gener
Generalized estimating equations
Hardin, James W
2002-01-01
Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine th
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Systematic Equation Formulation
DEFF Research Database (Denmark)
Lindberg, Erik
2007-01-01
A tutorial giving a very simple introduction to the set-up of the equations used as a model for an electrical/electronic circuit. The aim is to find a method which is as simple and general as possible with respect to implementation in a computer program. The “Modified Nodal Approach”, MNA, and th......, and the “Controlled Source Approach”, CSA, for systematic equation formulation are investigated. It is suggested that the kernel of the P Spice program based on MNA is reprogrammed....
Test equating methods and practices
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...
Conservation laws for equations related to soil water equations
C. M. Khalique; F. M. Mahomed
2005-01-01
We obtain all nontrivial conservation laws for a class of ( 2+1 ) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Conservation laws for equations related to soil water equations
Directory of Open Access Journals (Sweden)
Khalique C. M.
2005-01-01
Full Text Available We obtain all nontrivial conservation laws for a class of ( 2+1 nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Abstract. In this paper, coupled Higgs field equation and Hamiltonian amplitude equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
In this paper, coupled Higgs field equation are studied using the Lie classical method. Symmetry reductions and exact solutions are reported for Higgs equation and Hamiltonian amplitude equation. We also establish the travelling wave solutions involving parameters of the coupled Higgs equation and Hamiltonian ...
Kadowaki, Tadashi
2018-02-01
We propose a method to interpolate dynamics of von Neumann and classical master equations with an arbitrary mixing parameter to investigate the thermal effects in quantum dynamics. The two dynamics are mixed by intervening to continuously modify their solutions, thus coupling them indirectly instead of directly introducing a coupling term. This maintains the quantum system in a pure state even after the introduction of thermal effects and obtains not only a density matrix but also a state vector representation. Further, we demonstrate that the dynamics of a two-level system can be rewritten as a set of standard differential equations, resulting in quantum dynamics that includes thermal relaxation. These equations are equivalent to the optical Bloch equations at the weak coupling and asymptotic limits, implying that the dynamics cause thermal effects naturally. Numerical simulations of ferromagnetic and frustrated systems support this idea. Finally, we use this method to study thermal effects in quantum annealing, revealing nontrivial performance improvements for a spin glass model over a certain range of annealing time. This result may enable us to optimize the annealing time of real annealing machines.
African Journals Online (AJOL)
Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
Indian Academy of Sciences (India)
Design of Four-Link Mechanisms. Ashitava Ghosal. Ashitava Ghosal is a. Professor in the Depart- ment of Mechanical. Engineering and Centre for Product Design, IISc,. Bangalore. His research interests are in the areas of analysis and design of mechanisms and ... Freudenstein's thesis and the equation named af- ter him.
Indian Academy of Sciences (India)
Amalkumar Raychaudhuri's remarkable paper [1] for the first time gave a general derivation of the fundamental equation of gravitational attraction for pressure- free matter, showing the repulsive nature of a positive cosmological constant, and underlying the basic singularity theorem (see below). He used special coordinates.
Solving Equations Applet Project
Thatcher, Kimberly
2011-01-01
The purpose of this paper is to summarize a Masters Project for the MMath Degree. The purpose of the project was to create and evaluate an applet that maintains the advantages of the existent manipulatives (Hands-On Equations® and the NLVM applet) while also overcoming the limitations of each. Another product of this project is accompanying lesson plans for teachers.
Differential Equations as Actions
DEFF Research Database (Denmark)
Ronkko, Mauno; Ravn, Anders P.
1997-01-01
We extend a conventional action system with a primitive action consisting of a differential equation and an evolution invariant. The semantics is given by a predicate transformer. The weakest liberal precondition is chosen, because it is not always desirable that steps corresponding to differential...
Stochastic nonlinear beam equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Maslowski, Bohdan; Seidler, Jan
2005-01-01
Roč. 132, č. 1 (2005), s. 119-149 ISSN 0178-8051 R&D Projects: GA ČR(CZ) GA201/01/1197 Institutional research plan: CEZ:AV0Z10190503 Keywords : stochastic beam equation * stability Subject RIV: BA - General Mathematics Impact factor: 0.896, year: 2005
Fay, Temple H.
2010-01-01
Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…
Differential Equation of Equilibrium
African Journals Online (AJOL)
user
Department of Civil Engineering. University of Nigeria Nsukka. ABSTRACT. Analysis of underground circular cylindrical shell is carried out in this work. The forth order differential equation of equilibrium, comparable to that of beam on elastic foundation, was derived from static principles on the assumptions of P. L Pasternak.
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 15; Issue 8. The Freudenstein Equation - Design of Four-Link Mechanisms. Ashitava Ghosal. General Article Volume 15 Issue 8 August 2010 pp 699-710. Fulltext. Click here to view fulltext PDF. Permanent link:
Equational binary decision diagrams
J.F. Groote (Jan Friso); J.C. van de Pol (Jaco)
2000-01-01
textabstractWe incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs satisfiability and
International Nuclear Information System (INIS)
Tian Chou.
1991-05-01
It is important but difficult to find the invariant groups for the differential equations. We found a new invariant group for the MKdV equation. In this paper, we present a new invariance for the CDF equation. By using this invariance, we obtain some new solutions of CDF equation. (author). 5 refs
Lectures on partial differential equations
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.
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)
Anticipated backward stochastic differential equations
Peng, Shige; Yang, Zhe
2007-01-01
In this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations (anticipated BSDEs). In these equations the generator includes not only the values of solutions of the present but also the future. We show that these anticipated BSDEs have unique solutions, a comparison theorem for their solutions, and a duality between them and stochastic differential delay equations.
Elements of partial differential equations
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
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.
Classical Diophantine equations
1993-01-01
The author had initiated a revision and translation of "Classical Diophantine Equations" prior to his death. Given the rapid advances in transcendence theory and diophantine approximation over recent years, one might fear that the present work, originally published in Russian in 1982, is mostly superseded. That is not so. A certain amount of updating had been prepared by the author himself before his untimely death. Some further revision was prepared by close colleagues. The first seven chapters provide a detailed, virtually exhaustive, discussion of the theory of lower bounds for linear forms in the logarithms of algebraic numbers and its applications to obtaining upper bounds for solutions to the eponymous classical diophantine equations. The detail may seem stark--- the author fears that the reader may react much as does the tourist on first seeing the centre Pompidou; notwithstanding that, Sprind zuk maintainsa pleasant and chatty approach, full of wise and interesting remarks. His emphases well warrant, ...
DEFF Research Database (Denmark)
Dyre, Jeppe
1995-01-01
energies chosen randomly according to a Gaussian. The random-walk model is here derived from Newton's laws by making a number of simplifying assumptions. In the second part of the paper an approximate low-temperature description of energy fluctuations in the random-walk modelthe energy master equation...... (EME)is arrived at. The EME is one dimensional and involves only energy; it is derived by arguing that percolation dominates the relaxational properties of the random-walk model at low temperatures. The approximate EME description of the random-walk model is expected to be valid at low temperatures...... of the random-walk model. The EME allows a calculation of the energy probability distribution at realistic laboratory time scales for an arbitrarily varying temperature as function of time. The EME is probably the only realistic equation available today with this property that is also explicitly consistent...
Damped nonlinear Schrodinger equation
International Nuclear Information System (INIS)
Nicholson, D.R.; Goldman, M.V.
1976-01-01
High frequency electrostatic plasma oscillations described by the nonlinear Schrodinger equation in the presence of damping, collisional or Landau, are considered. At early times, Landau damping of an initial soliton profile results in a broader, but smaller amplitude soliton, while collisional damping reduces the soliton size everywhere; soliton speeds at early times are unchanged by either kind of damping. For collisional damping, soliton speeds are unchanged for all time
Differential equations with Mathematica
Abell, Martha L
2004-01-01
The Third Edition of the Differential Equations with Mathematica integrates new applications from a variety of fields,especially biology, physics, and engineering. The new handbook is also completely compatible with recent versions of Mathematica and is a perfect introduction for Mathematica beginners.* Focuses on the most often used features of Mathematica for the beginning Mathematica user* New applications from a variety of fields, including engineering, biology, and physics* All applications were completed using recent versions of Mathematica
Fun with Differential Equations
Indian Academy of Sciences (India)
IAS Admin
tion of ® with ¼=2. One can use the uniqueness of solutions of differential equations to prove the addition formulae for sin(t1 +t2), etc. But instead of continuing with this thought process, let us do something more interesting. Now we shall consider another system. Fix 0 < < 1. I am looking for three real-valued functions x(t), ...
Ansari, Rizwan A; Kaur, Manpreet; Ahmad, Firoz; Rahman, Shakilur; Rashid, Hina; Islam, Fakhrul; Raisuddin, Sheikh
2009-10-01
Deltamethrin, an alpha-cyano class of pyrethroid insecticide is used in insect pest control and antimalaria programs in several countries including India. Although various toxic manifestations of deltamethrin are reported in mammals, its ecotoxicologic dimensions are not adequately researched in ecologically and commercially important fishes. In this study, we report genotoxic effect of deltamethrin in a biomarker fish Channa punctata (Bloch). Adult fish were exposed to three concentrations of technical grade deltamethrin (0.4, 0.8, and 1.2 microg/L) for 48 and 72 h. Ethyl methane sulfonate was used as a positive control. Fish were analyzed for induction of micronucleus (MN), nuclear abnormalities (NAs), and oxidative stress biomarkers in erythrocytes. Deltamethrin significantly induced MN and NAs accompanied by increased lipid peroxidation. Activity of antioxidant enzyme superoxide dismutase was significantly decreased but an increase was observed in reduced glutathione level after 72 h of exposure. The NAs in exposed fish included blebbed, lobed and notched nuclei, and binucleated erythrocytes. Our findings suggest that oxidative stress may, in part, be contributing to deltamethrin-induced genotoxic damage to erythrocytes. Although MN induction is a nonspecific biomarker, it may provide an indication of pollution load of deltamethrin in the affected fish population when used as part of suite of other biomarkers.
Chaudhary, Anshu; Molnár, Kálmán; Gupta, Abhishek; Cech, Gábor; Singh, Hridaya S; Székely, Csaba
2017-03-01
During a survey of myxosporean parasites of freshwater fishes in Meerut, Uttar Pradesh (UP), India, spores of Henneguya chaudhuryi (Bajpai & Haldar, 1982) were found in the gill lamellae of the spotted snakehead fish Channa punctata (Bloch) (Perciformes: Channidae). This species was described lacking several characteristics in the original description, which makes challenging the accurate diagnosis. Here, we supplemented its description based on morphological, histological and molecular data. Plasmodia of H. chaudhuryi are oval, measuring 60-100 × 40-68 µm, located intralamellarly. Mature spores are elongate, measuring 10.5-13.2 × 3.6-4.2 µm, with two slightly unequal polar capsules with 6-7 filamental turns and two straight, equal caudal appendages, 10-17 µm long. Scanning electron microscopy revealed a flat surface. The 18S rDNA sequence for H. chaudhuryi did not show a close relationship with those of any other Henneguya spp., represented in the GenBank.
Ransangan, Julian; Manin, Benny Obrain
2010-09-28
Culture of Asian seabass, Lates calcarifer (Bloch) is a popular aquaculture activity in Malaysia. This fish is in high demand and fetches a good price in the local market. The seed for this fish is commercially produced by induced spawning in hatcheries. However, the seed supply is affected by frequent mass mortality of larvae aged between 15 and 60 dph. The clinical signs shown by the affected larvae include lethargy, loss of appetite, uncoordinated swimming, unusual spiral movement pattern and dark coloration. Histological examination of brain and eye of the affected specimens revealed extensive cell vacuolation in larvae aged 15-25 dph. Partial nucleotide sequence of the nervous necrosis virus coat protein gene of the affected larvae showed 94.0-96.1% homology to the nucleotide sequences of coat protein gene from nervous necrosis virus isolated from other countries in the Southeast Asia and Australia. This study provides scientific evidence based on molecular technique that many episodes of mass mortality in seabass larvae in Sabah is associated with the viral nervous necrosis. Because no effective treatment has been reported for this infection, stringent biosecurity measures must be adopted for exclusion of the pathogen from the culture system. (c) 2010 Elsevier B.V. All rights reserved.
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
Dokumaci, Ayse Sila; Pouymayou, Bertrand; Kreis, Roland; Boesch, Chris
2016-05-01
To reliably determine the amplitude of the transmit radiofrequency ( B1+) field in moving organs like the liver and heart, where most current techniques are usually not feasible. B1+ field measurement based on the Bloch-Siegert shift induced by a pair of Fermi pulses in a double-triggered modified Point RESolved Spectroscopy (PRESS) sequence with motion-compensated crusher gradients has been developed. Performance of the sequence was tested in moving phantoms and in muscle, liver, and heart of six healthy volunteers each, using different arrangements of transmit/receive coils. B1+ determination in a moving phantom was almost independent of type and amplitude of the motion and agreed well with theory. In vivo, repeated measurements led to very small coefficients of variance (CV) if the amplitude of the Fermi pulse was chosen above an appropriate level (CV in muscle 0.6%, liver 1.6%, heart 2.3% with moderate amplitude of the Fermi pulses and 1.2% with stronger Fermi pulses). The proposed sequence shows a very robust determination of B1+ in a single voxel even under challenging conditions (transmission with a surface coil or measurements in the heart without breath-hold). © 2015 Wiley Periodicals, Inc.
Kritsky, Delane C; Bullard, Stephen A; Ruiz, Carlos F; Warren, Micah B
2017-09-01
A new species of Empruthotrema Johnston & Tiegs, 1922 is described based on specimens collected from the olfactory sacs of smooth butterfly rays Gymnura micrura (Bloch & Schneider) captured in Mobile Bay (northcentral Gulf of Mexico), Alabama, USA. Empruthotrema longipenis n. sp. is most similar to the type-species Empruthotrema raiae (MacCallum, 1916) Johnston & Tiegs, 1922 by having 12 marginal and two interhamular loculi with members of haptoral hook pair 1 located midway along the periphery of each interhamular loculus and those of hook pair 2 located at the marginal termini of the bilateral septa flanking the interhamular loculi. Empruthotrema longipenis n. sp. differs from E. raiae by having a much longer male copulatory organ and from its remaining congeners by the sinistral and extracecal ejaculatory bulb flanking the pharynx, the number of interhamular and marginal septa, and the distribution of hook pairs 1 and 2 along the haptoral margin. This is the first report of a monocotylid from the smooth butterfly ray and from Mobile Bay. The diversity of haptoral morphotypes among the currently accepted species of Empruthotrema is detailed and discussed in the context of monophyly of the genus.
Generalized reduced MHD equations
International Nuclear Information System (INIS)
Kruger, S.E.; Hegna, C.C.; Callen, J.D.
1998-07-01
A new derivation of reduced magnetohydrodynamic (MHD) equations is presented. A multiple-time-scale expansion is employed. It has the advantage of clearly separating the three time scales of the problem associated with (1) MHD equilibrium, (2) fluctuations whose wave vector is aligned perpendicular to the magnetic field, and (3) those aligned parallel to the magnetic field. The derivation is carried out without relying on a large aspect ratio assumption; therefore this model can be applied to any general toroidal configuration. By accounting for the MHD equilibrium and constraints to eliminate the fast perpendicular waves, equations are derived to evolve scalar potential quantities on a time scale associated with the parallel wave vector (shear-alfven wave time scale), which is the time scale of interest for MHD instability studies. Careful attention is given in the derivation to satisfy energy conservation and to have manifestly divergence-free magnetic fields to all orders in the expansion parameter. Additionally, neoclassical closures and equilibrium shear flow effects are easily accounted for in this model. Equations for the inner resistive layer are derived which reproduce the linear ideal and resistive stability criterion of Glasser, Greene, and Johnson
Mathematics and Maxwell's equations
International Nuclear Information System (INIS)
Boozer, Allen H
2010-01-01
The universality of mathematics and Maxwell's equations is not shared by specific plasma models. Computations become more reliable, efficient and transparent if specific plasma models are used to obtain only the information that would otherwise be missing. Constraints of high universality, such as those from mathematics and Maxwell's equations, can be obscured or lost by integrated computations. Recognition of subtle constraints of high universality is important for (1) focusing the design of control systems for magnetic field errors in tokamaks from perturbations that have little effect on the plasma to those that do, (2) clarifying the limits of applicability to astrophysics of computations of magnetic reconnection in fields that have a double periodicity or have B-vector =0 on a surface, as in a Harris sheet. Both require a degree of symmetry not expected in natural systems. Mathematics and Maxwell's equations imply that neighboring magnetic field lines characteristically separate exponentially with distance along a line. This remarkably universal phenomenon has been largely ignored, though it defines a trigger for reconnection through a critical magnitude of exponentiation. These and other examples of the importance of making distinctions and understanding constraints of high universality are explained.
Computing generalized Langevin equations and generalized Fokker-Planck equations.
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.
Bitsadze, A V
1963-01-01
Equations of the Mixed Type compiles a series of lectures on certain fundamental questions in the theory of equations of mixed type. This book investigates the series of problems concerning linear partial differential equations of the second order in two variables, and possessing the property that the type of the equation changes either on the boundary of or inside the considered domain. Topics covered include general remarks on linear partial differential equations of mixed type; study of the solutions of second order hyperbolic equations with initial conditions given along the lines of parab
Ordinary differential equations
Cox, William
1995-01-01
Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Partial differential equations
Sloan, D; Süli, E
2001-01-01
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight in
Elliptic partial differential equations
Han, Qing
2011-01-01
Elliptic Partial Differential Equations by Qing Han and FangHua Lin is one of the best textbooks I know. It is the perfect introduction to PDE. In 150 pages or so it covers an amazing amount of wonderful and extraordinary useful material. I have used it as a textbook at both graduate and undergraduate levels which is possible since it only requires very little background material yet it covers an enormous amount of material. In my opinion it is a must read for all interested in analysis and geometry, and for all of my own PhD students it is indeed just that. I cannot say enough good things abo
Hyperbolic partial differential equations
Lax, Peter D
2006-01-01
The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of soluti
Partial differential equations
Levine, Harold
1997-01-01
The subject matter, partial differential equations (PDEs), has a long history (dating from the 18th century) and an active contemporary phase. An early phase (with a separate focus on taut string vibrations and heat flow through solid bodies) stimulated developments of great importance for mathematical analysis, such as a wider concept of functions and integration and the existence of trigonometric or Fourier series representations. The direct relevance of PDEs to all manner of mathematical, physical and technical problems continues. This book presents a reasonably broad introductory account of the subject, with due regard for analytical detail, applications and historical matters.
Nonelliptic Partial Differential Equations
Tartakoff, David S
2011-01-01
This book provides a very readable description of a technique, developed by the author years ago but as current as ever, for proving that solutions to certain (non-elliptic) partial differential equations only have real analytic solutions when the data are real analytic (locally). The technique is completely elementary but relies on a construction, a kind of a non-commutative power series, to localize the analysis of high powers of derivatives in the so-called bad direction. It is hoped that this work will permit a far greater audience of researchers to come to a deep understanding of this tec
Kuznetsov equation with variable coefficients
Indian Academy of Sciences (India)
like solutions of the PDE in (2+1) dimension with variable coefficients. ... Shivamoggi [12] gives only four polynomial conservation laws of the ZK equation ..... [3] P J Olver, Application of Lie group to differential equation (Springer, New York,.
Conservational PDF Equations of Turbulence
Shih, Tsan-Hsing; Liu, Nan-Suey
2010-01-01
Recently we have revisited the traditional probability density function (PDF) equations for the velocity and species in turbulent incompressible flows. They are all unclosed due to the appearance of various conditional means which are modeled empirically. However, we have observed that it is possible to establish a closed velocity PDF equation and a closed joint velocity and species PDF equation through conditions derived from the integral form of the Navier-Stokes equations. Although, in theory, the resulted PDF equations are neither general nor unique, they nevertheless lead to the exact transport equations for the first moment as well as all higher order moments. We refer these PDF equations as the conservational PDF equations. This observation is worth further exploration for its validity and CFD application
Functional equations for Feynman integrals
International Nuclear Information System (INIS)
Tarasov, O.V.
2011-01-01
New types of equations for Feynman integrals are found. It is shown that Feynman integrals satisfy functional equations connecting integrals with different kinematics. A regular method is proposed for obtaining such relations. The derivation of functional equations for one-loop two-, three- and four-point functions with arbitrary masses and external momenta is given. It is demonstrated that functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains
Classical solutions of quasielliptic equations
International Nuclear Information System (INIS)
Belonosov, V S
1999-01-01
Fundamental solutions of quasielliptic equations are constructed; this allows the author to develop a relevant theory of volume potentials, establish estimates for the Holder norms of solutions of equations with constant coefficients, and extend them after that to equations with variable coefficients. As a result, sharp Schauder-type interior estimates are obtained, of which the well-known classical results for elliptic and parabolic equations are special cases
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...... features that justify the development of specialized solution algorithms....
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity. Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity; loop quantum cosmology. PACS Nos 04.20.Jb; 04.2 ...
Successfully Transitioning to Linear Equations
Colton, Connie; Smith, Wendy M.
2014-01-01
The Common Core State Standards for Mathematics (CCSSI 2010) asks students in as early as fourth grade to solve word problems using equations with variables. Equations studied at this level generate a single solution, such as the equation x + 10 = 25. For students in fifth grade, the Common Core standard for algebraic thinking expects them to…
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...
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.)
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 ...
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.
Discovering evolution equations with applications
McKibben, Mark
2011-01-01
Most existing books on evolution equations tend either to cover a particular class of equations in too much depth for beginners or focus on a very specific research direction. Thus, the field can be daunting for newcomers to the field who need access to preliminary material and behind-the-scenes detail. Taking an applications-oriented, conversational approach, Discovering Evolution Equations with Applications: Volume 2-Stochastic Equations provides an introductory understanding of stochastic evolution equations. The text begins with hands-on introductions to the essentials of real and stochast
Directory of Open Access Journals (Sweden)
Taouil Hajer
2012-08-01
Full Text Available This paper is devoted to the helices processes, i.e. the solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω of the helix equation egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,oonumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω where Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω is a dynamical system on a measurable space (Ω, ℱ. More precisely, we investigate dominated solutions and non differentiable solutions of the helix equation. For the last case, the Wiener helix plays a fundamental role. Moreover, some relations with the cocycle equation defined by Φ, are investigated. Ce papier est consacré aux hélices, c’est-à-dire les solutions H : ℝ × Ω → ℝd, (t, ω ↦ H(t, ω de l’équation fonctionnelle egin{eqnarray} H(0,o=0; quad H(s+t,o= H(s,Phi(t,o +H(t,o onumber end{eqnarray} H ( 0 ,ω = 0 ; H ( s + t,ω = H ( s, Φ ( t,ω + H ( t,ω où Φ : ℝ × Ω → Ω, (t, ω ↦ Φ(t, ω est un système dynamique défini sur un espace mesurable (Ω, ℱ. Plus présisément, nous déterminons d’abord les hélices dominées puis nous caractérisons les hélices non différentiables. Dans ce dernier cas, l’hélice de Wiener joue un rôle important. Nous précisons aussi quelques relations des hélices avec les cocycles définis par Φ.
p-Euler equations and p-Navier-Stokes equations
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.
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)
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2015-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree structures that separate a data set recursively into subsets with significantly different parameter estimates in a SEM. SEM Trees provide means for finding covariates and covariate interactions that predict differences in structural parameters in observed as well as in latent space and facilitate theory-guided exploration of empirical data. We describe the methodology, discuss theoretical and practical implications, and demonstrate applications to a factor model and a linear growth curve model. PMID:22984789
Energy Technology Data Exchange (ETDEWEB)
Cardona, Carlos [Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University,Hsinchu, Taiwan 30013 (China); Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-16
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a ℂP{sup 2} space. We show that for the simplest integrand, namely the n−gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ−algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
Energy Technology Data Exchange (ETDEWEB)
Gomez, Humberto [Instituto de Fisica - Universidade de São Paulo,Caixa Postal 66318, 05315-970 São Paulo, SP (Brazil); Facultad de Ciencias Basicas, Universidad Santiago de Cali,Calle 5 62-00 Barrio Pampalinda, Cali, Valle (Colombia)
2016-06-17
The CHY representation of scattering amplitudes is based on integrals over the moduli space of a punctured sphere. We replace the punctured sphere by a double-cover version. The resulting scattering equations depend on a parameter Λ controlling the opening of a branch cut. The new representation of scattering amplitudes possesses an enhanced redundancy which can be used to fix, modulo branches, the location of four punctures while promoting Λ to a variable. Via residue theorems we show how CHY formulas break up into sums of products of smaller (off-shell) ones times a propagator. This leads to a powerful way of evaluating CHY integrals of generic rational functions, which we call the Λ algorithm.
Scaling of differential equations
Langtangen, Hans Petter
2016-01-01
The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and exam...
Differential equations with involutions
Cabada, Alberto
2015-01-01
This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.
Parabolized stability equations
Herbert, Thorwald
1994-01-01
The parabolized stability equations (PSE) are a new approach to analyze the streamwise evolution of single or interacting Fourier modes in weakly nonparallel flows such as boundary layers. The concept rests on the decomposition of every mode into a slowly varying amplitude function and a wave function with slowly varying wave number. The neglect of the small second derivatives of the slowly varying functions with respect to the streamwise variable leads to an initial boundary-value problem that can be solved by numerical marching procedures. The PSE approach is valid in convectively unstable flows. The equations for a single mode are closely related to those of the traditional eigenvalue problems for linear stability analysis. However, the PSE approach does not exploit the homogeneity of the problem and, therefore, can be utilized to analyze forced modes and the nonlinear growth and interaction of an initial disturbance field. In contrast to the traditional patching of local solutions, the PSE provide the spatial evolution of modes with proper account for their history. The PSE approach allows studies of secondary instabilities without the constraints of the Floquet analysis and reproduces the established experimental, theoretical, and computational benchmark results on transition up to the breakdown stage. The method matches or exceeds the demonstrated capabilities of current spatial Navier-Stokes solvers at a small fraction of their computational cost. Recent applications include studies on localized or distributed receptivity and prediction of transition in model environments for realistic engineering problems. This report describes the basis, intricacies, and some applications of the PSE methodology.
Semiclassical dye-laser equations and the unidirectional single-frequency operation
Fu, Hong; Haken, H.
1987-11-01
A semiclassical description for dye lasers is proposed, where the energy-level diagram of the dye molecule is assumed to consist of a continuous bandlike ground state and an excited singlet state. Unidirectional single-frequency (s.f.) operation is discussed. The linear-stability analysis for this operation reveals a very low threshold instability, which may appear generally in practical lasers. The ratio of the instability threshold to the lasing threshold may be of any value greater than 1, depending mainly on the bandwidth and the distribution of the dipole moments on the band, but it is independent of the cavity loss. This instability may account for that observed in recent experiments by Hillman, Krasinki, Boyd, and Stroud [Phys. Rev. Lett. 52, 1605 (1984)]. A general approach to analyzing the linear stability of the s.f. operation of the Maxwell-Bloch equations is also proposed, which states that only the eigenvalues of a 2×2 matrix are relevant: one concerns the stability of the s.f. operation near the lasing threshold, the other determines the instability threshold of this operation.
Mode decomposition evolution equations.
Wang, Yang; Wei, Guo-Wei; Yang, Siyang
2012-03-01
Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Europhys. Lett., 59(6): 814, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett., 6(7): 165, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be
Integral equations and their applications
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...
Differential equations methods and applications
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. .
Introduction to partial differential equations
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.
Equations Holding in Hilbert Lattices
Mayet, René
2006-07-01
We produce and study several sequences of equations, in the language of orthomodular lattices, which hold in the ortholattice of closed subspaces of any classical Hilbert space, but not in all orthomodular lattices. Most of these equations hold in any orthomodular lattice admitting a strong set of states whose values are in a real Hilbert space. For some of these equations, we give conditions under which they hold in the ortholattice of closed subspaces of a generalised Hilbert space. These conditions are relative to the dimension of the Hilbert space and to the characteristic of its division ring of scalars. In some cases, we show that these equations cannot be deduced from the already known equations, and we study their mutual independence. To conclude, we suggest a new method for obtaining such equations, using the tensorial product.
Stochastic partial differential equations
Lototsky, Sergey V
2017-01-01
Taking readers with a basic knowledge of probability and real analysis to the frontiers of a very active research discipline, this textbook provides all the necessary background from functional analysis and the theory of PDEs. It covers the main types of equations (elliptic, hyperbolic and parabolic) and discusses different types of random forcing. The objective is to give the reader the necessary tools to understand the proofs of existing theorems about SPDEs (from other sources) and perhaps even to formulate and prove a few new ones. Most of the material could be covered in about 40 hours of lectures, as long as not too much time is spent on the general discussion of stochastic analysis in infinite dimensions. As the subject of SPDEs is currently making the transition from the research level to that of a graduate or even undergraduate course, the book attempts to present enough exercise material to fill potential exams and homework assignments. Exercises appear throughout and are usually directly connected ...
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Laboratory
2015-12-15
The JWL equation of state (EOS) is frequently used for the products (and sometimes reactants) of a high explosive (HE). Here we review and systematically derive important properties. The JWL EOS is of the Mie-Grueneisen form with a constant Grueneisen coefficient and a constants specific heat. It is thermodynamically consistent to specify the temperature at a reference state. However, increasing the reference state temperature restricts the EOS domain in the (V, e)-plane of phase space. The restrictions are due to the conditions that P ≥ 0, T ≥ 0, and the isothermal bulk modulus is positive. Typically, this limits the low temperature regime in expansion. The domain restrictions can result in the P-T equilibrium EOS of a partly burned HE failing to have a solution in some cases. For application to HE, the heat of detonation is discussed. Example JWL parameters for an HE, both products and reactions, are used to illustrate the restrictions on the domain of the EOS.
Hyperbolic Methods for Einstein's Equations
Directory of Open Access Journals (Sweden)
Reula Oscar
1998-01-01
Full Text Available I review evolutionary aspects of general relativity, in particular those related to the hyperbolic character of the field equations and to the applications or consequences that this property entails. I look at several approaches to obtaining symmetric hyperbolic systems of equations out of Einstein's equations by either removing some gauge freedoms from them, or by considering certain linear combinations of a subset of them.
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.
Correct Linearization of Einstein's Equations
Directory of Open Access Journals (Sweden)
Rabounski D.
2006-06-01
Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.
Half-linear differential equations
Dosly, Ondrej
2005-01-01
The book presents a systematic and compact treatment of the qualitative theory of half-lineardifferential equations. It contains the most updated and comprehensive material and represents the first attempt to present the results of the rapidly developing theory of half-linear differential equations in a unified form. The main topics covered by the book are oscillation and asymptotic theory and the theory of boundary value problems associated with half-linear equations, but the book also contains a treatment of related topics like PDE's with p-Laplacian, half-linear difference equations and var
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.)
Equations of motion for cross term modified gravitational field equations
Energy Technology Data Exchange (ETDEWEB)
Mueller, V. (Akademie der Wissenschaften der DDR, Potsdam-Babelsberg. Zentralinstitut fuer Astrophysik)
1982-01-01
As proposed by Treder, possible consequences of a unitary field theory may be described phenomenologically by additional cross terms in Einstein's equations. The violation of the weak principle of equivalence and potential observable effects are discussed in deriving hydrodynamic EIH equations. Conclusions on gravitational instabilities follow in the quasistatic approximation.
Difference equations theory, applications and advanced topics
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...
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 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.
Karimi, F.; Davoody, A. H.; Knezevic, I.
2016-05-01
We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master-equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO2 and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.
Directory of Open Access Journals (Sweden)
T. Sharamok
2017-09-01
Full Text Available Purpose. To detect the effect of elevated copper ion concentrations (10 aquaculture Maximum Permissible Limits on morphological and cytometric parameters of erythrocytes of age-2 Prussian carp (Carassius gibelio Bloch, 1782 in experimental and natural conditions. Methodology. During the work, summarized results of studies performed in 2015-2016 were used. Morphological and cytometric parameters of Prussian carp erythrocytes were determined in the conditions of natural habitats (Zaporizhzhia reservoir and an experiment. Copper ion concentration both in the experiment and natural conditions was similar and was 0.01 mg/L (10 aquaculture Maximum Permissible Limits. Experimental studies were performed during 21 days. In the control aquarium, fish were kept in the settled tap water; while in the experimental aquaria, intoxication of fish with copper ions was modelled by introducing CuSO4 in water. Blood smears were examined under 40x and 100 x magnifications with the use of microphotography (digital camera Sciencelab T500 5.17 M. Findings. The performed hematological studies showed that under the conditions of experimental chronic intoxication with copper ions (0.01 mg/L, age-2 Prussian carp had an increase in the share of immature forms of erythrocytes, increase in the number of erythrocytes with pathological signs (cell wall destruction, atypical forms, increase in the nucleus-cytoplasm ration, but the difference in cytometric parameters of erythrocytes between experimental and control fish was not significant. When comparing the morphometric parameters of erythrocytes of fish kept in experimental and natural conditions with similar copper ion concentrations (0.01 mg/L, a significant increase in the nucleus areas of mature erythrocytes was detected and, correspondingly, an increase in the nucleus-cytoplasm ratio of erythrocytes (by almost 30% in fish in experimental conditions compared to fish, which lived in the Zaporizhzhia reservoir. An increase
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.
Solutions to Arithmetic Convolution Equations
Czech Academy of Sciences Publication Activity Database
Glöckner, H.; Lucht, L.G.; Porubský, Štefan
2007-01-01
Roč. 135, č. 6 (2007), s. 1619-1629 ISSN 0002-9939 R&D Projects: GA ČR GA201/04/0381 Institutional research plan: CEZ:AV0Z10300504 Keywords : arithmetic functions * Dirichlet convolution * polynomial equations * analytic equations * topological algebras * holomorphic functional calculus Subject RIV: BA - General Mathematics Impact factor: 0.520, year: 2007
Introduction to nonlinear dispersive equations
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...
Averaging of multivalued differential equations
Directory of Open Access Journals (Sweden)
G. Grammel
2003-04-01
Full Text Available Nonlinear multivalued differential equations with slow and fast subsystems are considered. Under transitivity conditions on the fast subsystem, the slow subsystem can be approximated by an averaged multivalued differential equation. The approximation in the Hausdorff sense is of order O(ÃÂµ1/3 as ÃÂµÃ¢Â†Â’0.
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
Enclosing Solutions of Integral Equations
DEFF Research Database (Denmark)
Madsen, Kaj; NA NA NA Caprani, Ole; Stauning, Ole
1996-01-01
We present a method for enclosing the solution of an integral equation. It is assumed that a solution exists and that the corresponding integral operator T is a contraction near y. When solving the integral equation by iteration we obtain a result which is normally different from y because...
On asymptotics for difference equations
Rafei, M.
2012-01-01
In this thesis a class of nonlinear oscillator equations is studied. Asymptotic approximations of first integrals for nonlinear difference equations are constructed by using the recently developed perturbation method based on invariance vectors. The asymptotic approximations of the solutions of the
Students' Understanding of Quadratic Equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-01-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…
On the Saha Ionization Equation
Indian Academy of Sciences (India)
An example of the soci- etal impact of the famous equation can be discerned in a .... gaseous state and they behaved like a dilute classical gas, as in. Maxwell's kinetic theory. That is to say, the atoms do .... the Sackur–Tetrode equation for the entropy of an ideal gas at high temperatures, that Saha was quite aware of [13].
Higher order equations of motion
International Nuclear Information System (INIS)
Bollini, C.G.; Giambiagi, J.J.
1989-01-01
The possibility that the motion of elementary particles be described by higher order differential equations induced by supersymmetry in higher dimensional space-time is discussed. The specific example of six dimensions writing the corresponding Lagrangian and equations of motion, is presented. (author) [pt
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
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.)
Discovering Evolution Equations with Applications, 1 Deterministic Equations
McKibben, Mark A
2010-01-01
Most books written on evolution equations either provide a thorough in-depth treatment of a particular class of equations for beginners or present an assimilation of materials devoted to a very particular timely research direction. This volume offers an engaging, accessible account of a rudimentary core of theoretical results that should be understood by anyone studying evolution equations. The text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. The author's conversational style sets the stage for the next step of theoretical deve
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…
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
Stochastic differential equations, backward SDEs, partial differential equations
Pardoux, Etienne
2014-01-01
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics. It pays special attention to the relations between SDEs/BSDEs and second order PDEs under minimal regularity assumptions, and also extends those results to equations with multivalued coefficients. The authors present in particular the theory of reflected SDEs in the above mentioned framework and include exercises at the end of each chapter. Stochastic calculus and stochastic differential equations (SDEs) were first introduced by K. Itô in the 1940s, in order to construct the path of diffusion processes (which are continuous time Markov processes with continuous trajectories taking their values in a finite dimensional vector space or manifold), which had been studied from a more analytic point of view by Kolmogorov in the 1930s. Since then, this topic has...
Fractional delayed damped Mathieu equation
Mesbahi, Afshin; Haeri, Mohammad; Nazari, Morad; Butcher, Eric A.
2015-03-01
This paper investigates the dynamical behaviour of the fractional delayed damped Mathieu equation. This system includes three different phenomena (fractional order, time delay, parametric resonance). The method of harmonic balance is employed to achieve approximate expressions for the transition curves in the parameter plane. The n = 0 and n = 1 transition curves (both lower and higher order approximations) are obtained. The dependencies of these curves on the system parameters and fractional orders are determined. Previous results for the transition curves reported for the damped Mathieu equation, delayed second-order oscillator, and fractional Mathieu equation are confirmed as special cases of the results for the current system.
Soliton equations and pseudospherical surfaces
International Nuclear Information System (INIS)
Sasaki, R.
1979-03-01
All the soliton equations in 1+1 dimensions that can be solved by the AKNS 2x2 inverse scattering method (for example, the sine-Gordon, KdV or Modified KdV equations) are shown to describe pseudospherical surfaces, i.e. surfaces of constant negative Gaussian curvature. This result provides a unified picture of all these soliton equations. Geometrical interpretations of characteristic properties like infinite numbers of conservation laws, and Baecklund transformations and of the soliton solutions themselves are presented. The important role of scale transformations as generating one parameter families of pseudospherical surfaces is pointed out. (Auth.)
Galois theory of difference equations
Put, Marius
1997-01-01
This book lays the algebraic foundations of a Galois theory of linear difference equations and shows its relationship to the analytic problem of finding meromorphic functions asymptotic to formal solutions of difference equations. Classically, this latter question was attacked by Birkhoff and Tritzinsky and the present work corrects and greatly generalizes their contributions. In addition results are presented concerning the inverse problem in Galois theory, effective computation of Galois groups, algebraic properties of sequences, phenomena in positive characteristics, and q-difference equations. The book is aimed at advanced graduate researchers and researchers.
Soliton equations and Hamiltonian systems
Dickey, L A
2002-01-01
The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this output followed one single work by Gardner, Green, Kruskal, and Mizura on the Korteweg-de Vries equation (KdV), which had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water. Besides its obvious practical use, this theory is attractive also becau
Integral equation methods for electromagnetics
Volakis, John
2012-01-01
This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the mo
Tian, Gang
2002-11-26
We discuss some recent progress on the regularity theory of the elliptic Yang-Mills equation. We start with some basic properties of the elliptic Yang-Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang-Mills connections and compactness theorems on Yang-Mills connections with bounded L(2) norm of curvature. We also discuss in some detail self-dual solutions of the Yang-Mills equation and describe a compactification of their moduli space.
Tian, Gang
2002-01-01
We discuss some recent progress on the regularity theory of the elliptic Yang–Mills equation. We start with some basic properties of the elliptic Yang–Mills equation, such as Coulomb gauges, monotonicity, and curvature estimates. Next we discuss singularity of stationary Yang–Mills connections and compactness theorems on Yang–Mills connections with bounded L2 norm of curvature. We also discuss in some detail self-dual solutions of the Yang–Mills equation and describe a compactification of the...
Lectures on ordinary differential equations
Hurewicz, Witold
1958-01-01
Hailed by The American Mathematical Monthly as ""a rigorous and lively introduction,"" this text explores a topic of perennial interest in mathematics. The author, a distinguished mathematician and formulator of the Hurewicz theorem, presents a clear and lucid treatment that emphasizes geometric methods. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown funct
Iterative Splitting Methods for Differential Equations
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
Nonlinear integrodifferential equations as discrete systems
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.
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)
1955-01-01
"First stone" ceremony for the SC : authorities in the audience. From right: Sir Ben Lockspeiser, President of the CERN Council, Felix Bloch, Francois Perreard, President of the Council of State of the canton of Geneva, C.J. Bakker and A.Pennetta
Indian Academy of Sciences (India)
IAS Admin
They set up a joint seminar on theoretical physics, meeting alternately in. Berkeley or Stanford and occasionally elsewhere on the West Coast. Because of Felix's reputation and presence at Stanford, prominent physicists visited him, most often in the summer, and stayed for a few weeks or longer. Among these many visitors ...
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
Analytical Solution of Mathieu Equation
Yerchuck, Dmitri; Dovlatova, Alla; Yerchak, Yauhen; Borovik, Felix
2014-01-01
The general solution of the homogeneous damped Mathieu equation in the analytical form, allowing its practical using in many applications, including superconductivity studies, without numerical calculations has been found.
International Nuclear Information System (INIS)
Skyrme, T.H.R.
1994-01-01
In a model quantum theory of interacting mesons, the motion of certain conserved particle-like structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation. (author)
Saha equation in Rindler space
Indian Academy of Sciences (India)
The Saha equations for the photoionization process of hydrogen atoms and the creation of electron–positron pairs at high temperature are investigated in a reference frame undergoing a uniform accelerated motion. It is known as the Rindler space.
An Investigation on Quadratic Equations.
Hirst, Keith
1988-01-01
Argues that exploring a familiar topic or examination question in a novel manner is a useful way to find topics for mathematical investigation in the classroom. The example used to illustrate the premise is a quadratic equation. (PK)
Solutions of Nonlocal -Laplacian Equations
Directory of Open Access Journals (Sweden)
Mustafa Avci
2013-01-01
Full Text Available In view of variational approach we discuss a nonlocal problem, that is, a Kirchhoff-type equation involving -Laplace operator. Establishing some suitable conditions, we prove the existence and multiplicity of solutions.
The quasilinear parabolic kirchhoff equation
Directory of Open Access Journals (Sweden)
Dawidowski Łukasz
2017-04-01
Full Text Available In this paper the existence of solution of a quasilinear generalized Kirchhoff equation with initial – boundary conditions of Dirichlet type will be studied using the Leray – Schauder principle.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
2015-11-27
Keywords. Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quantum gravity; loop quantum cosmology. ... Proceedings of the International Workshop/Conference on Computational Condensed Matter Physics and Materials Science (IWCCMP-2015). Posted on November 27, 2015. Guest Editors: Anurag ...
Geophysical interpretation using integral equations
Eskola, L
1992-01-01
Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu med to have a back...
Hidden Statistics of Schroedinger Equation
Zak, Michail
2011-01-01
Work was carried out in determination of the mathematical origin of randomness in quantum mechanics and creating a hidden statistics of Schr dinger equation; i.e., to expose the transitional stochastic process as a "bridge" to the quantum world. The governing equations of hidden statistics would preserve such properties of quantum physics as superposition, entanglement, and direct-product decomposability while allowing one to measure its state variables using classical methods.
Wave equations for pulse propagation
Energy Technology Data Exchange (ETDEWEB)
Shore, B.W.
1987-06-24
Theoretical discussions of the propagation of pulses of laser radiation through atomic or molecular vapor rely on a number of traditional approximations for idealizing the radiation and the molecules, and for quantifying their mutual interaction by various equations of propagation (for the radiation) and excitation (for the molecules). In treating short-pulse phenomena it is essential to consider coherent excitation phenomena of the sort that is manifest in Rabi oscillations of atomic or molecular populations. Such processes are not adequately treated by rate equations for excitation nor by rate equations for radiation. As part of a more comprehensive treatment of the coupled equations that describe propagation of short pulses, this memo presents background discussion of the equations that describe the field. This memo discusses the origin, in Maxwell's equations, of the wave equation used in the description of pulse propagation. It notes the separation into lamellar and solenoidal (or longitudinal and transverse) and positive and negative frequency parts. It mentions the possibility of separating the polarization field into linear and nonlinear parts, in order to define a susceptibility or index of refraction and, from these, a phase and group velocity. The memo discusses various ways of characterizing the polarization characteristics of plane waves, that is, of parameterizing a transverse unit vector, such as the Jones vector, the Stokes vector, and the Poincare sphere. It discusses the connection between macroscopically defined quantities, such as the intensity or, more generally, the Stokes parameters, and microscopic field amplitudes. The material presented here is a portion of a more extensive treatment of propagation to be presented separately. The equations presented here have been described in various books and articles. They are collected here as a summary and review of theory needed when treating pulse propagation.
Geometrical Solutions of Quadratic Equations.
Grewal, A. S.; Godloza, L.
1999-01-01
Demonstrates that the equation of a circle (x-h)2 + (y-k)2 = r2 with center (h; k) and radius r reduces to a quadratic equation x2-2xh + (h2 + k2 -r2) = O at the intersection with the x-axis. Illustrates how to determine the center of a circle as well as a point on a circle. (Author/ASK)
Feynman integrals and difference equations
International Nuclear Information System (INIS)
Moch, S.; Schneider, C.
2007-09-01
We report on the calculation of multi-loop Feynman integrals for single-scale problems by means of difference equations in Mellin space. The solution to these difference equations in terms of harmonic sums can be constructed algorithmically over difference fields, the so-called ΠΣ * -fields. We test the implementation of the Mathematica package Sigma on examples from recent higher order perturbative calculations in Quantum Chromodynamics. (orig.)
Computational partial differential equations using Matlab
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
Equationally Compact Acts : Coproducts / Peeter Normak
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
The soil moisture velocity equation
Ogden, Fred L.; Allen, Myron B.; Lai, Wencong; Zhu, Jianting; Seo, Mookwon; Douglas, Craig C.; Talbot, Cary A.
2017-06-01
Numerical solution of the one-dimensional Richards' equation is the recommended method for coupling groundwater to the atmosphere through the vadose zone in hyperresolution Earth system models, but requires fine spatial discretization, is computationally expensive, and may not converge due to mathematical degeneracy or when sharp wetting fronts occur. We transformed the one-dimensional Richards' equation into a new equation that describes the velocity of moisture content values in an unsaturated soil under the actions of capillarity and gravity. We call this new equation the Soil Moisture Velocity Equation (SMVE). The SMVE consists of two terms: an advection-like term that accounts for gravity and the integrated capillary drive of the wetting front, and a diffusion-like term that describes the flux due to the shape of the wetting front capillarity profile divided by the vertical gradient of the capillary pressure head. The SMVE advection-like term can be converted to a relatively easy to solve ordinary differential equation (ODE) using the method of lines and solved using a finite moisture-content discretization. Comparing against analytical solutions of Richards' equation shows that the SMVE advection-like term is >99% accurate for calculating infiltration fluxes neglecting the diffusion-like term. The ODE solution of the SMVE advection-like term is accurate, computationally efficient and reliable for calculating one-dimensional vadose zone fluxes in Earth system and large-scale coupled models of land-atmosphere interaction. It is also well suited for use in inverse problems such as when repeat remote sensing observations are used to infer soil hydraulic properties or soil moisture.type="synopsis">type="main">Plain Language SummarySince its original publication in 1922, the so-called Richards' equation has been the only rigorous way to couple groundwater to the land surface through the unsaturated zone that lies between the water table and land surface. The soil
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.)
Approximations of Stochastic Partial Differential Equations
Di Nunno, Giulia; Zhang, Tusheng
2014-01-01
In this paper we show that solutions of stochastic partial differ- ential equations driven by Brownian motion can be approximated by stochastic partial differential equations forced by pure jump noise/random kicks. Applications to stochastic Burgers equations are discussed.
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.)
Abstract methods in partial differential equations
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.
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
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
First-order partial differential equations
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
Hypergeometric solutions to Schr\\"odinger equations for the quantum Painlev\\'e equations
Nagoya, Hajime
2011-01-01
We consider Schr\\"odinger equations for the quantum Painlev\\'e equations. We present hypergeometric solutions of the Schr\\"odinger equations for the quantum Painlev\\'e equations, as particular solutions. We also give a representation theoretic correspondence between Hamiltonians of the Schr\\"odinger equations for the quantum Painlev\\'e equations and those of the KZ equation or the confluent KZ equations.
Students' understanding of quadratic equations
López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael
2016-05-01
Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.
Integration of quantum hydrodynamical equation
Ulyanova, Vera G.; Sanin, Andrey L.
2007-04-01
Quantum hydrodynamics equations describing the dynamics of quantum fluid are a subject of this report (QFD).These equations can be used to decide the wide class of problem. But there are the calculated difficulties for the equations, which take place for nonlinear hyperbolic systems. In this connection, It is necessary to impose the additional restrictions which assure the existence and unique of solutions. As test sample, we use the free wave packet and study its behavior at the different initial and boundary conditions. The calculations of wave packet propagation cause in numerical algorithm the division. In numerical algorithm at the calculations of wave packet propagation, there arises the problem of division by zero. To overcome this problem we have to sew together discrete numerical and analytical continuous solutions on the boundary. We demonstrate here for the free wave packet that the numerical solution corresponds to the analytical solution.
Dynamics of partial differential equations
Wayne, C Eugene
2015-01-01
This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties, and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equ...
Introductory course on differential equations
Gorain, Ganesh C
2014-01-01
Introductory Course on DIFFERENTIAL EQUATIONS provides an excellent exposition of the fundamentals of ordinary and partial differential equations and is ideally suited for a first course of undergraduate students of mathematics, physics and engineering. The aim of this book is to present the elementary theories of differential equations in the forms suitable for use of those students whose main interest in the subject are based on simple mathematical ideas. KEY FEATURES: Discusses the subject in a systematic manner without sacrificing mathematical rigour. A variety of exercises drill the students in problem solving in view of the mathematical theories explained in the book. Worked out examples illustrated according to the theories developed in the book with possible alternatives. Exhaustive collection of problems and the simplicity of presentation differentiate this book from several others. Material contained will help teachers as well as aspiring students of different competitive examinations.
Integration rules for scattering equations
Energy Technology Data Exchange (ETDEWEB)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H. [Niels Bohr International Academy and Discovery Center,Niels Bohr Institute, University of Copenhagen,Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark)
2015-09-21
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
Numerical integration of variational equations.
Skokos, Ch; Gerlach, E
2010-09-01
We present and compare different numerical schemes for the integration of the variational equations of autonomous Hamiltonian systems whose kinetic energy is quadratic in the generalized momenta and whose potential is a function of the generalized positions. We apply these techniques to Hamiltonian systems of various degrees of freedom and investigate their efficiency in accurately reproducing well-known properties of chaos indicators such as the Lyapunov characteristic exponents and the generalized alignment indices. We find that the best numerical performance is exhibited by the "tangent map method," a scheme based on symplectic integration techniques which proves to be optimal in speed and accuracy. According to this method, a symplectic integrator is used to approximate the solution of the Hamilton equations of motion by the repeated action of a symplectic map S , while the corresponding tangent map TS is used for the integration of the variational equations. A simple and systematic technique to construct TS is also presented.
Integration rules for scattering equations
International Nuclear Information System (INIS)
Baadsgaard, Christian; Bjerrum-Bohr, N.E.J.; Bourjaily, Jacob L.; Damgaard, Poul H.
2015-01-01
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
The respiratory system in equations
Maury, Bertrand
2013-01-01
The book proposes an introduction to the mathematical modeling of the respiratory system. A detailed introduction on the physiological aspects makes it accessible to a large audience without any prior knowledge on the lung. Different levels of description are proposed, from the lumped models with a small number of parameters (Ordinary Differential Equations), up to infinite dimensional models based on Partial Differential Equations. Besides these two types of differential equations, two chapters are dedicated to resistive networks, and to the way they can be used to investigate the dependence of the resistance of the lung upon geometrical characteristics. The theoretical analysis of the various models is provided, together with state-of-the-art techniques to compute approximate solutions, allowing comparisons with experimental measurements. The book contains several exercises, most of which are accessible to advanced undergraduate students.
Quantum Gross-Pitaevskii Equation
Directory of Open Access Journals (Sweden)
Jutho Haegeman, Damian Draxler, Vid Stojevic, J. Ignacio Cirac, Tobias J. Osborne, Frank Verstraete
2017-07-01
Full Text Available We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
(G /G)-expansion method for finding exact travelling wave solutions of Higgs field equa- tion. Section 3.2 is devoted to find travelling wave solutions of Hamiltonian amplitude equation. In §4, some conclusions are given. 2. Lie symmetry analysis. Lie's method [8–10] is an effective method and is the simplest among group ...
FMTLxLyLz DIMENSIONAL EQUAT DIMENSIONAL EQUATION ...
African Journals Online (AJOL)
eobe
rived equation based on the concept of specific resistance, was used to i was used to i drying bed as a slud ... the sludge, it was observed that the specific resistance decreases with incr ng results: D ng results: Dosage increase of 10g, ..... Assessment of the Suitability of Anaerobic Digestion. Effluent for Direct Application as ...
Coupled Higgs field equation and Hamiltonian amplitude equation ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 79; Issue 1. Coupled Higgs ﬁeld equation and ... School of Mathematics and Computer Applications, Thapar University, Patiala 147 004, India; Department of Mathematics, Jaypee University of Information Technology, Waknaghat, Distt. Solan 173 234, India ...
Stability theory of differential equations
Bellman, Richard Ernest
1953-01-01
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies.The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from
Fundamentals of equations of state
Eliezer, Shalom; Hora, Heinrich
2002-01-01
The equation of state was originally developed for ideal gases, and proved central to the development of early molecular and atomic physics. Increasingly sophisticated equations of state have been developed to take into account molecular interactions, quantization, relativistic effects, etc. Extreme conditions of matter are encountered both in nature and in the laboratory, for example in the centres of stars, in relativistic collisions of heavy nuclei, in inertial confinement fusion (where a temperature of 10 9 K and a pressure exceeding a billion atmospheres can be achieved). A sound knowledg
Nielsen number and differential equations
Directory of Open Access Journals (Sweden)
Andres Jan
2005-01-01
Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.
International Nuclear Information System (INIS)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab
Energy Technology Data Exchange (ETDEWEB)
Kahana, S.
1986-01-01
The role of the nuclear equation of state in determining the fate of the collapsing cores of massive stars is examined in light of both recent theoretical advances in this subject and recent experimental measurements with relativistic heavy ions. The difficulties existing in attempts to bring the softer nuclear matter apparently required by the theory of Type II supernovae into consonance with the heavy ion data are discussed. Relativistic mean field theory is introduced as a candidate for derivation of the equation of state, and a simple form for the saturation compressibility is obtained. 28 refs., 4 figs., 1 tab.
Applied analysis and differential equations
Cârj, Ovidiu
2007-01-01
This volume contains refereed research articles written by experts in the field of applied analysis, differential equations and related topics. Well-known leading mathematicians worldwide and prominent young scientists cover a diverse range of topics, including the most exciting recent developments. A broad range of topics of recent interest are treated: existence, uniqueness, viability, asymptotic stability, viscosity solutions, controllability and numerical analysis for ODE, PDE and stochastic equations. The scope of the book is wide, ranging from pure mathematics to various applied fields such as classical mechanics, biomedicine, and population dynamics.
Group analysis of differential equations
Ovsiannikov, L V
1982-01-01
Group Analysis of Differential Equations provides a systematic exposition of the theory of Lie groups and Lie algebras and its application to creating algorithms for solving the problems of the group analysis of differential equations.This text is organized into eight chapters. Chapters I to III describe the one-parameter group with its tangential field of vectors. The nonstandard treatment of the Banach Lie groups is reviewed in Chapter IV, including a discussion of the complete theory of Lie group transformations. Chapters V and VI cover the construction of partial solution classes for the g
Partial differential equations an introduction
Colton, David
2004-01-01
Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of
Basic linear partial differential equations
Treves, Francois
1975-01-01
Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students features most of the basic classical results. The methods, however, are decidedly nontraditional: in practically every instance, they tend toward a high level of abstraction. This approach recalls classical material to contemporary analysts in a language they can understand, as well as exploiting the field's wealth of examples as an introduction to modern theories.The four-part treatment covers the basic examples of linear partial differential equations and their
Einstein Equations from Varying Complexity
Czech, Bartłomiej
2018-01-01
A recent proposal equates the circuit complexity of a quantum gravity state with the gravitational action of a certain patch of spacetime. Since Einstein's equations follow from varying the action, it should be possible to derive them by varying complexity. I present such a derivation for vacuum solutions of pure Einstein gravity in three-dimensional asymptotically anti-de Sitter space. The argument relies on known facts about holography and on properties of tensor network renormalization, an algorithm for coarse-graining (and optimizing) tensor networks.
Sequent Calculus and Equational Programming
Directory of Open Access Journals (Sweden)
Nicolas Guenot
2015-07-01
Full Text Available Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.
Radar equations for modern radar
Barton, David K
2012-01-01
Based on the classic Radar Range-Performance Analysis from 1980, this practical volume extends that work to ensure applicability of radar equations to the design and analysis of modern radars. This unique book helps you identify what information on the radar and its environment is needed to predict detection range. Moreover, it provides equations and data to improve the accuracy of range calculations. You find detailed information on propagation effects, methods of range calculation in environments that include clutter, jamming and thermal noise, as well as loss factors that reduce radar perfo
Indian Academy of Sciences (India)
is to study the interaction properties between the periodic waves. Here, we take the (2+1)-dimensional KdV equation .... In fact, such limit for the present family of doubly periodic waves is especially rich, since one can proceed with the long .... ematical Society, Providence, 1997). [11] K Chandrasekharan, Elliptic functions ...
Stability of Functional Differential Equations
Lemm, Jeffrey M
1986-01-01
This book provides an introduction to the structure and stability properties of solutions of functional differential equations. Numerous examples of applications (such as feedback systrems with aftereffect, two-reflector antennae, nuclear reactors, mathematical models in immunology, viscoelastic bodies, aeroautoelastic phenomena and so on) are considered in detail. The development is illustrated by numerous figures and tables.
Sonar equations for planetary exploration.
Ainslie, Michael A; Leighton, Timothy G
2016-08-01
The set of formulations commonly known as "the sonar equations" have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and localize objects submerged in seawater. The efficacy of the sonar equations, with individual terms evaluated in decibels, is well established in Earth's oceans. The sonar equations have been used in the past for missions to other planets and moons in the solar system, for which they are shown to be less suitable. While it would be preferable to undertake high-fidelity acoustical calculations to support planning, execution, and interpretation of acoustic data from planetary probes, to avoid possible errors for planned missions to such extraterrestrial bodies in future, doing so requires awareness of the pitfalls pointed out in this paper. There is a need to reexamine the assumptions, practices, and calibrations that work well for Earth to ensure that the sonar equations can be accurately applied in combination with the decibel to extraterrestrial scenarios. Examples are given for icy oceans such as exist on Europa and Ganymede, Titan's hydrocarbon lakes, and for the gaseous atmospheres of (for example) Jupiter and Venus.
Sonar equations for planetary exploration
Ainslie, M.A.; Leighton, T.G.
2016-01-01
The set of formulations commonly known as “the sonar equations” have for many decades been used to quantify the performance of sonar systems in terms of their ability to detect and ocalize objects submerged in seawater. The efficacy of the sonar equations, with individualterms evaluated in decibels,
Saha equation in Rindler space
Indian Academy of Sciences (India)
Sanchari De
MS received 21 October 2016; revised 3 January 2017; accepted 25 January 2017; published online 31 May 2017. Abstract. The Saha equations for the photoionization process of hydrogen atoms .... [3] C W Misner, Kip S Thorne and J A Wheeler, Gravitation (W.H.. Freeman and Company, New York, 1972). [4] W Rindler ...
Equations for formally real meadows
Bergstra, J.A.; Bethke, I.; Ponse, A.
2015-01-01
We consider the signatures Σm = (0,1,−,+,⋅,−1) of meadows and (Σm,s) of signed meadows. We give two complete axiomatizations of the equational theories of the real numbers with respect to these signatures. In the first case, we extend the axiomatization of zero-totalized fields by a single axiom
On the Saha Ionization Equation
Indian Academy of Sciences (India)
On the Saha Ionization Equation. Sushanta Dattagupta. General Article Volume 23 Issue 1 January 2018 pp 41-55. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/023/01/0041-0055. Keywords. Ionization, astrophysics, spectroscopy, chemical reaction, transition state. Abstract.
Pendulum Motion and Differential Equations
Reid, Thomas F.; King, Stephen C.
2009-01-01
A common example of real-world motion that can be modeled by a differential equation, and one easily understood by the student, is the simple pendulum. Simplifying assumptions are necessary for closed-form solutions to exist, and frequently there is little discussion of the impact if those assumptions are not met. This article presents a…
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
Transport equation and shock waves
International Nuclear Information System (INIS)
Besnard, D.
1981-04-01
A multi-group method is derived from a one dimensional transport equation for the slowing down and spatial transport of energetic positive ions in a plasma. This method is used to calculate the behaviour of energetic charged particles in non homogeneous and non stationary plasma, and the effect of energy deposition of the particles on the heating of the plasma. In that purpose, an equation for the density of fast ions is obtained from the Fokker-Planck equation, and a closure condition for the second moment of this equation is deduced from phenomenological considerations. This method leads to a numerical method, simple and very efficient, which doesn't require much computer storage. Two types of numerical results are obtained. First, results on the slowing down of 3.5 MeV alpha particles in a 50 keV plasma plublished by Corman and al and Moses are compared with the results obtained with both our method and a Monte Carlo type method. Good agreement was obtained, even for energy deposition on the ions of the plasma. Secondly, we have calculated propagation of alpha particles heating a cold plasma. These results are in very good agreement with those given by an accurate Monte Carlo method, for both the thermal velocity, and the energy deposition in the plasma
Indian Academy of Sciences (India)
Abstract. By applying the bifurcation theory of dynamical system to the generalized. KP–BBM equation, the phase portraits of the travelling wave system are obtained. It can be shown that singular straight line in the travelling wave system is the reason why smooth periodic waves converge to periodic cusp waves.
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
birth of the Universe in a Big Bang. Nothing could be happier and more persuasive than the observation verifying the prediction of theory. This gave rise to a general belief that singularities were inevitable in general relativity (GR) so long as the dynamics were governed by Einstein's equations and more over positive energy ...
Renaissance Learning Equating Study. Report
Sewell, Julie; Sainsbury, Marian; Pyle, Katie; Keogh, Nikki; Styles, Ben
2007-01-01
An equating study was carried out in autumn 2006 by the National Foundation for Educational Research (NFER) on behalf of Renaissance Learning, to provide validation evidence for the use of the Renaissance Star Reading and Star Mathematics tests in English schools. The study investigated the correlation between the Star tests and established tests.…
A generalized advection dispersion equation
Indian Academy of Sciences (India)
This paper examines a possible effect of uncertainties, variability or heterogeneity of any dynamic system when being included in its evolution rule; the notion is illustrated with the advection dispersion equation, which describes the groundwater pollution model. An uncertain derivative is defined; some properties of.
Elizarova, Tatiana G
2009-01-01
This book presents two interconnected mathematical models generalizing the Navier-Stokes system. The models, called the quasi-gas-dynamic and quasi-hydrodynamic equations, are then used as the basis of numerical methods solving gas- and fluid-dynamic problems.
Slave equations for spin models
International Nuclear Information System (INIS)
Catterall, S.M.; Drummond, I.T.; Horgan, R.R.
1992-01-01
We apply an accelerated Langevin algorithm to the simulation of continuous spin models on the lattice. In conjunction with the evolution equation for the spins we use slave equations to compute estimators for the connected correlation functions of the model. In situations for which the symmetry of the model is sufficiently strongly broken by an external field these estimators work well and yield a signal-to-noise ratio for the Green function at large time separations more favourable than that resulting from the standard method. With the restoration of symmetry, however, the slave equation estimators exhibit an intrinsic instability associated with the growth of a power law tail in the probability distributions for the measured quantities. Once this tail has grown sufficiently strong it results in a divergence of the variance of the estimator which then ceases to be useful for measurement purposes. The instability of the slave equation method in circumstances of weak symmetry breaking precludes its use in determining the mass gap in non-linear sigma models. (orig.)
Solutions of equations in languages
Hesselink, Wim H.
A context-free grammar corresponds to a system of equations in languages. The language generated by the grammar is the smallest solution of the system. We give a necessary and sufficient condition for an arbitrary solution to be the smallest one. We revive an old criterion to decide that a grammar
A Versatile Technique for Solving Quintic Equations
Kulkarni, Raghavendra G.
2006-01-01
In this paper we present a versatile technique to solve several types of solvable quintic equations. In the technique described here, the given quintic is first converted to a sextic equation by adding a root, and the resulting sextic equation is decomposed into two cubic polynomials as factors in a novel fashion. The resultant cubic equations are…
Functional equations in matrix normed spaces
Indian Academy of Sciences (India)
Cauchy additive functional equation and the quadratic functional equation in matrix normed spaces. Keywords. Operator space; fixed point; Hyers–Ulam stability; Cauchy additive functional equation; quadratic functional equation. 2000 Mathematics Subject Classification. 47L25, 47H10, 39B82, 46L07, 39B52. 1.
Analytical solution of population balance equation involving ...
Indian Academy of Sciences (India)
This paper presents an effective analytical simulation to solve population balance equation (PBE), involving particulate aggregation and breakage, by making use of appropriate solution(s) of associated complementary equation via auxiliary equation method (AEM). Travelling wave solutions of the complementary equation ...
An analytical solution of fractional burgers equation
Directory of Open Access Journals (Sweden)
Pang Jing
2017-01-01
Full Text Available Using the fractional complex transform, the fractional partial differential equations can be reduced to ordinary differential equations which can be solved by the auxiliary equation method. Non-linear superposition formulation of Riccati equation is applied, and a complex infinite sequence solution is obtained.
The Complexity of One-Step Equations
Ngu, Bing
2014-01-01
An analysis of one-step equations from a cognitive load theory perspective uncovers variation within one-step equations. The complexity of one-step equations arises from the element interactivity across the operational and relational lines. The higher the number of operational and relational lines, the greater the complexity of the equations.…
Algebraic entropy for differential-delay equations
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.
Interplays between Harper and Mathieu equations.
Papp, E; Micu, C
2001-11-01
This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Mathieu equation. This leads to the derivation of two kinds of energy formulas working in terms of cubic and quadratic algebraic equations, respectively. Combining such results yields quadratic equations to the energy description of the Harper equation, incorporating all parameters needed.
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....
Maxwell's equations of electrodynamics an explanation
Ball, David W
2012-01-01
Maxwell's Equations of Electrodynamics: An Explanation is a concise discussion of Maxwell's four equations of electrodynamics - the fundamental theory of electricity, magnetism, and light. It guides readers step-by-step through the vector calculus and development of each equation. Pictures and diagrams illustrate what the equations mean in basic terms. The book not only provides a fundamental description of our universe but also explains how these equations predict the fact that light is better described as "electromagnetic radiation."
The equations icons of knowledge
Bais, Sander
2005-01-01
For thousands of years mankind has tried to understand nature. Exploring the world on all scales with instruments of ever more ingenuity, we have been able to unravel some of the great mysteries that surround us. While collecting an overwhelming multitude of observational facts, we discovered fundamental laws that govern the structure and evolution of physical reality. We know that nature speaks to us in the language of mathematics. In this language most of our basic understanding of the physical world can be expressed in an unambiguous and concise way. The most artificial language turns out to be the most natural of all. The laws of nature correspond to equations. These equations are the icons of knowledge that mark crucial turning points in our thinking about the world we happen to live in. They form the symbolic representation of most of what we know, and as such constitute an important and robust part of our culture.
Nonlocal higher order evolution equations
Rossi, Julio D.
2010-06-01
In this article, we study the asymptotic behaviour of solutions to the nonlocal operator ut(x, t)1/4(-1)n-1 (J*Id -1)n (u(x, t)), x ∈ ℝN, which is the nonlocal analogous to the higher order local evolution equation vt(-1)n-1(Δ)nv. We prove that the solutions of the nonlocal problem converge to the solution of the higher order problem with the right-hand side given by powers of the Laplacian when the kernel J is rescaled in an appropriate way. Moreover, we prove that solutions to both equations have the same asymptotic decay rate as t goes to infinity. © 2010 Taylor & Francis.
MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE
Directory of Open Access Journals (Sweden)
Francisco Frutos Alfaro
2017-04-01
Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.
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.
Equation of State Project Overview
Energy Technology Data Exchange (ETDEWEB)
Crockett, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2015-09-11
A general overview of the Equation of State (EOS) Project will be presented. The goal is to provide the audience with an introduction of what our more advanced methods entail (DFT, QMD, etc.. ) and how these models are being utilized to better constrain the thermodynamic models. These models substantially reduce our regions of interpolation between the various thermodynamic limits. I will also present a variety example of recent EOS work.
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Multiplication. If ux, f (x) and g(x) are differentiable in the opened interval D, then: D ux [f(x) · g(x)]=g(x)f (x) + f(x)g (x). + (gf + fg )(x)ux + u x. (f(x)g(x)). (2.5) ..... for solution of various nonlinear problems without usual restrictive assumptions. To solve equation. (4.2) by means of variational iteration method, we put (4.2) as ...
BERNULLI DIFFERENTIAL EQUATION AND CHAOS
Directory of Open Access Journals (Sweden)
V. Ye. Belozerov
2013-03-01
Full Text Available Existence conditions of homoclinic orbits for some systems of ordinary quadratic differential equations with singular linear part are founded. A realization of these conditions guarantees the existence of chaotic attractors at 3-D autonomous quadratic systems. In addition, a chaotic behavior of the solutions of these systems is determined by one-dimensional discrete map at some values of parameters. Examples are given.
Handbook of structural equation modeling
Hoyle, Rick H
2012-01-01
The first comprehensive structural equation modeling (SEM) handbook, this accessible volume presents both the mechanics of SEM and specific SEM strategies and applications. The editor, contributors, and editorial advisory board are leading methodologists who have organized the book to move from simpler material to more statistically complex modeling approaches. Sections cover the foundations of SEM; statistical underpinnings, from assumptions to model modifications; steps in implementation, from data preparation through writing the SEM report; and basic and advanced applications, inclu
Integration of Chandrasekhar's integral equation
International Nuclear Information System (INIS)
Tanaka, Tasuku
2003-01-01
We solve Chandrasekhar's integration equation for radiative transfer in the plane-parallel atmosphere by iterative integration. The primary thrust in radiative transfer has been to solve the forward problem, i.e., to evaluate the radiance, given the optical thickness and the scattering phase function. In the area of satellite remote sensing, our problem is the inverse problem: to retrieve the surface reflectance and the optical thickness of the atmosphere from the radiance measured by satellites. In order to retrieve the optical thickness and the surface reflectance from the radiance at the top-of-the atmosphere (TOA), we should express the radiance at TOA 'explicitly' in the optical thickness and the surface reflectance. Chandrasekhar formalized radiative transfer in the plane-parallel atmosphere in a simultaneous integral equation, and he obtained the second approximation. Since then no higher approximation has been reported. In this paper, we obtain the third approximation of the scattering function. We integrate functions derived from the second approximation in the integral interval from 1 to ∞ of the inverse of the cos of zenith angles. We can obtain the indefinite integral rather easily in the form of a series expansion. However, the integrals at the upper limit, ∞, are not yet known to us. We can assess the converged values of those series expansions at ∞ through calculus. For integration, we choose coupling pairs to avoid unnecessary terms in the outcome of integral and discover that the simultaneous integral equation can be deduced to the mere integral equation. Through algebraic calculation, we obtain the third approximation as a polynomial of the third degree in the atmospheric optical thickness
Deriving the bond pricing equation
Directory of Open Access Journals (Sweden)
Kožul Nataša
2014-01-01
Full Text Available Given the recent focus on Eurozone debt crisis and the credit rating downgrade not only of US debt, but that of other countries and many UK major banking institutions, this paper aims to explain the concept of bond yield, its different measures and bond pricing equation. Yields on capital market instruments are rarely quoted on the same basis, which makes direct comparison between different as investment choices impossible. Some debt instruments are quoted on discount basis, whilst coupon-bearing ones accrue interest differently, offer different compounding opportunities, have different coupon payment frequencies, and manage non-business day maturity dates differently. Moreover, rules governing debt vary across countries, markets and currencies, making yield calculation and comparison a rather complex issue. Thus, some fundamental concepts applicable to debt instrument yield measurement, with focus on bond equation, are presented here. In addition, bond equation expressed in annuity form and used to apply Newton-Raphson algorithm to derive true bond yield is also shown.
Wave equations in higher dimensions
Dong, Shi-Hai
2011-01-01
Higher dimensional theories have attracted much attention because they make it possible to reduce much of physics in a concise, elegant fashion that unifies the two great theories of the 20th century: Quantum Theory and Relativity. This book provides an elementary description of quantum wave equations in higher dimensions at an advanced level so as to put all current mathematical and physical concepts and techniques at the reader’s disposal. A comprehensive description of quantum wave equations in higher dimensions and their broad range of applications in quantum mechanics is provided, which complements the traditional coverage found in the existing quantum mechanics textbooks and gives scientists a fresh outlook on quantum systems in all branches of physics. In Parts I and II the basic properties of the SO(n) group are reviewed and basic theories and techniques related to wave equations in higher dimensions are introduced. Parts III and IV cover important quantum systems in the framework of non-relativisti...
Effective Schroedinger equations on submanifolds
Energy Technology Data Exchange (ETDEWEB)
Wachsmuth, Jakob
2010-02-11
In this thesis the time dependent Schroedinger equation is considered on a Riemannian manifold A with a potential that localizes a certain class of states close to a fixed submanifold C, the constraint manifold. When the potential is scaled in the directions normal to C by a small parameter epsilon, the solutions concentrate in an epsilon-neighborhood of the submanifold. An effective Schroedinger equation on the submanifold C is derived and it is shown that its solutions, suitably lifted to A, approximate the solutions of the original equation on A up to errors of order {epsilon}{sup 3} vertical stroke t vertical stroke at time t. Furthermore, it is proved that, under reasonable conditions, the eigenvalues of the corresponding Hamiltonians below a certain energy coincide upto errors of order {epsilon}{sup 3}. These results holds in the situation where tangential and normal energies are of the same order, and where exchange between normal and tangential energies occurs. In earlier results tangential energies were assumed to be small compared to normal energies, and rather restrictive assumptions were needed, to ensure that the separation of energies is maintained during the time evolution. The most important consequence of this thesis is that now constraining potentials that change their shape along the submanifold can be treated, which is the typical situation in applications like molecular dynamics and quantum waveguides.
Handbook of differential equations stationary partial differential equations
Chipot, Michel
2006-01-01
This handbook is volume III in a series devoted to stationary partial differential quations. Similarly as volumes I and II, it is a collection of self contained state-of-the-art surveys written by well known experts in the field. The topics covered by this handbook include singular and higher order equations, problems near critically, problems with anisotropic nonlinearities, dam problem, T-convergence and Schauder-type estimates. These surveys will be useful for both beginners and experts and speed up the progress of corresponding (rapidly developing and fascinating) areas of mathematics. Ke
Partial differential equations of mathematical physics and integral equations
Guenther, Ronald B
1996-01-01
This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the t
Partial differential equations for scientists and engineers
Farlow, Stanley J
1993-01-01
Most physical phenomena, whether in the domain of fluid dynamics, electricity, magnetism, mechanics, optics, or heat flow, can be described in general by partial differential equations. Indeed, such equations are crucial to mathematical physics. Although simplifications can be made that reduce these equations to ordinary differential equations, nevertheless the complete description of physical systems resides in the general area of partial differential equations.This highly useful text shows the reader how to formulate a partial differential equation from the physical problem (constructing th
Semilinear Schrödinger equations
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
General and exact pressure evolution equation
Toutant, Adrien
2017-11-01
A crucial issue in fluid dynamics is related to the knowledge of the fluid pressure. A new general pressure equation is derived from compressible Navier-Stokes equation. This new pressure equation is valid for all real dense fluids for which the pressure tensor is isotropic. It is argued that this new pressure equation allows unifying compressible, low-Mach and incompressible approaches. Moreover, this equation should be able to replace the Poisson equation in isothermal incompressible fluids. For computational fluid dynamics, it can be seen as an alternative to Lattice Boltzmann methods and as the physical justification of artificial compressibility.
Using fundamental equations to describe basic phenomena
DEFF Research Database (Denmark)
Jakobsen, Arne; Rasmussen, Bjarne D.
1999-01-01
When the fundamental thermodynamic balance equations (mass, energy, and momentum) are used to describe the processes in a simple refrigeration system, then one finds that the resulting equation system will have a degree of freedom equal to one. Further investigations reveal that it is the equation...... and subcooling are introduced. Since the degree of freedom was equal to one, using both the superheat and subcooling require that one of the fundamental equations must be omitted from the equation system.The main purpose of the paper is to clarify the relation between the fundamental balance equations...
International Workshop on Elliptic and Parabolic Equations
Schrohe, Elmar; Seiler, Jörg; Walker, Christoph
2015-01-01
This volume covers the latest research on elliptic and parabolic equations and originates from the international Workshop on Elliptic and Parabolic Equations, held September 10-12, 2013 at the Leibniz Universität Hannover. It represents a collection of refereed research papers and survey articles written by eminent scientist on advances in different fields of elliptic and parabolic partial differential equations, including singular Riemannian manifolds, spectral analysis on manifolds, nonlinear dispersive equations, Brownian motion and kernel estimates, Euler equations, porous medium type equations, pseudodifferential calculus, free boundary problems, and bifurcation analysis.
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
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
Cox, S.G.
2012-01-01
The thesis deals with various aspects of the study of stochastic partial differential equations driven by Gaussian noise. The approach taken is functional analytic rather than probabilistic: the stochastic partial differential equation is interpreted as an ordinary stochastic differential equation
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.
Reduction of lattice equations to the Painlevé equations: PIV and PV
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.
Techniques for estimating allometric equations.
Manaster, B J; Manaster, S
1975-11-01
Morphologists have long been aware that differential size relationships of variables can be fo great value when studying shape. Allometric patterns have been the basis of many interpretations of adaptations, biomechanisms, and taxonomies. It is of importance that the parameters of the allometric equation be as accurate estimates as possible since they are so commonly used in such interpretations. Since the error term may come into the allometric relation either exponentially or additively, there are at least two methods of estimating the parameters of the allometric equation. That most commonly used assumes exponentiality of the error term, and operates by forming a linear function by a logarithmic transformation and then solving by the method of ordinary least squares. On the other hand, if the rrror term comes into the equation in an additive way, a nonlinear method may be used, searching the parameter space for those parameters which minimize the sum of squared residuals. Study of data on body weight and metabolism in birds explores the issues involved in discriminating between the two models by working through a specific example and shows that these two methods of estimation can yield highly different results. Not only minimizing the sum of squared residuals, but also the distribution and randomness of the residuals must be considered in determing which model more precisely estimates the parameters. In general there is no a priori way to tell which model will be best. Given the importance often attached to the parameter estimates, it may be well worth considerable effort to find which method of solution is appropriate for a given set of data.
Differential Equations and Computational Simulations
1999-06-18
given in (6),(7) in Taylor series of e. Equating coefficients of same power of e in both side of equity , we obtain a sequence of linear boundary value...fields, 3). structural instability and block stability of divergence-free vector fields on 2D compact manifolds with nonzero genus , and 4). structural...circle bands. Definition 3.1 Let N be a compact manifold without boundary and with genus k > 0. A closed domain fi C N is called a pseudo-manifold
Ising models and soliton equations
International Nuclear Information System (INIS)
Perk, J.H.H.; Au-Yang, H.
1985-01-01
Several new results for the critical point of correlation functions of the Hirota equation are derived within the two-dimensional Ising model. The recent success of the conformal-invariance approach in the determination of a critical two-spin correration function is analyzed. The two-spin correlation function is predicted to be rotationally invariant and to decay with a power law in this approach. In the approach suggested here systematic corrections due to the underlying lattice breaking the rotational invariance are obtained
BMN correlators by loop equations
International Nuclear Information System (INIS)
Eynard, Bertrand; Kristjansen, Charlotte
2002-01-01
In the BMN approach to N=4 SYM a large class of correlators of interest are expressible in terms of expectation values of traces of words in a zero-dimensional gaussian complex matrix model. We develop a loop-equation based, analytic strategy for evaluating such expectation values to any order in the genus expansion. We reproduce the expectation values which were needed for the calculation of the one-loop, genus one correction to the anomalous dimension of BMN-operators and which were earlier obtained by combinatorial means. Furthermore, we present the expectation values needed for the calculation of the one-loop, genus two correction. (author)
Numerical Solution of Parabolic Equations
DEFF Research Database (Denmark)
Østerby, Ole
approximations which depend on a step size, such as numerical integration and solution of ordinary and partial differential equations. An integral part of the error estimation is the estimation of the order of the method and can thus satisfy the inquisitive mind: Is the order what we expect it to be from theopry...... ? and how do boundary value approximations affect the overall order of the method. Knowledge of a reliable order and error estimate enables us to determine (near-)optimal step sizes to meet a prescribed error tolerance, and possibly to extrapolate to get (higher order and) better accuracy at a minimal...
Introduction to partial differential equations with applications
Zachmanoglou, E C
1988-01-01
This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.
Feedback stabilization of semilinear heat equations
Directory of Open Access Journals (Sweden)
V. Barbu
2003-01-01
Full Text Available This paper is concerned with the internal and boundary stabilization of the steady-state solutions to quasilinear heat equations via internal linear feedback controllers provided by an LQ control problem associated with the linearized equation.
Regional Screening Levels (RSLs) - Equations (November 2017 )
Regional Screening Level RSL equations page provides quick access to the equations used in the Chemical Risk Assessment preliminary remediation goal PRG risk based concentration RBC and risk calculator for the assessment of human Health.
On oscillatory solutions of certain difference equations
Directory of Open Access Journals (Sweden)
Grzegorz Grzegorczyk
2006-01-01
Full Text Available Some difference equations with deviating arguments are discussed in the context of the oscillation problem. The aim of this paper is to present the sufficient conditions for oscillation of solutions of the equations discussed.
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
The stochastic Swift-Hohenberg equation
Gao, Peng
2017-09-01
In this paper, we will study the stochastic Swift-Hohenberg equation. The weak martingale solution, stationary martingale solution, invariant measures, mild solution, large deviation principle and random attractors for the stochastic Swift-Hohenberg equation will be considered.
On linear equations with general polynomial solutions
Laradji, A.
2018-04-01
We provide necessary and sufficient conditions for which an nth-order linear differential equation has a general polynomial solution. We also give necessary conditions that can directly be ascertained from the coefficient functions of the equation.
PARALLEL SOLUTION METHODS OF PARTIAL DIFFERENTIAL EQUATIONS
Directory of Open Access Journals (Sweden)
Korhan KARABULUT
1998-03-01
Full Text Available Partial differential equations arise in almost all fields of science and engineering. Computer time spent in solving partial differential equations is much more than that of in any other problem class. For this reason, partial differential equations are suitable to be solved on parallel computers that offer great computation power. In this study, parallel solution to partial differential equations with Jacobi, Gauss-Siedel, SOR (Succesive OverRelaxation and SSOR (Symmetric SOR algorithms is studied.
Partial differential equations of mathematical physics
Sobolev, S L
1964-01-01
Partial Differential Equations of Mathematical Physics emphasizes the study of second-order partial differential equations of mathematical physics, which is deemed as the foundation of investigations into waves, heat conduction, hydrodynamics, and other physical problems. The book discusses in detail a wide spectrum of topics related to partial differential equations, such as the theories of sets and of Lebesgue integration, integral equations, Green's function, and the proof of the Fourier method. Theoretical physicists, experimental physicists, mathematicians engaged in pure and applied math
About the solvability of matrix polynomial equations
Netzer, Tim; Thom, Andreas
2016-01-01
We study self-adjoint matrix polynomial equations in a single variable and prove existence of self-adjoint solutions under some assumptions on the leading form. Our main result is that any self-adjoint matrix polynomial equation of odd degree with non-degenerate leading form can be solved in self-adjoint matrices. We also study equations of even degree and equations in many variables.
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)
Solutions manual to accompany Ordinary differential equations
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
Numerical methods for stochastic differential equations.
Wilkie, Joshua
2004-01-01
Stochastic differential equations (SDE's) play an important role in physics but existing numerical methods for solving such equations are of low accuracy and poor stability. A general strategy for developing accurate and efficient schemes for solving stochastic equations is outlined here. High-order numerical methods are developed for the integration of stochastic differential equations with strong solutions. We demonstrate the accuracy of the resulting integration schemes by computing the errors in approximate solutions for SDE's which have known exact solutions.
Notes on the infinity Laplace equation
Lindqvist, Peter
2016-01-01
This BCAM SpringerBriefs is a treaty of the Infinity-Laplace Equation, which has inherited many features from the ordinary Laplace Equation, and is based on lectures by the author. The Infinity.Laplace Equation has delightful counterparts to the Dirichlet integral, the mean value property, the Brownian motion, Harnack's inequality, and so on. This "fully non-linear" equation has applications to image processing and to mass transfer problems, and it provides optimal Lipschitz extensions of boundary values.
Ramanujan's modular equations of degree 5
Indian Academy of Sciences (India)
Abstract. We provide alternative derivations of theta function identities associ- ated with modular equations of degree 5. We then use the identities to derive the corresponding modular equations. Keywords. Theta-function; elliptic integral; modular equation; multiplier. 1. Introduction. Ramanujan's general theta-function f (a, ...
Explicit solutions of the Rand Equation
African Journals Online (AJOL)
user
We perform a classical Lie Group analysis to analyze the point symmetries. By using a similarity ... Keywords: Nonlinear partial differential equations, evolution equations, symmetries, similarity solutions, Rand Equation. PACS-Code: .... The table is skew-symmetric and the diagonal elements vanish. The coefficient kji.
Fuzzy Stability of Quadratic Functional Equations
Directory of Open Access Journals (Sweden)
Jang Sun-Young
2010-01-01
Full Text Available The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces.
Fuzzy Stability of Quadratic Functional Equations
Dong Yun Shin; Choonkil Park; Sun-Young Jang; Jung Rye Lee
2010-01-01
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces.
Some Functional Equations Originating from Number Theory
Indian Academy of Sciences (India)
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
Some functional equations originating from number theory
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations. Keywords. Functional equation; stability; multiplicative function. 1. Introduction. In 1940, Ulam gave a wide ranging talk before the Mathematics ...
Some functional equations originating from number theory
Indian Academy of Sciences (India)
We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.
Managing Element Interactivity in Equation Solving
Ngu, Bing Hiong; Phan, Huy P.; Yeung, Alexander Seeshing; Chung, Siu Fung
2018-01-01
Between two popular teaching methods (i.e., balance method vs. inverse method) for equation solving, the main difference occurs at the operational line (e.g., +2 on both sides vs. -2 becomes +2), whereby it alters the state of the equation and yet maintains its equality. Element interactivity occurs on both sides of the equation in the balance…
A reliable treatment for nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.
2007-01-01
Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation
On the (colored Yang-Baxter Equation
Directory of Open Access Journals (Sweden)
Florin Felix Nichita
2010-06-01
Full Text Available The quantum Yang-Baxter equation ¯rst appeared in theoretical physics and statistical mechanics. Afterwards, it has proved to be
important also in knot theory, quantum groups, etc. This paper deals with the (colored Yang-Baxter equation and computational methods. A new result about the set-theoretical Yang-Baxter equation is presented.
Elliptic Hypergeometric Solutions to Elliptic Difference Equations
Directory of Open Access Journals (Sweden)
Alphonse P. Magnus
2009-03-01
Full Text Available It is shown how to define difference equations on particular lattices {x_n}, n in Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice. Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.
Elliptic Hypergeometric Solutions to Elliptic Difference Equations
Magnus, Alphonse P.
2009-03-01
It is shown how to define difference equations on particular lattices {xn}, n Î Z, made of values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations have remarkable simple interpolatory expansions. Only linear difference equations of first order are considered here.
New solitons connected to the Dirac equation
International Nuclear Information System (INIS)
Grosse, H.
1984-01-01
Imposing isospectral invariance for the one dimensional Dirac operator leads to systems of nonlinear partial differential equations. By constructing reflectionless potentials of the Dirac equation we obtain a new type of solitons for a system of modified Korteweg-de Vries equations. (Author)
Comparison of the Schrodinger and Salpeter equations
International Nuclear Information System (INIS)
Jacobs, S.; Olsson, M.G.
1985-01-01
A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation
Numerical Solutions to Fractional Perturbed Volterra Equations
Directory of Open Access Journals (Sweden)
B. Bandrowski
2012-01-01
Full Text Available In the paper, a class of perturbed Volterra equations of convolution type with three kernel functions is considered. The kernel functions , , , correspond to the class of equations interpolating heat and wave equations. The results obtained generalize our previous results from 2010.
Equations of state for light water
International Nuclear Information System (INIS)
Rubin, G.A.; Granziera, M.R.
1983-01-01
The equations of state for light water were developed, based on the tables of Keenan and Keyes. Equations are presented, describing the specific volume, internal energy, enthalpy and entropy of saturated steam, superheated vapor and subcooled liquid as a function of pressure and temperature. For each property, several equations are shown, with different precisions and different degress of complexity. (Author) [pt
Derivation of the neutron diffusion equation
International Nuclear Information System (INIS)
Mika, J.R.; Banasiak, J.
1994-01-01
We discuss the diffusion equation as an asymptotic limit of the neutron transport equation for large scattering cross sections. We show that the classical asymptotic expansion procedure does not lead to the diffusion equation and present two modified approaches to overcome this difficulty. The effect of the initial layer is also discussed. (authors). 9 refs
The Modified Enskog Equation for Mixtures
Beijeren, H. van; Ernst, M.H.
1973-01-01
In a previous paper it was shown that a modified form of the Enskog equation, applied to mixtures of hard spheres, should be considered as the correct extension of the usual Enskog equation to the case of mixtures. The main argument was that the modified Enskog equation leads to linear transport
Completely integrable operator evolution equations. II
International Nuclear Information System (INIS)
Chudnovsky, D.V.
1979-01-01
The author continues the investigation of operator classical completely integrable systems. The main attention is devoted to the stationary operator non-linear Schroedinger equation. It is shown that this equation can be used for separation of variables for a large class of completely integrable equations. (Auth.)
Symmetries of nonlinear ordinary differential equations: The ...
Indian Academy of Sciences (India)
2015-10-21
Oct 21, 2015 ... equation and showed that it admits sl(3, R) algebra and constructed a linearizing trans- formation from ... ers of ˙x to zero, one obtains a set of linear partial differential equations for the unknown functions ξ and η. ...... [11] N H Ibragimov, Elementary Lie group analysis and ordinary differential equations (John.
Positive Integer Solutions of Certain Diophantine Equations
Indian Academy of Sciences (India)
29
An important area of number theory is devoted to finding solutions of equations where the solutions are restricted to the set of integers. Diophantine equations get their name from Diophantus of. Alexandria and they are algebraic equations for which rational or integer solutions are sought. Many researchers considered the ...