Continuity, the Bloch-Torrey equation, and Diffusion MRI
Hall, Matt G
2016-01-01
The Bloch equation describes the evolution of classical particles tagged with a magnetisation vector in a strong magnetic field and is fundamental to many NMR and MRI contrast methods. The equation can be generalised to include the effects of spin motion by including a spin flux, which typically contains a Fickian diffusive term and/or a coherent velocity term. This form is known as the Bloch-Torrey equation, and is fundamental to MR modalities which are sensitive to spin dynamics such as diffusion MRI. Such modalities have received a great deal of interest in the research literature over the last few years, resulting in a huge range of models and methods. In this work we make make use of a more general Bloch-Torrey equation with a generalised flux term. We show that many commonly employed approaches in Diffusion MRI may be viewed as different choices for the flux terms in this equation. This viewpoint, although obvious theoretically, is not usually emphasised in the diffusion MR literature and points to inte...
Derivation of Bloch equations from the time convolution less generalized master equation
International Nuclear Information System (INIS)
The generalized Bloch equations (GBE) describing the temporal evolution of a single two-level atom interacting with a classical external field of arbitrary intensity and with a thermodynamic bath are obtained from the time convolutionless generalized master equation or equivalently from the Tokuyama-Mori identity. These GBE are then used to calculate the absorption spectrum of a single two-level atom with frequency modulated by dichotomic noise with time-dependent transition probability. (author)
Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems
Tscherbul, Timur V.; Brumer, Paul
2014-01-01
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an un...
A Floquet-Bloch decomposition of Maxwell's equations, applied to homogenization
Sjöberg, Daniel; Engström, Christian; Kristensson, Gerhard; Wall, David J.N.; Wellander, Niklas
2003-01-01
Using Bloch waves to represent the full solution of Maxwell’s equations in periodic media, we study the limit where the material’s period becomes much smaller than the wavelength. It is seen that for steady-state ﬁelds, only a few of the Bloch waves contribute to the full solution. Effective material parameters can be explicitly represented in terms of dyadic products of the mean values of the non-vanishing Bloch waves, providing a new means of homogenization. The representa...
Wieser, R
2016-10-01
The derivation of the time dependent Schrödinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical Landau-Lifshitz-Bloch equation the transition to quantum mechanics has been performed and the corresponding von-Neumann equation deduced. In a second step the time Schrödinger equation has been derived. Analytical proofs and computer simulations show the correctness and applicability of the derived Schrödinger equation. PMID:27494599
Quantum Maxwell-Bloch equations for spontaneous emission in optical semiconductor devices
Hess, Ortwin; Hofmann, Holger F.
1998-01-01
We present quantum Maxwell-Bloch equations (QMBE) for spatially inhomogeneous optical semiconductor devices taking into account the quantum noise effects which cause spontaneous emission and amplified spontaneous emission. Analytical expressions derived from the QMBE are presented for the spontaneous emission factor beta and the far field pattern of amplified spontaneous emission in broad area quantum well lasers.
Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
Hatsugai, Yasuhiro; Kohmoto, Mahito; Wu, Yong-Shi
1994-01-01
For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations of Wiegmann and Zabrodin. When the magnetic flux per plaquette is 1 / Q with Q an odd integer, distribution of the roots of the Bethe ansatz equation is uniform except at two points on the unit circle in the complex plane. For the semiclassical limit Q→∞, the wave function is
Modified Bloch-Redfield Master Equation for Incoherent Excitation of Multilevel Quantum Systems
Tscherbul, Timur V
2014-01-01
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The modified Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis, and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a fi...
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...
Chaos synchronization in bi-axial magnets modeled by Bloch equation
International Nuclear Information System (INIS)
In this paper, we show that the bi-axial magnetic material modelled by Bloch equation admits chaotic solutions for a certain set of numerical values assigned to the system of parameters and initial conditions. Using the unidirectional linear and nonlinear feedback schemes, we demonstrate that two such systems can be synchronized together. The chaotic synchronization is discussed in the context of complete synchronization which means that the difference of the states of two relevant systems converge to zero. (author)
Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes
Bidégaray-Fesquet, Brigitte
2010-01-01
International audience The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies...
Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes
Bidégaray-Fesquet, Brigitte
2010-10-01
The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature, we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena.
Positiveness and Pauli exception principle in raw Bloch equations for quantum boxes
International Nuclear Information System (INIS)
The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature, we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena.
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...... unstaggered. The stability of these states is investigated analytically and numerically. The nonlinear dynamics of the Bloch states are described by a complex Ginzburg-Landau equation with linear and nonlinear parametric driving. The switching between the staggered and unstaggered Bloch states under the...
Modified-Bloch-equation description of EPR transient nutations and free induction decay in solids
International Nuclear Information System (INIS)
Based on the experimental work by Boscaino et al on the EPR transient nutations (TNs) and free induction decay (FID) in solids, we propose the modified Bloch equations (MBEs). In addition to the Tomita expression for power-dependent parameter T2u, we give an original phenomenological expression for power-dependent parameter T2v and tuning Δ. Both analytical (in the form of a Torrey solution with these parameters) and numerical solutions of MBE are obtained for TN and for different FID regimes with very good agreement between theory and experiment. We also discuss the meaning and role of the instantaneous diffusion mechanism in the transient pulse experiments. (author)
Explicit Solutions of the Bethe Ansatz Equations for Bloch Electrons in a Magnetic Field
Hatsugai, Yasuhiro; Kohmoto, Mahito; Wu, Yong-Shi
1994-01-01
For Bloch electrons in a magnetic field, explicit solutions are obtained at the center of the spectrum for the Bethe ansatz equations recently proposed by Wiegmann and Zabrodin. When the magnetic flux per plaquette is $1/Q$ where $Q$ is an odd integer, distribution of the roots is uniform on the unit circle in the complex plane. For the semi-classical limit, $ Q\\rightarrow\\infty$, the wavefunction obeys the power low and is given by $|\\psi(x)|^2=(2/ \\sin \\pi x)$ which is critical and unnormal...
Tscherbul, Timur V.; Brumer, Paul
2015-03-01
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
Energy Technology Data Exchange (ETDEWEB)
Tscherbul, Timur V., E-mail: ttscherb@chem.utoronto.ca; Brumer, Paul [Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)
2015-03-14
We present an efficient theoretical method for calculating the time evolution of the density matrix of a multilevel quantum system weakly interacting with incoherent light. The method combines the Bloch-Redfield theory with a partial secular approximation for one-photon coherences, resulting in a master equation that explicitly exposes the reliance on transition rates and the angles between transition dipole moments in the energy basis. The partial secular Bloch-Redfield master equation allows an unambiguous distinction between the regimes of quantum coherent vs. incoherent energy transfer under incoherent light illumination. The fully incoherent regime is characterized by orthogonal transition dipole moments in the energy basis, leading to a dynamical evolution governed by a coherence-free Pauli-type master equation. The coherent regime requires non-orthogonal transition dipole moments in the energy basis and leads to the generation of noise-induced quantum coherences and population-to-coherence couplings. As a first application, we consider the dynamics of excited state coherences arising under incoherent light excitation from a single ground state and observe population-to-coherence transfer and the formation of non-equilibrium quasisteady states in the regime of small excited state splitting. Analytical expressions derived earlier for the V-type system [T. V. Tscherbul and P. Brumer, Phys. Rev. Lett. 113, 113601 (2014)] are found to provide a nearly quantitative description of multilevel excited-state populations and coherences in both the small- and large-molecule limits.
A Bloch-Torrey Equation for Diffusion in a Deforming Media
International Nuclear Information System (INIS)
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
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
International Nuclear Information System (INIS)
The equations of fluid mechanics, coupled with those that describe matter transportation at the molecular level must be handled effectively. Putting the fluid into equations, we model the Bloch NMR flow equations into the harmonic wave equation for the analysis of general fluid flow. We derived the solution of the modelled harmonic equation in non relativistic quantum mechanics and discuss its semi classical application to illustrate its potential wide-ranging usefulness in the search for the best possible data obtainable for general fluid flow analysis. Representing the solution of the derived harmonic wave equation by a normalized state function is quite useful in generating the properly normalized wave functions and in the efficient evaluation of expectation values of many operators that can be fundamental to the analysis of fluid flow especially at the microscopic level. (author)
Zhang, Wen-Zhuo
2012-01-01
We derive a set of optical Bloch equations (OBEs) directly from the minimal-coupling Hamiltonian density of the bound-state quantum electrodynamics (bound-state QED). Such optical Bloch equations are beyond the former widely-used ones due to that there is no electric dipole approximation (EDA) on the minimal-coupling Hamiltonian density of the bound-state QED. Then our optical Bloch equations can describe a two-level atom interacting with a monochromatic light of arbitrary wavelength, which are suitable to study the spectroscopy and the Rabi oscillations of two-level atoms in X-ray laser beams since that the wavelength of X-ray is close to an atom to make the electric dipole approximation (EDA) invalid.
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
Dynamics of the time dependent Bloch NMR equations for complex rFB1(t) magnetic field
International Nuclear Information System (INIS)
This study examines the dynamical changes produced by a complex time-dependent rFB1(t) magnetic field in an initially unperturbed magnetic resonance system. The analysis uses the Green's function algorithm as a tool to solve the transverse component of the time-dependent Bloch NMR equations with complex rFB1(t) field. The time development of the system is studied in the Hersenberg picture in which the operators are subject to unitary transformation as the applied rFB1(t) field changes the state of the NMR system from its initial ground state into another coherent state. The detailed features of the rFB1(t) field essentially affect the evolution of the state during its application. The state of the system after the complete cessation of the radio-frequency field is determined exclusively by a Fourier component which is in resonance with the NMR system. The unitary operator allows us to determine all the physically relevant information about the system in terms of a NMR relaxation parameter. (author)
Chen, Wen-Jun; Ma, Hong; Yu, De; Zeng, Xiao-Hu
2016-08-01
A novel nuclear magnetic resonance (NMR) experimental scheme, called wideband continuous wave NMR (WB-CW-NMR), is presented in this article. This experimental scheme has promising applications in pulsed magnetic fields, and can dramatically improve the utilization of the pulsed field. The feasibility of WB-CW-NMR scheme is verified by numerically solving modified Bloch equations. In the numerical simulation, the applied magnetic field is a pulsed magnetic field up to 80 T, and the wideband continuous radio frequency (RF) excitation is a band-limited (0.68–3.40 GHz) white noise. Furthermore, the influences of some experimental parameters, such as relaxation time, applied magnetic field strength and wideband continuous RF power, on the WB-CW-NMR signal are analyzed briefly. Finally, a multi-channel system framework for transmitting and receiving ultra wideband signals is proposed, and the basic requirements of this experimental system are discussed. Meanwhile, the amplitude of the NMR signal, the level of noise and RF interference in WB-CW-NMR experiments are estimated, and a preliminary adaptive cancellation plan is given for detecting WB-CW-NMR signal from large background interference. Supported by National Natural Science Foundation of China (11475067), the Innovative Research Foundation of Huazhong University of Science and Technology (2015 ZDTD017) and the Experimental Apparatus Research Project of Wuhan Pulsed High Magnetic Field Center (2015KF17)
Gherase, Mihai R
2012-01-01
Diffusive spin exchange is one of the most important relaxation mechanisms in the Nuclear Magnetic Resonance (NMR) applications to medicine and biology. Two models based on the Bloch-McConnell (B-M) and the Bloch-Torrey (B-T) equations are commonly used for modelling the physical processes which determine the NMR lineshapes. Qualitative arguments for each of the two methods can be found in various studies in the literature. However, there is a lack of systematic quantitative investigations of the diffusive exchange spectra calculated with the two methods for the same physical system or model. In this work exact frequency-domain transverse magnetization solutions of the B-M and the B-T equations with boundary conditions for a two-compartment radial diffusive exchange model are presented. Theoretical spectra and the two corresponding metrics were computed by varying three different parameters: diffusive permeability of the separating membrane between the two compartments (P), the radius of the inner spherical c...
Richter, Marten; Renger, Thomas; Knorr, Andreas
2008-01-01
On the basis of the recent progress in the resolution of the structure of the antenna light harvesting complex II (LHC II) of the photosystem II, we propose a microscopically motivated theory to predict excitation intensity-dependent spectra. We show that optical Bloch equations provide the means to include all 2( N ) excited states of an oligomer complex of N coupled two-level systems and analyze the effects of Pauli Blocking and exciton-exciton annihilation on pump-probe spectra. We use LHC Bloch equations for 14 Coulomb coupled two-level systems, which describe the S (0) and S (1) level of every chlorophyll molecule. All parameter introduced into the Hamiltonian are based on microscopic structure and a quantum chemical model. The derived Bloch equations describe not only linear absorption but also the intensity dependence of optical spectra in a regime where the interplay of Pauli Blocking effects as well as exciton-exciton annihilation effects are important. As an example, pump-probe spectra are discussed. The observed saturation of the spectra for high intensities can be viewed as a relaxation channel blockade on short time scales due to Pauli blocking. The theoretical investigation is useful for the interpretation of the experimental data, if the experimental conditions exceed the low intensity pump limit and effects like strong Pauli Blocking and exciton-exciton annihilation need to be considered. These effects become important when multiple excitations are generated by the pump pulse in the complex. PMID:17924202
Wu, Xiao-Yu; Tian, Bo; Zhen, Hui-Ling; Sun, Wen-Rong; Sun, Ya
2016-03-01
Under investigation in this paper is a set of the ?-dimensional nonlinear Schrödinger-Maxwell-Bloch (NLS-MB) equations, which describes the optical pulse propagation in an erbium-doped fibre. Employing the Hirota method and symbolic computation, we obtain the one- two- and N-soliton solutions. We prove that the interactions between the two solitons are elastic through the asymptotic analysis on the soliton solutions. Figures are plotted to show the one soliton and the interaction between the two solitons. We find that the decrease of the frequency shift from the resonance can make the angle between the propagation directions and the amplitudes of the two MB solitons bigger, implying that the change of the amplitudes of the two MB solitons is closely related to the propagation directions of the two NLS solitons.
Meißner, Holger; Steinborn, E. Otto
1997-08-01
Recently, we proposed an iteration method for solving the eigenvalue problem of the time-independent Schrödinger equation [H. Meiβner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997)]. This method, which is based on the generalized Bloch equation, calculates iteratively certain matrix elements of the wave operator which are the wave-function expansion coefficients (WECs). It is valid for boson as well as fermion systems. In this article we show that the WEC-iteration method, together with a renormalization technique, allows us to calculate energy eigenvalues for the ground state and excited states of the quartic, sextic, and octic anharmonic oscillator with very high accuracy. In order to overcome slow convergence in the iteration scheme we use a renormalization technique introduced by F. Vinette and J. Čížek [J. Math. Phys. (N.Y.) 32, 3392 (1991)] and show that this method is equivalent to the renormalization scheme based on the Bogoliubov transformation [N. N. Bogoliubov, Izv. Akad. Nauk SSSR, Ser. Fiz. 11, 77 (1947)] which is frequently used for the treatment of anharmonic oscillators in second quantization.
Bloch-Floquet type waves in periodic ferromagnetic layered structure
Directory of Open Access Journals (Sweden)
Danoyan Z.N.
2014-06-01
Full Text Available The Bloch-Floquet type waves existence and propagation in ferromagnetic periodic layered structure are investigated. The dispersion equation obtained and investigated. It is shown that the waves spectrum contains forbidden zones.
Bloch space structure, the qutrit wave function and atom-field entanglement in three-level systems
Sen, Surajit; Nath, Mihir Ranjan; Dey, Tushar Kanti; Gangopadhyay, Gautam
2011-01-01
We have given a novel formulation of the exact solutions for the lambda, vee and cascade three-level systems where the Hamiltonian of each configuration is expressed in the SU(3) basis. The solutions are discussed from the perspective of the Bloch equation and the atom-field entanglement scenario. For the semiclassical systems, the Bloch space structure of each configuration is studied by solving the corresponding Bloch equation and it is shown that at resonance, the eight-dimensional Bloch s...
The Bloch Oscillating Transistor
Seppä, H.; Hassel, J.
2003-01-01
We introduce a new mesoscopic transistor, which consists of a superconducting island connected to superconducting and normal electrodes via two mesoscopic tunnel junctions. Furthermore, the island is being charged through a resistor. The interplay between Bloch oscillations, single-electron effects and ohmic current leads to a device having a high current gain. The operation and characteristics of the transistor are analyzed with a numerical model.
Wiegmann, P. B.; Zabrodin, A. V.
1993-01-01
We present a new approach to the problem of Bloch electrons in magnetic field,\\\\ by making explicit a natural relation between magnetic translations and the\\\\quantum group $U_{q}(sl_2)$. The approach allows to express the spectrum and\\\\\\ the Bloch function as solutions of the Bethe-Ansatz equations typical for com\\\\pletely integrable quantum systems
Allaire, Grégoire; Briane, Marc; Vanninathan, Muthusamy
2016-01-01
in press International audience In this paper we make a comparison between the two-scale asymptotic expansion method for periodic homogenization and the so-called Bloch wave method. It is well-known that the homogenized tensor coincides with the Hessian matrix of the first Bloch eigenvalue when the Bloch parameter vanishes. In the context of the two-scale asymptotic expansion method, there is the notion of high order homogenized equation [5] where the homogenized equation can be improve...
Entangled Bloch Spheres: Bloch Matrix And Two Qubit State Space
Gamel, Omar
2016-01-01
We represent a two qubit density matrix in the basis of Pauli matrix tensor products, with the coefficients constituting a Bloch matrix, analogous to the single qubit Bloch vector. We find the quantum state positivity requirements on the Bloch matrix components, leading to three important inequalities, allowing us to parameterize and visualize the two qubit state space. Applying the singular value decomposition naturally separates the degrees of freedom to local and nonlocal, and simplifies the positivity inequalities. It also allows us to geometrically represent a state as two entangled Bloch spheres with superimposed correlation axes. It is shown that unitary transformations, local or nonlocal, have simple interpretations as axis rotations or mixing of certain degrees of freedom. The nonlocal unitary invariants of the state are then derived in terms of local unitary invariants. The positive partial transpose criterion for entanglement is generalized, and interpreted as a reflection, or a change of a single ...
Watkins, Nicholas Wynn; Waxman, David
2004-01-01
Quantum information processing has greatly increased interest in the phenomenon of environmentally-induced decoherence. The spin boson model is widely used to study the interaction between a spin-modelling a quantum particle moving in a double well potential-and its environment-modelled by a heat bath of harmonic oscillators. This paper extends a previous analysis of the static spin boson study to the driven spin boson case, with the derivation of an exact integro-differential equation for th...
Differential Bloch Oscillating Transistor Pair
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti J.
2013-01-01
We examine a Bloch Oscillating Transistor pair as a differential stage for cryogenic low-noise measurements. Using two oppositely biased, nearly symmetric Bloch Oscillating Transistors, we measured the sum and difference signals in the current gain and transconductance modes while changing the common mode signal, either voltage or current. From the common mode rejection ratio we find values $\\sim 20$ dB even under non-optimal conditions. We also characterize the noise properties and obtain ex...
Unit quaternions and the Bloch sphere
International Nuclear Information System (INIS)
The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to ‘second order qubits’ would imply either a larger gauge freedom or a natural space of hidden variables. (paper)
Unit quaternions and the Bloch sphere
Wharton, K. B.; Koch, D.
2015-06-01
The spinor representation of spin-1/2 states can equally well be mapped to a single unit quaternion, yielding a new perspective despite the equivalent mathematics. This paper first demonstrates a useable map that allows Bloch-sphere rotations to be represented as quaternionic multiplications, simplifying the form of the dynamical equations. Left-multiplications generally correspond to non-unitary transformations, providing a simpler (essentially classical) analysis of time-reversal. But the quaternion viewpoint also reveals a surprisingly large broken symmetry, as well as a potential way to restore it, via a natural expansion of the state space that has parallels to second order fermions. This expansion to ‘second order qubits’ would imply either a larger gauge freedom or a natural space of hidden variables.
An extended q-deformed su(2) algebra and the Bloch electron problem
Fujikawa, Kazuo; KUBO, HARUNOBU
1997-01-01
It is shown that an extended q-deformed $su(2)$ algebra with an extra (``Schwinger '') term can describe Bloch electrons in a uniform magnetic field with an additional periodic potential. This is a generalization of the analysis of Bloch electrons by Wiegmann and Zabrodin. By using a representation theory of this q-deformed algebra, we obtain functional Bethe ansatz equations whose solutions should be functions of finite degree. It is also shown that the zero energy solution is expressed in t...
Wave impedance retrieving via Bloch modes analysis
DEFF Research Database (Denmark)
Andryieuski, Andrei; Ha, S.; Sukhorukov, A.; Malureanu, Radu; Kivshar, Y.; Lavrinenko, Andrei
-ciples violation, like antiresonance behaviour with Im(ε) <0, Im(μ) <0. We employ the Bloch mode analysis of periodic metamaterials to extract the dominating (fundamental) Bloch mode. Then it is possible to determine the Bloch and 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...
The Bloch Vector for N-Level Systems
Kimura, Gen
2003-01-01
We determine the set of the Bloch vectors for N-level systems, generalizing the familiar Bloch ball in 2-level systems. An origin of the structural difference from the Bloch ball in 2-level systems is clarified.
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.
Electric dipoles on the Bloch sphere
Vutha, Amar C.
2015-03-01
The time evolution of a two-level quantum mechanical system can be geometrically described using the Bloch sphere. By mapping the Bloch sphere evolution onto the dynamics of oscillating electric dipoles, we provide a physically intuitive link between classical electromagnetism and the electric dipole transitions of atomic and molecular physics.
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 cal...
Bloch oscillations of bosonic lattice polarons
Grusdt, F.; Shashi, A.; Abanin, D.; Demler, E.
2014-12-01
We consider a single-impurity atom confined to an optical lattice and immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the impurity with the phonon modes of the BEC leads to the formation of a stable quasiparticle, the polaron. We use a variational mean-field approach to study dispersion renormalization and derive equations describing nonequilibrium dynamics of polarons by projecting equations of motion into mean-field-type wave functions. As a concrete example, we apply our method to study dynamics of impurity atoms in response to a suddenly applied force and explore the interplay of coherent Bloch oscillations and incoherent drift. We obtain a nonlinear dependence of the drift velocity on the applied force, including a sub-Ohmic dependence for small forces for dimensionality d >1 of the BEC. For the case of heavy impurity atoms, we derive a closed analytical expression for the drift velocity. Our results show considerable differences with the commonly used phenomenological Esaki-Tsu model.
``Bloch wave'' modification of stimulated Raman by stimulated Brillouin scattering
Dodd, E. S.; Vu, H. X.; DuBois, D. F.; Bezzerides, B.
2013-03-01
Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at kLW˜kIAW/2˜k0 (kLW, kIAW, and k0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are
First Bloch eigenvalue in high contrast media
Briane, Marc; Vanninathan, Muthusamy
2014-01-01
This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast ɛY-periodic conductivity. When the conductivity is bounded in L1 and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ɛ-2, the first Bloch eigenvalue converges as ɛ → 0 to a limit which preserves the second-order expansion with respect to the Bloch parameter. In dimension two the expansion of the limit can be improved until the fourth-order under the same hypotheses. On the contrary, in dimension three a fibers reinforced medium combined with a L1-unbounded conductivity leads us to a discontinuity of the limit first Bloch eigenvalue as the Bloch parameter tends to zero but remains not orthogonal to the direction of the fibers. Therefore, the high contrast conductivity of the microstructure induces an anomalous effect, since for a given low-contrast conductivity the first Bloch eigenvalue is known to be analytic with respect to the Bloch parameter around zero.
First Bloch eigenvalue in high contrast media
Energy Technology Data Exchange (ETDEWEB)
Briane, Marc, E-mail: mbriane@insa-rennes.fr [Institut de Recherche Mathématique de Rennes, INSA de Rennes (France); Vanninathan, Muthusamy, E-mail: vanni@math.tifrbng.res.in [TIFR-CAM, Bangalore (India)
2014-01-15
This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast εY-periodic conductivity. When the conductivity is bounded in L{sup 1} and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to ε{sup −2}, the first Bloch eigenvalue converges as ε → 0 to a limit which preserves the second-order expansion with respect to the Bloch parameter. In dimension two the expansion of the limit can be improved until the fourth-order under the same hypotheses. On the contrary, in dimension three a fibers reinforced medium combined with a L{sup 1}-unbounded conductivity leads us to a discontinuity of the limit first Bloch eigenvalue as the Bloch parameter tends to zero but remains not orthogonal to the direction of the fibers. Therefore, the high contrast conductivity of the microstructure induces an anomalous effect, since for a given low-contrast conductivity the first Bloch eigenvalue is known to be analytic with respect to the Bloch parameter around zero.
Behaviour of neutrons passing through the Bloch wall
International Nuclear Information System (INIS)
In part I of the present paper the pertinent knowledge about Bloch walls is presented and developed insofar as it appears necessary for the experiments with neutrons, that is to say the direction of magnetization within the domains, the calculation of the variation of magnetization in the wall, the wall thickness, and the zigzag structure of the Bloch wall. In part II it is first clarified why the Bloch wall can be treated as a continuum problem. It shows that this is possible far away from Laue reflexes. For angles far away from Laure-reflex angles the interaction of the periodic structure of the magnetization can be described with the aid of an averaged magnetic flux density. The consequence of it is the possibility of treating the problem by means of a Schroedinger equation with continous interaction. This leads to a law of refraction. The question of the possibilities for explaining the intensity behavior is treated in part III. This part, from different aspects, describes the fact, which already was pointed out in Schaerpf, O., Vehoff, H., Schwink, Ch. 1973, that the spin of the neutrons in passing through the wall is partly taken along by the magnetization gradually rotating in the wall. (orig./WBU)
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.
First Bloch eigenvalue in high contrast media
Briane, Marc; Vanninathan, Muthusamy
2014-01-01
16 pages International audience This paper deals with the asymptotic behavior of the first Bloch eigenvalue in a heterogeneous medium with a high contrast $\\varepsilon Y$-periodic conductivity. When the conductivity is bounded in $L^1$ and the constant of the Poincaré-Wirtinger weighted by the conductivity is very small with respect to $\\varepsilon^{-2}$, the first Bloch eigenvalue converges as $\\varepsilon\\to 0$ to a limit which preserves the second-order expansion with respect to the ...
Dhar, Abhishek; Sriram Shastry, B.
2000-09-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1D for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. They are identified as generalized quantum Bloch wall states, and a simple physical picture is provided for the same.
Dhar, Abhishek; Shastry, B. Sriram
2000-01-01
We present a calculation of the lowest excited states of the Heisenberg ferromagnet in 1-d for any wave vector. These turn out to be string solutions of Bethe's equations with a macroscopic number of particles in them. These are identified as generalized quantum Bloch wall states, and a simple physical picture provided for the same.
Bloch-like wave dynamics in disordered potentials based on supersymmetry
Yu, Sunkyu; Hong, Jiho; Park, Namkyoo
2015-01-01
Bloch's theorem for the description of waves in crystals was a major milestone, establishing the principle of bandgaps for electrical, optical, and vibrational waves. Although it was once believed that bandgaps could form only under conditions of periodicity and long-range correlations as the prerequisites for Bloch's theorem, this restriction was disproven by the groundbreaking discoveries of amorphous media and quasicrystals. While network and liquid models have been suggested for the interpretation of Bloch-like waves in disordered media, these approaches 'searching' for random networks with bandgaps have failed in the deterministic creation of bandgaps. Here, we reveal a deterministic pathway to bandgap engineering in disordered media, by applying the notion of supersymmetry to the fundamental wave equation. Inspired by the problem for isospectrality, we follow a methodology in stark contrast to previous methods: we 'transform' ordered potentials into disordered potentials while 'preserving' bandgaps. Our...
Serkin, Vladimir N.; Belyaeva, T. L.
2001-11-01
It is shown that optical solitons in nonlinear fibre-optic communication systems and soliton lasers can be represented as nonlinear Bloch waves in periodic structures. The Bloch theorem is proved for solitons of the nonlinear Schrodinger equation in systems with the dispersion, the nonlinearity, and the gain (absorption coefficient) periodically changing over the length. The dynamics of formation and interaction, as well as stability of the coupled states of nonlinear Bloch waves are investigated. It is shown that soliton Bloch waves exist only under certain self-matching conditions for the basic parameters of the system and reveal a structural instability with respect to the mismatch between the periods of spatial modulation of the dispersion, nonlinearity or gain.
Observation of Bloch oscillations in molecular rotation
Floß, Johannes; Averbukh, Ilya Sh; Bucksbaum, Philip H
2015-01-01
The periodically kicked quantum rotor is known for non-classical effects such as quantum localisation in angular momentum space or quantum resonances in rotational excitation. These phenomena have been studied in diverse systems mimicking the kicked rotor, such as cold atoms in optical lattices, or coupled photonic structures. Recently, it was predicted that several solid state quantum localisation phenomena - Anderson localisation, Bloch oscillations, and Tamm-Shockley surface states - may manifest themselves in the rotational dynamics of laser-kicked molecules. Here, we report the first observation of rotational Bloch oscillations in a gas of nitrogen molecules kicked by a periodic train of femtosecond laser pulses. A controllable detuning from the quantum resonance creates an effective accelerating potential in angular momentum space, inducing Bloch-like oscillations of the rotational excitation. These oscillations are measured via the temporal modulation of the refractive index of the gas. Our results int...
Fractional Bloch oscillations in photonic lattices
Corrielli, Giacomo; Della Valle, Giuseppe; Longhi, Stefano; Osellame, Roberto; 10.1038/ncomms2578
2013-01-01
Bloch oscillations, the oscillatory motion of a quantum particle in a periodic potential, are one of the most fascinating effects of coherent quantum transport. Originally studied in the context of electrons in crystals, Bloch oscillations manifest the wave nature of matter and are found in a wide variety of different physical systems. Here we report on the first experimental observation of fractional Bloch oscillations, using a photonic lattice as a model system of a two-particle extended Bose-Hubbard Hamiltonian. In our photonic simulator, the dynamics of two correlated particles hopping on a one-dimensional lattice is mapped into the motion of a single particle in a two-dimensional lattice with engineered defects and mimicked by light transport in a square waveguide lattice with a bent axis.
Sandwich reactor lattices and Bloch's theorem
International Nuclear Information System (INIS)
The study of the neutron flux distribution in repetitive sandwiches of reactor material leads to results analogous to the 1-dimensional form of Bloch's theorem for the electronic structure in crystals. This principle makes it possible to perform analytically accurate homogenisations of sandwich lattices The method has been extended to cover multi group diffusion and transport theory. (author)
Fractional Bloch Oscillations in photonic lattices
Directory of Open Access Journals (Sweden)
Corrielli G.
2013-11-01
Full Text Available We present the photonic analogy of the Fractional Bloch Oscillations [1]: the oscillatory motion of interacting particles moving in a periodic potential, under the presence of a static force. The analogy is implemented with the propagation of classical light in a specially engineered photonic waveguides lattice, fabricated in fused silica substrate via femtosecond laser micromachining.
Extended Cesaro Operator from to Bloch Space
Mingzhu Yang
2009-01-01
Let g be a holomorphic function of the unit ball B in several complex variables, and denote by the induced extended Cesaro operator. This paper discussed the boundedness and compactness of acting from to Bloch space in the unit ball.
Computation and visualization of photonic quasicrystal spectra via Blochs theorem
Rodriguez, Alejandro W; Avniel, Yehuda; Johnson, Steven G
2007-01-01
Previous methods for determining photonic quasicrystal (PQC) spectra have relied on the use of large supercells to compute the eigenfrequencies and/or local density of states (LDOS). In this manuscript, we present a method by which the energy spectrum and the eigenstates of a PQC can be obtained by solving Maxwells equations in higher dimensions for any PQC defined by the standard cut-and-project construction, to which a generalization of Blochs theorem applies. In addition, we demonstrate how one can compute band structures with defect states in the higher-dimensional superspace with no additional computational cost. As a proof of concept, these general ideas are demonstrated for the simple case of one-dimensional quasicrystals, which can also be solved by simple transfer-matrix techniques.
Pogrebnyak, Victor A.; Furlani, Edward P.
2016-05-01
We study wave propagation in uniform materials with periodic boundary profiles and introduce for the first time Bloch resonances and Bloch gaps. Bloch resonances are due to transverse phase matching, i.e., the coupling of two transverse standing waves corresponding to different harmonics. These are distinct from well-known Bragg resonances that result from longitudinal phase matching. We show that Bloch gaps can be engineered over the entire first Brillouin zone up to an infinite wavelength, i.e., kx=0 , where kx is the wave number in the direction of propagation. This is in contrast to Bragg gaps that open at a fixed wavelength, twice the period of the structure. Bloch resonances and gaps can be tuned by reconfiguring the boundary profile and we derive analytical expressions that predict these phenomena when the amplitude of the profile is small. The theory is fundamental as it broadly applies to wave phenomena that span the quantum to continuum scale with applications that range from condensed matter to acoustics. We validate the theory experimentally for the electromagnetic field at GHz frequencies. We also discuss potential photonic and electronic applications of the theory such as a white-light distributed feedback laser and a two-dimensional electron gas transistor.
Pogrebnyak, Victor A; Furlani, Edward P
2016-05-20
We study wave propagation in uniform materials with periodic boundary profiles and introduce for the first time Bloch resonances and Bloch gaps. Bloch resonances are due to transverse phase matching, i.e., the coupling of two transverse standing waves corresponding to different harmonics. These are distinct from well-known Bragg resonances that result from longitudinal phase matching. We show that Bloch gaps can be engineered over the entire first Brillouin zone up to an infinite wavelength, i.e., k_{x}=0, where k_{x} is the wave number in the direction of propagation. This is in contrast to Bragg gaps that open at a fixed wavelength, twice the period of the structure. Bloch resonances and gaps can be tuned by reconfiguring the boundary profile and we derive analytical expressions that predict these phenomena when the amplitude of the profile is small. The theory is fundamental as it broadly applies to wave phenomena that span the quantum to continuum scale with applications that range from condensed matter to acoustics. We validate the theory experimentally for the electromagnetic field at GHz frequencies. We also discuss potential photonic and electronic applications of the theory such as a white-light distributed feedback laser and a two-dimensional electron gas transistor. PMID:27258880
Theory of the Bloch Oscillating Transistor
Hassel, J.; Seppa, H.
2004-01-01
The Bloch oscillating transistor (BOT) is a device, where single electron current through a normal tunnel junction can be used to enhance Cooper pair current in a mesoscopic Josephson junction leading to signal amplification. In this paper we develop a theory, where the BOT dynamics is described as a two-level system. The theory is used to predict current-voltage characteristics and small-signal response. Transition from stable operation into hysteretic regime is studied. By identifying the t...
Quantum state transfer via Bloch oscillations
Tamascelli, Dario; Olivares, Stefano; Rossotti, Stefano; Osellame, Roberto; Paris, Matteo G. A.
2016-01-01
The realization of reliable quantum channels, able to transfer a quantum state with high fidelity, is a fundamental step in the construction of scalable quantum devices. In this paper we describe a transmission scheme based on the genuinely quantum effect known as Bloch oscillations. The proposed protocol makes it possible to carry a quantum state over different distances with a minimal engineering of the transmission medium and can be implemented and verified on current quantum technology hardware. PMID:27189630
A Refresher of the Original Bloch's Law Paper (Bloch, July 1885).
Gorea, Andrei
2015-08-01
In 1885, Adolphe-Moïse Bloch asked the following simple question "Is there a law describing the relationship between the duration of a light and its perceived intensity?" Based on a series of experiments using a Foucault regulator and a candle, Bloch concluded that "when the lighting duration varies from 0.00173 to 0.0518 seconds (…) the [visible] light is markedly in inverse proportion to its duration"-his famous law. As this law pertains to the more general and hotly debated question of accumulation of sensory information over time, it is timely to offer the public a full translation of Bloch's original paper (from French) and to present it within the context of contemporary research. PMID:27433317
Bloch's Theorem in the Context of Quaternion Analysis
Gürlebeck, K
2012-01-01
The classical theorem of Bloch (1924) asserts that if $f$ is a holomorphic function on a region that contains the closed unit disk $|z|\\leq 1$ such that $f(0) = 0$ and $|f'(0)| = 1$, then the image domain contains discs of radius $3/2-\\sqrt{2} > 1/12$. The optimal value is known as Bloch's constant and 1/12 is not the best possible. In this paper we give a direct generalization of Bloch's theorem to the three-dimensional Euclidean space in the framework of quaternion analysis. We compute explicitly a lower bound for the Bloch constant.
An approximation formula for the Bloch-Siegert shift of the Rabi model
Rapedius, K
2015-01-01
So far the Bloch-Siegert shift of the Rabi model has only been calculated numerically or by means of perturbation theory valid in either the weak or strong driving regime only. Recently Yan, L\\"u, and Zheng [Phys.~Rev.~A {\\bf 91}, 053834 (2015)] showed how to reduce the problem to solving a system of three nonlinear equations. Here, we pursue an alternative approach based on a perturbation expansion extrapolation technique. We are thus able to derive an explicit analytical approximation formula for the Bloch-Siegert shift of the Rabi model which is valid for all parameter regimes from weak to strong driving. Comparison with numerically exact results reveals an excellent agreement over the entire driving-strength range.
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 ...
Bloch spaces on bounded symmetric domains in complex Banach spaces
Institute of Scientific and Technical Information of China (English)
DENG; Fangwen
2006-01-01
We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.
Improved Separability Criteria Based on Bloch Representation of Density Matrices.
Shen, Shu-Qian; Yu, Juan; Li, Ming; Fei, Shao-Ming
2016-01-01
The correlation matrices or tensors in the Bloch representation of density matrices are encoded with entanglement properties. In this paper, based on the Bloch representation of density matrices, we give some new separability criteria for bipartite and multipartite quantum states. Theoretical analysis and some examples show that the proposed criteria can be more efficient than the previous related criteria. PMID:27350031
Bloch-Like Oscillations in Finite Quantum Structures
DEFF Research Database (Denmark)
Duggen, Lars; Willatzen, Morten; Lassen, Benny;
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 ...
“Bloch wave” modification of stimulated Raman by stimulated Brillouin scattering
International Nuclear Information System (INIS)
Using the reduced-description particle-in-cell (RPIC) method, we study the coupling of backward stimulated Raman scattering (BSRS) and backward stimulated Brillouin scattering (BSBS) in regimes where the reflectivity involves the nonlinear behavior of particles trapped in the daughter plasma waves. The temporal envelope of a Langmuir wave (LW) obeys a Schrödinger equation where the potential is the periodic electron density fluctuation resulting from an ion-acoustic wave (IAW). The BSRS-driven LWs in this case have a Bloch wave structure and a modified dispersion due to the BSBS-driven spatially periodic IAW, which includes frequency band gaps at kLW∼kIAW/2∼k0 (kLW, kIAW, and k0 are the wave number of the LW, IAW, and incident pump electromagnetic wave, respectively). This band structure and the associated Bloch wave harmonic components are distinctly observed in RPIC calculations of the electron density fluctuation spectra and this structure may be observable in Thomson scatter. Bloch wave components grow up in the LW spectrum, and are not the result of isolated BSRS. Self-Thomson scattered light from these Bloch wave components can have forward scattering components. The distortion of the LW dispersion curve implies that the usual relationship connecting the frequency shift of the BSRS-scattered light and the density of origin of this light may become inaccurate. The modified LW frequency results in a time-dependent frequency shift that increases as the IAW grows, detunes the BSRS frequency matching condition, and reduces BSRS growth. A dependence of the BSRS reflectivity on the IAW Landau damping results because this damping determines the levels of IAWs. The time-dependent reflectivity in our simulations is characterized by bursts of sub-picosecond pulses of BSRS alternating with multi-ps pulses of BSBS, and BSRS is observed to decline precipitously as soon as SBS begins to grow from low levels. In strong BSBS regimes, the Bloch wave effects in BSRS are
Bloch vector, disclination and exotic quantum holonomy
International Nuclear Information System (INIS)
A topological formulation of the eigenspace anholonomy, where eigenspaces are interchanged by adiabatic cycles, is introduced. The anholonomy in two-level systems is identified with a disclination of the director (headless vector) of a Bloch vector, which characterizes eigenprojectors. The covering map structure behind the exotic quantum holonomy and the role of the homotopy classification of adiabatic cycles are elucidated. The extensions of this formulation to nonadiabatic cycles and N-level systems are outlined. - Highlights: • A topological formulation of the eigenspace anholonomy is proposed. • The covering map structure behind the anholonomy is identified. • The role of homotopy classification of adiabatic cycles is explained. • The anholonomy in two-level systems is associated with disclinations. • The present formulation offers an extension to nonadiabatic cycles
Bloch state tomography using Wilson lines.
Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; Bloch, Immanuel; Schneider, Ulrich
2016-05-27
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z₂ numbers. PMID:27230376
Bloch state tomography using Wilson lines
Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; Bloch, Immanuel; Schneider, Ulrich
2016-05-01
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high-energy theories, quantum information, and condensed-matter physics. In condensed-matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multiband systems. Using an ultracold gas of rubidium atoms loaded in a honeycomb optical lattice, we realize strong-force dynamics in Bloch bands that are described by Wilson lines and observe an evolution in the band populations that directly reveals the band geometry. Our technique enables a full determination of band eigenstates, Berry curvature, and topological invariants, including single- and multiband Chern and Z2 numbers.
Bloch inductance in small-capacitance Josephson junctions
Zorin, A. B.
2005-01-01
We show that the electrical impedance of a small-capacitance Josephson junction includes besides the capacitive term $-i/\\omega C_B$ also an inductive term $i\\omega L_B$. Similar to the known Bloch capacitance $C_B(q)$, the Bloch inductance $L_B(q)$ also depends periodically on the quasicharge $q$, and its maximum value achieved at $q=e (\\textrm{mod} 2e)$ always exceeds the value of the Josephson inductance of this junction $L_J(\\phi)$ at fixed $\\phi=0$. The effect of the Bloch inductance on ...
Bloch Inductance in Small-Capacitance Josephson Junctions
International Nuclear Information System (INIS)
We show that the electrical impedance of a small-capacitance Josephson junction also includes, in addition to the capacitive term -i/ωCB, an inductive term iωLB. Similar to the known Bloch capacitance CB(q), the Bloch inductance LB(q) also depends periodically on the quasicharge, q, and its maximum value achieved at q=e(mod 2e) always exceeds the value of the Josephson inductance of this junction LJ(φ) at fixed φ=0. The effect of the Bloch inductance on the dynamics of a single junction and a one-dimensional array is described
Estimates on Bloch constants for planar harmonic mappings
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The Bloch constants for quasiregular harmonic mappings and open planar harmonic mappings are considered. Better estimates are obtained. The results, presented in this paper, improve the one made by Chen et al. and Grigoryan.
Bloch-mode analysis for effective parameters restoration
DEFF Research Database (Denmark)
Lavrinenko, Andrei; Andryieuski, Andrei; Ha, Sangwoo; Sukhorukov, Andrey A.; Kivshar, Yuri S.
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 on the...... nature of microfields returned by Maxwell's solvers, showing that ignoring of difference between magnetic strength and induction lead to incorrect determination of the Poynting vector....
Intersubband gain in a Bloch oscillator and Quantum cascade laser
Willenberg, Harald; Dohler, Gottfried H.; Faist, Jerome
2002-01-01
The link between the inversion gain of quantum cascade structures and the Bloch gain in periodic superlattices is presented. The proposed theoretical model based on the density matrix formalism is able to treat the gain mechanism of the Bloch oscillator and Quantum cascade laser on the same footing by taking into account in-plane momentum relaxation. The model predicts a dispersive contribution in addition to the (usual) population-inversion-dependent intersubband gain in quantum cascade stru...
Calculation of the relativistic Bloch correction to stopping power
Ahlen, S. P.
1982-01-01
Bloch's technique of joining the nonrelativistic Bethe and Bohr stopping-power expressions by taking into account wave-packet effects for close collisions is extended to the relativistic case. It is found that Bloch's nonrelativistic correction term must be modified and that charge asymmetric terms appear. Excellent agreement is observed by comparing the results of these calculations to recent data on the stopping power of relativistic heavy ions.
Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field
Hatsugai, Y.; Kohmoto, M.; Wu, Y.-S.
1995-01-01
The wave functions for two dimensional Bloch electrons in a uniform magnetic field at the mid-band points are studied with the help of the algebraic structure of the quantum group $U_q(sl_2)$. A linear combination of its generators gives the Hamiltonian. We obtain analytical and numerical solutions for the wave functions by solving the Bethe Ansatz equations, proposed by Wiegmann and Zabrodin on the basis of above observation. The semi-classical case with the flux per plaquette $\\phi=1/Q$ is ...
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.
COMPOSITION OPERATORS ON THE LITTLE BLOCH SPACE IN POLYDISCS
Institute of Scientific and Technical Information of China (English)
Zhou Zehua; Zhu Min; Shi Jihuai
2005-01-01
Let Un be the unit polydisc of Cn and φ = (φ1,…,φn) a holomorphic self map of Un. This paper shows that the composition operator Cφ induced by φ is bounded on the little Bloch space β0*(Un) if and only if φ∈β0*(Un) for every l=1,2,…,n, and also gives a sufficient and necessary condition for the composition operator Cφ to be compact on the little Bloch spaceβ0* (Un).
Bloch-wave engineering of quantum dot-micropillars for cavity quantum electrodynamics experiments
DEFF Research Database (Denmark)
Lermer, Matthias; Gregersen, Niels; Dunzer, Florian;
2012-01-01
We have employed Bloch-wave engineering to realize submicron diameter ultra-high quality factor GaAs/AlAs micropillars (MPs). The design features a tapered cavity in which the fundamental Bloch mode is subject to an adiabatic transition to match the Bragg mirror Bloch mode. The resulting reduced ...
Bloch oscillations of bosonic lattice polarons
Grusdt, Fabian; Shashi, A.; Abanin, Dmitry; Demler, Eugene A.
2014-01-01
We consider a single-impurity atom confined to an optical lattice and immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the impurity with the phonon modes of the BEC leads to the formation of a stable quasiparticle, the polaron. We use a variational mean-field approach to study dispersion renormalization and derive equations describing nonequilibrium dynamics of polarons by projecting equations of motion into mean-field-type wave functions. As a concrete example, we app...
Bloch oscillations of bosonic lattice polarons
Grusdt, Fabian; Shashi, Aditya; Abanin, Dmitry; Demler, Eugene
2014-01-01
We consider a single impurity atom confined to an optical lattice and immersed in a homogeneous Bose-Einstein condensate (BEC). Interaction of the impurity with the phonon modes of the BEC leads to the formation of a stable quasiparticle, the polaron. We use a variational mean-field approach to study dispersion renormalization and derive equations describing non-equilibrium dynamics of polarons by projecting equations of motion into mean-field (MF) type wavefunctions. As a concrete example, w...
International Nuclear Information System (INIS)
This paper describes an analytical method for the wave field induced by a moving load on a periodically supported beam. The Green's function for an Euler beam without support is evaluated by using the direct integration. Afterwards, it introduces the supports into the model established by using the superposition principle which states that the response from all the sleeper points and from the external point force add up linearly to give a total response. The periodicity of the supports is described by Bloch's theorem. The homogeneous system thus obtained represents a linear differential equation which governs rail response. It is initially solved in the homogeneous case, and it admits a no null solution if its determinant is null, this permits the establishment the dispersion equation to Bloch waves and wave bands. The Bloch waves and dispersion curves contain all the physics of the dynamic problem and the wave field induced by a dynamic load applied to the system is finally obtained by decomposition into Bloch waves, similarly to the usual decomposition into dynamic modes on a finite structure. The method is applied to obtain the field induced by a load moving at constant velocity on a thin beam supported by periodic elastic supports.
Quantum Properties of Bloch Point as Nanosized Soliton in Ferromagnetics
Directory of Open Access Journals (Sweden)
M.Yu. Barabash
2014-11-01
Full Text Available It is established that magnetic soliton – Bloch point – has quantum properties which are manifested in the effects of tunneling and above-barrier reflection in a subhelium temperature range. The conditions of the given phenomena are determined.
Geometric optics of Bloch waves in a chiral and dissipative medium
International Nuclear Information System (INIS)
We present a geometric optics theory for the transport of quantum particles (or classical waves) in a chiral and dissipative periodic crystal subject to slowly varying perturbations in space and time. Taking account of some properties of particles and media neglected in previous theory, we find important additional terms in the equations of motion of particles. The (energy) current density field, which traces the geometric optics rays, is not only governed by the Bloch band energy dispersion but also involves there additional fields. These are the angular momentum of the particle, the dissipation dipole density, and various geometric gauge fields in the extended phase space spanned by space time and its reciprocal, momentum, and frequency. For simplicity, the theory is presented using light propagation in photonic crystals.
A note on the Königs domain of compact composition operators on the Bloch space
Directory of Open Access Journals (Sweden)
Jones Matthew
2011-01-01
Full Text Available Abstract Let be the unit disk in the complex plane. We define to be the little Bloch space of functions f analytic in which satisfy lim|z|→1 (1 - |z|2|f'(z| = 0. If is analytic then the composition operator Cφ : f ↦ f ∘ φ is a continuous operator that maps into itself. In this paper, we show that the compactness of Cφ , as an operator on , can be modelled geometrically by its principal eigenfunction. In particular, under certain necessary conditions, we relate the compactness of Cφ to the geometry of , where σ satisfies Schöder's functional equation σ ∘ φ = φ'(0σ. 2000 Mathematics Subject Classification: Primary 30D05; 47B33 Secondary 30D45.
Bloch waves in an arbitrary two-dimensional lattice of subwavelength Dirichlet scatterers
Schnitzer, Ory
2016-01-01
We study waves governed by the planar Helmholtz equation, propagating in an infinite lattice of subwavelength Dirichlet scatterers, the periodicity being comparable to the wavelength. Applying the method of matched asymptotic expansions, the scatterers are effectively replaced by asymptotic point constraints. The resulting coarse-grained Bloch-wave dispersion problem is solved by a generalised Fourier series, whose singular asymptotics in the vicinities of scatterers yield the dispersion relation governing modes that are strongly perturbed from plane-wave solutions existing in the absence of the scatterers; there are also empty-lattice waves that are only weakly perturbed. Characterising the latter is useful in interpreting and potentially designing the dispersion diagrams of such lattices. The method presented, that simplifies and expands on Krynkin & McIver [Waves Random Complex, 19 347 2009], could be applied in the future to study more sophisticated designs entailing resonant subwavelength elements di...
Surface Bloch waves mediated heat transfer between two photonic crystals
Ben-Abdallah, Philippe; Joulain, Karl; Pryamikov, Andrey
2010-01-01
submitted to Applied Physics Letters We theoretically investigate the non-radiative heat transfer between two photonic crystals separated by a small gap in non-equilibrium thermal situation. We predict that the surface Bloch states coupling supported by these media can make heat exchanges larger than those measured at the same separation distance between two massive homogeneous materials made with the elementary components of photonic crystals. These results could find broad applications i...
Dynamics of Bloch oscillating transistor near the bifurcation threshold
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti J.
2013-01-01
The tendency to bifurcate can often be utilized to improve performance characteristics of amplifiers or even to build detectors. The Bloch oscillating transistor is such a device. Here, we show that bistable behavior can be approached by tuning the base current and that the critical value depends on the Josephson coupling energy EJ of the device. We demonstrate current-gain enhancement for the device operating near the bifurcation point at small EJ. From our results for the current gains at v...
Experimental reconstruction of Wilson lines in Bloch bands
Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; Bloch, Immanuel; Schneider, Ulrich
2015-01-01
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multi-band systems. By realizing strong-force dynamics in Bloch bands that are described by Wilson lines, we observe an ev...
Experimental reconstruction of Wilson lines in Bloch bands
Li, Tracy; Duca, Lucia; Reitter, Martin; Grusdt, Fabian; Demler, Eugene; Endres, Manuel; Schleier-Smith, Monika; BLOCH, Immanuel; Schneider, Ulrich
2015-01-01
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of phenomena stem from the geometry of the band eigenstates, which is encoded in the matrix-valued Wilson line for general multi-band systems. By realizing strong-force dynamics in Bloch bands that are described by Wilson lines, we observe an evolution of band po...
Super Bloch Oscillation in a PT symmetric system
Turker, Z
2016-01-01
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.
Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays
Beneke, M.; Braun, Vladimir M.; Zakharov, V. I.
1994-01-01
We investigate the one-loop radiative corrections to the semileptonic decay of a charged particle at finite gauge boson mass. Extending the Bloch-Nordsieck cancellation of infrared logarithms, the subsequent non-analytic terms are also found to vanish after eliminating the pole mass in favor of a mass defined at short distances. This observation justifies the operator product expansion for inclusive decays of heavy mesons and implies that infrared effects associated with the summation of the ...
Orbital magnetism of Bloch electrons I. General formula
International Nuclear Information System (INIS)
We derive an exact formula of orbital susceptibility expressed in terms of Bloch wave functions, starting from the exact one-line formula by Fukuyama in terms of Green's functions. The obtained formula contains four contributions: (1) Landau-Peierls susceptibility, (2) interband contribution, (3) Fermi surface contribution, and (4) contribution from occupied states. Except for the Landau-Peierls susceptibility, the other three contributions involve the crystal-momentum derivatives of Bloch wave functions. Physical meaning of each term is clarified. The present formula is simplified compared with those obtained previously by Hebborn et al. Based on the formula, it is seen first of all that diamagnetism from core electrons and Van Vleck susceptibility are the only contributions in the atomic limit. The band effects are then studied in terms of linear combination of atomic orbital treating overlap integrals between atomic orbitals as a perturbation and the itinerant feature of Bloch electrons in solids are clarified systematically for the first time. (author)
Directory of Open Access Journals (Sweden)
Bernhard Streck
2012-10-01
Full Text Available The essay wants to deconstruct the genre of utopias so popular in the 20th century political writings. Human history shows manifold respect to stories about non-existent worlds which mix reality and non-reality, but outside the area of Abrahamitic beliefs there was rarely hope for a future. The secular version of such eschatological teachings begins with Karl Marx in the 19th century and culminates in the prophetic as well as revolutionary writings of Ernst Bloch around the terrible wars of the 20th century. This philosopher succeeded in both parts of post-war Germany and is still venerated inside and outside the academias. Compared with the so-called dystopias of Max Weber, Aldous Huxley or George Orwell the political visions of Bloch lack any sense of reality and seem to be quite useless to the understanding of present tendencies in world politics.
Zhou Zehua; Liu Yan
2006-01-01
Let be the unit polydisc of and a holomorphic self-map of . , and denote the -Bloch space, little -Bloch space, and little star -Bloch space in the unit polydisc , respectively, where . This paper gives the estimates of the essential norms of bounded composition operators induced by between ( or ) and ( or ). As their applications, some necessary and sufficient conditions for the (bounded) composition operators to be compact from ( or ) into ( or ) are obtained.
Properties of Floquet-Bloch space harmonics in 1D periodic magneto-dielectric structures
DEFF Research Database (Denmark)
Breinbjerg, O.
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-dimensi......-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....
Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems
International Nuclear Information System (INIS)
We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The case studied is the second harmonic generation from metallodielectric multilayer filters. In particular, we have applied the Bloch vector analysis to Ag/Ta2O5 thin-film multilayer samples and shown the importance of the phase matching calculated through the Bloch vector. The nonlinear coefficients extracted from experimental results are consistent with previous studies. Nowadays, metal-based nanostructures play a fundamental role in nonlinear nanophotonics and nanoplasmonics. Our results clearly suggest that even in these forefront fields the Bloch vector continues to play an essential role.
Excitation of Bloch-like surface waves in quasi-crystals and aperiodic dielectric multilayers.
Koju, Vijay; Robertson, William M
2016-07-01
The existence of Bloch surface waves in periodic dielectric multilayer structures with a surface defect is well known. Not yet recognized is that quasi-crystals and aperiodic dielectric multilayers can also support Bloch-like surface waves. In this work, we numerically show the excitation of Bloch-like surface waves in Fibonacci quasi-crystals and Thue-Morse aperiodic dielectric multilayers using the prism coupling method. We report improved surface electric field intensity and penetration depth of Bloch-like surface waves in the air side in such structures compared to their periodic counterparts. PMID:27367064
Nonreciprocal Bloch Oscillations in Magneto-Optic Waveguide Arrays
Levy, Miguel
2010-01-01
We show that nonreciprocal optical Bloch-like oscillations can emerge in transversely magnetized waveguide arrays in the presence of an effective index step between the waveguides. Normal modes of the system are shown to acquire different wavenumbers in opposite propagation directions. Significant differences in phase coherence and decoherence between these normal modes are presented and discussed. Non-reciprocity is established by imposing unequal vertical refractive index gradients at the substrate/core, and core/cover interfaces in the presence of transverse magnetization.
Dynamics of Bloch oscillating transistor near bifurcation threshold
Sarkar, Jayanta; Puska, Antti; Hassel, Juha; Hakonen, Pertti J.
2013-01-01
Tendency to bifurcate can often be utilized to improve performance characteristics of amplifiers or even to build detectors. Bloch oscillating transistor is such a device. Here we show that bistable behaviour can be approached by tuning the base current and that the critical value depends on the Josephson coupling energy $E_J$ of the device. We demonstrate record-large current gains for device operation near the bifurcation point at small $E_J$. From our results for the current gains at vario...
Fast algorithm for periodic density fitting for Bloch waves
Lu, Jianfeng
2015-01-01
We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The computational cost of the algorithm scales as $\\mathcal{O}\\bigl(N_{\\text{grid}} N^2 + N_{\\text{grid}} NK \\log (NK)\\bigr)$, where $N_{\\text{grid}}$ is number of spatial grid points, $K$ is the number of sampling $k$-points in first Brillouin zone, and $N$ is the number of bands under consideration. We validate the algorithm by numerical examples in both two and three dimensions.
Truncated-Bloch-wave solitons in optical lattices
Wang, Jiandong; Alexander, Tristram J; Kivshar, Yuri S
2009-01-01
We study self-trapped localized nonlinear states in the form of truncated Bloch waves in one-dimensional optical lattices, which appear in the gaps of the linear bandgap spectrum. We demonstrate the existence of families of such localized states which differ by the number of intensity peaks. These families do not bifurcate from the band edge, and their power curves exhibit double branches. Linear stability analysis demonstrates that in deep lattice potentials the states corresponding to the lower branches are stable, whereas those corresponding to the upper branches are unstable, independently of the number of peaks.
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
A formula for the Bloch vector of some Lindblad quantum systems
Salgado, D; Sanchez-Gomez, J. L.
2003-01-01
Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators.
A formula for the Bloch vector of some Lindblad quantum systems
International Nuclear Information System (INIS)
Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators
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...
Bloch-Zener oscillations in a tunable optical honeycomb lattice
Energy Technology Data Exchange (ETDEWEB)
Uehlinger, Thomas; Greif, Daniel; Jotzu, Gregor; Esslinger, Tilman [Institute for Quantum Electronics, ETH Zurich, 8093 Zurich (Switzerland); Tarruell, Leticia [Institute for Quantum Electronics, ETH Zurich, 8093 Zurich, Switzerland and LP2N, Universite Bordeaux 1, IOGS, CNRS, 351 cours de la Liberation, 33405 Talence (France)
2013-12-04
Ultracold gases in optical lattices have proved to be a flexible tool to simulate many different phenomena of solid state physics [1, 2]. Recently, optical lattices with complex geometries have been realized [3, 4, 5, 6, 7], paving the way to simulating more realistic systems. The honeycomb structure has recently become accessible in an optical lattice composed of mutually perpendicular laser beams. This lattice structure exhibits topological features in its band structure – the Dirac points. At these points, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In optical lattices, Bloch oscillations [8] resolved both in time and in quasi-momentum space can be directly observed. We make use of such Bloch-Zener oscillations to probe the vanishing energy gap at the Dirac points as well as their position in the band structure. In small band gap regions, we observe Landau-Zener tunneling [7, 9] to the second band and the regions of maximum transfer can be identified with the position of the Dirac points.
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.
Shear Bloch waves and coupled phonon-polariton in periodic piezoelectric waveguides.
Piliposyan, D G; Ghazaryan, K B; Piliposian, G T
2014-02-01
Coupled electro-elastic SH waves propagating in a periodic piezoelectric finite-width waveguide are considered in the framework of the full system of Maxwell's electrodynamic equations. We investigate Bloch-Floquet waves under homogeneous or alternating boundary conditions for the elastic and electromagnetic fields along the guide walls. Zero frequency stop bands, trapped modes as well as some anomalous features due to piezoelectricity are identified. For mixed boundary conditions, by modulating the ratio of the length of the unit cell to the width of the waveguide, the minimum widths of the stop bands can be moved to the middle of the Brillouin zone. The dispersion equation has been investigated also for phonon-polariton band gaps. It is shown that for waveguides at acoustic frequencies, acousto-optic coupling gives rise to polariton behavior at wavelengths much larger than the length of the unit cell but at optical frequencies polariton resonance occurs at wavelengths comparable with the period of the waveguide. PMID:24139302
Entanglement and the three-dimensionality of the Bloch ball
Energy Technology Data Exchange (ETDEWEB)
Masanes, Ll., E-mail: ll.masanes@gmail.com [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom); Müller, M. P. [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany); Pérez-García, D. [Departamento de Analisis Matematico and IMI, Universidad Complutense de Madrid, 28040 Madrid (Spain); Augusiak, R. [ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona (Spain)
2014-12-15
We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.
Engineering of slow Bloch modes for optical trapping
Energy Technology Data Exchange (ETDEWEB)
Milord, L.; Gerelli, E.; Jamois, C.; Harouri, A.; Benyattou, T., E-mail: taha.benyattou@insa-lyon.fr [Institut des Nanotechnologies de Lyon (INL), CNRS UMR5270, Université de Lyon, INSA-Lyon, Bât “Blaise Pascal,” 7 avenue Jean Capelle, Villeurbanne F-69621 (France); Chevalier, C.; Viktorovitch, P.; Letartre, X. [Institut des Nanotechnologies de Lyon (INL), CNRS UMR5270, Ecole Centrale de Lyon, 36 avenue Guy de Collongue, Ecully F-69134 (France)
2015-03-23
In the present paper, we propose an approach based on slow Bloch mode microcavity that enables the optical trapping of small nanoparticles over a broad surface. A specific design based on a double-period photonic crystal is presented. It enables an easy coupling using a wide free-space Gaussian beam and the cavity Q factor can be tuned at will. Moreover, the microcavity mode is mainly localized within the photonic crystal holes, meaning that each hole of the microcavity behaves as efficient nanotweezers. Experimental studies have shown that 200 nm and 100 nm particles can be trapped within the microcavity, in a spatial region that corresponds to the size of one hole (200 nm wide). The experimental trap stiffness has been extracted. It shows that this approach is among the most performant ones if we take into account the size of the cavity.
Staying positive: going beyond Lindblad with perturbative master equations
Whitney, Robert S.
2008-05-01
The perturbative master equation (Bloch-Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima-Zwanzig or Schoeller-Schön equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch-Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.
On Bloch approximation and the boundedness of integration operator on $H^\\infty$
Smith, Wayne; Stolyarov, Dmitriy M.; Volberg, Alexander
2016-01-01
We obtain a necessary and sufficient condition for the operator of integration to be bounded on $H^\\infty$ in a simply connected domain. The main ingredient of the proof is a new result on approximation of Bloch functions.
Spatiotemporal control of light by Bloch-mode dispersion in multi-core fibers
DEFF Research Database (Denmark)
Rasmussen, Per Dalgaard; Sukhorukov, A.A.; Neshev, D.N.;
2008-01-01
We study theoretically the dispersion properties of Bloch modes and nonlinearly-induced defect states in two-dimensional waveguide arrays. We define the conditions for achieving anomalous group-velocity dispersion and discuss possibilities for generation of spatiotemporal solitons....
A dorsal fold in Gymnura micrura (Bloch and Scheneider, 1801 (Chondrichthyes: Gymnuridae
Directory of Open Access Journals (Sweden)
Jorge Luiz Silva Nunes
2009-04-01
Full Text Available This paper reports a dorsal fold which is a membranous structure located on the tail of two juvenile butterfly rays, Gymnura micrura (Bloch & Scheneider, 1801, caught through artisanal fishery in the shallow waters of Maranhão State (Brazil.Neste manuscrito registra-se uma nadadeira dorsal em dois espécimes juvenis de Gymnura micrura (Bloch and Scheneider, 1801 capturadas pela pesca artesanal em águas rasas do estado do Maranhão (Brasil.
Weighted Composition Operators from Bergman-Type Spaces into Bloch Spaces
Indian Academy of Sciences (India)
Songxiao Li; Stevo Stević
2007-08-01
Let be an analytic self-map and be a fixed analytic function on the open unit disk in the complex plane $\\mathbb{C}$. The weighted composition operator is defined by $$u C_\\varphi f=u\\cdot p (f\\circ\\varphi), f\\in H(D).$$ Weighted composition operators from Bergman-type spaces into Bloch spaces and little Bloch spaces are characterized by function theoretic properties of their inducing maps.
Optimal cloning of qubits given by arbitrary axisymmetric distribution on Bloch sphere
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 analyt...
Bloch Oscillations of Two-Component Bose-Einstein Condensates in Optical Lattices
Institute of Scientific and Technical Information of China (English)
GU Huai-Qiang; WANG Zhi-Cheng; JIN Kang; TAN Lei
2006-01-01
@@ We study the Bloch oscillations of two-component Bose-Einstein condensates trapped in spin-dependent optical lattices. The influence of the intercomponent atom interaction on the system is discussed in detail Accelerated breakdown of the Bloch oscillations and revival phenomena are found respectively for the repulsive and attractive case. For both the cases, the system will finally be set in a quantum self-trapping state due to dynamical instability.
Landau levels from the Bethe Ansatz equations
Hoshi, K.; Hatsugai, Y.
2000-01-01
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak-field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
Landau Levels from the Bethe Ansatz Equations
Hoshi, K.; Hatsugai, Y.
1999-01-01
The Bethe ansatz (BA) equations for the two-dimensional Bloch electrons in a uniform magnetic field are treated in the weak field limit. We have calculated energies near the lower boundary of the energy spectrum up to the first nontrivial order. It corresponds to calculating a finite size correction for the excitation energies of the BA solvable lattice models and gives the Landau levels in the present problem.
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...
Geometry of the generalized Bloch sphere for qutrit
Goyal, Sandeep K; Singh, Rajeev; Simon, Sudhavathani
2011-01-01
The geometry of the generalized Bloch sphere $\\Omega_3$, the state space of a qutrit is studied. Closed form expressions for $\\Omega_3$, its boundary $\\partial \\Omega_3$, and the set of extremals $\\Omega_3^{\\rm ext}$ are obtained by use of an elementary observation. These expressions and analytic methods are used to classify the 28 two-sections and the 56 three-sections of $\\Omega_3$ into unitary equivalence classes, completing the works of earlier authors. It is shown, in particular, that there are families of two-sections and of three-sections which are equivalent geometrically but not unitarily, a feature that does not appear to have been appreciated earlier. A family of three-sections of obese-tetrahedral shape whose symmetry corresponds to the 24-element tetrahedral point group $T_d$ is examined in detail. This symmetry is traced to the reduction of the adjoint representation of SU(3), the symmetry underlying $\\Omega_3$, into direct sum of the two-dimensional and the two (inequivalent) three-dimensional ...
Hidden structures in time evolution of Bloch vector under thermal Jaynes-Cummings model
Azuma, Hiroo
2012-01-01
We reveal hidden structures of time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, the Bloch vector seems to be in complete disorder and confusion. Because of the thermal photon distribution, both its norm and direction change hard at random, so that the Bloch vector shows a quasichaotic behaviour. However, if we take a different viewpoint compared with ones that we have been used to, we can find some novel structures in the Bloch vector's trajectories plotted at constant time intervals. In this paper, at first, we try to give an explanation of emergence of the quasichaotic behaviour by drawing an analogy between the dynamics of the Bloch vector and that of a compressible fluid. Next, we discuss the following two facts: (1) If we adj...
Quasiperiodicity in time evolution of the Bloch vector under the thermal Jaynes-Cummings model
Azuma, Hiroo; Ban, Masashi
2014-07-01
We study a quasiperiodic structure in the time evolution of the Bloch vector, whose dynamics is governed by the thermal Jaynes-Cummings model (JCM). Putting the two-level atom into a certain pure state and the cavity field into a mixed state in thermal equilibrium at initial time, we let the whole system evolve according to the JCM Hamiltonian. During this time evolution, motion of the Bloch vector seems to be in disorder. Because of the thermal photon distribution, both a norm and a direction of the Bloch vector change hard at random. In this paper, taking a different viewpoint compared with ones that we have been used to, we investigate quasiperiodicity of the Bloch vector’s trajectories. Introducing the concept of the quasiperiodic motion, we can explain the confused behaviour of the system as an intermediate state between periodic and chaotic motions. More specifically, we discuss the following two facts: (1) If we adjust the time interval Δt properly, figures consisting of plotted dots at the constant time interval acquire scale invariance under replacement of Δt by sΔt, where s(>1) is an arbitrary real but not transcendental number. (2) We can compute values of the time variable t, which let |Sz(t)| (the absolute value of the z-component of the Bloch vector) be very small, with the Diophantine approximation (a rational approximation of an irrational number).
Probing the intrinsic optical Bloch-mode emission from a 3D photonic crystal.
Hsieh, Mei-Li; Bur, James A; Du, Qingguo; John, Sajeev; Lin, Shawn-Yu
2016-10-14
We report experimental observation of intrinsic Bloch-mode emission from a 3D tungsten photonic crystal at low thermal excitation. After the successful removal of conventional metallic emission (normal emission), it is possible to make an accurate comparison of the Bloch-mode and the normal emission. For all biases, we found that the emission intensity of the Bloch-mode is higher than that of the normal emission. The Bloch-mode emission also exhibits a slower dependence on [Formula: see text] than that of the normal emission. The observed higher emission intensity and a different T-dependence is attributed to Bloch-mode assisted emission where emitters have been located into a medium having local density of states different than the isotropic case. Furthermore, our finite-difference time-domain (FDTD) simulation shows the presence of localized spots at metal-air boundaries and corners, having intense electric field. The enhanced plasmonic field and local non-equilibrium could induce a strong thermally stimulated emission and may be the cause of our unusual observation. PMID:27606574
Several Growth Characteristics of an Invasive Cyprinid Fish (Carassius gibelio Bloch, 1782
Directory of Open Access Journals (Sweden)
Sait BULUT
2013-05-01
Full Text Available Age composition, length-weight relationships, growth, and condition factors of the gibel carp (Carassius gibelio Bloch, 1782 were determined using specimens collected from Seyitler Reservoir between July 2005 to June 2006. A total of 149 gibel carp were observed and examined. The age composition of the samples ranged between I and VII years of age. It has been determined than 82.55% of the obtained samples are comprised of females, 16.11% is comprised of males and 1.34% is comprised of immature. The population is dominated by females able to reproduce gynogenetically. The mean fork lengths and mean weights of the population were 14.8-32.5 cm and 43.1-807.3 g respectively. The length-weight relation were calculated as W = 0.0696 L2.132, r=0.838 for females, for males W = 0.2942 L2.6417 r=0.784 and W = 0.0274 L2.9382, r=0.813 for all samples. The mean Fulton Condition Factor was calculated as 2.342 for females, 2.064 for males and 2.276 for all samples. Age-length and age-weight relations were determined according to von Bertalanffy growth equation formula. Growth parameters of the population were Lt = 48.09 [1-e-0.093(t+0.29], and Wt=2323.62 [1-e-0.093(t+0.29]2.9382. The growth performance index value (Ø´ was computed as 5.37 for all specimens.
Hung, Yu-Ju; Lin, I-Sheng
2016-07-11
This paper reports a novel approach to the direct observation of Bloch surface waves, wherein a layer of fluorescent material is deposited directly on the surface of a semi-infinite periodic layered cell. A set of surface nano-gratings is used to couple pumping light to Bloch surface waves, while the sample is rotated until the pumping light meets the quasi-phase matching conditions. This study investigated the directional propagation of waves on stripe and circular one-dimensional grating structures by analyzing the dispersion relationship of the first two eigen modes. Our results demonstrate the efficacy of the proposed scheme in visualizing Bloch surface waves, which could be extended to a variety of other devices. PMID:27410869
Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice
Xu, Ye-Long; Fegadolli, William S.; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng
2016-01-01
As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform. PMID:27095533
Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice.
Xu, Ye-Long; Fegadolli, William S; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng
2016-01-01
As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform. PMID:27095533
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.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Christodoulides, Demetrios; Peschel, Ulf
2016-01-01
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 ...
Bloch mode synthesis: Ultrafast methodology for elastic band-structure calculations
Krattiger, Dimitri; Hussein, Mahmoud I.
2014-12-01
We present a methodology for fast band-structure calculations that is generally applicable to problems of elastic wave propagation in periodic media. The methodology, called Bloch mode synthesis, represents an extension of component mode synthesis, a set of substructuring techniques originally developed for structural dynamics analysis. In Bloch mode synthesis, the unit cell is divided into interior and boundary degrees-of-freedom, which are described, respectively, by a set of normal modes and a set of constraint modes. A combination of these mode sets then forms a reduced basis for the band structure eigenvalue problem. The reduction is demonstrated on a phononic-crystal model and a locally resonant elastic-metamaterial model and is shown to accurately predict the frequencies and Bloch mode shapes with a dramatic decrease in computation time in excess of two orders of magnitude.
On averaging the Kubo-Hall conductivity of magnetic Bloch bands leading to Chern numbers
International Nuclear Information System (INIS)
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 k1, k2 and the two continuous integration parameters α1, α2. The average over the parameter domain 0 ≤ αj 1, k2. They show how this can be transformed into a single integral over the continuous magnetic Brillouin zone 0 ≤ αj j, j = 1, 2, nj = number of unit cells in j-direction, keeping k1, k2 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
Experimental realization of Bloch oscillations in a parity-time synthetic silicon photonic lattice
Xu, Ye-Long; Fegadolli, William S.; Gan, Lin; Lu, Ming-Hui; Liu, Xiao-Ping; Li, Zhi-Yuan; Scherer, Axel; Chen, Yan-Feng
2016-04-01
As an important electron transportation phenomenon, Bloch oscillations have been extensively studied in condensed matter. Due to the similarity in wave properties between electrons and other quantum particles, Bloch oscillations have been observed in atom lattices, photonic lattices, and so on. One of the many distinct advantages for choosing these systems over the regular electronic systems is the versatility in engineering artificial potentials. Here by utilizing dissipative elements in a CMOS-compatible photonic platform to create a periodic complex potential and by exploiting the emerging concept of parity-time synthetic photonics, we experimentally realize spatial Bloch oscillations in a non-Hermitian photonic system on a chip level. Our demonstration may have significant impact in the field of quantum simulation by following the recent trend of moving complicated table-top quantum optics experiments onto the fully integrated CMOS-compatible silicon platform.
Non-destructive monitoring of Bloch oscillations in an optical cavity
Keßler, H; Venkatesh, B P; Georges, Ch; Hemmerich, A
2016-01-01
Bloch oscillations are a hallmark of coherent wave dynamics in periodic potentials. They occur as the response of quantum mechanical particles in a lattice if a weak force is applied. In optical lattices with their perfect periodic structure they can be readily observed and employed as a quantum mechanical force sensor, for example, for precise measurements of the gravitational acceleration. However, the destructive character of the measurement process in previous experimental implementations poses serious limitations for the precision of such measurements. In this article we show that the use of an optical cavity operating in the regime of strong cooperative coupling allows one to directly monitor Bloch oscillations of a cloud of cold atoms in the light leaking out of the cavity. Hence, with a single atomic sample the Bloch oscillation dynamics can be mapped out, while in previous experiments, each data point required the preparation of a new atom cloud. The use of a cavity-based monitor should greatly impro...
The Barkas-Effect Correction to Bethe-Bloch Stopping Power
Porter, L. E.
A brief history of the discovery of the Barkas-effect correction to the Bethe-Bloch stopping power formula is presented, followed by a recounting of the initial theoretical calculations prepared as a quantitative explanation. A current version of the modified Bethe-Bloch formula is described in detail. An overview of the current capability to assess the validity of several existing formalisms for calculating the Barkas-effect correction term is provided, in the course of which discussion of numerous sources of uncertainty ensues. Finally, an opinion on the significance of this departure from Bethe-Bloch theory is offered, along with a presentation of a few recent developments and of some areas for focus in future exploration in the field of the stopping power of matter for charged particles.
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.
International Nuclear Information System (INIS)
The non-Bloch LCAO wave functions for cubic crystals are discussed and applied to the calculation of the matrix elements for electron transitions in an external electric field. The sum of transitions between non-Bloch electron states is compared with the matrix element for a conventional nearly free electron transition. 26 refs., 2 tabs
Sreekumari, T.; Aravindan, C.M.
1993-01-01
Satiation amount, satiation time and handling time of Anabas testudineus (Bloch), an air breathing predatory fish was experimentally estimated using guppy (Lebistes reticulatus) as prey. Weight of the fish and satiation time influenced prey handling time. As satiation time is related to the level of hunger, level of hunger was found to influence handling time of prey.
Floquet-Bloch waves and suppression of vibrations in multi-scale fluid-solid systems
Carta, Giorgio; Movchan, Alexander B
2016-01-01
The paper presents a mathematical model for an industry inspired problem of vibration isolation applied to a cluster of elastic fluid-filled containers. We develop a systematic approach employing full fluid-solid interaction and Floquet-Bloch waves in periodic multi-scale systems. The analytical findings are accompanied by numerical simulations, including frequency response analyses and computations in the transient regime.
Identification of Bloch-modes in hollow-core Photonic Crystal Fiber cladding
DEFF Research Database (Denmark)
Couny, F.; Benabid, F.; Roberts, John; Burnett, M.T.; Maier, S.A.
2007-01-01
We report on the experimental visualization of the cladding Bloch-modes of a hollow-core photonic crystal fiber. Both spectral and spatial field information is extracted using the approach, which is based on measurement of the near-field and Fresnel-zone that results after propagation over a short...
Decoherence of a qubit as a diffusion on the Bloch sphere
International Nuclear Information System (INIS)
We analyze qubit decoherence in the framework of geometric quantum mechanics. In this framework the qubit density operators are represented by probability distributions which are also the Kähler functions on the Bloch sphere. Interestingly, the complete positivity of the quantum evolution is recovered as ellipticity of the second order differential operator (deformed Laplacian) which governs the evolution of the probability distribution. (paper)
Thermal Two Point Function of a Heavy Muon in hot QED plasma within Bloch Nordsieck Approximation
Takashiba, K.
1995-01-01
The thermal propagator of a heavy muon propagating in a hot QED plasma is examined within the Bloch-Nordsieck approximation, which is valid in the infrared region. It is shown that the muon damping rate is finite, in contrast to the lower-order calculation with hard thermal loop resummations taken into account.
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
Institute of Scientific and Technical Information of China (English)
LIU Jing; LI Chunsheng; NING Ping
2013-01-01
Pampus cinereus (Bloch,1795) (Stromateidae),a species believed to be widely distributed throughout the Indo-Western Pacific region,was redescribed and a neotype was designated.The designation of a neotype was necessary because of ambiguous data in Bloch's original description and the loss of the original type specimen.Morphological data indicated that 10 recently-collected specimens from the coasts of southern China agreed well with Bloch's original description and figure ofP.cinereus.A neotype for this species was selected from among the 10 specimens,and a detailed description is presented in this paper.
International Nuclear Information System (INIS)
The motion of the charged particle in a one-dimensional periodic potential of the Kronig-Penney type is considered. The energy band structure, Bloch wave functions (BWF) in coordinate and momentum representation are investigated in detail. Two sharply distinguished groups of states, i.e. below-the-barrier and above-the-barrier, are extracted, and the role of both positively and negatively charged particles in the channeling is explained. It is shown that only with use of a dispersion equation form one can obtain the information on the symmetry properties of the BWF at the edges of energy bands. The estimate of the corresponding regions of the edge coherence in the Brillouin zone is given. In above-the-barrier case the nontrivial effect of parity interchange violation of BWF at the edges of energy bands, connected with the nullification of the reflection coefficient either from the single barrier or well is found. Oscillation behaviour of both allowed and forbidden band widths is revealed. The analytical results for different values of the parameters are illustrated by computer calculations
Homogenization of the Schrodinger equation with a time oscillating potential
Allaire, Grégoire; Vanninathan, M.
2005-01-01
International audience We study the homogenization of a Schrodinger equation in a periodic medium with a time dependent potential. This is a model for semiconductors excited by an external electromagnetic wave. We prove that, for a suitable choice of oscillating (both in time and space) potential, one can partially transfer electrons from one Bloch band to another. This justifies the famous "Fermi golden rule" for the transition probability between two such states which is at the basis of ...
Bloch oscillations as generators of polarons in a 1D crystal
Nazareno, H. N.; Brito, P. E. de
2016-08-01
The main purpose of this work is to characterize the kind of propagation/localization of carriers in a one-dimensional crystalline structure along the tight-binding model while the electron-phonon interaction is taken into account through a deformation potential and the system is under the action of a dc electric field. The lattice was treated in the classical formalism of harmonic vibrations. A remarkable effect is obtained due to the presence of the electric field. On one side the particle performs Bloch oscillations and at the same time it interacts with the lattice and as a result at each turning point of its trajectory phonons are generated that carry with them a fraction of the electronic wave packet, it is the polaron formation. This way the Bloch oscillations pump polarons into the system. We explain why the polaron is formed at returning points of the oscillations.
Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction
Tallarico, Domenico; Movchan, Alexander B; Colquitt, Daniel J
2016-01-01
We consider a vibrating triangular mass-truss lattice whose unit cell contains a resonator of a triangular shape. The resonators are connected to the triangular lattice by trusses. Each resonator is tilted, i.e. it is rotated with respect to the triangular lattice's unit cell through an angle $\\vartheta_0$. This geometrical parameter is responsible for the emergence of a resonant mode in the Bloch spectrum for elastic waves and strongly affects the dispersive properties of the lattice. Additionally, the tilting angle $\\vartheta_0$ triggers the opening of a band gap at a Dirac-like point. We provide a physical interpretation of these phenomena and discuss the dynamical implications on elastic Bloch waves. The dispersion properties are used to design a structured interface containing tilted resonators which exhibit negative refraction and focussing, as in a "flat elastic lens".
Measuring h /mCs and the Fine Structure Constant with Bragg Diffraction and Bloch Oscillations
Parker, Richard
2016-05-01
We have demonstrated a new scheme for atom interferometry based on large-momentum-transfer Bragg beam splitters and Bloch oscillations. In this new scheme, we have achieved a resolution of δα / α =0.25ppb in the fine structure constant measurement, which gives up to 4.4 million radians of phase difference between freely evolving matter waves. We suppress many systematic effects, e.g., Zeeman shifts and effects from Earth's gravity and vibrations, use Bloch oscillations to increase the signal and reduce the diffraction phase, simulate multi-atom Bragg diffraction to understand sub-ppb systematic effects, and implement spatial filtering to further suppress systematic effects. We present our recent progress toward a measurement of the fine structure constant, which will provide a stringent test of the standard model of particle physics.
Interplay between Point-Group Symmetries and the Choice of the Bloch Basis in Multiband Models
Directory of Open Access Journals (Sweden)
Qiang-Hua Wang
2013-11-01
Full Text Available We analyze the point-group symmetries of generic multiband tight-binding models with respect to the transformation properties of the effective interactions. While the vertex functions in the orbital language may transform non-trivially under point-group operations, their point-group behavior in the band language can be simplified by choosing a suitable Bloch basis. We first give two analytically accessible examples. Then, we show that, for a large class of models, a natural Bloch basis exists, in which the vertex functions in the band language transform trivially under all point-group operations. As a consequence, the point-group symmetries can be used to reduce the computational effort in perturbative many-particle approaches, such as the functional renormalization group.
Laura Ghigliotti; Julius Nielsen; Jorgen Schou Christiansen; Eva Pisano
2015-01-01
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 unde...
Norm equivalence and composition operators between Bloch/Lipschitz spaces of the ball
Stević Stevo; Clahane Dana D
2006-01-01
For , let and denote, respectively, the -Bloch and holomorphic -Lipschitz spaces of the open unit ball in . It is known that and are equal as sets when . We prove that these spaces are additionally norm-equivalent, thus extending known results for and the polydisk. As an application, we generalize work by Madigan on the disk by investigating boundedness of the composition operator from to .
Institute of Scientific and Technical Information of China (English)
Robert F.Allen
2014-01-01
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient condi-tions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ”computable” estimates on the operator norm.
Floquet-Bloch vs. Nicolson-Ross-Weir Extraction for Magneto-Dielectric Bragg Stacks
DEFF Research Database (Denmark)
Clausen, Niels Christian Jerichau; Arslanagic, Samel; Breinbjerg, Olav
We extract and compare the permittivity and permeability from a dielectric and a magnetodielectric Bragg stack with the Floquet-Bloch (FB) method for the infinite stack and the Nicolson-Ross- Weir (NRW) method for the finite stack. While the extracted propagation constants are identical, the wave...... impedances are different. Moreover, the NRWmethod yields magnetic effects for the dielectric Bragg stack, while the FB method gives the expected vacuum permeability, also in the bandgab....
Grating-Coupling-Based Excitation of Bloch Surface Waves for Lab-on-Fiber Nanoprobes
Scaravilli, Michele; Castaldi, Giuseppe; Cusano, Andrea; Galdi, Vincenzo
2016-01-01
In this paper, we investigate for the first time the possibility to excite Bloch surface waves (BSWs) on the tip of single-mode optical fibers. Within this framework, we first demonstrate the possibility to exploit a grating-coupling mechanism for on-tip excitation of BSWs, and highlight the flexibility of the proposed design as well as its intrinsic robustness to unavoidable fabrication tolerances. Subsequently, with a view towards label-free chemical and biological sensing, we present an op...
International Nuclear Information System (INIS)
We study nonlinear wave phenomena in coupled ring resonator optical waveguides in the tight coupling regime. A discrete model for the system dynamics is put forward and its steady-state nonlinear Bloch modes are derived. The switching behaviour of the transmission system is addressed numerically and the results are explained in the light of this analytical result. We also present a numerical study on the spontaneous generation of Bragg solitons from a continuous-wave input. (paper)
Muthusamy RAJASEKAR; Muthusamy THANGARAJ; Thathiredypalli R. BARATHKUMAR; Jayachandran SUBBURAJ; Kaliyan MUTHAZHAGAN
2012-01-01
Lates calcarifer (Bloch 1790) is one of the major economically important cultivable fish species in India. In this study, three populations of L. calcarifer was selected to assess the genetic diversity. Of which, two wild (Mudaslodai, Muthupettai) and one captive (Mutukadu) population. The genetic diversity of three populations of this species was studied using Random Amplified Polymorphic DNA (RAPD) markers. Ten random primers were used for the assessment of their genetic diversity and const...
The ℋ∞ synchronization of nonlinear Bloch systems via dynamic feedback control approach
International Nuclear Information System (INIS)
We consider an ℋ∞ synchronization problem in nonlinear Bloch systems. Based on Lyapunov stability theory and linear matrix inequality formulation, a dynamic feedback controller is designed to guarantee asymptotic stability of the master-slave synchronization. Moreover, this controller reduces the effect of an external disturbance to the ℋ∞ norm constraint. A numerical example is given to validate the proposed synchronization scheme. (general)
Zitterbewegung, Bloch Oscillations and Landau-Zener Tunneling in a Quantum Walk
Regensburger, Alois; Hinrichs, Benjamin; Onishchukov, Georgy; Schreiber, Andreas; Silberhorn, Christine; Peschel, Ulf
2011-01-01
We experimentally investigate a discrete time quantum walk in a system of coupled fiber loops and observe typical phenomena known from the wave propagation in periodic structures as ballistic spreading or an oscillation between two internal quantum states similar to Zitterbewegung (trembling motion). If a position-dependent phase gradient is applied we find localization and Bloch oscillations of the field for moderate as well as Landau-Zener tunneling for strong phase gradients.
Dynamic scattering of electron vortex beams – A Bloch wave analysis
International Nuclear Information System (INIS)
Two important applications of electron vortex beams are in electron magnetic chiral dichroism (EMCD) measurements and nanoparticle manipulation. In both cases orbital angular momentum (
Representability of Bloch states on Projector-augmented-wave (PAW) basis sets
Agapito, Luis; Ferretti, Andrea; Curtarolo, Stefano; Buongiorno Nardelli, Marco
2015-03-01
Design of small, yet `complete', localized basis sets is necessary for an efficient dual representation of Bloch states on both plane-wave and localized basis. Such simultaneous dual representation permits the development of faster more accurate (beyond DFT) electronic-structure methods for atomistic materials (e.g. the ACBN0 method.) by benefiting from algorithms (real and reciprocal space) and hardware acceleration (e.g. GPUs) used in the quantum-chemistry and solid-state communities. Finding a `complete' atomic-orbital basis (partial waves) is also a requirement in the generation of robust and transferable PAW pseudopotentials. We have employed the atomic-orbital basis from available PAW data sets, which extends through most of the periodic table, and tested the representability of Bloch states on such basis. Our results show that PAW data sets allow systematic and accurate representability of the PAW Bloch states, better than with traditional quantum-chemistry double-zeta- and double-zeta-polarized-quality basis sets.
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.
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.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
2015-12-01
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.
Role of confined Bloch waves in the near field heat transfer between two photonic crystals
International Nuclear Information System (INIS)
The near field heat transfer between two finite size one-dimensional photonic crystals separated by a small vacuum gap and maintained in nonequilibrium thermal situation is theoretically investigated. The main features of this electromagnetic transfer are discussed and compared with what is generally observed with media that support surface polaritons. It is shown that the presence of surface Bloch waves can significantly enhance heat transfers beyond the far field limit for both polarization states of electromagnetic field at subwavelength separation distances. A specific attention is addressed to the consequence of the slopes of surface Bloch waves dispersion curves on the heat transfer. In particular, it is shown that the localization of surface Bloch waves close to the light line allows to observe a transfer exaltaion at larger separation distances than the Wien wavelength. These results could open new possibilities for the development of innovative near-field technologies such as near-field thermophotovoltaic conversion, plasmon assisted nanophotolitography or near-field spectroscopy.
Bloch walls and the non-ideal bose gas spectrum
International Nuclear Information System (INIS)
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)
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)
Prolongation Loop Algebras for a Solitonic System of Equations
Directory of Open Access Journals (Sweden)
Maria A. Agrotis
2006-11-01
Full Text Available We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.
Extraction of optical Bloch modes in a photonic-crystal waveguide
Huisman, S R; Stobbe, S; Herek, J L; Lodahl, P; Vos, W L; Pinkse, P W H
2011-01-01
We perform phase-sensitive near-field scanning optical microscopy on photonic-crystal waveguides. The observed intricate field patterns are analyzed by spatial Fourier transformations, revealing several guided TE- and TM-like modes. Using the reconstruction algorithm proposed by Ha, et al. (Opt. Lett. 34 (2009)), we decompose the measured two-dimensional field pattern in a superposition of propagating Bloch modes. This opens new possibilities to study specific modes in near-field measurements. We apply the method to study the transverse behavior of a guided TE-like mode, where the mode extends deeper in the surrounding photonic crystal when the band edge is approached.
Energy Technology Data Exchange (ETDEWEB)
Lyo, Sungkwun Kenneth; Pan, Wei; Reno, John Louis; Wendt, Joel Robert; Barton, Daniel Lee
2008-09-01
We have investigated the physics of Bloch oscillations (BO) of electrons, engineered in high mobility quantum wells patterned into lateral periodic arrays of nanostructures, i.e. two-dimensional (2D) quantum dot superlattices (QDSLs). A BO occurs when an electron moves out of the Brillouin zone (BZ) in response to a DC electric field, passing back into the BZ on the opposite side. This results in quantum oscillations of the electron--i.e., a high frequency AC current in response to a DC voltage. Thus, engineering a BO will yield continuously electrically tunable high-frequency sources (and detectors) for sensor applications, and be a physics tour-de-force. More than a decade ago, Bloch oscillation (BO) was observed in a quantum well superlattice (QWSL) in short-pulse optical experiments. However, its potential as electrically biased high frequency source and detector so far has not been realized. This is partially due to fast damping of BO in QWSLs. In this project, we have investigated the possibility of improving the stability of BO by fabricating lateral superlattices of periodic coupled nanostructures, such as metal grid, quantum (anti)dots arrays, in high quality GaAs/Al{sub x}Ga{sub 1-x}As heterostructures. In these nanostructures, the lateral quantum confinement has been shown theoretically to suppress the optical-phonon scattering, believed to be the main mechanism for fast damping of BO in QWSLs. Over the last three years, we have made great progress toward demonstrating Bloch oscillations in QDSLs. In the first two years of this project, we studied the negative differential conductance and the Bloch radiation induced edge-magnetoplasmon resonance. Recently, in collaboration with Prof. Kono's group at Rice University, we investigated the time-domain THz magneto-spectroscopy measurements in QDSLs and two-dimensional electron systems. A surprising DC electrical field induced THz phase flip was observed. More measurements are planned to investigate this
Institute of Scientific and Technical Information of China (English)
CHEN Li-Xue(陈历学); KIM Dalwoo; SONG Ying-Lin(宋瑛琳); DING Wei-Qiang(丁卫强); LI Wen-Hui(李文惠); LIU Shu-Tian(刘树田)
2004-01-01
One-dimensional photonic crystal of second-order nonlinearity is studied. Among the three waves of the parametric interaction process of down-conversion with a nondispersive medium, two gap-edge localized modes and one travelling-mode are proposed, and an exact phase matching condition is realized using the periodic condition of the Bloch phase. Numerical simulation is implemented by the slow-envelope finite difference time domain method. In the case of a pulse wave pump of amplitude half-width 5.2 × 10-13 s, an intense optical parametric pulse with half-width about 5 × 10-14 s is observed.
DEFF Research Database (Denmark)
de Lasson, Jakob Rosenkrantz; Kristensen, Philip Trøst; Mørk, Jesper;
2014-01-01
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 nite-dierence time-domain method and the nite element method, the present approach satises automatically the outgoing wave boundary condition in the propagation direction which represents a signicant advantage of our new method. The scheme...
Fornasari, Lucia; Floris, Francesco; Patrini, Maddalena; Comoretto, Davide; Marabelli, Franco
2016-05-18
An all-polymer photonic structure constituted by a distributed Bragg reflector topped with an ultrathin fluorescent polymer film has been studied. A Bloch surface wave resonance has been exploited to improve pumping efficiency. A strongly polarization and angle dependent fluorescence signal is found with respect to the light pumping beam and the emitted wavelength. Matching the most favorable condition for the pump coupling and the collection geometry, the signal obtained from the structure appears to be two orders of magnitude larger than the one of the bare emitting film. PMID:27158698
Experimental reconstruction of the Berry curvature in a topological Bloch band
Weitenberg, Christof; Flaeschner, Nick; Rem, Benno; Tarnowski, Matthias; Vogel, Dominik; Luehmann, Dirk-Soeren; Sengstock, Klaus
2016-05-01
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry of the eigenstates across the Brillouin zone. Employing fermionic ultracold atoms in a hexagonal optical lattice, we engineer the Berry curvature of the Bloch bands using resonant driving and measure it with full momentum resolution. Our results pave the way to explore intriguing phases of matter with interactions in topological band structures.
Sturmberg, Björn C. P.; Dossou, Kokou B.; Lawrence, Felix J.; Poulton, Christopher G.; McPhedran, Ross C.; de Sterke, C. Martijn; Botten, Lindsay C.
2016-05-01
We describe EMUstack, an open-source implementation of the Scattering Matrix Method (SMM) for solving field problems in layered media. The fields inside nanostructured layers are described in terms of Bloch modes that are found using the Finite Element Method (FEM). Direct access to these modes allows the physical intuition of thin film optics to be extended to complex structures. The combination of the SMM and the FEM makes EMUstack ideally suited for studying lossy, high-index contrast structures, which challenge conventional SMMs.
International Nuclear Information System (INIS)
We propose a photonic structure stacked sequentially by one-dimensional photonic crystals and cavities. The whole structure is composed of single-negative and double-negative materials. The optical Wannier–Stark ladder (WSL) can be obtained in a low frequency region by modulating the widths of the cavities in order. We simulate the dynamical behavior of the electromagnetic wave passing through the proposed photonic structure. Due to the dispersive characteristics of the metamaterials, a very narrow WSL can be obtained. The long-period electromagnetic Bloch oscillation is demonstrated theoretically to have a period on a microsecond time scale. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
International Nuclear Information System (INIS)
The author performed the histological analysis of the oocytes of golden (Chinese) carp, Carassius auratus gibelio (Bloch). Its habitat was radioactive-contaminated Belarusian reservoirs within Chernobyl zone. The obtained results revealed that the oocytes underwent some degenerative alterations such as irregular nucleus shape and karyolysis. That was witnessed by examination of the fish of Perstok Lake where water was characterized by the high level of radioactive contamination. It was shown that the alterations were connected with the high level of natural habitat contamination. These alterations were also caused by the high content of radionuclides in fish tissuies and organs
Bloch-type domain walls in rhombohedral BaTiO.sub.3./sub..
Czech Academy of Sciences Publication Activity Database
Taherinejad, M.; Vanderbilt, D.; Márton, Pavel; Stepkova, Vilgelmina; Hlinka, Jiří
2012-01-01
Roč. 86, č. 15 (2012), "155138-1"-"155138-8". ISSN 1098-0121 R&D Projects: GA ČR GA202/09/0430; GA ČR GAP204/10/0616 Institutional research plan: CEZ:AV0Z10100520 Keywords : domain walls * Bloch domain walls * rhombohedral phase * phase-field approach * first-principles approach Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.767, year: 2012 http://prb.aps.org/abstract/PRB/v86/i15/e155138
UGROŽENE VRSTE RIBA U SVIJETU: Mystus vittatus (Bloch, 1794) (Siluriformes: Bagridae)
Hossain, Yeamin
2014-01-01
Autohtona vrsta, Mystus vittatus (Bloch, 1794), pripadnik porodice Bagridae, široke je distribucije u azijskim zemljama, uključujući Bangladeš, Indiju, Pakistan, Šri Lanku, Nepal i Mianmar. Međutim, prirodne populacije ozbiljno opadaju zbog visokog ribolovnog pritiska, gubitka staništa, zagađenja, prirodnih katastrofa, sanacije močvara i prekomjernog poplavnog zamuljivanja pa se stoga nalazi se u kategoriji osjetljive vrste. U članku se predlažu mjere za očuvanje ostatka izolirane populacije ...
Institute of Scientific and Technical Information of China (English)
SUN Hui-Yuan; HU Yun-Zhi; LIU Li-Hu
2009-01-01
The diameters of the ordinary hard bubbles (OHBs) and soft bubbles in epitaxial garnet films are measured under the microscope at various temperatures. It is found that the bubble diameters of OHBs increase with temperature, and it is concluded that the equilibrium separation between two neighbouring vertical Bloch lines (VBLs) Seq is widened with increasing temperature. At the same time, the results can be understood simply as that there are more VBLs in the domain walls of the first dumbbell domains (IDs) than those in walls of OH Bs at the same temperature.
Weighted Composition Operators from α-Bloch Spaces to H∞%α-Bloch空间到H∞的加权复合算子
Institute of Scientific and Technical Information of China (English)
唐笑敏
2007-01-01
The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces(or little α-Bloch spaces) to H∞, but also gives some estimates for the norm of the weighted composition operator.
International Nuclear Information System (INIS)
Small-angle scattering of neutrons allows the determination of the orientation of Bloch walls in the interior of bulk single crystals. The zigzag angle psi=280 of the 900 Bloch wall and its field dependence are measured. We also observe walls or wall pieces with psi=00. With 1800 walls we measure zigzag angles of psi approximately equal to 300. (orig.)
Matveev, V. I.; Makarov, D. N.
2011-09-01
A simple method including nonperturbative shell corrections has been developed for calculating energy losses on complex atoms. The energy losses of fast highly charged ions on neon, argon, krypton, and xenon atoms have been calculated and compared with experimental data. It has been shown that the inclusion of the non-perturbative shell corrections noticeably improves agreement with experimental data as compared to calculations by the Bethe-Bloch formula with the standard corrections. This undoubtedly helps to reduce the number of fitting parameters in various modifications of the Bethe-Bloch formula, which are usually determined semiempirically.
Raman fingerprints on the Bloch sphere of a spinor Bose-Einstein condensate
Schultz, Justin T; Murphree, Joseph D; Jayaseelan, Maitreyi; Bigelow, Nicholas P
2016-01-01
We explore the geometric interpretation of a diabatic, two-photon Raman process as a rotation on the Bloch sphere for a pseudo-spin-1/2 system. The spin state of a spin-1/2 quantum system can be described by a point on the surface of the Bloch sphere, and its evolution during a Raman pulse is a trajectory on the sphere determined by properties of the optical beams: the pulse area, the relative intensities and phases, and the relative frequencies. We experimentally demonstrate key features of this model with a $^{87}$Rb spinor Bose-Einstein condensate, which allows us to examine spatially dependent signatures of the Raman beams. The two-photon detuning allows us to precisely control the spin density and imprinted relative phase profiles, as we show with a coreless vortex. With this comprehensive understanding and intuitive geometric interpretation, we use the Raman process to create and tailor as well as study and characterize exotic topological spin textures in spinor BECs.
Creating full-Bloch Bose–Einstein condensates with Raman q-plates
Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.
2016-06-01
A coherent two-photon optical Raman interaction in a pseudo-spin-1/2 Bose–Einstein condensate (BEC) serves as a q-plate for atoms, converting spin to orbital angular momentum. This Raman q-plate has a singular pattern in its polarization distribution in analogy to the singular birefringent q-plates used in singular optics. The vortex winding direction and magnitude as well as the final spin state of the BEC depend on the initial spin state and the topology of the optical Raman q-plate beams. Drawing on the mathematical and geometric foundations of singular optics, we derive the equivalent Jones matrix for this Raman q-plate and use it to create and characterize atomic spin singularities in the BEC that are analogous to optical C-point singularities in polarization. By tuning the optical Raman parameters, we can generate a coreless vortex spin texture which contains every possible superposition in a two-state system. We identify this spin texture as a full-Bloch BEC since every point on the Bloch sphere is represented at some point in the cross section of the atomic cloud. This spin–orbit interaction and the spin textures it generates may allow for the observation of interesting geometric phases in matter waves and lead to schemes for topological quantum computation with spinor BECs.
Wannier-Bloch approach to localization in high harmonics generation in solids
Osika, Edyta N; Ortmann, Lisa; Suárez, Noslen; Pérez-Hernández, Jose Antonio; Szafran, Bartłomiej; Ciappina, Marcelo F; Sols, Fernando; Landsman, Alexandra S; Lewenstein, Maciej
2016-01-01
Emission of high-order harmonics from solids provides a new avenue in attosecond science. On one hand, it allows to investigate fundamental processes of the non-linear response of electrons driven by a strong laser pulse in a periodic crystal lattice. On the other hand, it opens new paths toward efficient attosecond pulse generation, novel imaging of electronic wave functions, and enhancement of high-order harmonic generation (HHG) intensity. A key feature of HHG in a solid (as compared to the well-understood phenomena of HHG in an atomic gas) is the delocalization of the process, whereby an electron ionized from one site in the periodic lattice may recombine with any other. Here, we develop an analytic model, based on the localized Wannier wave functions in the valence band and delocalized Bloch functions in the conduction band. This Wannier-Bloch approach assesses the contributions of individual lattice sites to the HHG process, and hence addresses precisely the question of localization of harmonic emission...
Institute of Scientific and Technical Information of China (English)
无
2004-01-01
At the beginning of 16th century, mathematicians found it easy to solve equations of the first degree(linear equations, involving x) and of the second degree(quadratic equatiorts, involving x2). Equations of the third degree(cubic equations, involving x3)defeated them.
Bazeia, D
2004-01-01
We investigate a system described by two real scalar fields coupled with gravity in (4, 1) dimensions in warped spacetime involving one extra dimension. The results show that the parameter which controls the way the two scalar fields interact induces the appearence of thick brane which engenders internal structure, driving the energy density to localize inside the brane in a very specific way.
Asymptotic behavior for a dissipative plate equation in $R^N$ with periodic coefficients
Directory of Open Access Journals (Sweden)
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.
Bethe-ansatz equations for quantum Heisenberg chains with elliptic exchange
Inozemtsev, V. I.
1999-01-01
The eigenvectors of the Hamiltonian ${\\cal H}_{N}$ of $N$-sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero-Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Bethe-ansatz type which is presented in explicit form.
Multiflavor bosonic Hubbard models in the first excited Bloch band of an optical lattice
International Nuclear Information System (INIS)
We propose that by exciting ultracold atoms from the zeroth to the first Bloch band in an optical lattice, multiflavor bosonic Hubbard Hamiltonians can be realized in a different way. In these systems, each flavor hops in a separate direction and on-site exchange terms allow pairwise conversion between different flavors. Using band-structure calculations, we determine the parameters entering these Hamiltonians and derive the mean-field ground-state phase diagram for two effective Hamiltonians (two dimensional, two flavors, and three dimensional, three flavors). Further, we estimate the stability of atoms in the first band using second-order perturbation theory and find lifetimes that can be considerably (10-100 times) longer than the relevant time scale associated with intersite hopping dynamics, suggesting that quasiequilibrium can be achieved in these metastable states
Effects of gamma radiations on certain tissues of heteropneustes fossils bloch
International Nuclear Information System (INIS)
In the present investigation effect of gamma radiation on certain tissues (kidney, stomach and gills) of Heteropneustes fossilis Bloch, an Indian Cat fish, were studied. The fish were irradiated with 10 Gy of gamma radiations at the dose rate of 1.60 Gy/minute from a 60Co source. Five fish were autopsied at each post-irradiation time of 1,2,3,7,15 and 30 days. Radiation induced histopathology was observed in all the tissues studied. The radio lesions appeared on day-1 after exposure which became exaggerated on day-2 and 3. Signs of recovery were noticed on day-7 which progressed on day-15 and normal histology was observed on day-30. (author). 18 refs
Bloch oscillations of ultracold atoms and measurement of the fine structure constant
International Nuclear Information System (INIS)
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)
Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC
Stirling, W. J.; Vryonidou, E.
2013-04-01
We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2 → 2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/γ+jet and also the ratio of Z to γ production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak corrections. We also comment on the effect of electroweak corrections and the presence of BN violation for QCD processes, in particular dijet production, and also for purely electroweak processes such as W + H and W + Z associated production.
Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC
Stirling, W J
2013-01-01
We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2-to-2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/photon+jet and also the ratio of Z to photon production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak corrections. We also comment on the effect of electroweak corrections and the presence of BN violation for QCD processes, in particular dijet production, and also for purely electroweak processes such as W + H and W + Z associated production.
Measuring the fine structure constant with Bragg diffraction and Bloch oscillations
Yu, Chenghui; Estey, Brian; Parker, Richard; Dudley, Jordan; Müller, Holger
2016-05-01
We have demonstrated a new scheme for atom interferometry based on large-momentum-transfer Bragg beam splitters and Bloch oscillations. In this new scheme, we have achieved a resolution of δα / α =0.25ppb in the fine structure constant measurement, which gives up to 4.4 million radians of phase difference between freely evolving matter waves. We have suppressed many systematic effects known in most atom interferometers with Raman beam splitters such as light shift, Zeeman effect shift as well as vibration. We have also simulated multi-atom Bragg diffraction to understand sub-ppb systematic effects, and implemented spatial filtering to further suppress systematic effects. We present our recent progress toward a measurement of the fine structure constant, which will provide a stringent test of the standard model of particle physics.
Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices
Graefe, E M; Rush, A
2016-01-01
Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.
Dynamics of cold bosons in optical lattices: effects of higher Bloch bands
Łącki, Mateusz; Delande, Dominique; Zakrzewski, Jakub
2013-01-01
The extended effective multiorbital Bose-Hubbard-type Hamiltonian which takes into account higher Bloch bands is discussed for boson systems in optical lattices, with emphasis on dynamical properties, in relation to current experiments. It is shown that the renormalization of Hamiltonian parameters depends on the dimension of the problem studied. Therefore, mean-field phase diagrams do not scale with the coordination number of the lattice. The effect of Hamiltonian parameters renormalization on the dynamics in reduced one-dimensional optical lattice potential is analyzed. We study both the quasi-adiabatic quench through the superfluid-Mott insulator transition and the absorption spectroscopy, that is, the energy absorption rate when the lattice depth is periodically modulated.
Sub-cycle control of terahertz high-harmonic generation by dynamical Bloch oscillations
Schubert, O; Langer, F; Urbanek, B; Lange, C; Huttner, U; Golde, D; Meier, T; Kira, M; Koch, S W; Huber, R
2016-01-01
Ultrafast charge transport in strongly biased semiconductors is at the heart of highspeed electronics, electro-optics, and fundamental solid-state physics. Intense light pulses in the terahertz (THz) spectral range have opened fascinating vistas: Since THz photon energies are far below typical electronic interband resonances, a stable electromagnetic waveform may serve as a precisely adjustable bias. Novel quantum phenomena have been anticipated for THz amplitudes reaching atomic field strengths. We exploit controlled THz waveforms with peak fields of 72 MV/cm to drive coherent interband polarization combined with dynamical Bloch oscillations in semiconducting gallium selenide. These dynamics entail the emission of phase-stable high-harmonic transients, covering the entire THz-to-visible spectral domain between 0.1 and 675 THz. Quantum interference of different ionization paths of accelerated charge carriers is controlled via the waveform of the driving field and explained by a quantum theory of inter- and in...
Directory of Open Access Journals (Sweden)
Claudiu Alexandru Baciu
2015-12-01
Full Text Available In our researches we have determined the variation of certain physiological indexes, such as the oxygen consume, the breathing rhythm, the glycaemia and the number of red blood cells under the action of Coragen insecticide on Carassius auratus gibelio Bloch. Under the action of Coragen, we have registered significant changes in the oxygen consume, the breathing rhythm, the number of red blood cells and glycemia at the Carassius auratus gibelio Bloch items, considered as answers to the stress provoked by emissions. The highest variations of the physiological indexes, from the perspective of the percentage, were noticed at the glycemia, which at the mark was 28 mg/dl, and in the treated sample, with 0.1 ml/l Coragen is 42 mg/dl, representing a 50% growth and at the breathing rhythm in 24 hours, where values significantly decreased with 41.18% at the concentration of 0.07 ml/l and with 39.33% at the concentrations of 0.05 and 0.1 ml/l Coragen. The slightest variations of the physiological indexes, from the perspective of percentage, were noticed at the oxygen consumption, which, at the mark is of 55.302 ml oxygen/kg/hour, and for the treated sample, with 0.1 ml/l Coragen is 34.81 ml oxygen/kg/hour, representing a decrease of 37.06% in 24 hours and the number of red blood cells, where the values have significantly decrease with 9.58%, 13.48%, respectively 18.44% for the concentrations of 0.05, 0.07 and 0.1 ml/l Coragen.
Origin of the Bloch-type polarization components at the 180° domain walls in ferroelectric PbTiO3
International Nuclear Information System (INIS)
Determination of atomic and electronic structures of ferroelectric domain walls is crucial to understand and explore their unusual properties. Using first-principles calculations based on the density functional theory, we explored the atomic and electronic structures of 180° domain walls in PbTiO3, in order to understand the origin of Bloch-type polarization components. It is found that Bloch-type polarization components originate from the large displacements of Pb atoms and the Pb-O hybridization at the domain walls. The development of Bloch-type polarization components significantly reduce the domain wall energies and change the Peierls barriers of domain wall motion in different orientations
Dynamics of open quantum spin systems: An assessment of the quantum master equation approach
Zhao, P; Miyashita, S; Jin, F; Michielsen, K
2016-01-01
Data of the numerical solution of the time-dependent Schr\\"odinger equation of a system containing one spin-1/2 particle interacting with a bath of up to 32 spin-1/2 particles is used to construct a Markovian quantum master equation describing the dynamics of the system spin. The procedure of obtaining this quantum master equation, which takes the form of a Bloch equation with time-independent coefficients, accounts for all non-Markovian effects in as much the general structure of the quantum master equation allows. Our simulation results show that, with a few rather exotic exceptions, the Bloch-like equation with time-independent coefficients provides a simple and accurate description of the dynamics of a spin-1/2 particle in contact with a thermal bath. A calculation of the coefficients that appear in the Redfield master equation in the Markovian limit shows that this equation yields a rather poor description of the original data.
Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation
Lindgren, I.; Salomonson, S.; Hedendahl, D.
2005-03-01
The connection between many-body perturbation theory (MBPT) and quantum electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based on the recently developed covariant-evolution-operator method for QED calculations (I. Lindgren, S. Salomonson, and B. Asen. Phys. Rep. 389, 161 (2004)), which is quite similar in structure to MBPT. At the same time, this procedure is closely related to the S-matrix and Green's-function formalisms and can therefore serve as a bridge connecting various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schrodinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. This is a multi-state equation that has the same relation to the single-state BS equation as the standard Bloch equation has to the ordinary Schrodinger equation. It can be used to generate a perturbation expansion compatible with the BS equation even in the case of a quasi-degenerate model space.
String equation from field equation
Gurovich, V T
1996-01-01
It is shown that the string equation can be obtain from field equations. Such work is performed to scalar field. The equation obtained in nonrelativistic limit describes the nonlinear string. Such string has the effective elasticity connencted with the local string curvature. Some examples of the movement such nonlinear elastic string are considered.
A semiclassical optics derivation of Einstein's rate equations
Hoeppner, Robert; Roldán, Eugenio
2011-01-01
We provide a semiclassical derivation of Einstein's rate equations (ERE) for a two-level system illuminated by a broadband light field, setting a limit for their validity that depends on the light spectral properties (namely on the height and width of its spectrum). Starting from the optical Bloch equations for individual atoms, the ensemble averaged atomic inversion is shown to follow ERE under two concurrent hypotheses: (i) the decorrelation of the inversion at a given time from the field at later times, and (ii) a Markov approximation owed to the short correlation time of the light field. The latter is then relaxed, leading to effective Bloch equations for the ensemble average in which the atomic polarization decay rate is increased by an amount equal to the width of the light spectrum, what allows its adiabatic elimination for large enough spectral width. Finally the use of a phase-diffusion model of light allows us to check all the results and hypotheses through numerical simulations of the corresponding...
Luciano Neves dos Santos; Alejandra Filippo Gonzalez; Francisco Gerson de Araújo
2001-01-01
The diet of Cichla monoculus (Bloch & Schneider, 1801) in Lajes's Reservoir, a major impoundment in Rio de Janeiro State, Brazil, was assessed, from fishes collected in 1994,1996 and 1999/2000. Gut contents in individuals was analyzed by the index of relative importance (IRI) which deals with numerical, gravimetrical and frequency of occurrence. Cichla monoculus showed a strong piscivorous habits feeding on Cichlidae, Characidae and Pimelodidae, in decreasing order of importance, with a remar...
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
International Nuclear Information System (INIS)
In this paper, a generalized variable-coefficient Hirota–Maxwell–Bloch system is investigated, which can describe the propagation of optical solitons in an erbium-doped optical fiber. Higher-step generalized Darboux transformation and rogue-wave solutions are obtained. Rogue-wave interaction is analyzed as follows: (1) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the first-step rogue waves for the modulus of the normalized slowly varying amplitude of the complex pulse envelope, modulus of the measure of the polarization of the resonant medium and extant population inversion; (2) Variable coefficients in the system affect the shape, background and number of the wave crests and troughs of the second-step rogue-wave interaction. Those phenomena can not be attained through the existing Hirota–Maxwell–Bloch system
Institute of Scientific and Technical Information of China (English)
Zhang Bing-Zhi; Cui Hu; Li Xiang-Heng; She Wei-Long
2009-01-01
We theoretically study the beam dynamical hehaviour in a modulated optical lattice with a quadratic potential in a photovoltaic photorefractive crystal. We find that two different Bloch oscillation patterns appear for the excitation of both broad and narrow light beams. One kind of optical Landau-Zener tunnelling also appears upon the Bloch oscillation and can be controlled by adjusting the parameter of the optical lattice. Unlike the case of linear potential, the energy radiation due to Landau-Zener tunnelling can be confined in modulated lattices of this kind. For high input intensity levels, the Landau-Zener tunnelling is suppressed by the photovoltaic photorefractive nonlinearity and a symmetry breaking of beam propagation from the modulational instability appears.
Directory of Open Access Journals (Sweden)
B. Prasanna Venkatesh
2015-12-01
Full Text Available In this paper we give a new description, in terms of optomechanics, of previous work on the problem of an atomic Bose–Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a bias force, such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a high-finesse optical cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice depth at the Bloch frequency which can in turn transport the atoms up or down the lattice. In the optomechanical picture, the transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the Bloch oscillator. Depending on the sign of the pump-cavity detuning, atoms are transported either with or against the bias force accompanied by an up- or down-conversion of the frequency of the pump laser light. We also evaluate the prospects for using the optomechanical Bloch oscillator to make continuous measurements of forces by reading out the Bloch frequency. In this context, we establish the significant result that the optical spring effect is absent and the Bloch frequency is not modified by the backaction.
Hartog, den, J.M.P.
1997-01-01
The genus Amphiprion Bloch & Schneider, 1801, is represented in the Seychelles by two species, A. akallopisos Bleeker, 1853, and the endemic A. fuscocaudatus Allen, 1972. Throughout its distributional range Amphiprion akallopisos has exclusively been recorded to associate with the clownfish anemones Heteractis magnifica (Quoy & Gaimard, 1833) and Stichodactyla mertensii Brandt, 1835. During the Netherlands Indian Ocean Programme (NIOP) Seychelles Expedition 19921993 this was confirmed for the...
Savoie, Baptiste
2012-01-01
Starting with a nearest-neighbors tight-binding model, we rigorously investigate the bulk zero-field orbital susceptibility of a non-interacting Bloch electrons gas in graphene-like solids at fixed temperature and density of particles. In the zero-temperature limit and in the semiconducting situation, we derive a complete expression which holds for an arbitrary number of bands with possible degeneracies. In the particular case of a two-bands gapped model, all involved quantities are exactly written down. Besides the formula we obtain have the special feature to be suitable for numerical computations since it only involves the eigenvalues and associated eigenfunctions of the Bloch Hamiltonian, together with the derivatives (up to the second order) w.r.t. the quasi-momentum of the matrix-elements of the Bloch Hamiltonian. Finally we give a simple application for the two-bands gapped model by considering the case of a dispersion law which is linear w.r.t. the quasi-momentum in the gapless limit. Through this ins...
Directory of Open Access Journals (Sweden)
Laura Ghigliotti
2015-11-01
Full Text Available The Greenland shark Somniosus microcephalus (Bloch and Schneider, 1801 is the largest predatory fish in Arctic waters. The socio-economic significance of Greenland shark is demonstrated by its impact on the fishing cultures in Greenland, Scandinavia and Iceland for centuries. The fundamental biology and ecological role of Greenland shark, on the other hand, is virtually unknown. Although knowledge of its life history is limited, increasing evidence indicates that the Greenland shark may undertake long-distance migrations and perform vertical movements from the surface to the deep sea. It is an omnivorous species feeding on carrion and a wide variety of pelagic and bottom-dwelling organisms ranging from invertebrates to mammals, and including active species such as fishes and seals. Accordingly, Greenland shark should be recognized as a top predator, with a strong potential to influence the trophic dynamics of the Arctic marine ecosystem. The sensory biology of Greenland shark is scarcely studied, and considering the importance of olfaction in chemoreception, feeding and other behavioral traits, we examined the architecture of the peripheral olfactory organ where olfactory cues are received from the environment – the olfactory rosette. The structural organization of the olfactory rosette, in terms of histological features of the sensory epithelium, number of primary lamellae and total sensory surface area, provides a first proxy of the olfactory capability of Greenland shark. Based on own results and published studies, the overall morphology of the olfactory rosette is viewed in context of the functional and trophic ecology among other elasmobranch species.
A Bloch wave analysis of optical sectioning in aberration-corrected STEM
International Nuclear Information System (INIS)
The reduction in the focal depth of field that occurs through the use of larger apertures in aberration-corrected STEM allows three-dimensional information to be retrieved by optical depth sectioning. This paper explores depth sectioning in zone-axis crystals using Bloch wave calculations. By decomposing the calculation into the contribution from individual states and from individual partial plane waves in the convergent cone of illumination, we explain the form of the electron intensity in the crystal as a function of depth. Two separate effects are found that can cause the intensity maximum to deviate from that of the expected defocus value. Firstly it is found that the unbound, high angle excited states give rise to a behaviour similar to that of the probe focusing in the vacuum, but with a prefocusing effect due to the lensing effect of the potential of the atomic column. Superimposed upon this prefocused peak is an oscillation due to interference between the channelling 1s state and the rest of the wavefunction. This oscillation can actually prevent an intensity maximum being formed at certain depths in the crystal, and will complicate the interpretation of optical sectioning data
Grating-Coupling-Based Excitation of Bloch Surface Waves for Lab-on-Fiber Nanoprobes
Scaravilli, Michele; Cusano, Andrea; Galdi, Vincenzo
2016-01-01
In this paper, we investigate for the first time the possibility to excite Bloch surface waves (BSWs) on the tip of single-mode optical fibers. Within this framework, we first demonstrate the possibility to exploit a grating-coupling mechanism for on-tip excitation of BSWs, and highlight the flexibility of the proposed design as well as its intrinsic robustness to unavoidable fabrication tolerances. Subsequently, with a view towards label-free chemical and biological sensing, we present an optimized design to maximize the sensitivity (in terms of wavelength shift) of the arising resonances with respect to changes in the refractive properties of the surrounding environment. Numerical results indicate that the attained sensitivities are in line with those exhibited by state-of-the-art plasmonic nanoprobes, with the key advantage of exhibiting much narrower spectral resonances. This prototype study paves the way for a new class of miniaturized high-performance surface-wave fiber-optic devices for high-resolution...
Establishment of a cell line from kidney of seabass, Lates calcarifer (Bloch
Directory of Open Access Journals (Sweden)
Phromkunthong, W.
2003-01-01
Full Text Available Primary cell culture from caudal fin and kidney of seabass (Lates calcarifer Bloch using tissue explant method were cultured in three different medias with various salt concentrations. Only seabass kidney (SK cells grew well in Leibovitze's-15 medium containing 8 g/l of NaCl supplemented with 10 % fetal bovine serum at an optimum temperature of 25 oC. Over a period of 24 months, SK cells were subcultured over than 75 passages and exhibited epithelial-like cells. The chromosome number of SK cells was 42. The cells were found to be free from bacterial, fungal and mycoplasma contamination. Seabass cells can be kept at -80 oC and/or in liquid nitrogen (-196 oC for at least 24 months with a survival rate of 83.20 and 74.50 %, respectively. Nine fish viruses were tested for their infectivity and this SK cells were susceptible to sand goby virus (SGV, chub reovirus (CRV, snake-head rhabdovirus (SHRV, red seabream iridovirus (RSIV, seabass iridovirus (SIV and grouper iridovirus-2 (GIV-2.
Application of Berry's phase to the effective mass of Bloch electrons
International Nuclear Information System (INIS)
Berry's phase, although well known since 1984, has received little attention among textbook authors of solid state physics. We attempt to address this lack by showing how the presence of the Berry's phase significantly changes a standard concept (effective mass) found in most solid state texts. Specifically, we show that the presence of a non-zero Berry curvature in Bloch systems makes the traditional concept of an inverse effective mass tensor M-1 problematic, since a routine application of Newton's second law leads to a circular definition. As a consequence, the related concept of cyclotron effective mass m* also requires modification. It is shown that m* is magnetic-field dependent in non-inversion symmetric systems. This has important ramifications for cyclotron resonance experiments, since such experiments yield m* and thereby purportedly give the components of M-1. This work represents a 'case study' in how Berry's phase effects can modify 'standard' solid-state topics in ways that students and instructors may find surprising.
Mass Spectrum of Fermion on Bloch Branes with New Scalar-fermion Coupling
Xie, Qun-Ying; Zhao, Zhen-Hua; Du, Yun-Zhi; Zhang, Yu-Peng
2015-01-01
In order to localize a left- or right-handed fermion zero mode on a thick brane, one usually introduces the Yukawa coupling $\\eta \\bar{\\Psi} F(\\chi) \\Psi$ between a bulk fermion and the background scalar field $\\chi$. However, the Yukawa coupling will do not work if the background scalar is an even function of the extra dimension. Recently, Ref. [Phy. Rev. \\textbf{D} 89 (2014) 086001] has presented a new scalar-fermion coupling form $\\lambda \\bar \\Psi \\Gamma^M \\partial_M F(\\chi) \\gamma^5 \\Psi$ in order to deal with this problem. In this paper, we investigate the localization and mass spectrum of fermion on the Bloch brane by using the new scalar-fermion coupling with $F(\\chi)=\\chi^n$. It is found that the effective potentials have rich structure and may be volcano-like, finite square well-like, and infinite potentials, which depend on the parameter $n$. As a result, there may appear some resonant KK fermions, finite or infinite numbers of bound KK fermions.
Effects of the projectile electronic structure on Bethe-Bloch stopping parameters for Ag
Moussa, D.; Damache, S.; Ouichaoui, S.
2010-06-01
Energy losses of protons and alpha particles in silver have been accurately measured under the same experimental conditions over the velocity range E=(0.192-2.595) MeV/amu using the transmission method. Deduced S(E) stopping powers are compared to most accurate ones from the literature, to values generated by the SRIM-2008 computer code and to ICRU-49 compilation. They were analyzed in the framework of modified Bethe-Bloch theory for extracting Ag target mean excitation and ionization potential, I, and Barkas effect parameter, b. Values of ( 466±5) eV and 1.20±0.01 for these two parameters were inferred from the proton S(E) data while the alpha particle data yielded values of (438±4) eV and 1.38±0.01, respectively. The ( I, b) stopping parameters thus exhibit opposite variations as the projectile charge increases, similarly as we have found previously for nickel [6]. This can be ascribed only to an effect of the projectile electronic structure at low velocities. The obtained results are discussed in comparison to previous ones reported in the literature.
Bloch oscillations in non-Hermitian lattices with trajectories in the complex plane
Longhi, Stefano
2015-10-01
Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.
Directory of Open Access Journals (Sweden)
Muthusamy RAJASEKAR
2012-08-01
Full Text Available Lates calcarifer (Bloch 1790 is one of the major economically important cultivable fish species in India. In this study, three populations of L. calcarifer was selected to assess the genetic diversity. Of which, two wild (Mudaslodai, Muthupettai and one captive (Mutukadu population. The genetic diversity of three populations of this species was studied using Random Amplified Polymorphic DNA (RAPD markers. Ten random primers were used for the assessment of their genetic diversity and construction of the dendrogram. A total of 589 scorable bands were obtained, 93.12% of them were polymorphic. The Nei�s gene diversity (H of two wild populations were more (0.0504 � 0.0670 and 0.0519 � 0.0953 than the captive population (0.0489 � 0.0850. The clustering pattern obtained by UPGMA method emphasized the wild populations were clustered in one clade and captive population was deviated into another clade. This study proved that RAPD analysis has the ability to discriminate L. calcarifer populations. Further molecular studies, comprising a higher number of molecular tools are still required to precisely evaluate the genetic structure of all seabass populations along the Indian coast.
Tricomi, FG
2012-01-01
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 differential
Institute of Scientific and Technical Information of China (English)
Palanivel Bharadhirajan; Natarajan Periyasamy; Sambantham Murugan
2014-01-01
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: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 results of proximate composition in M. maculata showed that the percentage of 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)
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.
Reflection of fast electrons in DPO approximation of transport equation
International Nuclear Information System (INIS)
Reflection of high energy electrons from solids is treated by the approximative analytic solution of linearized transport equation. For the scattering of electrons on target atoms determined by screened Coulomb interaction and energy loss defined by Be-the-Bloch formula, the mean number of large angle deflections of an electron before slowing down to rest has been introduced. The approach is applicable in wide range of electron energy - from several tens of keV to several MeV - and for materials where the mean number of large angle deflections is large. The isotropic approximation of collision integral is accepted and the Boltzmann equation in Laplace transformed form over relative path length is analytically treated by the ordinary DPN method. In the lowest order of approximation, we derived the expressions for energy distributions of backscattered electrons as well as particle and energy reflection coefficients. Comparison of our results with data of the computational bipartition model is presented. (author)
Venkatesh, B Prasanna; Goldwin, J
2015-01-01
We analyze the optomechanics of an atomic Bose-Einstein condensate interacting with the optical lattice inside a laser-pumped optical cavity and subject to a uniform bias force such as gravity. An atomic wave packet in a tilted lattice undergoes Bloch oscillations; in a cavity the backaction of the atoms on the light leads to a time-dependent modulation of the intracavity lattice at the Bloch frequency. When the Bloch frequency is on the order of the cavity damping rate we find transport of the atoms either up or down the lattice. The transport dynamics can be interpreted as a manifestation of dynamical backaction-induced sideband damping/amplification of the optomechanical 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...
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.
Hochstadt, Harry
2012-01-01
Modern approach to differential equations presents subject in terms of ideas and concepts rather than special cases and tricks which traditional courses emphasized. No prerequisites needed other than a good calculus course. Certain concepts from linear algebra used throughout. Problem section at end of each chapter.
Viljamaa, Panu; Jacobs, J. Richard; Chris; JamesHyman; Halma, Matthew; EricNolan; Coxon, Paul
2014-07-01
In reply to a Physics World infographic (part of which is given above) about a study showing that Euler's equation was deemed most beautiful by a group of mathematicians who had been hooked up to a functional magnetic-resonance image (fMRI) machine while viewing mathematical expressions (14 May, http://ow.ly/xHUFi).
Antes, desde y para el exilio. Herencia de esta época (1935/1962 de Ernst Bloch
Directory of Open Access Journals (Sweden)
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.
Lawrence, Felix J; Dossou, Kokou B; McPhedran, R C; de Sterke, C Martijn
2011-01-01
We present a flexible method that can calculate Bloch modes, complex band structures, and impedances of two-dimensional photonic crystals from scattering data produced by widely available numerical tools. The method generalizes previous work which relied on specialized multipole and FEM techniques underpinning transfer matrix methods. We describe the numerical technique for mode extraction, and apply it to calculate a complex band structure and to design two photonic crystal antireflection coatings. We do this for frequencies at which other methods fail, but which nevertheless are of significant practical interest.
RELACIONES TALLA-PESO DEL BARBUL (Pimelodus clarias f.c. Bloch, 1785) EN LA CUENCA DEL RIO SINU,
Iliana Santos-Sanes,; Charles Olaya-Nieto; Fredys Segura-Guevara; Samir Brú-Cordero; Glenys Tordecilla-Petro
2006-01-01
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 (�...
Bloch k-selective resonant inelastic scattering of hard X-rays from valence electrons of 3d-metals
Enkisch, Hartmut
2002-01-01
Die Form von resonant angeregen Valenz-Fluoreszenzspektren hängt sowohl vonder Energie der einfallenden Strahlung, als auch von Größe und Richtung desImpulsübertrags q ab, falls harte Röntgenstrahlen benutzt werden. DieserEffekt ist auf die elektronische Bandstruktur der Valenz- undLeitungselektronen der Probe, in Kombination mit der Energie- undImpulserhaltung des Streuprozesses zurückzuführen, woraus dieBloch-k-Impulserhaltung des resonant inelastischen Streuprozesses folgt.In dieser Arbeit...
DEFF Research Database (Denmark)
Breinbjerg, Olav; Yaghjian, Arthur D.
For an infinite 1D periodic structure with unit cells consisting of two planar slabs of magnetodielectric materials, the electric field – as well as magnetic field, electric flux density, magnetic flux density, polarization, and magnetization – can be expressed as infinite series of Floquet......-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...
International Nuclear Information System (INIS)
With the aid of symbolic computation, the coupled Hirota-Maxwell-Bloch system is investigated with third-order dispersion and higher-order nonlinear effects, which govern the nonlinear pulse propagation in an erbium-doped optical fiber medium. In addition, the Lax pair for the system is explicitly constructed and the soliton-like solutions are derived using the Darboux transformation, which makes it possible to generate the multi-soliton solutions in a recursive manner. Through the graphical analysis of some obtained analytic one- and two-soliton-like solutions, stable propagation and collision between two solitons are discussed. Furthermore, the conservation laws for the system are presented.
1998-09-21
In the late 1950s to early 1960s Rudolph A. Marcus developed a theory for treating the rates of outer-sphere electron-transfer reactions. Outer-sphere reactions are reactions in which an electron is transferred from a donor to an acceptor without any chemical bonds being made or broken. (Electron-transfer reactions in which bonds are made or broken are referred to as inner-sphere reactions.) Marcus derived several very useful expressions, one of which has come to be known as the Marcus cross-relation or, more simply, as the Marcus equation. It is widely used for correlating and predicting electron-transfer rates. For his contributions to the understanding of electron-transfer reactions, Marcus received the 1992 Nobel Prize in Chemistry. This paper discusses the development and use of the Marcus equation. Topics include self-exchange reactions; net electron-transfer reactions; Marcus cross-relation; and proton, hydride, atom and group transfers.
Directory of Open Access Journals (Sweden)
Alexander V. Baryshev
2014-12-01
Full Text Available A one-dimensional photonic crystal (PhC with termination by a metal film—a plasmonic photonic-crystal slab—has been theoretically analyzed for its optical response at a variation of the dielectric permittivity of an analyte and at a condition simulating the molecular binding event. Visualization of the Bloch surface wave resonance (SWR was done with the aid of plasmon absorption in a dielectric/metal/dielectric sandwich terminating a PhC. An SWR peak in spectra of such a plasmonic photonic crystal (PPhC slab comprising a noble or base metal layer was shown to be sensitive to a negligible variation of refractive index of a medium adjoining to the slab. As a consequence, the considered PPhC-based optical sensors exhibited an enhanced sensitivity and a good robustness in comparison with the conventional surface-plasmon and Bloch surface wave sensors. The PPhC biosensors can be of practical importance because the metal layer is protected by a capping dielectric layer from contact with analytes and, consequently, from deterioration.
Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.
2014-01-01
Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in gene...
Tricomi, Francesco Giacomo
1957-01-01
This classic text on integral equations by the late Professor F. G. Tricomi, of the Mathematics Faculty of the University of Turin, Italy, presents an authoritative, well-written treatment of the subject at the graduate or advanced undergraduate level. To render the book accessible to as wide an audience as possible, the author has kept the mathematical knowledge required on the part of the reader to a minimum; a solid foundation in differential and integral calculus, together with some knowledge of the theory of functions is sufficient. The book is divided into four chapters, with two useful
Derivation of Ray Optics Equations in Photonic Crystals Via a Semiclassical Limit
De Nittis, Giuseppe; Lein, Max
2015-01-01
In this work we present a novel approach to the ray optics limit: we rewrite the dynamical Maxwell equations in Schr\\"odinger form and prove Egorov-type theorems, a robust semiclassical technique. We implement this scheme for periodic light conductors, photonic crystals, thereby making the quantum-light analogy between semiclassics for the Bloch electron and ray optics in photonic crystals rigorous. Our main results, Theorems 3.3 and 4.1, give a ray optics limit for quadratic observables and,...
Padmanabha Chakrabarti; Saroj Kumar Ghosh
2015-01-01
The histological analysis, disposition and histochemical localization of tryptophan were investigated in the pancreas to compare the cellular organization and histochemical characterization in the pancreas of Labeo rohita (Hamilton, 1822), Mystus vittatus (Bloch, 1790) and Notopterus notopterus (Pallas, 1769) having different feeding habits. Histological analysis demonstrated that the exocrine pancreatic tissues were dispersed within the hepatic parenchyma and spleen in L. rohita. Thin septa ...
Directory of Open Access Journals (Sweden)
Luciano Neves dos Santos
2001-07-01
Full Text Available The diet of Cichla monoculus (Bloch & Schneider, 1801 in Lajes's Reservoir, a major impoundment in Rio de Janeiro State, Brazil, was assessed, from fishes collected in 1994,1996 and 1999/2000. Gut contents in individuals was analyzed by the index of relative importance (IRI which deals with numerical, gravimetrical and frequency of occurrence. Cichla monoculus showed a strong piscivorous habits feeding on Cichlidae, Characidae and Pimelodidae, in decreasing order of importance, with a remarkable cannibalism on young-of-the-year. Others minor items in the diet were Macrobrachium sp. and Odonata. Changes in feeding composition varied with reservoir's zones and seasons, with higher diversity in Autumn and peaks of cannibalism in lower zone during Spring/Summer. Overall, only one third of fish species composition in the reservoir are predated by C. monoculus. Condition factor (k and fullness index varied closely with higher values in lower zone, and lower records in Winter.
Hao, Hui-Qin; Zhang, Jian-Wen
2015-05-01
In this paper, we investigate the inhomogeneous reduced Maxwell-Bloch system, which describes the propagation of the intense ultra-short optical pulses through an inhomogeneous two-level dielectric medium. Through symbolic computation, the integrability aspects including the Painlevé integrable condition, Lax pair and infinite conservation laws are derived. By virtue of the Darboux transformation method, one- and two-soliton solutions are generated on the nonvanishing background, including the bright solitons, dark solitons, periodic solutions and some two-soliton solutions. The asymptotic analysis method is performed to verify the elastic interaction between two solitons. Furthermore, by virtue of some figures, the dynamic properties of those solitons are discussed. The results may be useful in the study of the ultrashort pulses propagation in such situations as the model of the two-level dielectric media.
Ammi, H.; Zemih, R.; Mammeri, S.; Allab, M.
2005-04-01
Recent stopping power measurements in thin polymeric films have been performed for protons of 0.4-3.5 MeV energies using the indirect transmission technique [H. Ammi, S. Mammeri, M. Chekirine, B. Bouzid, M. Allab, Nucl. Instr. and Meth. B 198 (2002) 5]. Experimental stopping data have been analyzed with the modified Bethe-Bloch formula and the mean excitation energies I have been then extracted from the data. Resulting values for each thin film are 76 ± 1 eV in Mylar, 70.8 ± 1 eV in Makrofol, 82.2 ± 1.2 eV in LR-115 and 55.4 ± 1 eV in Polypropylene. The I-extracted values are compared to those IB calculated by using the Bragg's rule.
Sych, Denis V.; Grishanin, Boris A.; Zadkov, Victor N.
2005-06-01
Possibilities of improving characteristics of quantum key distribution (QKD) protocols via variation of character set in quantum alphabets are investigated. QKD protocols with discrete alphabets letters of which form regular polyhedrons on the Bloch sphere (tetrahedron octahedron cube icosahedron and dodecahedron which have 4, 6, 8, 12, and 20 vertexes) and QKD protocol with continuous alphabet which corresponds to the limiting case of a polyhedron with infinitive number of vertexes are considered. Stability of such QKD protocols to the interceptresend and optimal eavesdropping strategies at the individual attacks is studied in detail. It is shown that in case of optimal eavesdropping strategy after safety bases reconciliation critical error rate of the QKD protocol with continuous alphabet surpasses all other protocols. Without basis reconciliation the highest critical error rate have the protocol with tetrahedron-type alphabet.
Bloch Oscillations, Zener Tunneling, and Wannier-Stark Ladders in the Time Domain
DEFF Research Database (Denmark)
Rotvig, Jon; Jauho, Antti-Pekka; Smith, Henrik
1995-01-01
We present a time-domain analysis of carrier dynamics in a semiconductor superlattice with two minibands. Integration of the density-matrix equations of motion reveals a number of new features: (i) for certain values of the applied static electric field strong interminiband transitions occur; (ii...
Complex solitary waves and soliton trains in KdV and mKdV equations
Modak, Subhrajit; Pratap Singh, Akhil; Panigrahi, Prasanta Kumar
2016-06-01
We demonstrate the existence of complex solitary wave and periodic solutions of the Korteweg-de Vries (KdV) and modified Korteweg-de Vries (mKdV) equations. The solutions of the KdV (mKdV) equation appear in complex-conjugate pairs and are even (odd) under the simultaneous actions of parity (𝓟) and time-reversal (𝓣) operations. The corresponding localized solitons are hydrodynamic analogs of Bloch soliton in magnetic system, with asymptotically vanishing intensity. The 𝓟𝓣-odd complex soliton solution is shown to be iso-spectrally connected to the fundamental sech2 solution through supersymmetry. Physically, these complex solutions are analogous to the experimentally observed grey solitons of non-liner Schödinger equation, governing the dynamics of shallow water waves and hence may also find physical verification.
Directory of Open Access Journals (Sweden)
César Roberto Goes Carqueija
1995-01-01
Full Text Available The occurence of Decapoda crustaceans in the diet of Dasyatis guttata (Bloch & Schneider, 1801 (Elasmobranchii. Dasyatididae is reported. Inferences are also made about some aspects of the predator - prey relationship in the area around the Ecological Station.
Stevo Stević
2008-01-01
We introduce an integral-type operator, denoted by PÃÂ†g, on the space of holomorphic functions on the unit ball BÃ¢ÂŠÂ‚Ã¢Â„Â‚n, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of PÃÂ†g from the weighted Bergman space AÃŽÂ±p(B) to the Bloch-type space Ã¢Â„Â¬ÃŽÂ¼(B) or the little Bloch-type space Ã¢Â„Â¬ÃŽÂ¼,0(B) is calculated. The compactness of the operator is characterized in terms of inducing functions g and ÃÂ†. Upper and lower...
Prendergast, David; Louie, Steven G.
2009-12-01
We present an efficient generalization of the k -space interpolation scheme for electronic structure presented by Shirley [Phys. Rev. B 54, 16464 (1996)]. The method permits the construction of a compact k -dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of effective single-particle electronic-structure calculations (based on density-functional theory in this work). We provide some generalizations of the initial approach which reduce the number of required initial electronic-structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone center only for large systems. We also generalize the representation of nonlocal Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. Furthermore, accurate eigenfunctions—expressed in the optimal basis—provide easy access to useful matrix elements for simulating spectroscopy and we provide details for computing optical transition amplitudes. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.
Prendergast, David; Louie, Steven G.
2010-03-01
We present an efficient generalization of the k-space interpolation scheme for electronic structure presented by E. L. Shirley, Phys. Rev. B 54, 16464 (1996), which permits the construction of a compact k-dependent Hamiltonian using a numerically optimal basis derived from a coarse-grained set of density functional theory calculations. We provide some generalizations of the initial approach which reduce the number of required initial electronic structure calculations, enabling accurate interpolation over the entire Brillouin zone based on calculations at the zone-center only for large systems. We also generalize the representation of non-local Hamiltonians, leading to a more efficient implementation which permits the use of both norm-conserving and ultrasoft pseudopotentials in the input calculations. Numerically interpolated electronic eigenvalues with accuracy that is within 0.01 eV can be produced at very little computational cost. The approach is also applicable to other theoretical frameworks such as the Dyson equation for quasiparticle excitations or the Bethe-Salpeter equation for optical responses.
Energy Technology Data Exchange (ETDEWEB)
Myrzakulov, R.; Mamyrbekova, G.K.; Nugmanova, G.N.; Yesmakhanova, K.R. [Eurasian International Center for Theoretical Physics and Department of General and Theoretical Physics, Eurasian National University, Astana 010008 (Kazakhstan); Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India)
2014-06-13
Motion of curves and surfaces in R{sup 3} lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R{sup 3} in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs.
International Nuclear Information System (INIS)
Motion of curves and surfaces in R3 lead to nonlinear evolution equations which are often integrable. They are also intimately connected to the dynamics of spin chains in the continuum limit and integrable soliton systems through geometric and gauge symmetric connections/equivalence. Here we point out the fact that a more general situation in which the curves evolve in the presence of additional self-consistent vector potentials can lead to interesting generalized spin systems with self-consistent potentials or soliton equations with self-consistent potentials. We obtain the general form of the evolution equations of underlying curves and report specific examples of generalized spin chains and soliton equations. These include principal chiral model and various Myrzakulov spin equations in (1+1) dimensions and their geometrically equivalent generalized nonlinear Schrödinger (NLS) family of equations, including Hirota–Maxwell–Bloch equations, all in the presence of self-consistent potential fields. The associated gauge equivalent Lax pairs are also presented to confirm their integrability. - Highlights: • Geometry of continuum spin chain with self-consistent potentials explored. • Mapping on moving space curves in R3 in the presence of potential fields carried out. • Equivalent generalized nonlinear Schrödinger (NLS) family of equations identified. • Integrability of identified nonlinear systems proved by deducing appropriate Lax pairs
Mohammed Safwan Ali Khan; Abdul Manan Mat Jais; Javeed Hussain; Faiza Siddiqua; Gopala Reddy, A.; P. Shivakumar; Madhuri, D.
2014-01-01
Channa striata (Bloch.) is a fresh water fish belonging to the family Channidae. The stripped snakehead fish possesses wide range of medicinal properties. In view of traditional use of C. striata for wound healing, the present study was undertaken to investigate the beneficial effects of orally administered freeze dried aqueous extract of Channa striata (AECS) in experimentally induced gastric ulcers in Wistar rats. Aspirin induced ulcerogenesis in pyloric ligation model was used for the asse...
Vankara, Anu Prasanna; Vijayalakshmi, C.
2009-01-01
A total of 9 metazoan parasitic species were identified from Mystus vittatus (Bloch) in river Godavari during 2005–2007 including 2 monogeneans, 2 digeneans, 3 acanthocephalans and 2 copepods. Two species of monogeneans (Bifurcohaptor indicus and Thaparocleidus tengra), digeneans (Haplorchoides macrones and metacercariae of Isoparorchis hypselobagri), an acanthocephalan (Raosentis podderi) found during the present study are of common occurrence in this fish. M. vittatus constitutes a new host...
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.
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)
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.
Energy Technology Data Exchange (ETDEWEB)
Barber, D.P.
2015-10-15
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.
Directory of Open Access Journals (Sweden)
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.
Walker, Christopher M.; Bankson, James A.
2015-03-01
Magnetic resonance imaging (MRI) of hyperpolarized (HP) agents has the potential to probe in-vivo metabolism with sensitivity and specificity that was not previously possible. Biological conversion of HP agents specifically for cancer has been shown to correlate to presence of disease, stage and response to therapy. For such metabolic biomarkers derived from MRI of hyperpolarized agents to be clinically impactful, they need to be validated and well characterized. However, imaging of HP substrates is distinct from conventional MRI, due to the non-renewable nature of transient HP magnetization. Moreover, due to current practical limitations in generation and evolution of hyperpolarized agents, it is not feasible to fully experimentally characterize measurement and processing strategies. In this work we use a custom Bloch-McConnell simulator with pharmacokinetic modeling to characterize the performance of specific magnetic resonance spectroscopy sequences over a range of biological conditions. We performed numerical simulations to evaluate the effect of sequence parameters over a range of chemical conversion rates. Each simulation was analyzed repeatedly with the addition of noise in order to determine the accuracy and reproducibility of measurements. Results indicate that under both closed and perfused conditions, acquisition parameters can affect measurements in a tissue dependent manner, suggesting that great care needs to be taken when designing studies involving hyperpolarized agents. More modeling studies will be needed to determine what effect sequence parameters have on more advanced acquisitions and processing methods.
Delamare-Deboutteville, J; Bowater, R; Condon, K; Reynolds, A; Fisk, A; Aviles, F; Barnes, A C
2015-12-01
Since 2007, 96 wild Queensland groupers, Epinephelus lanceolatus, (Bloch), have been found dead in NE Australia. In some cases, Streptococcus agalactiae (Group B Streptococcus, GBS) was isolated. At present, a GBS isolate from a wild grouper case was employed in experimental challenge trials in hatchery-reared Queensland grouper by different routes of exposure. Injection resulted in rapid development of clinical signs including bilateral exophthalmia, hyperaemic skin or fins and abnormal swimming. Death occurred in, and GBS was re-isolated from, 98% fish injected and was detected by PCR in brain, head kidney and spleen from all fish, regardless of challenge dose. Challenge by immersion resulted in lower morbidity with a clear dose response. Whilst infection was established via oral challenge by admixture with feed, no mortality occurred. Histology showed pathology consistent with GBS infection in organs examined from all injected fish, from fish challenged with medium and high doses by immersion, and from high-dose oral challenge. These experimental challenges demonstrated that GBS isolated from wild Queensland grouper reproduced disease in experimentally challenged fish and resulted in pathology that was consistent with that seen in wild Queensland grouper infected with S. agalactiae. PMID:25117665
Guan, Yue-Yang; Tian, Bo; Zhen, Hui-Lin; Wang, Yu-Feng; Chai, Jun
2016-03-01
In this article, the generalised nonlinear Schrödinger-Maxwell-Bloch system is investigated, which describes the propagation of the optical solitons in an optical fibre doped with two-level resonant impurities like erbium with the fourth-order dispersion taken into account. Bilinear forms are derived via the Hirota method, symbolic computation, and the auxiliary function. Bright solitons can be obtained for the complex envelope of the field and the measure of the polarisation for the resonant medium, while the dark ones have been deduced for the extant population inversion. Propagation of the one and two solitons is analysed with the results that the solitons keep their shapes unchanged after the interaction, except for the phase shifts, which means that the interaction is elastic. Velocities of the solitons decrease when the effect of discreteness and higher-order dispersion increases. For the bound-state solitons, which can be formed among the solitons at the same velocity, the period decreases when the effect of discreteness and higher-order dispersion increases.
Higher Order Radial Derivatives of Bloch Type Functions%Bloch型函数的高阶径向导数
Institute of Scientific and Technical Information of China (English)
卓文新
2002-01-01
讨论了复超球上全纯函数的高阶导数的增长速度,证明了f∈Bα的充分必要条件是supa∈B(1-|z|2)m+α-1|Rmf(z)|＜∞,或supa∈B∫B(1-|z|2)(m+α-1)|Rmf(z)|pJRφα(z)dv(z)＜∞,或(1-|z|2)p(m+α-1)|Rmf(z)|pdv(z)是Bergman-Carleson测度.%In this paper, higher order radial derivatives of Bloch type functions in the unit ball of Cn is discussed and it is proved that for f∈H(B), f∈Bα if and only if supα∈B(1-|z|2)m+α-1|Rmf(z)|＜∞, if and only if supa∈B∫B(1-|z|2)P(m+α-1)|Rmf(z)|PJRφα(z)dv(z)＜∞, if and only if (1-|z|2)P(m+α-1)|Rmf(z)|Pdv(z) is a Bergman-Carleson measure.
International Nuclear Information System (INIS)
Recent measurements of the stopping powers of polysulfone for 0.66-1.74 MeV protons and 1.04-3.20 MeV alpha particles have been analyzed in terms of the modified Bethe-Bloch theory in order to extract values of the parameters characterizing the formalism utilized. Resulting values of mean excitation energy (I) and Barkas-effect parameter (b), respectively, were 83.3 eV and 1.05 for proton data, and 81.1 eV and 1.38 for alpha particle data. The lower energy alpha particle data were included by employing a single effective charge parameter (λ) evaluated at 1.63. The composite weighted value of mean excitation energy, 82.9 eV, lies some 6% above the additivity-based estimate, whereas the corresponding value of Barkas-effect parameter, 1.22, agrees quite well with the prescribed interval of 1.4±0.1
Directory of Open Access Journals (Sweden)
Bogdan Mihai Udroiu
2015-12-01
Full Text Available The main objective of this study is to see how the metylthiophanate fungicide influences the energetic metabolism and the breathing rhythm at Carassius auratus gibelio Bloch L. 1758. Experimental samples were subjected to under-lethal concentrations of 3.75mg/l, 7.5mg/l, 15mg/l and 30mg/l methyl-thiophanate fungicide from 24 to 336 hours. The physiologic parameter with the highest growth rate was the oxygen consumption, which, at the concentration of 7.5mg/l grew by 40.3% in 6 hours, compared to the witness values, registering the value of 179.52 mg oxygen/l/h compared to 127.95 mg oxygen/l/h. Also, the breathing rhythm grew at the concentration of 7.5 mg/l by 24.76% in 6 hours, compared to the witness values. At the concentration of 30mg/l, both physiologic parameters decreased. So, after 6 hours, the oxygen consumption decrease up to 31.38% from the witness values, registering the value of 51.503mg oxygen/l/h compared to 164.09mg oxygen/l/h, and the breathing rhythm decreased to 84.3% compared to the witness martor.
Frazier, Michael J.; Hussein, Mahmoud I.
2016-05-01
It is common for dispersion curves of damped periodic materials to be based on real frequencies as a function of complex wavenumbers or, conversely, real wavenumbers as a function of complex frequencies. The former condition corresponds to harmonic wave motion where a driving frequency is prescribed and where attenuation due to dissipation takes place only in space alongside spatial attenuation due to Bragg scattering. The latter condition, on the other hand, relates to free wave motion admitting attenuation due to energy loss only in time while spatial attenuation due to Bragg scattering also takes place. Here, we develop an algorithm for 1D systems that provides dispersion curves for damped free wave motion based on frequencies and wavenumbers that are permitted to be simultaneously complex. This represents a generalized application of Bloch's theorem and produces a dispersion band structure that fully describes all attenuation mechanisms, in space and in time. The algorithm is applied to a viscously damped mass-in-mass metamaterial exhibiting local resonance. A frequency-dependent effective mass for this damped infinite chain is also obtained. xml:lang="fr"
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.
Random diophantine equations, I
Brüdern, Jörg; Dietmann, Rainer
2012-01-01
We consider additive diophantine equations of degree $k$ in $s$ variables and establish that whenever $s\\ge 3k+2$ then almost all such equations satisfy the Hasse principle. The equations that are soluble form a set of positive density, and among the soluble ones almost all equations admit a small solution. Our bound for the smallest solution is nearly best possible.
The Generalized Jacobi Equation
Chicone, C.; Mashhoon, B.
2002-01-01
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighboring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analyzed in this paper. The tidal accelerat...
Spectral validation of the Whitham equations for periodic waves of lattice dynamical systems
Kabil, Buğra; Rodrigues, L. Miguel
2016-02-01
In the present contribution we investigate some features of dynamical lattice systems near periodic traveling waves. First, following the formal averaging method of Whitham, we derive modulation systems expected to drive at main order the time evolution of slowly modulated wavetrains. Then, for waves whose period is commensurable to the lattice, we prove that the formally-derived first-order averaged system must be at least weakly hyperbolic if the background waves are to be spectrally stable, and, when weak hyperbolicity is met, the characteristic velocities of the modulation system provide group velocities of the original system. Historically, for dynamical evolutions obeying partial differential equations, this has been proved, according to increasing level of algebraic complexity, first for systems of reaction-diffusion type, then for generic systems of balance laws, at last for Hamiltonian systems. Here, for their semi-discrete counterparts, we give at once simultaneous proofs for all these cases. Our main analytical tool is the discrete Bloch transform, a discrete analogue to the continuous Bloch transform. Nevertheless, we needed to overcome the absence of genuine space-translation invariance, a key ingredient of continuous analyses.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
EvangelosChaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similar fashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is done by replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vector potential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vector analysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHD equations.
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...
方波电场驱动下的Rabi振荡%Rabi Oscillations Between Bloch Bands in a Square-wave Electric Field
Institute of Scientific and Technical Information of China (English)
宫建平; 邵建立; 段素青; 赵宪庚
2006-01-01
We investigate double Bloch bands driven by a square-wave electric field with a tight-binding model. Using Fourier analysis, we analytically obtain resonance conditions of Rabi oscillation and Rabi frequency in the weak-coupling limit. The results are verified by numerical evolution of electrons.%研究了方波电场驱动下的双Bloch带的紧束缚模型.借助Fourier分析,得到了在弱耦合极限下Rabi振荡及Rabi频率的解析解;这些结果均由电子的数值演化所证实.
Vankara, Anu Prasanna; Vijayalakshmi, C
2009-12-01
A total of 9 metazoan parasitic species were identified from Mystus vittatus (Bloch) in river Godavari during 2005-2007 including 2 monogeneans, 2 digeneans, 3 acanthocephalans and 2 copepods. Two species of monogeneans (Bifurcohaptor indicus and Thaparocleidus tengra), digeneans (Haplorchoides macrones and metacercariae of Isoparorchis hypselobagri), an acanthocephalan (Raosentis podderi) found during the present study are of common occurrence in this fish. M. vittatus constitutes a new host record for an acanthocephalan, Raosentis thapari and 2 copepods, Argulus striatus and Lamproglena hospetensis. The occurrence of A. striatus represents unusual for M. vittatus. A new species of acanthocephala, Raosentis godavarensis sp. nov is reported, described and illustrated. PMID:23129893
Robillart, B.; Maynard, G.; Cros, B.; Boudaa, A.; Dubau, J.; Sebban, S.; Goddet, JP.
It has been recently demonstrated experimentally that seeding a high-harmonic pulse into an Optical-Field-Ionized gas can generate a coherent soft x-ray laser beam of up to 1üJ. In order to analyze the physical processes involved in the amplification of the x-ray laser pulse through the plasma amplifier a 3D numerical code named COFIXE_MB has been developed using a Maxwell-Bloch treatment. It brings detailed information about the x-ray pulse evolution, especially regarding the fast evolution of the pulse temporal profile and the spatial filtering of the wave front structure by the amplifier.
Indian Academy of Sciences (India)
George F R Ellis
2007-07-01
The Raychaudhuri equation is central to the understanding of gravitational attraction in astrophysics and cosmology, and in particular underlies the famous singularity theorems of general relativity theory. This paper reviews the derivation of the equation, and its significance in cosmology.
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
Ray C. Fair
2007-01-01
How inflation and unemployment are related in both the short run and long run is perhaps the key question in macroeconomics. This paper tests various price equations using quarterly U.S. data from 1952 to the present. Issues treated are the following. 1) Estimating price and wage equations in which wages affect prices and vice versa versus estimating "reduced form" price equations with no wage explanatory variables. 2) Estimating price equations in (log) level terms, first difference (i.e., i...
New unified evolution equation
Lim, Jyh-Liong; Li, Hsiang-nan
1998-01-01
We propose a new unified evolution equation for parton distribution functions appropriate for both large and small Bjorken variables $x$, which is an improved version of the Ciafaloni-Catani-Fiorani-Marchesini equation. In this new equation the cancellation of soft divergences between virtual and real gluon emissions is explicit without introducing infrared cutoffs, next-to-leading contributions to the Sudakov resummation can be included systematically. It is shown that the new equation reduc...
Goncalves, Patricia
2010-01-01
We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states are given by energy solutions of the KPZ equation. As a consequence, we prove that the Cole-Hofp solutions are also energy solutions of the KPZ equation.
Diophantine equations and identities
Directory of Open Access Journals (Sweden)
Malvina Baica
1985-01-01
Full Text Available The general diophantine equations of the second and third degree are far from being totally solved. The equations considered in this paper are i x2−my2=±1 ii x3+my3+m2z3−3mxyz=1iii Some fifth degree diopantine equations
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.
The Modified Magnetohydrodynamical Equations
Institute of Scientific and Technical Information of China (English)
Evangelos Chaliasos
2003-01-01
After finding the really self-consistent electromagnetic equations for a plasma, we proceed in a similarfashion to find how the magnetohydrodynamical equations have to be modified accordingly. Substantially this is doneby replacing the "Lorentz" force equation by the correct (in our case) force equation. Formally we have to use the vectorpotential instead of the magnetic field intensity. The appearance of the formulae presented is the one of classical vectoranalysis. We thus find a set of eight equations in eight unknowns, as previously known concerning the traditional MHDequations.
International Nuclear Information System (INIS)
It is possible to determine the h/mRb 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*10-9), 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 α-1 is 137.03599887(65). It is the best determination of alpha, independent from quantum electrodynamics
International Nuclear Information System (INIS)
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))=(A0(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.
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.
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.
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...
Fundamental Equation of Economics
Wayne, James J.
2013-01-01
Recent experience of the great recession of 2008 has renewed one of the oldest debates in economics: whether economics could ever become a scientific discipline like physics. This paper proves that economics is truly a branch of physics by establishing for the first time a fundamental equation of economics (FEOE), which is similar to many fundamental equations governing other subfields of physics, for example, Maxwell’s Equations for electromagnetism. From recently established physics laws of...
Solving Ordinary Differential Equations
Krogh, F. T.
1987-01-01
Initial-value ordinary differential equation solution via variable order Adams method (SIVA/DIVA) package is collection of subroutines for solution of nonstiff ordinary differential equations. There are versions for single-precision and double-precision arithmetic. Requires fewer evaluations of derivatives than other variable-order Adams predictor/ corrector methods. Option for direct integration of second-order equations makes integration of trajectory problems significantly more efficient. Written in FORTRAN 77.
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.
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.
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 eleven classes of vector-potentials of the electro-magnetic field A(t,x) 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...
International Nuclear Information System (INIS)
A new evolution equation is proposed for the gluon density relevant (GLR) for the region of small xB. It generalizes the GLR equation and allows deeper penetration in dense parton systems than the GLR equation does. This generalization consists of taking shadowing effects more comprehensively into account by including multi gluon correlations, and allowing for an arbitrary initial gluon distribution in a hadron. We solve the new equation for fixed αs. It is found that the effects of multi gluon correlations on the deep-inelastic structure function are small. (author) 15 refs, 5 figs, 2 tabs
Linear Equations: Equivalence = Success
Baratta, Wendy
2011-01-01
The ability to solve linear equations sets students up for success in many areas of mathematics and other disciplines requiring formula manipulations. There are many reasons why solving linear equations is a challenging skill for students to master. One major barrier for students is the inability to interpret the equals sign as anything other than…
Wetterich, C
2016-01-01
We propose a gauge invariant flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations, corresponding to a particular gauge fixing. The freedom in the precise choice of the macroscopic field can be exploited in order to keep the flow equation simple.
Ramirez, Erandy; Liddle, Andrew
2004-01-01
We generalize the flow equations approach to inflationary model building to the Randall–Sundrum Type II braneworld scenario. As the flow equations are quite insensitive to the expansion dynamics, we find results similar to, though not identical to, those found in the standard cosmology.
Zahari, N. M.; Sapar, S. H.; Mohd Atan, K. A.
2013-04-01
This paper discusses an integral solution (a, b, c) of the Diophantine equations x3n+y3n = 2z2n for n ≥ 2 and it is found that the integral solution of these equation are of the form a = b = t2, c = t3 for any integers t.
Some classical Diophantine equations
Directory of Open Access Journals (Sweden)
Nikita Bokarev
2014-09-01
Full Text Available An attempt to find common solutions complete some Diophantine equations of the second degree with three variables, traced some patterns, suggest a common approach, which being elementary, however, lead to a solution of such equations. Using arithmetic functions allowed to write down the solutions in a single formula with no restrictions on the parameters used.
Applied singular integral equations
Mandal, B N
2011-01-01
The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.
Alternative equations of gravitation
International Nuclear Information System (INIS)
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.)
International Nuclear Information System (INIS)
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
The relativistic Pauli equation
Delphenich, David
2012-01-01
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charged spinning particle in an external electromagnetic field then implies a second order equation in the matrix-valued wave functions that is of Klein-Gordon type and represents the relativistic analogue of the Pauli equation. We conclude by presenting the Lagrangian form for the relativistic Pauli equation.
The generalized Jacobi equation
International Nuclear Information System (INIS)
The Jacobi equation in pseudo-Riemannian geometry determines the linearized geodesic flow. The linearization ignores the relative velocity of the geodesics. The generalized Jacobi equation takes the relative velocity into account; that is, when the geodesics are neighbouring but their relative velocity is arbitrary the corresponding geodesic deviation equation is the generalized Jacobi equation. The Hamiltonian structure of this nonlinear equation is analysed in this paper. The tidal accelerations for test particles in the field of a plane gravitational wave and the exterior field of a rotating mass are investigated. In the latter case, the existence of an attractor of uniform relative radial motion with speed 2-1/2c ∼ 0.7c is pointed out. The astrophysical implication of this result for the terminal speed of a relativistic jet is briefly explored
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...
International Nuclear Information System (INIS)
The direct use of enlarged subsets of mathematically exact equations of change in moments of the velocity distribution function, each equation corresponding to one of the macroscopic variables to be retained, produces extended MHD models. The first relevant level of closure provides 'ten moment' equations in the density ρ, velocity v, scalar pressure p, and the traceless component of the pressure tensor t. The next 'thirteen moment' level also includes the thermal flux vector q, and further extended MHD models could be developed by including even higher level basic equations of change. Explicit invariant forms for the tensor t and the heat flux vector defining q follow from their respective basic equations of change. Except in the neighbourhood of a magnetic null, in magnetised plasma these forms may be resolved into known sums of their parallel, cross (or transverse) and perpendicular components. Parallel viscosity in an electron-ion plasma is specifically discussed. (author)
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.
Zeitoun, Philippe; Oliva, Eduardo; Fajardo, Marta; Ros, David; Sebban, Stéphane; Velarde, Pedro
2011-12-01
Seeding plasma-based soft x-ray laser (SXRL) demonstrated diffraction-limited, fully coherent in space and in time beam but with energy not exceeding 1 μJ per pulse. Quasi-steady-state (QSS) plasmas demonstrated to be able to store high amount of energy and then amplify incoherent SXRL up to several mJ. Using 1D time-dependant Bloch-Maxwell model including amplification of noise, we demonstrated that femtosecond HHG cannot be efficiently amplified in QSS plasmas. However, using Chirped Pulse Amplification concept on HHG seed allows to extract most of the stored energy, reaching up to 5 mJ in fully coherent pulses that can be compressed down to 130 fs.
Nonlinear gyrokinetic equations
International Nuclear Information System (INIS)
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed
Nonlinear gyrokinetic equations
Energy Technology Data Exchange (ETDEWEB)
Dubin, D.H.E.; Krommes, J.A.; Oberman, C.; Lee, W.W.
1983-03-01
Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, we emphasize the limit of electrostatic fluctuations in slab geometry; however, there is a straight-forward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and various of its limits are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev is derived from an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry-Horton and Hasegawa-Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed.
Standardized Referente Evapotranspiration Equation
M.D. Mundo–Molina
2009-01-01
In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude) it was selected tomake comparisons. The compared equations we re: a) CIANO weat her station, b) Penman–Monteith ASCE (PMA), Penman–Monteith FAO 56 (PM FAO 56), Penman–Monteith estan...
Stochastic Schroedinger equations
International Nuclear Information System (INIS)
A derivation of Belavkin's stochastic Schroedinger equations is given using quantum filtering theory. We study an open system in contact with its environment, the electromagnetic field. Continuous observation of the field yields information on the system: it is possible to keep track in real time of the best estimate of the system's quantum state given the observations made. This estimate satisfies a stochastic Schroedinger equation, which can be derived from the quantum stochastic differential equation for the interaction picture evolution of system and field together. Throughout the paper we focus on the basic example of resonance fluorescence
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
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.
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
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
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
Modern introduction to differential equations
Ricardo, Henry J
2009-01-01
A Modern Introduction to Differential Equations, Second Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical, and numerical aspects of first-order equations, including slope fields and phase lines. The discussions then cover methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients; systems of linear differential equations; the Laplace transform and its applications to the solution of differential equat
A Comparison of IRT Equating and Beta 4 Equating.
Kim, Dong-In; Brennan, Robert; Kolen, Michael
Four equating methods were compared using four equating criteria: first-order equity (FOE), second-order equity (SOE), conditional mean squared error (CMSE) difference, and the equipercentile equating property. The four methods were: (1) three parameter logistic (3PL) model true score equating; (2) 3PL observed score equating; (3) beta 4 true…
Nonlinear differential equations
International Nuclear Information System (INIS)
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
Garkavenko A. S.
2011-01-01
The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
Tsintsadze, Nodar L.; Tsintsadze, Levan N.
2008-01-01
A general derivation of the charging equation of a dust grain is presented, and indicated where and when it can be used. A problem of linear fluctuations of charges on the surface of the dust grain is discussed.
Diophantine Equations and Computation
Davis, Martin
Unless otherwise stated, we’ll work with the natural numbers: N = \\{0,1,2,3, dots\\}. Consider a Diophantine equation F(a1,a2,...,an,x1,x2,...,xm) = 0 with parameters a1,a2,...,an and unknowns x1,x2,...,xm For such a given equation, it is usual to ask: For which values of the parameters does the equation have a solution in the unknowns? In other words, find the set: \\{ mid exists x_1,ldots,x_m [F(a_1,ldots,x_1,ldots)=0] \\} Inverting this, we think of the equation F = 0 furnishing a definition of this set, and we distinguish three classes: a set is called Diophantine if it has such a definition in which F is a polynomial with integer coefficients. We write \\cal D for the class of Diophantine sets.
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...
Hedin Equations for Superconductors
Linscheid, A.; Essenberger, F.
2015-01-01
We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of s...
Resistive ballooning mode equation
Energy Technology Data Exchange (ETDEWEB)
Bateman, G.; Nelson, D. B.
1978-10-01
A second-order ordinary differential equation on each flux surface is derived for the high mode number limit of resistive MHD ballooning modes in tokamaks with arbitrary cross section, aspect ratio, and shear. The equation is structurally similar to that used to study ideal MHD ballooning modes computationally. The model used in this paper indicates that all tokamak plasmas are unstable, with growth rate proportional to resistivity when the pressure gradient is less than the critical value needed for ideal MHD stability.
Relativistic Guiding Center Equations
Energy Technology Data Exchange (ETDEWEB)
White, R. B. [PPPL; Gobbin, M. [Euratom-ENEA Association
2014-10-01
In toroidal fusion devices it is relatively easy that electrons achieve relativistic velocities, so to simulate runaway electrons and other high energy phenomena a nonrelativistic guiding center formalism is not sufficient. Relativistic guiding center equations including flute mode time dependent field perturbations are derived. The same variables as used in a previous nonrelativistic guiding center code are adopted, so that a straightforward modifications of those equations can produce a relativistic version.
SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER
Collier, D.M.; Meeks, L.A.; Palmer, J.P.
1960-05-10
A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.
Functional Equations and Fourier Analysis
Yang, Dilian
2010-01-01
By exploring the relations among functional equations, harmonic analysis and representation theory, we give a unified and very accessible approach to solve three important functional equations -- the d'Alembert equation, the Wilson equation, and the d'Alembert long equation, on compact groups.
Scaling Equation for Invariant Measure
Institute of Scientific and Technical Information of China (English)
LIU Shi-Kuo; FU Zun-Tao; LIU Shi-Da; REN Kui
2003-01-01
An iterated function system (IFS) is constructed. It is shown that the invariant measure of IFS satisfies the same equation as scaling equation for wavelet transform (WT). Obviously, IFS and scaling equation of WT both have contraction mapping principle.
Integral equations and computation problems
International Nuclear Information System (INIS)
Volterra's Integral Equations and Fredholm's Integral Equations of the second kind are discussed. Computational problems are found in the derivations and the computations. The theorem of the solution of the Fredholm's Integral Equation is discussed in detail. (author)
Transport equation solving methods
International Nuclear Information System (INIS)
This work is mainly devoted to Csub(N) and Fsub(N) methods. CN method: starting from a lemma stated by Placzek, an equivalence is established between two problems: the first one is defined in a finite medium bounded by a surface S, the second one is defined in the whole space. In the first problem the angular flux on the surface S is shown to be the solution of an integral equation. This equation is solved by Galerkin's method. The Csub(N) method is applied here to one-velocity problems: in plane geometry, slab albedo and transmission with Rayleigh scattering, calculation of the extrapolation length; in cylindrical geometry, albedo and extrapolation length calculation with linear scattering. Fsub(N) method: the basic integral transport equation of the Csub(N) method is integrated on Case's elementary distributions; another integral transport equation is obtained: this equation is solved by a collocation method. The plane problems solved by the Csub(N) method are also solved by the Fsub(N) method. The Fsub(N) method is extended to any polynomial scattering law. Some simple spherical problems are also studied. Chandrasekhar's method, collision probability method, Case's method are presented for comparison with Csub(N) and Fsub(N) methods. This comparison shows the respective advantages of the two methods: a) fast convergence and possible extension to various geometries for Csub(N) method; b) easy calculations and easy extension to polynomial scattering for Fsub(N) method
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.
Unified derivation of evolution equations
Li, Hsiang-nan
1998-01-01
We derive the evolution equations of parton distribution functions appropriate in different kinematic regions in a unified and simple way using the resummation technique. They include the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi equation for large momentum transfer $Q$, the Balitskii-Fadin-Kuraev-Lipatov equation for a small Bjorken variable $x$, and the Ciafaloni-Catani-Fiorani-Marchesini equation which embodies the above two equations. The relation among these equations is explored, and p...
The Equations of Magnetoquasigeostrophy
Umurhan, O M
2013-01-01
The dynamics contained in magnetized layers of exoplanet atmospheres are important to understand in order to characterize what observational signatures they may provide for future observations. It is important to develop a framework to begin studying and learning the physical processes possible under those conditions and what, if any, features contained in them may be observed in future observation missions. The aims of this study is to formally derive, from scaling arguments, a manageable reduced set of equations for analysis, i.e. a magnetic formulation of the equations of quasigeostrophy appropriate for a multi-layer atmosphere. The main goal is to provide a simpler theoretical platform to explore the dynamics possible within confined magnetized layers of exoplanet atmospheres. We primarily use scaling arguments to derive the reduced equations of "magnetoquasigeostrophy" which assumes dynamics to take place in an atmospheric layer which is vertically thin compared to its horizontal scales. The derived equa...
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...
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.
Steyerl, A; Müller, G; Malik, S S; Desai, A M; Golub, R
2014-01-01
Pendlebury $\\textit{et al.}$ [Phys. Rev. A $\\textbf{70}$, 032102 (2004)] were the first to investigate the role of geometric phases in searches for an electric dipole moment of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schr\\"odinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.
Steyerl, A.; Kaufman, C.; Müller, G.; Malik, S. S.; Desai, A. M.; Golub, R.
2014-05-01
Pendlebury etal . [Phys. Rev. A 70, 032102 (2004), 10.1103/PhysRevA.70.032102] were the first to investigate the role of geometric phases in searches for an electric dipole moment (EDM) of elementary particles based on Ramsey-separated oscillatory field magnetic resonance with trapped ultracold neutrons and comagnetometer atoms. Their work was based on the Bloch equation and later work using the density matrix corroborated the results and extended the scope to describe the dynamics of spins in general fields and in bounded geometries. We solve the Schrödinger equation directly for cylindrical trap geometry and obtain a full description of EDM-relevant spin behavior in general fields, including the short-time transients and vertical spin oscillation in the entire range of particle velocities. We apply this method to general macroscopic fields and to the field of a microscopic magnetic dipole.
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
Mirce Functionability Equation
Directory of Open Access Journals (Sweden)
Dr Jezdimir Knezevic
2014-08-01
Full Text Available Scientific principles and concepts expressed through the laws, equations and formulas are the bedrock for the prediction of the deign-in functionality performance of any engineering creation. However, there is no equivalent when the in-service functionability performance predictions have to be made. Hence, Mirce Mechanics has been created at the MIRCE Akademy to fulfil the roll. The main purpose of this paper is to present the development and application of Mirce Functionability Equation which is the bedrock for the prediction of the functionability performance of maintainable systems.
Obtaining Maxwell's equations heuristically
Diener, Gerhard; Weissbarth, Jürgen; Grossmann, Frank; Schmidt, Rüdiger
2013-02-01
Starting from the experimental fact that a moving charge experiences the Lorentz force and applying the fundamental principles of simplicity (first order derivatives only) and linearity (superposition principle), we show that the structure of the microscopic Maxwell equations for the electromagnetic fields can be deduced heuristically by using the transformation properties of the fields under space inversion and time reversal. Using the experimental facts of charge conservation and that electromagnetic waves propagate with the speed of light, together with Galilean invariance of the Lorentz force, allows us to finalize Maxwell's equations and to introduce arbitrary electrodynamics units naturally.
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
Institute of Scientific and Technical Information of China (English)
Ding Yi
2009-01-01
In this article, the author derives a functional equation η(s)=［(π/4)s-1/2√2/πг(1-s)sin(πs/2)]η(1-s) of the analytic function η(s) which is defined by η(s)=1-s-3-s-5-s+7-s…for complex variable s with Re s>1, and is defined by analytic continuation for other values of s. The author proves (1) by Ramanujan identity (see [1], [3]). Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.
Markley, F. Landis
1995-01-01
Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 10(exp 18), exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.
Amorim, R G G; Silva, Edilberto O
2015-01-01
Symplectic unitary representations for the Poincar\\'{e} group are studied. The formalism is based on the noncommutative structure of the star-product, and using group theory approach as a guide, a consistent physical theory in phase space is constructed. The state of a quantum mechanics system is described by a quasi-probability amplitude that is in association with the Wigner function. As a result, the Klein-Gordon and Dirac equations are derived in phase space. As an application, we study the Dirac equation with electromagnetic interaction in phase space.
The relativistic Pauli equation
Delphenich, David
2012-01-01
After discussing the way that C2 and the algebra of complex 2x2 matrices can be used for the representation of both non-relativistic rotations and Lorentz transformations, we show that Dirac bispinors can be more advantageously represented as 2x2 complex matrices. One can then give the Dirac equation a form for such matrix-valued wave functions that no longer necessitates the introduction of gamma matrices or a choice for their representation. The minimally-coupled Dirac equation for a charge...
Cira, Octavian; Smarandache, Florentin
2016-01-01
In this book a multitude of Diophantine equations and their partial or complete solutions are presented. How should we solve, for example, the equation {\\eta}({\\pi}(x)) = {\\pi}({\\eta}(x)), where {\\eta} is the Smarandache function and {\\pi} is Riemann function of counting the number of primes up to x, in the set of natural numbers? If an analytical method is not available, an idea would be to recall the empirical search for solutions. We establish a domain of searching for the solutions and th...
The Statistical Drake Equation
Maccone, Claudio
2010-12-01
We provide the statistical generalization of the Drake equation. From a simple product of seven positive numbers, the Drake equation is now turned into the product of seven positive random variables. We call this "the Statistical Drake Equation". The mathematical consequences of this transformation are then derived. The proof of our results is based on the Central Limit Theorem (CLT) of Statistics. In loose terms, the CLT states that the sum of any number of independent random variables, each of which may be ARBITRARILY distributed, approaches a Gaussian (i.e. normal) random variable. This is called the Lyapunov Form of the CLT, or the Lindeberg Form of the CLT, depending on the mathematical constraints assumed on the third moments of the various probability distributions. In conclusion, we show that: The new random variable N, yielding the number of communicating civilizations in the Galaxy, follows the LOGNORMAL distribution. Then, as a consequence, the mean value of this lognormal distribution is the ordinary N in the Drake equation. The standard deviation, mode, and all the moments of this lognormal N are also found. The seven factors in the ordinary Drake equation now become seven positive random variables. The probability distribution of each random variable may be ARBITRARY. The CLT in the so-called Lyapunov or Lindeberg forms (that both do not assume the factors to be identically distributed) allows for that. In other words, the CLT "translates" into our statistical Drake equation by allowing an arbitrary probability distribution for each factor. This is both physically realistic and practically very useful, of course. An application of our statistical Drake equation then follows. The (average) DISTANCE between any two neighboring and communicating civilizations in the Galaxy may be shown to be inversely proportional to the cubic root of N. Then, in our approach, this distance becomes a new random variable. We derive the relevant probability density
Comparison of Kernel Equating and Item Response Theory Equating Methods
Meng, Yu
2012-01-01
The kernel method of test equating is a unified approach to test equating with some advantages over traditional equating methods. Therefore, it is important to evaluate in a comprehensive way the usefulness and appropriateness of the Kernel equating (KE) method, as well as its advantages and disadvantages compared with several popular item…
On difference Riccati equations and second order linear difference equations
Ishizaki, Katsuya
2011-01-01
In this paper, we treat difference Riccati equations and second order linear difference equations in the complex plane. We give surveys of basic properties of these equations which are analogues in the differential case. We are concerned with the growth and value distributions of transcendental meromorphic solutions of these equations. Some examples are given.
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...
Variation principle of piezothermoelastic bodies, canonical equation and homogeneous equation
Institute of Scientific and Technical Information of China (English)
LIU Yan-hong; ZHANG Hui-ming
2007-01-01
Combining the symplectic variations theory, the homogeneous control equation and isoparametric element homogeneous formulations for piezothermoelastic hybrid laminates problems were deduced. Firstly, based on the generalized Hamilton variation principle, the non-homogeneous Hamilton canonical equation for piezothermoelastic bodies was derived. Then the symplectic relationship of variations in the thermal equilibrium formulations and gradient equations was considered, and the non-homogeneous canonical equation was transformed to homogeneous control equation for solving independently the coupling problem of piezothermoelastic bodies by the incensement of dimensions of the canonical equation. For the convenience of deriving Hamilton isoparametric element formulations with four nodes, one can consider the temperature gradient equation as constitutive relation and reconstruct new variation principle. The homogeneous equation simplifies greatly the solution programs which are often performed to solve nonhomogeneous equation and second order differential equation on the thermal equilibrium and gradient relationship.
Standardized Referente Evapotranspiration Equation
Directory of Open Access Journals (Sweden)
M.D. Mundo–Molina
2009-04-01
Full Text Available In this paper is presented a discussion on the necessity to standardize the Penman–Monteith equations in order to estimate ETo. The proposal is to define an accuracy and standarize equation based in Penman–Monteith. The automated weather station named CIANO (27° 22 ' 144 North latitude and 109" 55' west longitude it was selected tomake comparisons. The compared equations we re: a CIANO weat her station, b Penman–Monteith ASCE (PMA, Penman–Monteith FAO 56 (PM FAO 56, Penman–Monteith estandarizado ASCE (PM Std. ASCE. The results were: a There are important differences between PMA and CIANO weather station. The differences are attributed to the nonstandardization of the equation CIANO weather station, b The coefficient of correlation between both methods was of 0,92, with a standard deviation of 1,63 mm, an average quadratic error of 0,60 mm and one efficiency in the estimation of ETo with respect to the method pattern of 87%.
Calculus & ordinary differential equations
Pearson, David
1995-01-01
Professor Pearson's book starts with an introduction to the area and an explanation of the most commonly used functions. It then moves on through differentiation, special functions, derivatives, integrals and onto full differential equations. As with other books in the series the emphasis is on using worked examples and tutorial-based problem solving to gain the confidence of students.
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...
Chi, Do Minh
1999-01-01
We research the natural causality of the Universe. We find that the equation of causality provides very good results on physics. That is our first endeavour and success in describing a quantitative expression of the law of causality. Hence, our theoretical point suggests ideas to build other laws including the law of the Universe's evolution.
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
On rough differential equations
Lejay, Antoine
2009-01-01
We prove that the Ito map, that is the map that gives the solution of a differential equation controlled by a rough path of finite p-variation with p in [2,3) is locally Lipschitz continuous in all its arguments and could be extended to vector fields that have only a linear growth.
Directory of Open Access Journals (Sweden)
Garkavenko A. S.
2011-08-01
Full Text Available The rate equations of the exciton laser in the system of interacting excitons have been obtained and the inverted population conditions and generation have been derived. The possibility of creating radically new gamma-ray laser has been shown.
Kasari, Hikoya; Yamaguchi, Yoshio
2001-01-01
Contrary to the conventional belief, it was shown that the Breit equation has the eigenvalues for bound states of two oppositely charged Dirac particles interacting through the (static) Coulomb potential. All eigenvalues reduced to those of the Sch\\"odinger case in the non-relativistic limit.
Generalized reduced magnetohydrodynamic equations
International Nuclear Information System (INIS)
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 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. The equations have been programmed into a spectral initial value code and run with shear flow that is consistent with the equilibrium input into the code. Linear results of tearing modes with shear flow are presented which differentiate the effects of shear flow gradients in the layer with the effects of the shear flow decoupling multiple harmonics
Modelling by Differential Equations
Chaachoua, Hamid; Saglam, Ayse
2006-01-01
This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…
Do Differential Equations Swing?
Maruszewski, Richard F., Jr.
2006-01-01
One of the units of in a standard differential equations course is a discussion of the oscillatory motion of a spring and the associated material on forcing functions and resonance. During the presentation on practical resonance, the instructor may tell students that it is similar to when they take their siblings to the playground and help them on…
Kinetic equation of sociodynamics
Володимир Олександрович Касьянов
2014-01-01
This article aims to build a theory of social dynamics, similar to the kinetic theory of gases. In general, given model is hybrid because off static mechanics ideas. In particular, Boltsman equation, Jaynes’s principle of entropy optimality have been applied to preference distribution of first and second type.
Equational binary decision diagrams
Groote, J.F.; Pol, J.C. van de
2000-01-01
We 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 tautology checkin
Kinetic equation of sociodynamics
Directory of Open Access Journals (Sweden)
Володимир Олександрович Касьянов
2014-08-01
Full Text Available This article aims to build a theory of social dynamics, similar to the kinetic theory of gases. In general, given model is hybrid because off static mechanics ideas. In particular, Boltsman equation, Jaynes’s principle of entropy optimality have been applied to preference distribution of first and second type.
Directory of Open Access Journals (Sweden)
Hatem Mejjaoli
2008-12-01
Full Text Available We introduce and study the Dunkl symmetric systems. We prove the well-posedness results for the Cauchy problem for these systems. Eventually we describe the finite speed of it. Next the semi-linear Dunkl-wave equations are also studied.
International Nuclear Information System (INIS)
We present part of our (direct or indirect) knwoledge of the equation of state of nuclear matter in a density-temperature domain for which nucleonic effects are dominant (densities smaller than 2-4 times the saturation density and temperatures smaller than 10-20 MeV). The lectures are divided into three parts corresponding, respectiveley, to direct studies close to the saturation, to the astrophysical case and to the studies involving heavy-ion collisions. In chapter one, after a brief introduction to the concept of equation of state, we discuss the saturation property of nuclear matter. The notion of incompressibility modulus is also introduced and its value is discussed in detail. Nuclear matter calculations trying to reproduce saturation from a nucleon-nucleon interaction are also briefly presented. In chapter two we study the equation of state in the astrophysical context. The role of the nuclear component is discussed in detail for the final phase of the collapse of supernovae cores. A brief presentation of calculations of dense matter constituting neutron stars is also given. Chapter three is devoted to heavy-ion collisions below 500-600 MeV per nucleon. After a brief presentation of both theoretical and experimental frameworks, we focus on three particular aspects which could have a link with the nuclear matter equation of state: the formation of intermediate mass fragments, flow effects and subthreshold particle production
RPA equations and the instantaneous Bethe-Salpeter equation
Resag, J
1993-01-01
We give a derivation of the particle-hole RPA equations for an interacting multi-fermion system by applying the instantaneous approximation to the amputated two-fermion propagator of the system. In relativistic field theory the same approximation leads from the fermion-antifermion Bethe-Salpeter equation to the Salpeter equation. We show that RPA equations and Salpeter equation are indeed equivalent.
Lie Symmetries of Ishimori Equation
Institute of Scientific and Technical Information of China (English)
SONG Xu-Xia
2013-01-01
The Ishimori equation is one of the most important (2+1)-dimensional integrable models,which is an integrable generalization of (1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.
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.
Anticipated backward stochastic differential equations
Peng, Shige; Yang, Zhe
2009-01-01
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 N
2006-01-01
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
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Chaos in Partial Differential Equations
Li, Y. Charles
2009-01-01
This is a survey on Chaos in Partial Differential Equations. First we classify soliton equations into three categories: 1. (1+1)-dimensional soliton equations, 2. soliton lattices, 3. (1+n)-dimensional soliton equations (n greater than 1). A systematic program has been established by the author and collaborators, for proving the existence of chaos in soliton equations under perturbations. For each category, we pick a representative to present the results. Then we review some initial results o...
Energy Technology Data Exchange (ETDEWEB)
Su, Chuan-Qi; Gao, Yi-Tian; Yu, Xin [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Xue, Long [Beijing Univ. of Aeronautics and Astronautics (China). Ministry-of-Education Key Lab. of Fluid Mechanics and National Lab. for Computational Fluid Dynamics; Aviation Univ. of Air Force, Liaoning (China). Flight Training Base
2015-07-01
Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
International Nuclear Information System (INIS)
Under investigation in this article is a higher-order nonlinear Schroedinger-Maxwell-Bloch (HNLS-MB) system for the optical pulse propagation in an erbium-doped fiber. Lax pair, Darboux transformation (DT), and generalised DT for the HNLS-MB system are constructed. Soliton solutions and rogue wave solutions are derived based on the DT and generalised DT, respectively. Properties of the solitons and rogue waves are graphically presented. The third-order dispersion parameter, fourth-order dispersion parameter, and frequency detuning all influence the characteristic lines and velocities of the solitons. The frequency detuning also affects the amplitudes of solitons. The separating function has no effect on the properties of the first-order rogue waves, except for the locations where the first-order rogue waves appear. The third-order dispersion parameter affects the propagation directions and shapes of the rogue waves. The frequency detuning influences the rogue-wave types of the module for the measure of polarization of resonant medium and the extant population inversion. The fourth-order dispersion parameter impacts the rogue-wave interaction range and also has an effect on the rogue-wave type of the extant population inversion. The value of separating function affects the spatial-temporal separation of constituting elementary rogue waves for the second-order and third-order rogue waves. The second-order and third-order rogue waves can exhibit the triangular and pentagon patterns under different choices of separating functions.
Directory of Open Access Journals (Sweden)
Latif Taşkaya
2016-03-01
Full Text Available In this study, quality properties and shelf life for gibel carp (Carassius gibelio, Bloch 1782 marinades during stored at 4±1 °C in different sauces was investigated. The marinating process was carried out in 2.5% vinegar, 10% salt and water for 72h at 4±1 °C. After the marination process, fish were removed from the solutions, transferred in to glass jar contain with different sauces (Group A: sunflower oil and tomato paste, Group B: sunflower oil with garlic, red pepper, thyme, basil and mint and the control group: sun flower oil. Sensory, chemical, colour and microbiological analyses were performed during the storage. According the chemical analysis results TVB-N and TBA values of all groups were increased during the storage, but during the stored period did not exceed acceptible limit values. The highest TVB-N and TBA values were group A. (P<0,05. At the end of 135 days of storage, sensory analysis results pointed out that the marinades of group B did not exceed acceptible limit values (P<0,05. The overall microbial load of the fresh samples decreased through out the storage period (P<0,05. By sensory data, shelf life of sauced gibel carp marinades were 120 days (control, 105 days (group A and 135 days (group B.
Xie, Xi-Yang; Tian, Bo; Sun, Wen-Rong; Sun, Ya; Liu, De-Yin
2015-10-01
In this paper, we construct soliton solutions for a generalized variable-coefficient coupled Hirota-Maxwell-Bloch system, which can describe the ultrashort optical pulse propagation in a nonlinear, dispersive fiber doped with two-level resonant atoms. Under certain transformations and constraints, one- and two-soliton solutions are obtained via the Hirota method and symbolic computation, and soliton collisions are graphically presented and analyzed. One soliton is shown to maintain its amplitude and shape during the propagation. Soliton collision is elastic, while bright two-peak solitons and dark two-peak solitons are also observed. We discuss the influence of the coefficients for the group velocity, group-velocity dispersion (GVD), self-phase modulation, distribution of the dopant, and Stark shift on the soliton propagation and collision features, with those coefficients are set as some constants and functions, respectively. We find the group velocity and self-phase modulation can change the solitons' amplitudes and widths, and the solitons become curved when the GVD and distribution of the dopant are chosen as some functions. When the Stark shift is chosen as a certain constant, the two peaks of bright two-peak solitons and dark two-peak solitons are not parallel. In addition, we observe the periodic collision of the two solitons.
Ali Khan, Mohammed Safwan; Mat Jais, Abdul Manan; Hussain, Javeed; Siddiqua, Faiza; Gopala Reddy, A; Shivakumar, P; Madhuri, D
2014-01-01
Channa striata (Bloch.) is a fresh water fish belonging to the family Channidae. The stripped snakehead fish possesses wide range of medicinal properties. In view of traditional use of C. striata for wound healing, the present study was undertaken to investigate the beneficial effects of orally administered freeze dried aqueous extract of Channa striata (AECS) in experimentally induced gastric ulcers in Wistar rats. Aspirin induced ulcerogenesis in pyloric ligation model was used for the assessment of antiulcer activity and Ranitidine (50 mg/kg) was employed as the standard drug. The various gastric parameters like volume of gastric juice, pH, free and total acidities, ulcer index, and levels of antioxidant enzymes like catalase, superoxide dismutase, and lipid peroxidation marker malondialdehyde were determined. AECS at concentrations of 40% and 50% w/v significantly decreased the volume of gastric juice and increased the levels of catalase while considerable decrease in free and total acidities and increase in superoxide dismutase were observed with the treatment of standard drug and AECS (50% w/v). All the test doses of AECS markedly decreased ulcer index and malondialdehyde compared to the standard drug whereas AECS 30% w/v did not alter volume of gastric juice, pH, free and total acidities, catalase, and superoxide dismutase. From these findings, it can be concluded that AECS is devoid of acid neutralizing effects at lower doses and possesses antisecretory and antiulcer activities and this could be related to its antioxidant mechanism. PMID:24977051
Wang, Qi-Min; Gao, Yi-Tian; Su, Chuan-Qi; Zuo, Da-Wei
2015-10-01
In this paper, a higher-order nonlinear Schrödinger-Maxwell-Bloch system with quintic terms is investigated, which describes the propagation of ultrashort optical pulses, up to the attosecond duration, in an erbium-doped fiber. Multi-soliton, breather and rogue-wave solutions are derived by virtue of the Darboux transformation and the limiting procedure. Features and interaction patterns of the solitons, breathers and rogue waves are discussed. (i) The solitonic amplitudes, widths and velocities are exhibited, and solitonic amplitudes and widths are proved to have nothing to do with the higher-order terms. (ii) The higher-order terms and frequency detuning affect the growth rate of periodic modulation and skewing angle for the breathers, except for the range of the frequency of modulation. (iii) The quintic terms and frequency detuning have the effects on the temporal duration for the rogue waves. (iv) Breathers are classified into two types, according to the range of the modulation instability. (v) Interaction between the two solitons is elastic. When the two solitons interact with each other, the periodic structure occurs, which is affected by the higher-order terms and frequency detuning. (vi) Interaction between the two Akhmediev-like breathers or two Kuznetsov-Ma-like solitons shows the different patterns with different ratios of the relative modulation frequencies, while the interaction area induced by the two breathers looks like a higher-order rogue wave.
Directory of Open Access Journals (Sweden)
Padmanabha Chakrabarti
2015-01-01
Full Text Available The histological analysis, disposition and histochemical localization of tryptophan were investigated in the pancreas to compare the cellular organization and histochemical characterization in the pancreas of Labeo rohita (Hamilton, 1822, Mystus vittatus (Bloch, 1790 and Notopterus notopterus (Pallas, 1769 having different feeding habits. Histological analysis demonstrated that the exocrine pancreatic tissues were dispersed within the hepatic parenchyma and spleen in L. rohita. Thin septa of connective tissue separated parenchyma of liver and also the spleen from exocrine pancreatic cells. However, in M. vittatus, the discrete pancreatic tissue formed distinct oval or elongated acini interspersed with small area of islet of Langerhans and blood vessels. In N. notopterus, the rhomboidal acinar cells of discrete pancreatic tissue intercalated with comparatively clear and large islet of Langerhans. The exocrine acinar cells in all the three species were provided with prominent nuclei and densely packed zymogen granules. Histochemical localization revealed that the zymogen granules of exocrine acinar cells of all species exhibited varied intensities of tryptophan reaction, the precursor of various pancreatic enzymes which may be related to the food and feeding habits of the fishes under study.
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, ...
Multinomial diffusion equation
Balter, Ariel; Tartakovsky, Alexandre M.
2011-06-01
We describe a new, microscopic model for diffusion that captures diffusion induced fluctuations at scales where the concept of concentration gives way to discrete particles. We show that in the limit as the number of particles N→∞, our model is equivalent to the classical stochastic diffusion equation (SDE). We test our new model and the SDE against Langevin dynamics in numerical simulations, and show that our model successfully reproduces the correct ensemble statistics, while the classical model fails.
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
Directory of Open Access Journals (Sweden)
D. Diederen
2015-06-01
Full Text Available We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.
Directory of Open Access Journals (Sweden)
M. Paul Gough
2008-07-01
Full Text Available LandauerÃ¢Â€Â™s principle is applied to information in the universe. Once stars began forming there was a constant information energy density as the increasing proportion of matter at high stellar temperatures exactly compensated for the expanding universe. The information equation of state was close to the dark energy value, w = -1, for a wide range of redshifts, 10 > z > 0.8, over one half of cosmic time. A reasonable universe information bit content of only 1087 bits is sufficient for information energy to account for all dark energy. A time varying equation of state with a direct link between dark energy and matter, and linked to star formation in particular, is clearly relevant to the cosmic coincidence problem. In answering the Ã¢Â€Â˜Why now?Ã¢Â€Â™ question we wonder Ã¢Â€Â˜What next?Ã¢Â€Â™ as we expect the information equation of state to tend towards w = 0 in the future.c
Maxwell Equations as the One Photon Quantum Equation
International Nuclear Information System (INIS)
Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived from first principles. We have shown how all Maxwell equations can be derived simultaneously from first principles, similar to those which have been used to derive the Dirac relativistic electron equation. We have 'also- shown that equations for massless particles, derived by Dirac in 1936, lead to the same result. The complex wave function, being a linear combination of the electric and magnetic fields, is a locally measurable quantity. Therefore Maxwell equations should be used as a guideline for proper interpretations of quantum equations
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
Telegrapher's equation for light derived from the transport equation
Hoenders, Bernhard J.; Graaff, R.
2005-01-01
Shortcomings of diffusion theory when applied to turbid media such as biological tissue makes the development of more accurate equations desirable. Several authors developed telegrapher's equations in the well known P-1 approximation. The method used in this paper is different: it is based on the asymptotic evaluation of the solutions of the equation of radiative transport with respect to place and time for all values of the albedo. Various coefficients for the telegrapher's equations were de...
Converting fractional differential equations into partial differential equations
He Ji-Huan; Li Zheng-Biao
2012-01-01
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the entropy of some physical systems.
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
Stochastic Geometric Wave Equations
Czech Academy of Sciences Publication Activity Database
Brzezniak, Z.; Ondreját, Martin
Cham: Springer, 2015, s. 157-188. (Progress in Probability. 68). ISBN 978-3-0348-0908-5. ISSN 1050-6977. [Stochastic analysis and applications at the Centre Interfacultaire Bernoulli, Ecole Polytechnique Fédérale de Lausanne. Lausanne (CH), 09.01.2012-29.6.2012] R&D Projects: GA ČR GAP201/10/0752 Institutional research plan: CEZ:AV0Z10750506 Institutional support: RVO:67985556 Keywords : Stochastic wave equation * Riemannian manifold * homogeneous space Subject RIV: BA - General Mathematics http://library.utia.cas.cz/separaty/2015/SI/ondrejat-0447803.pdf
The nonlinear fragmentation equation
International Nuclear Information System (INIS)
We study the kinetics of nonlinear irreversible fragmentation. Here, fragmentation is induced by interactions/collisions between pairs of particles and modelled by general classes of interaction kernels, for several types of breakage models. We construct initial value and scaling solutions of the fragmentation equations, and apply the 'non-vanishing mass flux' criterion for the occurrence of shattering transitions. These properties enable us to determine the phase diagram for the occurrence of shattering states and of scaling states in the phase space of model parameters. (fast track communication)
Elliptic differential equations
Hackbusch, Wolfgang; Ion, PDF
2010-01-01
The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems. The author starts with a discussion of the Laplace equation in the classical formulation and its discretisation by finite differences and deals with topics of gradually increasing complexity in the following chapters. He introduces the variational formulation of boundary value problems together with the necessary background from functional analysis and describes the finite element method including the most important error estimates. A more advanced chapter leads the reader into the th
Dimensional Equations of Entropy
Sparavigna, Amelia Carolina
2015-01-01
Entropy is a quantity which is of great importance in physics and chemistry. The concept comes out of thermodynamics, proposed by Rudolf Clausius in his analysis of Carnot cycle and linked by Ludwig Boltzmann to the number of specific ways in which a physical system may be arranged. Any physics classroom, in its task of learning physics, has therefore to face this crucial concept. As we will show in this paper, the lectures can be enriched by discussing dimensional equations linked to the ent...
Lopez, Cesar
2014-01-01
MATLAB is a high-level language and environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java. MATLAB Differential Equations introduces you to the MATLAB language with practical hands-on instructions and results, allowing you to quickly achieve your goals. In addition to giving an introduct
Makkonen, Lasse
2016-04-01
Young's construction for a contact angle at a three-phase intersection forms the basis of all fields of science that involve wetting and capillary action. We find compelling evidence from recent experimental results on the deformation of a soft solid at the contact line, and displacement of an elastic wire immersed in a liquid, that Young's equation can only be interpreted by surface energies, and not as a balance of surface tensions. It follows that the a priori variable in finding equilibrium is not the position of the contact line, but the contact angle. This finding provides the explanation for the pinning of a contact line. PMID:26940644
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...... actions shall terminate. It is shown that the proposed differential action has a semantics which corresponds to a discrete approximation when the discrete step size goes to zero. The extension gives action systems the power to model real-time clocks and continuous evolutions within hybrid systems....
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
Program Transformation by Solving Equations
Institute of Scientific and Technical Information of China (English)
朱鸿
1991-01-01
Based on the theory of orthogonal program expansion[8-10],the paper proposes a method to transform programs by solving program equations.By the method,transformation goals are expressed in program equations,and achieved by solving these equations.Although such equations are usually too complicated to be solved directly,the orthogonal expansion of programs makes it possible to reduce such equations into systems of equations only containing simple constructors of programs.Then,the solutions of such equations can be derived by a system of solving and simplifying rules,and algebraic laws of programs.The paper discusses the methods to simplify and solve equations and gives some examples.
On Certain Dual Integral Equations
Directory of Open Access Journals (Sweden)
R. S. Pathak
1974-01-01
Full Text Available Dual integral equations involving H-Functions have been solved by using the theory of Mellin transforms. The proof is analogous to that of Busbridge on solutions of dual integral equations involving Bessel functions.
International Nuclear Information System (INIS)
This monograph treats most of the usual material to be found in texts on the Dirac equation such as the basic formalism of quantum mechanics, representations of Dirac matrices, covariant realization of the Dirac equation, interpretation of negative energies, Foldy-Wouthuysen transformation, Klein's paradox, spherically symmetric interactions and a treatment of the relativistic hydrogen atom, etc., and also provides excellent additional treatments of a variety of other relevant topics. The monograph contains an extensive treatment of the Lorentz and Poincare groups and their representations. The author discusses in depth Lie algebaic and projective representations, covering groups, and Mackey's theory and Wigner's realization of induced representations. A careful classification of external fields with respect to their behavior under Poincare transformations is supplemented by a basic account of self-adjointness and spectral properties of Dirac operators. A state-of-the-art treatment of relativistic scattering theory based on a time-dependent approach originally due to Enss is presented. An excellent introduction to quantum electrodynamics in external fields is provided. Various appendices containing further details, notes on each chapter commenting on the history involved and referring to original research papers and further developments in the literature, and a bibliography covering all relevant monographs and over 500 articles on the subject, complete this text. This book should satisfy the needs of a wide audience, ranging from graduate students in theoretical physics and mathematics to researchers interested in mathematical physics
Functional equations for Feynman integrals
International Nuclear Information System (INIS)
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
Growth Equation with Conservation Law
Lauritsen, Kent Baekgaard
1995-01-01
A growth equation with a generalized conservation law characterized by an integral kernel is introduced. The equation contains the Kardar-Parisi-Zhang, Sun-Guo-Grant, and Molecular-Beam Epitaxy growth equations as special cases and allows for a unified investigation of growth equations. From a dynamic renormalization-group analysis critical exponents and universality classes are determined for growth models with a conservation law.
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…
Hyperbolic Methods for Einstein's Equations
Reula Oscar
1998-01-01
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.
An Extented Wave Action Equation
Institute of Scientific and Technical Information of China (English)
左其华
2003-01-01
Based on the Navier-Stokes equation, an average wave energy equation and a generalized wave action conservation equation are presented in this paper. The turbulence effects on water particle velocity ui and wave surface elavation ξ as well as energy dissipation are included. Some simplified forms are also given.
The Schroedinger equation and spin
International Nuclear Information System (INIS)
Galilei invariance of the Schroedinger equation requires linearization of the operator by the introduction of anticommuting matrices as coefficients of the linear form. In an external field this leads directly to the Pauli equation, the non-relativistic limit of Dirac's equation. An overview of the complete argument that defines spin as a non-relativistic concept is presented. 9 refs
Resonantly coupled nonlinear evolution equations
International Nuclear Information System (INIS)
A differential matrix eigenvalue problem is used to generate systems of nonlinear evolution equations. They model triad, multitriad, self-modal, and quartet wave interactions. A nonlinear string equation is also recovered as a special case. A continuum limit of the eigenvalue problem and associated evolution equations are discussed. The initial value solution requires an investigation of the corresponding inverse-scattering problem. (auth)
Solving Nonlinear Coupled Differential Equations
Mitchell, L.; David, J.
1986-01-01
Harmonic balance method developed to obtain approximate steady-state solutions for nonlinear coupled ordinary differential equations. Method usable with transfer matrices commonly used to analyze shaft systems. Solution to nonlinear equation, with periodic forcing function represented as sum of series similar to Fourier series but with form of terms suggested by equation itself.
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...
Quadratic bundle and nonlinear equations
International Nuclear Information System (INIS)
The paper is aimed at giving an exhaustive description of the nonlinear evolution equations (NLEE), connected with the quadratic bundle (the spectral parameter lambda, which enters quadratically into the equations) and at describing Hamiltonian structure of these equations. The equations are solved through the inverse scattering method (ISM). The basic formulae for the scattering problem are given. The spectral expansion of the integrodifferential operator is used so that its eigenfunctions are the squared solutions of the equation. By using the notions of Hamiltonian structure hierarchy and gauge transformations it is shown how to single out physically interesting NLEE
Generalized Klein-Kramers equations
Fa, Kwok Sau
2012-12-01
A generalized Klein-Kramers equation for a particle interacting with an external field is proposed. The equation generalizes the fractional Klein-Kramers equation introduced by Barkai and Silbey [J. Phys. Chem. B 104, 3866 (2000), 10.1021/jp993491m]. Besides, the generalized Klein-Kramers equation can also recover the integro-differential Klein-Kramers equation for continuous-time random walk; this means that it can describe the subdiffusive and superdiffusive regimes in the long-time limit. Moreover, analytic solutions for first two moments both in velocity and displacement (for force-free case) are obtained, and their dynamic behaviors are investigated.
Chaliasos, Evangelos
2006-01-01
As we know, from the Einstein equations the vanishing of the four-divergence of the energy-momentum tensor follows. This is the case because the four-divergence of the Einstein tensor vanishes identically. Inversely, we find that from the vanishing of the four-divergence of the energy-momentum tensor not only the Einstein equations follow. Besides, the so-named anti-Einstein equations follow. These equations must be considered as complementary to the Einstein equations. And while from the Ein...
A generalized advection dispersion equation
Indian Academy of Sciences (India)
Abdon Atangana
2014-02-01
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 the operator are presented. The operator is used to generalize the advection dispersion equation. The generalized equation differs from the standard equation in four properties. The generalized equation is solved via the variational iteration technique. Some illustrative figures are presented.
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.
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 in
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
$\\Lambda$ Scattering Equations
Gomez, Humberto
2016-01-01
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 $\\Lambda$ 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 $\\Lambda$ 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 $\\Lambda$ algorithm.
Cardona, Carlos
2016-01-01
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 $\\mathbb{C}P^2$ space. We show that for the simplest integrand, namely the ${\\rm n-gon}$, our proposal indeed reproduces the expected result. By using the recently formulated $\\Lambda-$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.
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...
Comparison between characteristics of mild slope equations and Boussinesq equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Boussinesq-type equations and mild-slope equations are compared in terms of their basic forms and characteristics. It is concluded that linear mild-slope equations on dispersion relation are better than non-linear Boussinesq equations. In addition, Berkhoff experiments are computed and compared by the two models, and agreement between model results and available experimental data is found to be quite reasonable, which demonstrates the two models' capacity to simulate wave transformation. However they can deal with different physical processes respectively, and they have their own characteristics.
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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.
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. .
Spinor wave equation of photon
Wu, Xiang-Yao; Liu, Xiao-Jing; Zhang, Si-Qi; Wang, Jing; Li, Hong; Fan, Xi-Hui; Li, Jing-Wu
2012-01-01
In this paper, we give the spinor wave equations of free and unfree photon, which are the differential equation of space-time one order. For the free photon, the spinor wave equations are covariant, and the spinors $\\psi$ are corresponding to the the reducibility representations $D^{10}+D^{01}$ and $D^{10}+D^{01}+D^{1/2 1/2}$ of the proper Lorentz group.
Quaternion Dirac Equation and Supersymmetry
Rawat, Seema; Negi, O. P. S.
2007-01-01
Quaternion Dirac equation has been analyzed and its supersymetrization has been discussed consistently. It has been shown that the quaternion Dirac equation automatically describes the spin structure with its spin up and spin down components of two component quaternion Dirac spinors associated with positive and negative energies. It has also been shown that the supersymmetrization of quaternion Dirac equation works well for different cases associated with zero mass, non zero mass, scalar pote...
Differential Equations for Algebraic Functions
Bostan, Alin; Chyzak, Frédéric; Salvy, Bruno; Lecerf, Grégoire; Schost, Éric
2007-01-01
It is classical that univariate algebraic functions satisfy linear differential equations with polynomial coefficients. Linear recurrences follow for the coefficients of their power series expansions. We show that the linear differential equation of minimal order has coefficients whose degree is cubic in the degree of the function. We also show that there exists a linear differential equation of order linear in the degree whose coefficients are only of quadratic degree. Furthermore, we prove ...
Perturbed linear rough differential equations
Coutin, Laure; Lejay, Antoine
2014-01-01
We study linear rough differential equations and we solve perturbed linear rough differential equation using the Duhamel principle. These results provide us with the key technical point to study the regularity of the differential of the Itô map in a subsequent article. Also, the notion of linear rough differential equations leads to consider multiplicative functionals with values in Banach algebra more general than tensor algebra and to consider extensions of classical results such as the Mag...
THE ERMAKOV EQUATION: A COMMENTARY
P.G.L. Leach; Andriopoulos, K.
2008-01-01
We present a short history of the Ermakov Equation with an emphasis on its discovery by theWest and the subsequent boost to research into invariants for nonlinear systems although recognizing some of the significant developments in the East. We present the modern context of the Ermakov Equation in the algebraic and singularity theory of ordinary differential equations and applications to more divers fields. The reader is referred to the previous article (Appl. Anal. Discrete Math., 2 (2008), ...
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.
Luo, Da-Wei; Pyshkin, P. V.; Yu, Ting; Lin, Hai-Qing; You, J. Q.; Wu, Lian-Ao
2016-01-01
We provide an alternative approach to relativistic dynamics based on the Feshbach projection technique. Instead of directly studying the Dirac equation, we derive a two-component equation for the upper spinor. This approach allows one to investigate the underlying physics in a different perspective. For particles with small mass such as the neutrino, the leading order equation has a Hermitian effective Hamiltonian, implying there is no leakage between the upper and lower spinors. In the weak ...
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.
Introduction to ordinary differential equations
Rabenstein, Albert L
1966-01-01
Introduction to Ordinary Differential Equations is a 12-chapter text that describes useful elementary methods of finding solutions using ordinary differential equations. This book starts with an introduction to the properties and complex variable of linear differential equations. Considerable chapters covered topics that are of particular interest in applications, including Laplace transforms, eigenvalue problems, special functions, Fourier series, and boundary-value problems of mathematical physics. Other chapters are devoted to some topics that are not directly concerned with finding solutio
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...... electrodynamics. Although this ambitious attempt attracted some interest in 1926, its impact on the mainstream of development in quantum mechanics was virtually nil....
Temporal Fokker-Planck Equations
Boon, Jean Pierre; Lutsko, James F.
2016-01-01
The temporal Fokker-Plank equation [{\\it J. Stat. Phys.}, {\\bf 3/4}, 527 (2003)] or propagation-dispersion equation was derived to describe diffusive processes with temporal dispersion rather than spatial dispersion as in classical diffusion. %\\cite{boon-grosfils-lutsko}. We present two generalizations of the temporal Fokker-Plank equation for the first passage distribution function $f_j(r,t)$ of a particle moving on a substrate with time delays $\\tau_j$. Both generalizations follow from the ...
A modified electromagnetic wave equation
International Nuclear Information System (INIS)
The aim of this paper is to find an alternative to the usual electromagnetic wave equation: that is, we want to find a different equation with the same solutions. The final goal is to solve electromagnetic problems with iterative methods. The curl curl operator that appears in the electromagnetic wave equation is difficult to invert numerically, and this cannot be done iteratively. The addition of a higher order term that emphasizes the diagonal terms in the operator may help the solution of the problem, and the new equation should be solvable by an iterative algorithm. The additional mode is suppressed by suitable boundary conditions. (author) 5 figs., 9 refs
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.
Diffusion equations and turbulent transport
International Nuclear Information System (INIS)
One scrutinized transport equations differing essentially in form from the classical diffusion one. Description of diffusion under strong nonequilibrium and turbulence involved application of equations that took account of transport nonlocality and memory effects. One analyzed ways to derive the mentioned equations starting from quasi-linear approximation and up to equations with fractional derivatives. One points out the generality of the applied theoretical concepts in spite of the essential difference of the exact physical problems. One demonstrated the way of application of the theoretical and probabilistic ideas
Diffusion equations and turbulent transport
International Nuclear Information System (INIS)
Diffusion equations are considered that differ substantially in structure from classical ones. A description of diffusion under strongly nonequilibrium conditions in a highly turbulent plasma requires the use of equations that take into account memory effects and the nonlocal nature of transport. Different methods are developed for constructing such equations, ranging from those in the quasilinear approximation to those with fractional derivatives. It is emphasized that the theoretical concepts underlying the equations proposed are common for a very wide variety of specific physical problems. The ways of applying theoretical probabilistic ideas are demonstrated
Electronic representation of wave equation
Veigend, Petr; Kunovský, Jiří; Kocina, Filip; Nečasová, Gabriela; Šátek, Václav; Valenta, Václav
2016-06-01
The Taylor series method for solving differential equations represents a non-traditional way of a numerical solution. Even though this method is not much preferred in the literature, experimental calculations done at the Department of Intelligent Systems of the Faculty of Information Technology of TU Brno have verified that the accuracy and stability of the Taylor series method exceeds the currently used algorithms for numerically solving differential equations. This paper deals with solution of Telegraph equation using modelling of a series small pieces of the wire. Corresponding differential equations are solved by the Modern Taylor Series Method.
ON A CORRELATION BETWEEN DIFFERENTIAL EQUATIONS AND THEIR CHARACTERISTIC EQUATIONS
Boro M. Piperevski
2007-01-01
Abstract: The aim of this paper is to derive the dependence of the nature of a solution of a class of differential equations of n-th order with polynomial coefficients on the solutions of the corresponding characteristic algebraic equation of n-th degree.
Tippe Top Equations and Equations for the Related Mechanical Systems
Rutstam, Nils
2012-01-01
The equations of motion for the rolling and gliding Tippe Top (TT) are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis $\\mathbf{\\hat{3}}$ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT.
Tippe Top Equations and Equations for the Related Mechanical Systems
Directory of Open Access Journals (Sweden)
Nils Rutstam
2012-04-01
Full Text Available The equations of motion for the rolling and gliding Tippe Top (TT are nonintegrable and difficult to analyze. The only existing arguments about TT inversion are based on analysis of stability of asymptotic solutions and the LaSalle type theorem. They do not explain the dynamics of inversion. To approach this problem we review and analyze here the equations of motion for the rolling and gliding TT in three equivalent forms, each one providing different bits of information about motion of TT. They lead to the main equation for the TT, which describes well the oscillatory character of motion of the symmetry axis 3ˆ during the inversion. We show also that the equations of motion of TT give rise to equations of motion for two other simpler mechanical systems: the gliding heavy symmetric top and the gliding eccentric cylinder. These systems can be of aid in understanding the dynamics of the inverting TT.
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.
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
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.
Solving equations by topological methods
Lech Górniewicz
2005-01-01
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.
Partial Completion of Equational Theories
Institute of Scientific and Technical Information of China (English)
孙永强; 林凯; 陆朝俊
2000-01-01
In this paper, the notion of partial completion of equational theories is proposed, which is a procedure to construct a confluent term rewriting system from an equational theory without requirement of termination condition. A partial completion algorithm is presented with a brief description of its application in a program development system.
Differential equations a concise course
Bear, H S
2011-01-01
Concise introduction for undergraduates includes, among other topics, a survey of first order equations, discussions of complex-valued solutions, linear differential operators, inverse operators and variation of parameters method, the Laplace transform, Picard's existence theorem, and an exploration of various interpretations of systems of equations. Numerous clearly stated theorems and proofs, examples, and problems followed by solutions.
Differential equations and moving frames
Abib, Odinette Renée
2006-01-01
The purpose of the paper is to study the relationship between differential equations, Pfaffian systems and geometric structures, via the method of moving frames of E.Cartan. We show a local structure theorem. The Lie algebra aspects differential equations is studied too.
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 of...
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
International Nuclear Information System (INIS)
The Boltzmann-Uhlenbeck (BUU) equation, which is the time evolution of the wigner function of the single particle Green's function, is dervied by using the closed-time Green's function approach. The quantum mechanical approximation in derving the BUU equation is discussed
Phenomenological equations for reacting fluids
International Nuclear Information System (INIS)
A nonlocal phenomenological equation is introduced for a multicomponent fluid where chemical or nuclear reactions are taking place. The reciprocity between the nonlocal linear-coefficients is examined closely. An approximation reduces the nonlocal equation to the ordinary phenomenological relation with correction terms which show clearly a coupling of the reaction with the diffusion and the thermal conduction in an isotropic system. (auth.)
Uncertainty of empirical correlation equations
Feistel, R.; Lovell-Smith, J. W.; Saunders, P.; Seitz, S.
2016-08-01
The International Association for the Properties of Water and Steam (IAPWS) has published a set of empirical reference equations of state, forming the basis of the 2010 Thermodynamic Equation of Seawater (TEOS-10), from which all thermodynamic properties of seawater, ice, and humid air can be derived in a thermodynamically consistent manner. For each of the equations of state, the parameters have been found by simultaneously fitting equations for a range of different derived quantities using large sets of measurements of these quantities. In some cases, uncertainties in these fitted equations have been assigned based on the uncertainties of the measurement results. However, because uncertainties in the parameter values have not been determined, it is not possible to estimate the uncertainty in many of the useful quantities that can be calculated using the parameters. In this paper we demonstrate how the method of generalised least squares (GLS), in which the covariance of the input data is propagated into the values calculated by the fitted equation, and in particular into the covariance matrix of the fitted parameters, can be applied to one of the TEOS-10 equations of state, namely IAPWS-95 for fluid pure water. Using the calculated parameter covariance matrix, we provide some preliminary estimates of the uncertainties in derived quantities, namely the second and third virial coefficients for water. We recommend further investigation of the GLS method for use as a standard method for calculating and propagating the uncertainties of values computed from empirical equations.
Saturation and linear transport equation
Energy Technology Data Exchange (ETDEWEB)
Kutak, K.
2009-03-15
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)
Saturation and linear transport equation
International Nuclear Information System (INIS)
We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term. (orig.)
Kocak, M.; Gonul, B.
2007-01-01
The solutions, in terms of orthogonal polynomials, of Dirac equation with analytically solvable potentials are investigated within a novel formalism by transforming the relativistic equation into a Schrodinger like one. Earlier results are discussed in a unified framework and certain solutions of a large class of potentials are given.
Wigner transforms and Liouville equations
International Nuclear Information System (INIS)
Recent works concerning the semi-classical limit (h barred tending to zero) of the Quantum Mechanics linear and non linear models or equations, are presented. The non linear case is corresponding to mean field (or self consistent) models and gives, at the limit, the Vlasov equations of the Classical Statistical Mechanics. 48 refs
Singularity: Raychaudhuri equation once again
Indian Academy of Sciences (India)
Naresh Dadhich
2007-07-01
I first recount Raychaudhuri's deep involvement with the singularity problem in general relativity. I then argue that precisely the same situation has arisen today in loop quantum cosmology as obtained when Raychaudhuri discovered his celebrated equation. We thus need a new analogue of the Raychaudhuri equation in quantum gravity.
Nonlinear evolution equations and the Painleve test
International Nuclear Information System (INIS)
In this paper a survey is given of new results of the Painleve test and nonlinear evolution equations where ordinary- and partial-differential equations are considered. The authors study the semiclassical Haynes-Cumming model, the energy-eigenvalue-level-motion equation, the Kadomtsev-Petviashvili equation, the nonlinear Klein-Gordon equation and the self-dual Yang-Mills equation
Conservation Laws of Differential Equations in Finance
Institute of Scientific and Technical Information of China (English)
QIN Mao-Chang; MEI Feng-Xiang; SHANG Mei
2005-01-01
Conservation laws of some differential equations in fiance are studied in this paper. This method does not involve the use or existence of a variational principle. As an alternative, linearize the given equation and find adjoint equation of the linearized equation, the conservation laws can be constructed directly from the symmetries and adjoint symmetries of the associated linearized equation and its adjoint equation.
Integrability of equations for soliton's eigenfunctions
International Nuclear Information System (INIS)
Eigenfunctions of the auxiliary linear problems for the soliton equations obey the nonlinear evolution equations. It is shown that these eigenfunction equations are integrable by the inverse spectral transform method. Eigenfunction equations are also the generating equations. Several (1+1) and (2+1) dimensional eigenfunction equations and their properties are considered. 11 refs
Conservation laws of semidiscrete canonical Hamiltonian equations
International Nuclear Information System (INIS)
There are many evolution partial differential equations which can be cast into Hamiltonian form. Conservation laws of these equations are related to one-parameter Hamiltonian symmetries admitted by the PDEs. The same result holds for semidiscrete Hamiltonian equations. In this paper we consider semidiscrete canonical Hamiltonian equations. Using symmetries, we find conservation laws for the semidiscretized nonlinear wave equation and Schroedinger equation. (author)
Conservation Laws of Differential Equations in Finance
International Nuclear Information System (INIS)
Conservation laws of some differential equations in fiance are studied in this paper. This method does not involve the use or existence of a variational principle. As an alternative, linearize the given equation and find adjoint equation of the linearized equation, the conservation laws can be constructed directly from the symmetries and adjoint symmetries of the associated linearized equation and its adjoint equation.
Transport Equations for Oscillating Neutrinos
Zhang, Yunfan
2013-01-01
We derive a suite of generalized Boltzmann equations, based on the density-matrix formalism, that incorporates the physics of neutrino oscillations for two- and three-flavor oscillations, matter refraction, and self-refraction. The resulting equations are straightforward extensions of the classical transport equations that nevertheless contain the full physics of quantum oscillation phenomena. In this way, our broadened formalism provides a bridge between the familiar neutrino transport algorithms employed by supernova modelers and the more quantum-heavy approaches frequently employed to illuminate the various neutrino oscillation effects. We also provide the corresponding angular-moment versions of this generalized equation set. Our goal is to make it easier for astrophysicists to address oscillation phenomena in a language with which they are familiar. The equations we derive are simple and practical, and are intended to facilitate progress concerning oscillation phenomena in the context of core-collapse su...
Determining dynamical equations is hard
Cubitt, Toby S; Wolf, Michael M
2010-01-01
The behaviour of any physical system is governed by its underlying dynamical equations--the differential equations describing how the system evolves with time--and much of physics is ultimately concerned with discovering these dynamical equations and understanding their consequences. At the end of the day, any such dynamical law is identified by making measurements at different times, and computing the dynamical equation consistent with the acquired data. In this work, we show that, remarkably, this process is a provably computationally intractable problem (technically, it is NP-hard). That is, even for a moderately complex system, no matter how accurately we have specified the data, discovering its dynamical equations can take an infeasibly long time (unless P=NP). As such, we find a complexity-theoretic solution to both the quantum and the classical embedding problems; the classical version is a long-standing open problem, dating from 1937, which we finally lay to rest.
Nominal Logic with Equations Only
Clouston, Ranald
2011-01-01
Many formal systems, particularly in computer science, may be captured by equations modulated by side conditions asserting the "freshness of names"; these can be reasoned about with Nominal Equational Logic (NEL). Like most logics of this sort NEL employs this notion of freshness as a first class logical connective. However, this can become inconvenient when attempting to translate results from standard equational logic to the nominal setting. This paper presents proof rules for a logic whose only connectives are equations, which we call Nominal Equation-only Logic (NEoL). We prove that NEoL is just as expressive as NEL. We then give a simple description of equality in the empty NEoL-theory, then extend that result to describe freshness in the empty NEL-theory.
Generalizing the cosmic energy equation
International Nuclear Information System (INIS)
We generalize the cosmic energy equation to the case when massive particles interact via a modified gravitational potential of the form φ(a,r), which is allowed to explicitly depend upon the cosmological time through the expansion factor a(t). Using the nonrelativistic approximation for particle dynamics, we derive the equation for the cosmological expansion which has the form of the Friedmann equation with a renormalized gravitational constant. The generalized Layzer-Irvine cosmic energy equation and the associated cosmic virial theorem are applied to some recently proposed modifications of the Newtonian gravitational interaction between dark-matter particles. We also draw attention to the possibility that the cosmic energy equation may be used to probe the expansion history of the universe thereby throwing light on the nature of dark matter and dark energy.
Some Variations on Maxwell's Equations
Ascoli, G A; Ascoli, Giorgio A.; Goldin, Gerald A.
2006-01-01
In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work---a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems---one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\\it a priori\\/} by known physical ...
International Nuclear Information System (INIS)
It is known that many irreversible processes have a high degree of symmetry. Thus, spontaneous emission, thermal collisions, and the collisions of atoms or molecules of a gas with container walls lead to completely isotropic relaxation. The assumption of isotropy is also a good approximation in the presence of an external magnetic field if the energy of the Zeeman level splitting of the system is appreciably less than kT. Relaxation in the presence of a weak fluctuating perturbation, which is typical of liquids and gases, is also isotropic. In the presence of a strong magnetic field the environment is, as a rule, axisymmetric. In this connection, semigroups with different degrees of symmetry are widely used in the phenomenological description of the irreversible evolution of open quantum systems. In this paper, quantum Markov master equations of spin systems are classified (up to conjugation) with respect to the continuous symmetry groups of the environment. The Bloch equations are derived from the general theory of completely positive quantum dynamical semigroups
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.
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...
Higher derivative gravity: field equation as the equation of state
Dey, Ramit; Mohd, Arif
2016-01-01
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.
Higher derivative gravity: Field equation as the equation of state
Dey, Ramit; Liberati, Stefano; Mohd, Arif
2016-08-01
One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon. The extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades. In particular, equations of motion for minimally coupled higher-curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning. In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy. In this paper, we propose a new entropy density, closely related to the Noetheresque form, such that the field equation of any diffeomorphism-invariant metric theory of gravity can be derived by imposing the Clausius relation on a small patch of local causal horizon.
Extended Trial Equation Method for Nonlinear Partial Differential Equations
Gepreel, Khaled A.; Nofal, Taher A.
2015-04-01
The main objective of this paper is to use the extended trial equation method to construct a series of some new solutions for some nonlinear partial differential equations (PDEs) in mathematical physics. We will construct the solutions in many different functions such as hyperbolic function solutions, trigonometric function solutions, Jacobi elliptic function solutions, and rational functional solutions for the nonlinear PDEs when the balance number is a real number via the Zhiber-Shabat nonlinear differential equation. The balance number of this method is not constant as we shown in other methods, but it is changed by changing the trial equation derivative definition. This method allowed us to construct many new types of solutions. It is shown by using the Maple software package that all obtained solutions satisfy the original PDEs.
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
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.
Equational theories of tropical sernirings
DEFF Research Database (Denmark)
Aceto, Luca; Esik, Zoltan; Ingolfsdottir, Anna
2003-01-01
of these commutative idempotent weak semirings, the paper offers characterizations of the equations that hold in them, decidability results for their equational theories, explicit descriptions of the free algebras in the varieties they generate, and relative axiomatization results. Udgivelsesdato......This paper studies the equational theories of various exotic semirings presented in the literature. Exotic semirings are semirings whose underlying carrier set is some subset of the set of real numbers equipped with binary operations of minimum or maximum as sum, and addition as product. Two prime...
Lectures on ordinary differential equations
Hurewicz, Witold
2014-01-01
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
THE ERMAKOV EQUATION: A COMMENTARY
Directory of Open Access Journals (Sweden)
P. G. L. Leach
2008-08-01
Full Text Available We present a short history of the Ermakov Equation with an emphasis on its discovery by theWest and the subsequent boost to research into invariants for nonlinear systems although recognizing some of the significant developments in the East. We present the modern context of the Ermakov Equation in the algebraic and singularity theory of ordinary differential equations and applications to more divers fields. The reader is referred to the previous article (Appl. Anal. Discrete Math., 2 (2008, 123–145 for an English translation of Ermakov’s original paper.
Loop equations from differential systems
Eynard, Bertrand; Marchal, Olivier
2016-01-01
To any differential system $d\\Psi=\\Phi\\Psi$ where $\\Psi$ belongs to a Lie group (a fiber of a principal bundle) and $\\Phi$ is a Lie algebra $\\mathfrak g$ valued 1-form on a Riemann surface $\\Sigma$, is associated an infinite sequence of "correlators" $W_n$ that are symmetric $n$-forms on $\\Sigma^n$. The goal of this article is to prove that these correlators always satisfy "loop equations", the same equations satisfied by correlation functions in random matrix models, or the same equations as Virasoro or W-algebra constraints in CFT.
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
Vědec a „muž činu“: Marc Bloch a jeho výjimečné postavení v kontinuitě vývoje moderního dějepisectví
Czech Academy of Sciences Publication Activity Database
Řepa, Milan
Brno : Matice moravská, 2009 - (Hanuš, J.; Vlček, R.), s. 73-88 ISBN 978-80-86488-59-2. - (Země a kultura ve střední Evropě. 11) Institutional research plan: CEZ:AV0Z80150510 Keywords : Marc Bloch * History * Historiography Subject RIV: AB - History
Direct 'delay' reductions of the Toda equation
International Nuclear Information System (INIS)
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)