Magnus approximation in the adiabatic picture
International Nuclear Information System (INIS)
Klarsfeld, S.; Oteo, J.A.
1991-01-01
A simple approximate nonperturbative method is described for treating time-dependent problems that works well in the intermediate regime far from both the sudden and the adiabatic limits. The method consists of applying the Magnus expansion after transforming to the adiabatic basis defined by the eigenstates of the instantaneous Hamiltonian. A few exactly soluble examples are considered in order to assess the domain of validity of the approximation. (author) 32 refs., 4 figs
Quantum adiabatic approximation and the geometric phase
International Nuclear Information System (INIS)
Mostafazadeh, A.
1997-01-01
A precise definition of an adiabaticity parameter ν of a time-dependent Hamiltonian is proposed. A variation of the time-dependent perturbation theory is presented which yields a series expansion of the evolution operator U(τ)=summation scr(l) U (scr(l)) (τ) with U (scr(l)) (τ) being at least of the order ν scr(l) . In particular, U (0) (τ) corresponds to the adiabatic approximation and yields Berry close-quote s adiabatic phase. It is shown that this series expansion has nothing to do with the 1/τ expansion of U(τ). It is also shown that the nonadiabatic part of the evolution operator is generated by a transformed Hamiltonian which is off-diagonal in the eigenbasis of the initial Hamiltonian. This suggests the introduction of an adiabatic product expansion for U(τ) which turns out to yield exact expressions for U(τ) for a large number of quantum systems. In particular, a simple application of the adiabatic product expansion is used to show that for the Hamiltonian describing the dynamics of a magnetic dipole in an arbitrarily changing magnetic field, there exists another Hamiltonian with the same eigenvectors for which the Schroedinger equation is exactly solvable. Some related issues concerning geometric phases and their physical significance are also discussed. copyright 1997 The American Physical Society
Bond selective chemistry beyond the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Butler, L.J. [Univ. of Chicago, IL (United States)
1993-12-01
One of the most important challenges in chemistry is to develop predictive ability for the branching between energetically allowed chemical reaction pathways. Such predictive capability, coupled with a fundamental understanding of the important molecular interactions, is essential to the development and utilization of new fuels and the design of efficient combustion processes. Existing transition state and exact quantum theories successfully predict the branching between available product channels for systems in which each reaction coordinate can be adequately described by different paths along a single adiabatic potential energy surface. In particular, unimolecular dissociation following thermal, infrared multiphoton, or overtone excitation in the ground state yields a branching between energetically allowed product channels which can be successfully predicted by the application of statistical theories, i.e. the weakest bond breaks. (The predictions are particularly good for competing reactions in which when there is no saddle point along the reaction coordinates, as in simple bond fission reactions.) The predicted lack of bond selectivity results from the assumption of rapid internal vibrational energy redistribution and the implicit use of a single adiabatic Born-Oppenheimer potential energy surface for the reaction. However, the adiabatic approximation is not valid for the reaction of a wide variety of energetic materials and organic fuels; coupling between the electronic states of the reacting species play a a key role in determining the selectivity of the chemical reactions induced. The work described below investigated the central role played by coupling between electronic states in polyatomic molecules in determining the selective branching between energetically allowed fragmentation pathways in two key systems.
The adiabatic approximation in multichannel scattering
International Nuclear Information System (INIS)
Schulte, A.M.
1978-01-01
Using two-dimensional models, an attempt has been made to get an impression of the conditions of validity of the adiabatic approximation. For a nucleon bound to a rotating nucleus the Coriolis coupling is neglected and the relation between this nuclear Coriolis coupling and the classical Coriolis force has been examined. The approximation for particle scattering from an axially symmetric rotating nucleus based on a short duration of the collision, has been combined with an approximation based on the limitation of angular momentum transfer between particle and nucleus. Numerical calculations demonstrate the validity of the new combined method. The concept of time duration for quantum mechanical collisions has also been studied, as has the collective description of permanently deformed nuclei. (C.F.)
A note on the geometric phase in adiabatic approximation
International Nuclear Information System (INIS)
Tong, D.M.; Singh, K.; Kwek, L.C.; Fan, X.J.; Oh, C.H.
2005-01-01
The adiabatic theorem shows that the instantaneous eigenstate is a good approximation of the exact solution for a quantum system in adiabatic evolution. One may therefore expect that the geometric phase calculated by using the eigenstate should be also a good approximation of exact geometric phase. However, we find that the former phase may differ appreciably from the latter if the evolution time is large enough
Dynamic hysteresis of a uniaxial superparamagnet: Semi-adiabatic approximation
International Nuclear Information System (INIS)
Poperechny, I.S.; Raikher, Yu.L.; Stepanov, V.I.
2014-01-01
The semi-adiabatic theory of magnetic response of a uniaxial single-domain ferromagnetic particle is presented. The approach is developed in the context of the kinetic theory and allows for any orientation of the external field. Within this approximation, the dynamic magnetic hysteresis loops in an ac field are calculated. It is demonstrated that they very closely resemble those obtained by the full kinetic theory. The behavior of the effective coercive force is analyzed in detail, and for it a simple formula is proposed. This relation accounts not only for the temperature behavior of the coercive force, as the previous ones do, but also yields the dependence on the frequency and amplitude of the applied field
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
Calculation of a hydrogen molecule in the adiabatic approximation
International Nuclear Information System (INIS)
Vukajlovich, F.R.; Mogilevskij, O.A.; Ponomarev, L.I.
1979-01-01
The adiabatic approximation js used for calculating the energy levels of a hydrogen molecule, i.e. of the simplest four-body system with a Coulomb interaction. The aim of this paper is the investigation of the possible use of the adiabatic method in the molecular problems. The most effective regions of its application are discussed. An infinite system of integro-differential equations is constructed, which describes the hydrogen molecule in the adiabatic approximation with the effective potentials taking into account the corrections to the nuclear motion. The energy of the first three vibrational states of the hydrogen molecule is calculated and compared with the experimental data. The convergence of the method is discussed
Accuracy of the adiabatic-impulse approximation for closed and open quantum systems
Tomka, Michael; Campos Venuti, Lorenzo; Zanardi, Paolo
2018-03-01
We study the adiabatic-impulse approximation (AIA) as a tool to approximate the time evolution of quantum states when driven through a region of small gap. Such small-gap regions are a common situation in adiabatic quantum computing and having reliable approximations is important in this context. The AIA originates from the Kibble-Zurek theory applied to continuous quantum phase transitions. The Kibble-Zurek mechanism was developed to predict the power-law scaling of the defect density across a continuous quantum phase transition. Instead, here we quantify the accuracy of the AIA via the trace norm distance with respect to the exact evolved state. As expected, we find that for short times or fast protocols, the AIA outperforms the simple adiabatic approximation. However, for large times or slow protocols, the situation is actually reversed and the AIA provides a worse approximation. Nevertheless, we found a variation of the AIA that can perform better than the adiabatic one. This counterintuitive modification consists in crossing the region of small gap twice. Our findings are illustrated by several examples of driven closed and open quantum systems.
Generalized Gradient Approximation Made Simple
International Nuclear Information System (INIS)
Perdew, J.P.; Burke, K.; Ernzerhof, M.
1996-01-01
Generalized gradient approximations (GGA close-quote s) for the exchange-correlation energy improve upon the local spin density (LSD) description of atoms, molecules, and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental constants. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential. copyright 1996 The American Physical Society
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2012-01-01
The adiabatic connection fluctuation-dissipation theorem with the random phase approximation (RPA) has recently been applied with success to obtain correlation energies of a variety of chemical and solid state systems. The main merit of this approach is the improved description of dispersive forces...... while chemical bond strengths and absolute correlation energies are systematically underestimated. In this work we extend the RPA by including a parameter-free renormalized version of the adiabatic local-density (ALDA) exchange-correlation kernel. The renormalization consists of a (local) truncation...... of the ALDA kernel for wave vectors q > 2kF, which is found to yield excellent results for the homogeneous electron gas. In addition, the kernel significantly improves both the absolute correlation energies and atomization energies of small molecules over RPA and ALDA. The renormalization can...
International Nuclear Information System (INIS)
Cady, W.A.; Clark, A.P.; Dickinson, A.S.
1975-01-01
Recently a near-adiabatic (perturbed stationary states) approximation was used in an investigation the collinear vibrational excitation of a harmonic oscillator. This approximation reduced the problem to that of obtaining transition probabilities for a harmonic oscillator with time-dependent forcing function. Cady derived an apparently exact solution for this problem. It is shown that this solution is not exact but that the solution results from making a further adiabatic approximation and a derivation is given that clearly shows the adiabatic character of this further approximation
The adiabatic versus the diabatic approximation in the decoupling of electron and nuclear motion
International Nuclear Information System (INIS)
Every, A.G.
1975-01-01
There are two limiting approximations that are used as starting points for the analysis of a system of interacting electrons and nuclei. The more widely used is the adiabatic approximation in which one assumes that the electrons adjust adiabatically to the instantaneous configuration of the nuclei. This yields an effective internuclear potential. In treating the nuclear motion, this potential can legitimately be expanded to fourth order in nuclear displacements from equilibrium. The difficulties of extending this expansion further are discussed. In situations where two adiabatic potentials approach each other the so-called diabatic approximation has to be used. A novel application to non-radioactive processes in solids is discussed. (author)
A counterexample and a modification to the adiabatic approximation theorem in quantum mechanics
Gingold, H.
1991-01-01
A counterexample to the adiabatic approximation theorem is given when degeneracies are present. A formulation of an alternative version is proposed. A complete asymptotic decomposition for n dimensional self-adjoint Hamiltonian systems is restated and used.
Muonic molecules as three-body Coulomb problem in adiabatic approximation
International Nuclear Information System (INIS)
Decker, M.
1994-04-01
The three-body Coulomb problem is treated within the framework of the hyperspherical adiabatic approach. The surface functions are expanded into Faddeev-type components in order to ensure the equivalent representation of all possible two-body contributions. It is shown that this decomposition reduces the numerical effort considerably. The remaining radial equations are solved both in the extreme and the uncoupled adiabatic approximation to determine the binding energies of the systems (dtμ) and (d 3 Heμ). Whereas the ground state is described very well in the uncoupled adiabatic approximation, the excited states should be treated within the coupled adiabatic approximation to obtain good agreement with variational calculations. (orig.)
Adiabatic approximation in the ultrastrong-coupling regime of an oscillator and two qubits
Energy Technology Data Exchange (ETDEWEB)
Yang, Ping; Zou, Ping [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China); Zhang, Zhi-Ming, E-mail: zmzhang@scnu.edu.cn [Laboratory of Nanophotonic Functional Materials and Devices, SIPSE and LQIT, South China Normal University, Guangzhou 510006 (China)
2012-10-01
We present a system composed of two flux qubits and a transmission-line resonator. Instead of using the rotating wave approximation (RWA), we analyze the system by the adiabatic approximation methods under two opposite extreme conditions. Basic properties of the system are calculated and compared under these two different conditions. Relative energy-level spectrum of the system in the adiabatic displaced oscillator basis is shown, and the theoretical result is compared with the numerical solution. -- Highlights: ► Our work shows that the adiabatic approximations may work also in the ultrastrong coupling limit. ► Both of the approximation methods are valid in a large range of coupling strength, including the ultrastrong coupling regime. ► The results of the approximate formula meet well the exact numerical solution.
S-wave Qanti Qqanti q states in the adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Chao, K T [Oxford Univ. (UK). Dept. of Theoretical Physics
1981-06-01
The static potential energy for an S-wave Qanti Qqanti q system is discussed in an adiabatic (Born-Oppenheimer) approximation. Both spherical bag and arbitrary bag are considered. We concentrate on those Qanti Qqanti q states in which both (Qanti Q) and (qanti q) are colour singlets. Their energy level, wave function, and possible experimental observation are studied.
International Nuclear Information System (INIS)
Garis, N.S.; Karlsson, J.K.H.; Pazsit, I.
2000-01-01
The neutron noise, induced by a rod manoeuvring experiment in a pressurized water reactor, has been calculated by the incore fuel management code SIMULATE. The space- and frequency-dependent noise in the thermal group was calculated through the adiabatic approximation in three dimensions and two-group theory, with the spatial resolution of the nodal model underlying the SIMULATE algorithm. The calculated spatial noise profiles were interpreted on physical terms. They were also compared with model calculations in a 2-D one-group model, where various approximations as well as the full space-dependent response could be calculated. The adiabatic results obtained with SIMULATE can be regarded as reliable for sub-plateau frequencies (below 0.1 Hz). (orig.) [de
Simple Lie groups without the approximation property
DEFF Research Database (Denmark)
Haagerup, Uffe; de Laat, Tim
2013-01-01
For a locally compact group G, let A(G) denote its Fourier algebra, and let M0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-∗ topology...... on the space M0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely, SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center...
The analysis of the elastic scattering of 11Be and 6Li by adiabatic approximation
International Nuclear Information System (INIS)
Takagi, S.
2000-01-01
The unstable nuclei, particularly, the neutron halo nuclei which exist near by the neutron dripline, are recently one of the interesting topics in the nuclear physics. By the adiabatic approximation, R. C. Jhonson et al. have reproduced the experimental differential cross-section of the elastic scattering of the neutron halo nucleus 11 Be (+ l2 C) [1]. We have applied their method to the elastic scattering of another nucleus 6 Li which is not a halo nucleus but has the cluster structure as 11 Be. But it couldn't reproduce the experimental data, so that the method of Johnson et al. is poor in the case of 6 Li. (author)
Approximations to the non-adiabatic particle response in toroidal geometry
International Nuclear Information System (INIS)
Schep, T.J.; Braams, B.J.
1981-08-01
The non-adiabatic part of the particle response to low-frequency electromagnetic modes with long parallel wavelengths is discussed. Analytic approximations to the kernels of the integrals that relate the amplitudes of the perturbed potentials to the non-adiabatic part of the perturbed density in an axisymmetric toroidal configuration are presented and the results are compared with numerical calculations. It is shown that both in the plane slab and in toroidal geometry the kernel contains a logarithmic singularity. This singularity is associated with particles with vanishing parallel velocity so that, in toroidal geometry, it is related with the behaviour of trapped particles near their turning points. In contrast to the plane slab, in toroidal geometry this logarithmic singularity is mainly real and associated with non-resonant particles. Apart from this logarithmic term, the kernel contains a complex regular part arising from resonant as well as from non-resonant particles. The analytic approximations that will be presented make the dispersion relation of drift-type modes in toroidal geometry amenable to analytic as well as to simpler numerical calculation of the growth rate and of the spatial mode structure
Approximations of time-dependent phenomena in quantum mechanics: adiabatic versus sudden processes
International Nuclear Information System (INIS)
Melnichuk, S V; Dijk, W van; Nogami, Y
2005-01-01
By means of a one-dimensional model of a particle in an infinite square-well potential with one wall moving at a constant speed, we examine aspects of time-dependent phenomena in quantum mechanics such as adiabatic and sudden processes. The particle is assumed to be initially in the ground state of the potential with its initial width. The time dependence of the wavefunction of the particle in the well is generally more complicated when the potential well is compressed than when it is expanded. We are particularly interested in the case in which the potential well is suddenly compressed. The so-called sudden approximation is not applicable in this case. We also study the energy of the particle in the changing well as a function of time for expansion and contraction as well as for expansion followed by contraction and vice versa
Coherent states of quantum systems. [Hamiltonians, variable magnetic field, adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Trifonov, D A
1975-01-01
Time-evolution of coherent states and uncertainty relations for quantum systems are considered as well as the relation between the various types of coherent states. The most general form of the Hamiltonians that keep the uncertainty products at a minimum is found using the coherent states. The minimum uncertainty packets are shown to be coherent states of the type nonstationary-system coherent states. Two specific systems, namely that of a generalized N-dimensional oscillator and that of a charged particle moving in a variable magnetic field, are treated as examples. The adiabatic approximation to the uncertainty products for these systems is also discussed and the minimality is found to be retained with an exponential accuracy.
Hamiltonian term for a uniform dc electric field under the adiabatic approximation
Siu, Zhuo Bin; Jalil, Mansoor B. A.; Tan, Seng Ghee
2018-02-01
In this work, we show that the disorder-free Kubo formula for the nonequilibrium value of an observable due to a dc electric field, represented by Exx ̂ in the Hamiltonian, can be interpreted as the standard time-independent theory response of the observable due to a time- and position-independent perturbation HMF. We derive the explicit expression for HMF and show that it originates from the adiabatic approximation to Kubo formula and the time-independent perturbation theory, as well as the Sundaram-Niu wave-packet formalism, we show that HMF reproduces the effect of the E field, i.e., Exx ̂ , up to the first order. This replacement suggests the emergence of a spin current term that is not captured by the standard Kubo formula spin current calculation. We illustrate this via the exemplary spin current for the heavy-hole spin-3/2 Luttinger system.
International Nuclear Information System (INIS)
Armour, E.A.G.; Beker, C.A.; Farina, J.E.G.
1981-01-01
P-wave phaseshifts for positron-hydrogen elastic scattering are calculated using a new adiabatic approximation in which the length of the radius vector from the proton to the positron is fixed but its direction is allowed to vary. This adiabatic approximation makes possible the full inclusion in the calculation of virtual states in which angular momentum is transferred to the target H atom. The results obtained agree qualitatively with the highly accurate results of Bhatia and co-workers (Phys. Rev.; A9:219 (1974)) and are much closer to them than the results obtained using the usual adiabatic approximation in which the radius vector from the proton to the positron is fixed. (author)
Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
International Nuclear Information System (INIS)
Lidar, Daniel A.; Rezakhani, Ali T.; Hamma, Alioscia
2009-01-01
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.
Directory of Open Access Journals (Sweden)
Barban C.
2013-03-01
Full Text Available CoRoT and Kepler measurements reveal us that the amplitudes of solar-like oscillations detected in red giant stars scale from stars to stars in a characteristic way. This observed scaling relation is not yet fully understood but constitutes potentially a powerful diagnostic about mode physics. Quasi-adiabatic theoretical scaling relations in terms of mode amplitudes result in systematic and large differences with the measurements performed for red giant stars. The use of a non-adiabatic intensity-velocity relation derived from a non-adiabatic pulsation code significantly reduces the discrepancy with the CoRoT measurements. The origin of the remaining difference is still unknown. Departure from adiabatic eigenfunction is a very likely explanation that is investigated in the present work using a 3D hydrodynamical model of the surface layers of a representative red giant star.
A simple approximation method for dilute Ising systems
International Nuclear Information System (INIS)
Saber, M.
1996-10-01
We describe a simple approximate method to analyze dilute Ising systems. The method takes into consideration the fluctuations of the effective field, and is based on a probability distribution of random variables which correctly accounts for all the single site kinematic relations. It is shown that the simplest approximation gives satisfactory results when compared with other methods. (author). 12 refs, 2 tabs
A simple approximation of productivity scores of fuzzy production plans
DEFF Research Database (Denmark)
Hougaard, Jens Leth
2005-01-01
This paper suggests a simple approximation procedure for the assessment of productivity scores with respect to fuzzy production plans. The procedure has a clear economic interpretation and all the necessary calculations can be performed in a spreadsheet making it highly operational...
Transitionless driving on adiabatic search algorithm
Energy Technology Data Exchange (ETDEWEB)
Oh, Sangchul, E-mail: soh@qf.org.qa [Qatar Environment and Energy Research Institute, Qatar Foundation, Doha (Qatar); Kais, Sabre, E-mail: kais@purdue.edu [Qatar Environment and Energy Research Institute, Qatar Foundation, Doha (Qatar); Department of Chemistry, Department of Physics and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907 (United States)
2014-12-14
We study quantum dynamics of the adiabatic search algorithm with the equivalent two-level system. Its adiabatic and non-adiabatic evolution is studied and visualized as trajectories of Bloch vectors on a Bloch sphere. We find the change in the non-adiabatic transition probability from exponential decay for the short running time to inverse-square decay in asymptotic running time. The scaling of the critical running time is expressed in terms of the Lambert W function. We derive the transitionless driving Hamiltonian for the adiabatic search algorithm, which makes a quantum state follow the adiabatic path. We demonstrate that a uniform transitionless driving Hamiltonian, approximate to the exact time-dependent driving Hamiltonian, can alter the non-adiabatic transition probability from the inverse square decay to the inverse fourth power decay with the running time. This may open up a new but simple way of speeding up adiabatic quantum dynamics.
International Nuclear Information System (INIS)
Bardo, R.D.; Wolfsberg, M.
1977-01-01
The wave equation for a nonlinear polyatomic molecule is formulated in molecule-fixed coordinates by a method originally due to Hirschfelder and Wigner. Application is made to a triatomic molecule, and the wave equation is explicitly presented in a useful molecule-fixed coordinate system. The formula for the adiabatic correction to the Born--Oppenheimer approximation for a triatomic molecule is obtained. The extension of the present formulation to larger polyatomic molecules is pointed out. Some terms in the triatomic molecule wave equation are discussed in detail
International Nuclear Information System (INIS)
Bakalov, D.D.; Melezhik, V.S.
1987-01-01
The relativistic Hamiltonian for 3-spin particles with electromagnetic interaction has been represented in the form of a sum of terms with factorized dependence on spin, angular and spheroidal variable, and its matrix elements have been expressed in terms of the matrix elements of a small number of ''basic'' operators. The numerical values of the latter have been tabulated, thus allowing for the evaluation of the leading relativistic effects in any 3-body system (with unit particle charge) with and accuracy of ∼ 0(1/2M), where 1/2M=(M 1 -1 +M 2 -1 )/2(M 1 -1 +M 3 -1 ) is the small parameter of the adiabatic expansion (M i , i=1,2,3 being particle masses)
International Nuclear Information System (INIS)
Vinitskii, S.I.; Puzynin, I.V.; Puzynina, T.P.
1992-01-01
An effective adiabatic approach is given for the analysis of three-particle interactions that makes it possible, even in the simple two-level approximation, to reflect all the qualitative characteristics of mesic-atom resonance reactions and to obtain good qualitative agreement with various time-consuming calculations. 6 figs
The analysis of the elastic scattering of {sup 11}Be and {sup 6}Li by adiabatic approximation
Energy Technology Data Exchange (ETDEWEB)
Takagi, S. [Osaka City Univ. (Japan). Dept. of Physics
2000-01-01
The unstable nuclei, particularly, the neutron halo nuclei which exist near by the neutron dripline, are recently one of the interesting topics in the nuclear physics. By the adiabatic approximation, R. C. Jhonson et al. have reproduced the experimental differential cross-section of the elastic scattering of the neutron halo nucleus {sup 11}Be (+{sup l2}C) [1]. We have applied their method to the elastic scattering of another nucleus {sup 6}Li which is not a halo nucleus but has the cluster structure as {sup 11}Be. But it couldn't reproduce the experimental data, so that the method of Johnson et al. is poor in the case of {sup 6}Li. (author)
A simple semi-empirical approximation for bond energy
International Nuclear Information System (INIS)
Jorge, F.E.; Giambiagi, M.; Giambiagi, M.S. de.
1985-01-01
A simple semi-empirical expression for bond energy, related with a generalized bond index, is proposed and applied within the IEH framework. The correlation with experimental data is good for the intermolecular bond energy of base pairs of nucleic acids and other hydrogen bonded systems. The intramolecular bond energies for a sample of molecules containing typical bonds and for hydrides are discussed. The results are compared with those obtained by other methods. (Author) [pt
Simple Methods to Approximate CPC Shape to Preserve Collection Efficiency
Directory of Open Access Journals (Sweden)
David Jafrancesco
2012-01-01
Full Text Available The compound parabolic concentrator (CPC is the most efficient reflective geometry to collect light to an exit port. Anyway, to allow its actual use in solar plants or photovoltaic concentration systems, a tradeoff between system efficiency and cost reduction, the two key issues for sunlight exploitation, must be found. In this work, we analyze various methods to model an approximated CPC aimed to be simpler and more cost-effective than the ideal one, as well as to preserve the system efficiency. The manufacturing easiness arises from the use of truncated conic surfaces only, which can be realized by cheap machining techniques. We compare different configurations on the basis of their collection efficiency, evaluated by means of nonsequential ray-tracing software. Moreover, due to the fact that some configurations are beam dependent and for a closer approximation of a real case, the input beam is simulated as nonsymmetric, with a nonconstant irradiance on the CPC internal surface.
A simple proof of the existence of adiabatic invariants for perturbed reversible problems
International Nuclear Information System (INIS)
Chartier, P; Faou, E
2008-01-01
In this paper, we give a simple proof of the existence of invariants for reversible perturbations of action-angle systems. The originality of this proof is that it does not rely on canonical transformations that bring the system gradually closer to a normal form, but rather on a formal development of the invariant itself
A simple approximation for the current-voltage characteristics of high-power, relativistic diodes
Energy Technology Data Exchange (ETDEWEB)
Ekdahl, Carl, E-mail: cekdahl@lanl.gov [Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2016-06-15
A simple approximation for the current-voltage characteristics of a relativistic electron diode is presented. The approximation is accurate from non-relativistic through relativistic electron energies. Although it is empirically developed, it has many of the fundamental properties of the exact diode solutions. The approximation is simple enough to be remembered and worked on almost any pocket calculator, so it has proven to be quite useful on the laboratory floor.
Engel, D.; Klews, M.; Wunner, G.
2009-02-01
and to provide a program which allows users to calculate as comprehensively as possible energies, wavelengths, and oscillator strengths of medium-Z atoms and ions up to Z=26 in neutron star magnetic field strengths. Obviously, the method for achieving this goal must be highly efficient since for the calculation of synthetic spectra data of many thousands or even millions of atomic transitions may be required. Solution method: As in previous work on the problem (cf. [3,7]) we exploit the fact that a strong magnetic field results in an approximate decoupling of the dynamics of the electrons parallel and perpendicular to the field. In this adiabatic approximation the single-particle wave functions take the form: ψ(ρ,φ,z)=ϕ(ρ,φ)ṡP(z), where ϕ(ρ,φ) are Landau wave functions, describing the (fast) motion perpendicular to the field, and the P(z) are the longitudinal wave functions, describing the (slow) bound motion along the direction of the field. The spins of the electrons are all aligned antiparallel to the magnetic field and need not be accounted for explicitly. The total N-electron wave function is constructed as a Slater determinant of the single-particle wave functions, and the unknown longitudinal wave functions are determined from the Hartree-Fock equations, which follow from inserting the total N-electron wave function into Schrödinger's variational principle for the total energy. The novel feature of our approach [8] is to use finite-element and B-spline techniques to solve the Hartree-Fock equations for atoms in strong magnetic fields. This is accomplished through the following steps: 1) decomposition of the z-axis into finite elements with quadratically widening element borders; 2) sixth-order B-spline expansion of the single-particle wave functions on the individual finite elements; 3) formulation of the variational principle equivalent to the Hartree-Fock equations in terms of the expansion coefficients. This leads to a simple system of linear
Approximate design theory for a simple block design with random block effects
Christof, Karin
1985-01-01
Approximate design theory for a simple block design with random block effects / K. Christof ; F. Pukelsheim. - In: Linear statistical inference / ed. by T. Calinski ... - Berlin u. a. : Springer, 1985. - S. 20-28. - (Lecture notes in statistics ; 35)
Approximate Expressions for the Period of a Simple Pendulum Using a Taylor Series Expansion
Belendez, Augusto; Arribas, Enrique; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi
2011-01-01
An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the…
Simple approximations for the batch-arrival MX/G/1 queue
van Ommeren, Jan C.W.
1990-01-01
In this paper we consider the MX/G/I queueing system with batch arrivals. We give simple approximations for the waiting-time probabilities of individual customers. These approximations are checked numerically and they are found to perform very well for a wide variety of batch-size and service-timed
International Nuclear Information System (INIS)
Toledo Piza, A.F.R. de.
1987-01-01
The Random Phase Approximation (RPA) treatment of nuclear small amplitude vibrations including particle-hole continua is handled in terms of previously developed techniques to treat single-particle resonances in a reaction theoretical framework. A hierarchy of interpretable approximations is derived and a simple working approximation is proposed which involves a numerical effort no larger than that involved in standard, discrete RPA calculations. (Author) [pt
Pawlak, Mariusz; Ben-Asher, Anael; Moiseyev, Nimrod
2018-01-09
We present a simple expression and its derivation for reaction rate coefficients for cold anisotropic collision experiments based on adiabatic variational theory and time-independent non-Hermitian scattering theory. We demonstrate that only the eigenenergies of the resulting one-dimensional Schrödinger equation for different complex adiabats are required. The expression is applied to calculate the Penning ionization rate coefficients of an excited metastable helium atom with molecular hydrogen in an energy range spanning from hundreds of kelvins down to the millikelvin regime. Except for trivial quantities like the masses of the nuclei and the bond length of the diatomic molecule participating in the collision, one needs as input data only the complex potential energy surface (CPES). In calculations, we used recently obtained ab initio CPES by D. Bhattacharya et al. ( J. Chem. Theory Comput. 2017 , 13 , 1682 - 1690 ) without fitting parameters. The results show good accord with current measurements ( Nat. Phys. 2017 , 13 , 35 - 38 ).
Comment on 'Approximation for a large-angle simple pendulum period'
International Nuclear Information System (INIS)
Yuan Qingxin; Ding Pei
2009-01-01
In a recent letter, Belendez et al (2009 Eur. J. Phys. 30 L25-8) proposed an alternative of approximation for the period of a simple pendulum suggested earlier by Hite (2005 Phys. Teach. 43 290-2) who set out to improve on the Kidd and Fogg formula (2002 Phys. Teach. 40 81-3). As a response to the approximation scheme, we obtain another analytical approximation for the large-angle pendulum period, which owns the simplicity and accuracy in evaluating the exact period, and moreover, for amplitudes less than 144 deg. the analytical approximate expression is more accurate than others in the literature. (letters and comments)
Adiabatic compression of elongated field-reversed configurations
Energy Technology Data Exchange (ETDEWEB)
Spencer, R.L.; Tuszewski, M.; Linford, R.K.
1983-06-01
The adiabatic compression of an elongated field-reversed configuration (FRC) is computed by using a one-dimensional approximation. The one-dimensional results are checked against a two-dimensional equilibrium code. For ratios of FRC separatrix length to separatrix radius greater than about ten, the one-dimensional results are accurate within 10%. To this accuracy, the adiabatic compression of FRC's can be described by simple analytic formulas.
Adiabatic compression of elongated field-reversed configurations
International Nuclear Information System (INIS)
Spencer, R.L.; Tuszewski, M.; Linford, R.K.
1983-01-01
The adiabatic compression of an elongated field-reversed configuration (FRC) is computed by using a one-dimensional approximation. The one-dimensional results are checked against a two-dimensional equilibrium code. For ratios of FRC separatrix length to separatrix radius greater than about ten, the one-dimensional results are accurate within 10%. To this accuracy, the adiabatic compression of FRC's can be described by simple analytic formulas
Physical Applications of a Simple Approximation of Bessel Functions of Integer Order
Barsan, V.; Cojocaru, S.
2007-01-01
Applications of a simple approximation of Bessel functions of integer order, in terms of trigonometric functions, are discussed for several examples from electromagnetism and optics. The method may be applied in the intermediate regime, bridging the "small values regime" and the "asymptotic" one, and covering, in this way, an area of great…
A simple method to approximate liver size on cross-sectional images using living liver models
International Nuclear Information System (INIS)
Muggli, D.; Mueller, M.A.; Karlo, C.; Fornaro, J.; Marincek, B.; Frauenfelder, T.
2009-01-01
Aim: To assess whether a simple. diameter-based formula applicable to cross-sectional images can be used to calculate the total liver volume. Materials and methods: On 119 cross-sectional examinations (62 computed tomography and 57 magnetic resonance imaging) a simple, formula-based method to approximate the liver volume was evaluated. The total liver volume was approximated measuring the largest craniocaudal (cc), ventrodorsal (vd), and coronal (cor) diameters by two readers and implementing the equation: Vol estimated =ccxvdxcorx0.31. Inter-rater reliability, agreement, and correlation between liver volume calculation and virtual liver volumetry were analysed. Results: No significant disagreement between the two readers was found. The formula correlated significantly with the volumetric data (r > 0.85, p < 0.0001). In 81% of cases the error of the approximated volume was <10% and in 92% of cases <15% compared to the volumetric data. Conclusion: Total liver volume can be accurately estimated on cross-sectional images using a simple, diameter-based equation.
International Nuclear Information System (INIS)
Manchev, B.; Marinova, B.; Nenkova, B.
2001-01-01
The method described on this report provides a set of simple, easily understood 'approximate' models applicable to a large class of system architectures. Constructing a Markov model of each redundant subsystem and its replacement after that by a pseudo-component develops the approximation models. Of equal importance, the models can be easily understood even of non-experts, including managers, high-level decision-makers and unsophisticated consumers. A necessary requirement for their application is the systems to be repairable and the mean time to repair to be much smaller than the mean time to failure. This ia a case most often met in the real practice. Results of the 'approximate' model application on a technological system of Kozloduy NPP are also presented. The results obtained can be compared quite favorably with the results obtained by using SAPHIRE software
Approximate expressions for the period of a simple pendulum using a Taylor series expansion
International Nuclear Information System (INIS)
Belendez, Augusto; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi; Arribas, Enrique
2011-01-01
An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be performed which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the Kidd-Fogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.
Approximate expressions for the period of a simple pendulum using a Taylor series expansion
Energy Technology Data Exchange (ETDEWEB)
Belendez, Augusto; Marquez, Andres; Ortuno, Manuel; Gallego, Sergi [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Arribas, Enrique, E-mail: a.belendez@ua.es [Departamento de Fisica Aplicada, Escuela Superior de IngenierIa Informatica, Universidad de Castilla-La Mancha, Avda de Espana, s/n, E-02071 Albacete (Spain)
2011-09-15
An approximate scheme for obtaining the period of a simple pendulum for large-amplitude oscillations is analysed and discussed. When students express the exact frequency or the period of a simple pendulum as a function of the oscillation amplitude, and they are told to expand this function in a Taylor series, they always do so using the oscillation amplitude as the variable, without considering that if they change the variable (in this paper to the new variable m), a different Taylor series expansion may be performed which is in addition more accurate than previously published ones. Students tend to believe that there is one and only one way of performing a Taylor series expansion of a specific function. The approximate analytical formula for the period is obtained by means of a Taylor expansion of the exact frequency taking into account the Kidd-Fogg formula for the period. This approach based on the Taylor expansion of the frequency about a suitable value converges quickly even for large amplitudes. We believe that this method may be very useful for teaching undergraduate courses on classical mechanics and helping students understand nonlinear oscillations of a simple pendulum.
Geometry of the Adiabatic Theorem
Lobo, Augusto Cesar; Ribeiro, Rafael Antunes; Ribeiro, Clyffe de Assis; Dieguez, Pedro Ruas
2012-01-01
We present a simple and pedagogical derivation of the quantum adiabatic theorem for two-level systems (a single qubit) based on geometrical structures of quantum mechanics developed by Anandan and Aharonov, among others. We have chosen to use only the minimum geometric structure needed for the understanding of the adiabatic theorem for this case.…
International Nuclear Information System (INIS)
Smith, N.; Pritchard, D.E.
1981-01-01
We have recently demonstrated that the energy corrected sudden (ECS) scaling law of De Pristo et al. when conbined with the power law assumption for the basis rates k/sub l/→0proportional[l(l+1)]/sup -g/ can accurately fit a wide body of rotational energy transfer data. We develop a simple and accurate approximation to this fitting law, and in addition mathematically show the connection between it and our earlier proposed energy based law which also has been successful in describing both theoretical and experimental data on rotationally inelastic collisions
International Nuclear Information System (INIS)
Overcamp, T.J.; Fjeld, R.A.
1987-01-01
A simple approximation for estimating the centerline gamma absorbed dose rates due to a continuous Gaussian plume was developed. To simplify the integration of the dose integral, this approach makes use of the Gaussian cloud concentration distribution. The solution is expressed in terms of the I1 and I2 integrals which were developed for estimating long-term dose due to a sector-averaged Gaussian plume. Estimates of tissue absorbed dose rates for the new approach and for the uniform cloud model were compared to numerical integration of the dose integral over a Gaussian plume distribution
A simple approximative procedure for taking into account low cycle fatigue loads
Energy Technology Data Exchange (ETDEWEB)
Larsen, G; Thomsen, K
1996-09-01
In this paper a simple approximative algorithm for taking into account low cycle fatigue loads is presented. Traditionally, the fatigue life consumption of a wind turbine is estimated by considering a number of (independent) load cases and performing a rainflow counting analysis on each of those. These results are then subsequently synthesized into a total load spectrum by performing a weighed sum of the number of individual load case ranges. The fatigue life consumption is thus obtained by applying the Palmgren-Miner rule on the total load spectrum. However, due to the assumption of isolated basic load cases, the above procedure fail to represent the low-frequency contributions related to the transition between those load cases. The procedure to be described in the following aims at taking the fatigue contribution, related to the transitions between the defined load cases, into account in an approximative manner. (au)
Gabbay, Itay E; Gabbay, Uri
2013-01-01
Excess adverse events may be attributable to poor surgical performance but also to case-mix, which is controlled through the Standardized Incidence Ratio (SIR). SIR calculations can be complicated, resource consuming, and unfeasible in some settings. This article suggests a novel method for SIR approximation. In order to evaluate a potential SIR surrogate measure we predefined acceptance criteria. We developed a new measure - Approximate Risk Index (ARI). "Number Needed for Event" (NNE) is the theoretical number of patients needed "to produce" one adverse event. ARI is defined as the quotient of the group of patients needed for no observed events Ge by total patients treated Ga. Our evaluation compared 2500 surgical units and over 3 million heterogeneous risk surgical patients that were induced through a computerized simulation. Surgical unit's data were computed for SIR and ARI to evaluate compliance with the predefined criteria. Approximation was evaluated by correlation analysis and performance prediction capability by Receiver Operating Characteristics (ROC) analysis. ARI strongly correlates with SIR (r(2) = 0.87, p 0.9) 87% sensitivity and 91% specificity. ARI provides good approximation of SIR and excellent prediction capability. ARI is simple and cost-effective as it requires thorough risk evaluation of only the adverse events patients. ARI can provide a crucial screening and performance evaluation quality control tool. The ARI method may suit other clinical and epidemiological settings where relatively small fraction of the entire population is affected. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.
Dynamical constraints and adiabatic invariants in chemical reactions.
Lorquet, J C
2007-08-23
For long-range electrostatic potentials and, more generally, when the topography of the potential energy surface is locally simple, the reaction path coordinate is adiabatically separable from the perpendicular degrees of freedom. For the ion-permanent dipole and ion-quadrupole interactions, the Poisson bracket of the adiabatic invariant decreases with the interfragment distance more rapidly than the electrostatic potential. The smaller the translational momentum, the moment of inertia of the neutral fragment, and the dipole or quadrupole moments are, the more reliable the adiabatic approximation is, as expected from the usual argumentation. Closed-form expressions for an effective one-dimensional potential in an adiabatic Hamiltonian are given. Connection with a model where the decoupling is exact is obtained in the limit of an infinitely heavy dipole. The dynamics is also constrained by adiabatic invariance for a harmonic valley about a curved reaction path, as shown by the reaction path Hamiltonian method. The maximum entropy method reveals that, as a result of the invariance properties of the entropy, constraints whose validity has been demonstrated locally only subsist in all parts of phase space. However, their form varies continuously, and they are not necessarily expressed in simple terms as they are in the asymptotic region. Therefore, although the influence of adiabatic invariance has been demonstrated at asymptotically large values of the reaction coordinate only, it persists in more interesting ranges.
A learning rule for very simple universal approximators consisting of a single layer of perceptrons.
Auer, Peter; Burgsteiner, Harald; Maass, Wolfgang
2008-06-01
One may argue that the simplest type of neural networks beyond a single perceptron is an array of several perceptrons in parallel. In spite of their simplicity, such circuits can compute any Boolean function if one views the majority of the binary perceptron outputs as the binary output of the parallel perceptron, and they are universal approximators for arbitrary continuous functions with values in [0,1] if one views the fraction of perceptrons that output 1 as the analog output of the parallel perceptron. Note that in contrast to the familiar model of a "multi-layer perceptron" the parallel perceptron that we consider here has just binary values as outputs of gates on the hidden layer. For a long time one has thought that there exists no competitive learning algorithm for these extremely simple neural networks, which also came to be known as committee machines. It is commonly assumed that one has to replace the hard threshold gates on the hidden layer by sigmoidal gates (or RBF-gates) and that one has to tune the weights on at least two successive layers in order to achieve satisfactory learning results for any class of neural networks that yield universal approximators. We show that this assumption is not true, by exhibiting a simple learning algorithm for parallel perceptrons - the parallel delta rule (p-delta rule). In contrast to backprop for multi-layer perceptrons, the p-delta rule only has to tune a single layer of weights, and it does not require the computation and communication of analog values with high precision. Reduced communication also distinguishes our new learning rule from other learning rules for parallel perceptrons such as MADALINE. Obviously these features make the p-delta rule attractive as a biologically more realistic alternative to backprop in biological neural circuits, but also for implementations in special purpose hardware. We show that the p-delta rule also implements gradient descent-with regard to a suitable error measure
Simple polynomial approximation to modified Bethe formula low-energy electron stopping powers data
Energy Technology Data Exchange (ETDEWEB)
Taborda, A., E-mail: ana.taborda@irsn.fr [Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-HOM/SDI/LEDI, BP-17, 92262 Fontenay-aux-Roses (France); Desbrée, A. [Institut de Radioprotection et de Sûreté Nucléaire (IRSN), PRP-HOM/SDI/LEDI, BP-17, 92262 Fontenay-aux-Roses (France); Reis, M.A. [C" 2TN, Campus Tecnológico e Nuclear, Instituto Superior Técnico, Universidade de Lisboa, EN10 km139.7, 2685-066 Bobadela LRS (Portugal)
2015-08-01
A recently published detailed and exhaustive paper on cross-sections for ionisation induced by keV electrons clearly shows that electron phenomena occurring in parallel with X-ray processes may have been dramatically overlooked for many years, mainly when low atomic number species are involved since, in these cases, the fluorescence coefficient is smaller than the Auger yield. An immediate problem is encountered while attempting to tackle the issue. Accounting for electron phenomena requires the knowledge of the stopping power of electrons within, at least, a reasonably small error. Still, the Bethe formula for stopping powers is known to not be valid for electron energies below 30 keV, and its use leads to values far off experimental ones. Recently, a few authors have addressed this problem and both detailed tables of electron stopping powers for various atomic species and attempts to simplify the calculations, have emerged. Nevertheless, its implementation in software routines to efficiently calculate keV electron effects in materials quickly becomes a bit cumbersome. Following a procedure already used to establish efficient methods to calculate ionisation cross-sections by protons and alpha particles, it became clear that a simple polynomial approximation could be set, which allows retrieving the electronic stopping powers with errors of less than 20% for energies above 500 eV and less than 50% for energies between 50 eV and 500 eV. In this work, we present this approximation which, based on just six parameters, allows to recover electron stopping power values that are less than 20% different from recently published experimentally validated tabulated data.
A simple approximation to the bivariate normal distribution with large correlation coefficient
Albers, Willem/Wim; Kallenberg, W.C.M.
1994-01-01
The bivariate normal distribution function is approximated with emphasis on situations where the correlation coefficient is large. The high accuracy of the approximation is illustrated by numerical examples. Moreover, exact upper and lower bounds are presented as well as asymptotic results on the
A simple analytic approximation to the Rayleigh-Bénard stability threshold
Prosperetti, Andrea
2011-01-01
The Rayleigh-Bénard linear stability problem is solved by means of a Fourier series expansion. It is found that truncating the series to just the first term gives an excellent explicit approximation to the marginal stability relation between the Rayleigh number and the wave number of the
On the independent particle approximation of Gauge theories: a simple example
International Nuclear Information System (INIS)
Palladino, B.E.
1992-08-01
In this work, the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1+1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed. (author)
Ziegler, Tom; Krykunov, Mykhaylo; Autschbach, Jochen
2014-09-09
The random phase approximation (RPA) equation of adiabatic time dependent density functional ground state response theory (ATDDFT) has been used extensively in studies of excited states. It extracts information about excited states from frequency dependent ground state response properties and avoids, thus, in an elegant way, direct Kohn-Sham calculations on excited states in accordance with the status of DFT as a ground state theory. Thus, excitation energies can be found as resonance poles of frequency dependent ground state polarizability from the eigenvalues of the RPA equation. ATDDFT is approximate in that it makes use of a frequency independent energy kernel derived from the ground state functional. It is shown in this study that one can derive the RPA equation of ATDDFT from a purely variational approach in which stationary states above the ground state are located using our constricted variational DFT (CV-DFT) method and the ground state functional. Thus, locating stationary states above the ground state due to one-electron excitations with a ground state functional is completely equivalent to solving the RPA equation of TDDFT employing the same functional. The present study is an extension of a previous work in which we demonstrated the equivalence between ATDDFT and CV-DFT within the Tamm-Dancoff approximation.
International Nuclear Information System (INIS)
Abrashkevich, A.G.; Puzynin, I.V.; Vinitskij, S.I.
1997-01-01
A FORTRAN 77 program is presented which calculates asymptotics of potential curves and adiabatic potentials with an accuracy of O(ρ -2 ) in the framework of the hyperspherical adiabatic (HSA) approach. It is shown that matrix elements of the equivalent operator corresponding to the perturbation ρ -2 have a simple form in the basis of the Coulomb parabolic functions in the body-fixed frame and can be easily computed for high values of total orbital momentum and threshold number. The second-order corrections to the adiabatic curves are obtained as the solutions of the corresponding secular equation. The asymptotic potentials obtained can be used for the calculation of the energy levels and radial wave functions of two-electron systems in the adiabatic and coupled-channel approximations of the HSA approach
About the method of approximation of a simple closed plane curve with a sharp edge
Directory of Open Access Journals (Sweden)
Zelenyy A.S.
2017-02-01
Full Text Available it was noted in the article, that initially the problem of interpolation of the simple plane curve arose in the problem of simulation of subsonic flow around a body with the subsequent calculation of the velocity potential using the vortex panel method. However, as it turned out, the practical importance of this method is much wider. This algorithm can be successfully applied in any task that requires a discrete set of points which describe an arbitrary curve: potential function method, flow around an airfoil with the trailing edge (airfoil, liquid drop, etc., analytic expression, which is very difficult to obtain, creation of the font and logo and in some tasks of architecture and garment industry.
International Nuclear Information System (INIS)
Lima, F M S
2009-01-01
In a previous work, O'Connell (Phys. Teach. 40, 24 (2002)) investigated the time dependence of the tension in the string of a simple pendulum oscillating within the small-angle regime. In spite of the approximation sin θ ∼ θ being accurate only for amplitudes below 7 deg., his experimental results are for a pendulum oscillating with an amplitude of about 18 deg., therefore beyond the small-angle regime. This lapse may also be found in some textbooks, laboratory manuals and internet. By noting that the exact analytical solution for this problem involves the so-called Jacobi elliptic functions, which are unknown to most students (even instructors), I take into account a sinusoidal approximate solution for the pendulum equation I introduced in a recent work (Eur. J. Phys. 29 1091 (2008)) for deriving a simple trigonometric approximation for the tension valid for all possible amplitudes. This approximation is compared to both the O'Connell and the exact results, revealing that it is accurate enough for analysing large-angle pendulum experiments. (letters and comments)
Quantum adiabatic Markovian master equations
International Nuclear Information System (INIS)
Albash, Tameem; Zanardi, Paolo; Boixo, Sergio; Lidar, Daniel A
2012-01-01
We develop from first principles Markovian master equations suited for studying the time evolution of a system evolving adiabatically while coupled weakly to a thermal bath. We derive two sets of equations in the adiabatic limit, one using the rotating wave (secular) approximation that results in a master equation in Lindblad form, the other without the rotating wave approximation but not in Lindblad form. The two equations make markedly different predictions depending on whether or not the Lamb shift is included. Our analysis keeps track of the various time and energy scales associated with the various approximations we make, and thus allows for a systematic inclusion of higher order corrections, in particular beyond the adiabatic limit. We use our formalism to study the evolution of an Ising spin chain in a transverse field and coupled to a thermal bosonic bath, for which we identify four distinct evolution phases. While we do not expect this to be a generic feature, in one of these phases dissipation acts to increase the fidelity of the system state relative to the adiabatic ground state. (paper)
International Nuclear Information System (INIS)
Albayrak, Erhan; Keskin, Mustafa
2000-01-01
The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made
Albayrak, E
2000-01-01
The linear chain approximation is used to study the temperature dependence of the order parameters and the phase diagrams of the Blume-Emery-Griffiths model on the simple cubic lattice with dipole-dipole, quadrupole-quadrupole coupling strengths and a crystal-field interaction. The problem is approached introducing first a trial one-dimensional Hamiltonian whose free energy can be calculated exactly by the transfer matrix method. Then using the Bogoliubov variational principle, the free energy of the model is determined. It is assumed that the dipolar and quadrupolar intrachain coupling constants are much stronger than the corresponding interchain constants and confined the attention to the case of nearest-neighbor interactions. The phase transitions are examined and the phase diagrams are obtained for several values of the coupling strengths in the three different planes. A comparison with other approximate techniques is also made.
Directory of Open Access Journals (Sweden)
J. D. Biamonte
2011-06-01
Full Text Available In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator would be controllable, and built using existing technology. In some cases, moving away from gate-model-based implementations of quantum computing may offer a more feasible solution for particular experimental implementations. Here we consider an adiabatic quantum simulator which simulates the ground state properties of sparse Hamiltonians consisting of one- and two-local interaction terms, using sparse Hamiltonians with at most three-local interactions. Properties of such Hamiltonians can be well approximated with Hamiltonians containing only two-local terms. The register holding the simulated ground state is brought adiabatically into interaction with a probe qubit, followed by a single diabatic gate operation on the probe which then undergoes free evolution until measured. This allows one to recover e.g. the ground state energy of the Hamiltonian being simulated. Given a ground state, this scheme can be used to verify the QMA-complete problem LOCAL HAMILTONIAN, and is therefore likely more powerful than classical computing.
A Phase Matching, Adiabatic Accelerator
Energy Technology Data Exchange (ETDEWEB)
Lemery, Francois [Hamburg U.; Flöttmann, Klaus [DESY; Kärtner, Franz [CFEL, Hamburg; Piot, Philippe [Northern Illinois U.
2017-05-01
Tabletop accelerators are a thing of the future. Reducing their size will require scaling down electromagnetic wavelengths; however, without correspondingly high field gradients, particles will be more susceptible to phase-slippage – especially at low energy. We investigate how an adiabatically-tapered dielectric-lined waveguide could maintain phase-matching between the accelerating mode and electron bunch. We benchmark our simple model with CST and implement it into ASTRA; finally we provide a first glimpse into the beam dynamics in a phase-matching accelerator.
Hierarchical theory of quantum adiabatic evolution
International Nuclear Information System (INIS)
Zhang, Qi; Wu, Biao; Gong, Jiangbin
2014-01-01
Quantum adiabatic evolution is a dynamical evolution of a quantum system under slow external driving. According to the quantum adiabatic theorem, no transitions occur between nondegenerate instantaneous energy eigenstates in such a dynamical evolution. However, this is true only when the driving rate is infinitesimally small. For a small nonzero driving rate, there are generally small transition probabilities between the energy eigenstates. We develop a classical mechanics framework to address the small deviations from the quantum adiabatic theorem order by order. A hierarchy of Hamiltonians is constructed iteratively with the zeroth-order Hamiltonian being determined by the original system Hamiltonian. The kth-order deviations are governed by a kth-order Hamiltonian, which depends on the time derivatives of the adiabatic parameters up to the kth-order. Two simple examples, the Landau–Zener model and a spin-1/2 particle in a rotating magnetic field, are used to illustrate our hierarchical theory. Our analysis also exposes a deep, previously unknown connection between classical adiabatic theory and quantum adiabatic theory. (paper)
Nonadiabatic exchange dynamics during adiabatic frequency sweeps.
Barbara, Thomas M
2016-04-01
A Bloch equation analysis that includes relaxation and exchange effects during an adiabatic frequency swept pulse is presented. For a large class of sweeps, relaxation can be incorporated using simple first order perturbation theory. For anisochronous exchange, new expressions are derived for exchange augmented rotating frame relaxation. For isochronous exchange between sites with distinct relaxation rate constants outside the extreme narrowing limit, simple criteria for adiabatic exchange are derived and demonstrate that frequency sweeps commonly in use may not be adiabatic with regard to exchange unless the exchange rates are much larger than the relaxation rates. Otherwise, accurate assessment of the sensitivity to exchange dynamics will require numerical integration of the rate equations. Examples of this situation are given for experimentally relevant parameters believed to hold for in-vivo tissue. These results are of significance in the study of exchange induced contrast in magnetic resonance imaging. Copyright © 2016 Elsevier Inc. All rights reserved.
Lobe, Elisabeth; Stollenwerk, Tobias; Tröltzsch, Anke
2015-01-01
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic ...
Semi adiabatic theory of seasonal Markov processes
Energy Technology Data Exchange (ETDEWEB)
Talkner, P [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1999-08-01
The dynamics of many natural and technical systems are essentially influenced by a periodic forcing. Analytic solutions of the equations of motion for periodically driven systems are generally not known. Simulations, numerical solutions or in some limiting cases approximate analytic solutions represent the known approaches to study the dynamics of such systems. Besides the regime of weak periodic forces where linear response theory works, the limit of a slow driving force can often be treated analytically using an adiabatic approximation. For this approximation to hold all intrinsic processes must be fast on the time-scale of a period of the external driving force. We developed a perturbation theory for periodically driven Markovian systems that covers the adiabatic regime but also works if the system has a single slow mode that may even be slower than the driving force. We call it the semi adiabatic approximation. Some results of this approximation for a system exhibiting stochastic resonance which usually takes place within the semi adiabatic regime are indicated. (author) 1 fig., 8 refs.
Electron Correlation from the Adiabatic Connection for Multireference Wave Functions
Pernal, Katarzyna
2018-01-01
An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
Directory of Open Access Journals (Sweden)
Dave Bacon
2013-06-01
Full Text Available We describe a many-body quantum system that can be made to quantum compute by the adiabatic application of a large applied field to the system. Prior to the application of the field, quantum information is localized on one boundary of the device, and after the application of the field, this information propagates to the other side of the device, with a quantum circuit applied to the information. The applied circuit depends on the many-body Hamiltonian of the material, and the computation takes place in a degenerate ground space with symmetry-protected topological order. Such “adiabatic quantum transistors” are universal adiabatic quantum computing devices that have the added benefit of being modular. Here, we describe this model, provide arguments for why it is an efficient model of quantum computing, and examine these many-body systems in the presence of a noisy environment.
Wireless adiabatic power transfer
International Nuclear Information System (INIS)
Rangelov, A.A.; Suchowski, H.; Silberberg, Y.; Vitanov, N.V.
2011-01-01
Research highlights: → Efficient and robust mid-range wireless energy transfer between two coils. → The adiabatic energy transfer is analogous to adiabatic passage in quantum optics. → Wireless energy transfer is insensitive to any resonant constraints. → Wireless energy transfer is insensitive to noise in the neighborhood of the coils. - Abstract: We propose a technique for efficient mid-range wireless power transfer between two coils, by adapting the process of adiabatic passage for a coherently driven two-state quantum system to the realm of wireless energy transfer. The proposed technique is shown to be robust to noise, resonant constraints, and other interferences that exist in the neighborhood of the coils.
Adiabatic capture and debunching
International Nuclear Information System (INIS)
Ng, K.Y.
2012-01-01
In the study of beam preparation for the g-2 experiment, adiabatic debunching and adiabatic capture are revisited. The voltage programs for these adiabbatic processes are derived and their properties discussed. Comparison is made with some other form of adiabatic capture program. The muon g-2 experiment at Fermilab calls for intense proton bunches for the creation of muons. A booster batch of 84 bunches is injected into the Recycler Ring, where it is debunched and captured into 4 intense bunches with the 2.5-MHz rf. The experiment requires short bunches with total width less than 100 ns. The transport line from the Recycler to the muon-production target has a low momentum aperture of ∼ ±22 MeV. Thus each of the 4 intense proton bunches required to have an emittance less than ∼ 3.46 eVs. The incoming booster bunches have total emittance ∼ 8.4 eVs, or each one with an emittance ∼ 0.1 eVs. However, there is always emittance increase when the 84 booster bunches are debunched. There will be even larger emittance increase during adiabatic capture into the buckets of the 2.5-MHz rf. In addition, the incoming booster bunches may have emittances larger than 0.1 eVs. In this article, we will concentrate on the analysis of the adiabatic capture process with the intention of preserving the beam emittance as much as possible. At this moment, beam preparation experiment is being performed at the Main Injector. Since the Main Injector and the Recycler Ring have roughly the same lattice properties, we are referring to adiabatic capture in the Main Injector instead in our discussions.
Messica, A.
2016-10-01
The probability distribution function of a weighted sum of non-identical lognormal random variables is required in various fields of science and engineering and specifically in finance for portfolio management as well as exotic options valuation. Unfortunately, it has no known closed form and therefore has to be approximated. Most of the approximations presented to date are complex as well as complicated for implementation. This paper presents a simple, and easy to implement, approximation method via modified moments matching and a polynomial asymptotic series expansion correction for a central limit theorem of a finite sum. The method results in an intuitively-appealing and computation-efficient approximation for a finite sum of lognormals of at least ten summands and naturally improves as the number of summands increases. The accuracy of the method is tested against the results of Monte Carlo simulationsand also compared against the standard central limit theorem andthe commonly practiced Markowitz' portfolio equations.
Adiabatic and isothermal resistivities
International Nuclear Information System (INIS)
Fishman, R.S.
1989-01-01
The force-balance method is used to calculate the isothermal resistivity to first order in the electric field. To lowest order in the impurity potential, the isothermal resistivity disagrees with the adiabatic results of the Kubo formula and the Boltzmann equation. However, an expansion of the isothermal resistivity in powers of the impurity potential is divergent, with two sets of divergent terms. The first set arises from the density matrix of the relative electron-phonon system. The second set arises from the explicit dependence of the density matrix on the electric field, which was ignored by force-balance calculations. These divergent contributions are calculated inductively, by applying a recursion relation for the Green's functions. Using the λ 2 t→∞ limit of van Hove, I show that the resummation of these divergent terms yields the same result for the resistivity as the adiabatic calculations, in direct analogy with the work of Argyres and Sigel, and Huberman and Chester
Adiabatically steered open quantum systems: Master equation and optimal phase
International Nuclear Information System (INIS)
Salmilehto, J.; Solinas, P.; Ankerhold, J.; Moettoenen, M.
2010-01-01
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a nonsteered system in the first superadiabatic basis. It is potentially efficient in obtaining higher-order equations. Furthermore, we show how to select the phases of the adiabatic eigenstates to minimize the local adiabatic parameter and how this selection leads to states which are invariant under a local gauge change. We also discuss the effects of the adiabatic noncyclic geometric phase on the master equation.
Modeling non-adiabatic photoexcited reaction dynamics in condensed phases
International Nuclear Information System (INIS)
Coker, D.F.
2003-01-01
Reactions of photoexcited molecules, ions, and radicals in condensed phase environments involve non-adiabatic dynamics over coupled electronic surfaces. We focus on how local environmental symmetries can effect non-adiabatic coupling between excited electronic states and thus influence, in a possibly controllable way, the outcome of photo-excited reactions. Semi-classical and mixed quantum-classical non-adiabatic molecular dynamics methods, together with semi-empirical excited state potentials are used to probe the dynamical mixing of electronic states in different environments from molecular clusters, to simple liquids and solids, and photo-excited reactions in complex reaction environments such as zeolites
Improving the positive feedback adiabatic logic familiy
Directory of Open Access Journals (Sweden)
J. Fischer
2004-01-01
Full Text Available Positive Feedback Adiabatic Logic (PFAL shows the lowest energy dissipation among adiabatic logic families based on cross-coupled transistors, due to the reduction of both adiabatic and non-adiabatic losses. The dissipation primarily depends on the resistance of the charging path, which consists of a single p-channel MOSFET during the recovery phase. In this paper, a new logic family called Improved PFAL (IPFAL is proposed, where all n- and pchannel devices are swapped so that the charge can be recovered through an n-channel MOSFET. This allows to decrease the resistance of the charging path up to a factor of 2, and it enables a significant reduction of the energy dissipation. Simulations based on a 0.13µm CMOS process confirm the improvements in terms of power consumption over a large frequency range. However, the same simple design rule, which enables in PFAL an additional reduction of the dissipation by optimal transistor sizing, does not apply to IPFAL. Therefore, the influence of several sources of dissipation for a generic IPFAL gate is illustrated and discussed, in order to lower the power consumption and achieve better performance.
Convergence of hyperspherical adiabatic expansion for helium-like systems
International Nuclear Information System (INIS)
Abrashkevich, A.G.; Abrashkevich, D.G.; Pojda, V.Yu.; Vinitskij, S.I.; Kaschiev, M.S.; Puzynin, I.V.
1988-01-01
The convergence of hyperspherical adiabatic expansion has been studied numerically. The spectral problems arising after separation of variables are solved by the finite-difference and finite element methods. The energies of the ground and some doubly excited staes of a hydrogen ion are calculated in the six-channel approximation within the 10 -4 a.u. accuracy. Obtained results demonstrate a rapid convergence of the hyperspherical adiabatic expansion. 14 refs.; 5 tabs
Adiabatic analysis of collisions. III. Remarks on the spin model
International Nuclear Information System (INIS)
Fano, U.
1979-01-01
Analysis of a spin-rotation model illustrates how transitions between adiabatic channel states stem from the second, rather than from the first, rate of change of these states, provided that appropriate identification of channels and scaling of the independent variable are used. These remarks, like the earlier development of a post-adiabatic approach, aim at elucidating the surprising success of approximate separation of variables in the treatment of complex mechanical systems
Non-adiabatic generator-coordinate calculation of H2+
International Nuclear Information System (INIS)
Tostes, J.G.R.; Para Univ., Belem; Toledo Piza, A.F.R. de
1982-10-01
A non-adiabatic calculation of the few lowest J=O states in the H 2+ molecule done within the framework of the Generator Coordinate Method is reported. Substantial accuracy is achivied with the diagonalization of matrices of very modest dimensions. The resulting wavefunctions are strongly dominated by just a few basis states. The computational scheme is set up so as to take the best advantage of good analytical approximations to existing adiabatic molecular wavefunctions. (Author) [pt
Albash, Tameem; Lidar, Daniel A.
2018-01-01
Adiabatic quantum computing (AQC) started as an approach to solving optimization problems and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. This review gives an account of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. Several variants are presented of the adiabatic theorem, the cornerstone of AQC, and examples are given of explicit AQC algorithms that exhibit a quantum speedup. An overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory is given. Considerable space is devoted to stoquastic AQC, the setting of most AQC work to date, where obstructions to success and their possible resolutions are discussed.
Piecewise adiabatic following in non-Hermitian cycling
Gong, Jiangbin; Wang, Qing-hai
2018-05-01
The time evolution of periodically driven non-Hermitian systems is in general nonunitary but can be stable. It is hence of considerable interest to examine the adiabatic following dynamics in periodically driven non-Hermitian systems. We show in this work the possibility of piecewise adiabatic following interrupted by hopping between instantaneous system eigenstates. This phenomenon is first observed in a computational model and then theoretically explained, using an exactly solvable model, in terms of the Stokes phenomenon. In the latter case, the piecewise adiabatic following is shown to be a genuine critical behavior and the precise phase boundary in the parameter space is located. Interestingly, the critical boundary for piecewise adiabatic following is found to be unrelated to the domain for exceptional points. To characterize the adiabatic following dynamics, we also advocate a simple definition of the Aharonov-Anandan (AA) phase for nonunitary cyclic dynamics, which always yields real AA phases. In the slow driving limit, the AA phase reduces to the Berry phase if adiabatic following persists throughout the driving without hopping, but oscillates violently and does not approach any limit in cases of piecewise adiabatic following. This work exposes the rich features of nonunitary dynamics in cases of slow cycling and should stimulate future applications of nonunitary dynamics.
ADIABATIC HEATING OF CONTRACTING TURBULENT FLUIDS
International Nuclear Information System (INIS)
Robertson, Brant; Goldreich, Peter
2012-01-01
Turbulence influences the behavior of many astrophysical systems, frequently by providing non-thermal pressure support through random bulk motions. Although turbulence is commonly studied in systems with constant volume and mean density, turbulent astrophysical gases often expand or contract under the influence of pressure or gravity. Here, we examine the behavior of turbulence in contracting volumes using idealized models of compressed gases. Employing numerical simulations and an analytical model, we identify a simple mechanism by which the turbulent motions of contracting gases 'adiabatically heat', experiencing an increase in their random bulk velocities until the largest eddies in the gas circulate over a Hubble time of the contraction. Adiabatic heating provides a mechanism for sustaining turbulence in gases where no large-scale driving exists. We describe this mechanism in detail and discuss some potential applications to turbulence in astrophysical settings.
Landahl, Andrew
2012-10-01
Quantum computers promise to exploit counterintuitive quantum physics principles like superposition, entanglement, and uncertainty to solve problems using fundamentally fewer steps than any conventional computer ever could. The mere possibility of such a device has sharpened our understanding of quantum coherent information, just as lasers did for our understanding of coherent light. The chief obstacle to developing quantum computer technology is decoherence--one of the fastest phenomena in all of physics. In principle, decoherence can be overcome by using clever entangled redundancies in a process called fault-tolerant quantum error correction. However, the quality and scale of technology required to realize this solution appears distant. An exciting alternative is a proposal called ``adiabatic'' quantum computing (AQC), in which adiabatic quantum physics keeps the computer in its lowest-energy configuration throughout its operation, rendering it immune to many decoherence sources. The Adiabatic Quantum Architectures In Ultracold Systems (AQUARIUS) Grand Challenge Project at Sandia seeks to demonstrate this robustness in the laboratory and point a path forward for future hardware development. We are building devices in AQUARIUS that realize the AQC architecture on up to three quantum bits (``qubits'') in two platforms: Cs atoms laser-cooled to below 5 microkelvin and Si quantum dots cryo-cooled to below 100 millikelvin. We are also expanding theoretical frontiers by developing methods for scalable universal AQC in these platforms. We have successfully demonstrated operational qubits in both platforms and have even run modest one-qubit calculations using our Cs device. In the course of reaching our primary proof-of-principle demonstrations, we have developed multiple spinoff technologies including nanofabricated diffractive optical elements that define optical-tweezer trap arrays and atomic-scale Si lithography commensurate with placing individual donor atoms with
Adiabatic perturbation theory in quantum dynamics
Teufel, Stefan
2003-01-01
Separation of scales plays a fundamental role in the understanding of the dynamical behaviour of complex systems in physics and other natural sciences. A prominent example is the Born-Oppenheimer approximation in molecular dynamics. This book focuses on a recent approach to adiabatic perturbation theory, which emphasizes the role of effective equations of motion and the separation of the adiabatic limit from the semiclassical limit. A detailed introduction gives an overview of the subject and makes the later chapters accessible also to readers less familiar with the material. Although the general mathematical theory based on pseudodifferential calculus is presented in detail, there is an emphasis on concrete and relevant examples from physics. Applications range from molecular dynamics to the dynamics of electrons in a crystal and from the quantum mechanics of partially confined systems to Dirac particles and nonrelativistic QED.
Interacting adiabatic quantum motor
Bruch, Anton; Kusminskiy, Silvia Viola; Refael, Gil; von Oppen, Felix
2018-05-01
We present a field-theoretic treatment of an adiabatic quantum motor. We explicitly discuss a motor called the Thouless motor which is based on a Thouless pump operating in reverse. When a sliding periodic potential is considered to be the motor degree of freedom, a bias voltage applied to the electron channel sets the motor in motion. We investigate a Thouless motor whose electron channel is modeled as a Luttinger liquid. Interactions increase the gap opened by the periodic potential. For an infinite Luttinger liquid the coupling-induced friction is enhanced by electron-electron interactions. When the Luttinger liquid is ultimately coupled to Fermi liquid reservoirs, the dissipation reduces to its value for a noninteracting electron system for a constant motor velocity. Our results can also be applied to a motor based on a nanomagnet coupled to a quantum spin Hall edge.
Topology hidden behind the breakdown of adiabaticity
International Nuclear Information System (INIS)
Fu, L.-B.; Chen, S.-G.
2005-01-01
For classical Hamiltonian systems, the adiabatic condition may fail at some critical points. However, the breakdown of the adiabatic condition does not always cause the adiabatic evolution to be destroyed. In this paper, we suggest a supplemental condition of the adiabatic evolution for the fixed points of classical Hamiltonian systems when the adiabatic condition breaks down at the critical points. As an example, we investigate the adiabatic evolution of the fixed points of a classical Hamiltonian system which has a number of applications
Decoherence in adiabatic quantum computation
Albash, Tameem; Lidar, Daniel A.
2015-06-01
Recent experiments with increasingly larger numbers of qubits have sparked renewed interest in adiabatic quantum computation, and in particular quantum annealing. A central question that is repeatedly asked is whether quantum features of the evolution can survive over the long time scales used for quantum annealing relative to standard measures of the decoherence time. We reconsider the role of decoherence in adiabatic quantum computation and quantum annealing using the adiabatic quantum master-equation formalism. We restrict ourselves to the weak-coupling and singular-coupling limits, which correspond to decoherence in the energy eigenbasis and in the computational basis, respectively. We demonstrate that decoherence in the instantaneous energy eigenbasis does not necessarily detrimentally affect adiabatic quantum computation, and in particular that a short single-qubit T2 time need not imply adverse consequences for the success of the quantum adiabatic algorithm. We further demonstrate that boundary cancellation methods, designed to improve the fidelity of adiabatic quantum computing in the closed-system setting, remain beneficial in the open-system setting. To address the high computational cost of master-equation simulations, we also demonstrate that a quantum Monte Carlo algorithm that explicitly accounts for a thermal bosonic bath can be used to interpolate between classical and quantum annealing. Our study highlights and clarifies the significantly different role played by decoherence in the adiabatic and circuit models of quantum computing.
Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics
International Nuclear Information System (INIS)
White, Alexander J.; Gorshkov, Vyacheslav N.; Wang, Ruixi; Tretiak, Sergei; Mozyrsky, Dmitry
2014-01-01
Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantum mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement
Photoionization by a bichromatic field: Adiabatic theory
International Nuclear Information System (INIS)
Pazdzersky, V.A.; Yurovsky, V.A.
1995-01-01
Atom photoionization by the superposition of a fundamental field and its second harmonic is considered. The finite analytical expressions for the photoionization probability are obtained using the adiabatic approximation. They demonstrate that the photoelectron angular distribution has a polar symmetry when the electrical field strength has a maximal polar asymmetry and the distribution is asymmetrical when the field is symmetrical. A strict proof of the polar symmetry of the photoionization probability in the case of the electrical field with maximal asymmetry is deduced using the Keldysh-Faisal-Reiss theories. The obtained results are in agreement with the experimental data available
Neutron generator based on adiabatic trap
International Nuclear Information System (INIS)
Golovin, I.N.; Zhil'tsov, V.A.; Panov, D.A.; Skovoroda, A.A.; Shatalov, G.E.; Shcherbakov, A.G.
1988-01-01
A possibility of 14 MeV neutron generator (NG) production on the basis of axial-symmetric adiabatic trap with MHD cusped armature for the testing of materials and elements of the DT reactor first wall and blanket structure is discussed. General requirements to NG are formulated. It is shown that the NG variant discussed meets the requirements formulated. Approximate calculation of the NG parameters has shown that total energy consumption by the generator does not exceed 220 MW at neutron flux specific capacity of 2.5 MW/m 2 and radiation test area of 5-6 m 2
A simple method for one-loop renormalization in curved space-time
Energy Technology Data Exchange (ETDEWEB)
Markkanen, Tommi [Helsinki Institute of Physics and Department of Physics, P.O. Box 64, FI-00014, University of Helsinki (Finland); Tranberg, Anders, E-mail: tommi.markkanen@helsinki.fi, E-mail: anders.tranberg@uis.no [Niels Bohr International Academy and Discovery Center, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen (Denmark)
2013-08-01
We present a simple method for deriving the renormalization counterterms from the components of the energy-momentum tensor in curved space-time. This method allows control over the finite parts of the counterterms and provides explicit expressions for each term separately. As an example, the method is used for the self-interacting scalar field in a Friedmann-Robertson-Walker metric in the adiabatic approximation, where we calculate the renormalized equation of motion for the field and the renormalized components of the energy-momentum tensor to fourth adiabatic order while including interactions to one-loop order. Within this formalism the trace anomaly, including contributions from interactions, is shown to have a simple derivation. We compare our results to those obtained by two standard methods, finding agreement with the Schwinger-DeWitt expansion but disagreement with adiabatic subtractions for interacting theories.
Analysis of adiabatic transfer in cavity quantum electrodynamics
Indian Academy of Sciences (India)
adiabatic transfer process through the 'dark state' by a slow variation of the control laser intensity. ... control field of Rabi frequency C(t) transfers one photon in the cavity mode to a long- .... It gives an approximate statistical description of the.
Adiabatic temperature change from non-adiabatic measurements
Czech Academy of Sciences Publication Activity Database
Carvalho, A.M.G.; Mejía, C.S.; Ponte, C.A.; Silva, L.E.L.; Kaštil, Jiří; Kamarád, Jiří; Gomes, A.M.
2016-01-01
Roč. 122, č. 3 (2016), s. 1-5, č. článku 246. ISSN 0947-8396 Institutional support: RVO:68378271 Keywords : magnetocaloric effect * adiabatic temperature change * calorimetric device * gadolinium Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.455, year: 2016
Interplay between electric and magnetic effect in adiabatic polaritonic systems
Alabastri, Alessandro; Toma, Andrea; Liberale, Carlo; Chirumamilla, Manohar; Giugni, Andrea; De Angelis, Francesco De; Das, Gobind; Di Fabrizio, Enzo M.; Proietti Zaccaria, Remo
2013-01-01
We report on the possibility of realizing adiabatic compression of polaritonic wave on a metallic conical nano-structure through an oscillating electric potential (quasi dynamic regime). By comparing this result with an electromagnetic wave excitation, we were able to relate the classical lighting-rod effect to adiabatic compression. Furthermore, we show that while the magnetic contribution plays a marginal role in the formation of adiabatic compression, it provides a blue shift in the spectral region. In particular, magnetic permeability can be used as a free parameter for tuning the polaritonic resonances. The peculiar form of adiabatic compression is instead dictated by both the source and the metal permittivity. The analysis is performed by starting from a simple electrostatic system to end with the complete electromagnetic one through intermediate situations such as the quasi-electrostatic and quasi-dynamic regimes. Each configuration is defined by a particular set of equations which allows to clearly determine the individual role played by the electric and magnetic contribution in the generation of adiabatic compression. We notice that these findings can be applied for the realization of a THz nano-metric generator. © 2013 Optical Society of America.
Dynamics of ionizing shock waves on adiabatic motions of gases
International Nuclear Information System (INIS)
Zorev, N.N.; Sklizkov, G.V.; Shikanov, A.S.
1982-01-01
Results are presented of an experimental investigation of free (adiabatic) motion of a spherical ionizing wave in deuterium produced by an expanding laser plasma. It is shown that the discrepancy between the free movement of shock waves (which lead to total ionization of the gas) and the Sedov-Taylor model of a spontaneous point explosion is not related to variations in the adiabat exponent γ and the motion occurs for a constant γ=5/3. The effect is ascribed to the influence of the shock wave front structure on the dynamics of its propagation. An analytic expression for the motion of symmetric ionizing shock waves is found which has an accuracy of better than 1%. As a result the adiabat exponent was determined experimentally. A method for determining the energy of a shock wave on the basis of its dynamics of motion is developed which has an accuracy of approximately 5% [ru
Failure of geometric electromagnetism in the adiabatic vector Kepler problem
International Nuclear Information System (INIS)
Anglin, J.R.; Schmiedmayer, J.
2004-01-01
The magnetic moment of a particle orbiting a straight current-carrying wire may precess rapidly enough in the wire's magnetic field to justify an adiabatic approximation, eliminating the rapid time dependence of the magnetic moment and leaving only the particle position as a slow degree of freedom. To zeroth order in the adiabatic expansion, the orbits of the particle in the plane perpendicular to the wire are Keplerian ellipses. Higher-order postadiabatic corrections make the orbits precess, but recent analysis of this 'vector Kepler problem' has shown that the effective Hamiltonian incorporating a postadiabatic scalar potential ('geometric electromagnetism') fails to predict the precession correctly, while a heuristic alternative succeeds. In this paper we resolve the apparent failure of the postadiabatic approximation, by pointing out that the correct second-order analysis produces a third Hamiltonian, in which geometric electromagnetism is supplemented by a tensor potential. The heuristic Hamiltonian of Schmiedmayer and Scrinzi is then shown to be a canonical transformation of the correct adiabatic Hamiltonian, to second order. The transformation has the important advantage of removing a 1/r 3 singularity which is an artifact of the adiabatic approximation
International Nuclear Information System (INIS)
Habershon, Scott
2013-01-01
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency
Habershon, Scott
2013-09-14
We introduce a new approach for calculating quantum time-correlation functions and time-dependent expectation values in many-body thermal systems; both electronically adiabatic and non-adiabatic cases can be treated. Our approach uses a path integral simulation to sample an initial thermal density matrix; subsequent evolution of this density matrix is equivalent to solution of the time-dependent Schrödinger equation, which we perform using a linear expansion of Gaussian wavepacket basis functions which evolve according to simple classical-like trajectories. Overall, this methodology represents a formally exact approach for calculating time-dependent quantum properties; by introducing approximations into both the imaginary-time and real-time propagations, this approach can be adapted for complex many-particle systems interacting through arbitrary potentials. We demonstrate this method for the spin Boson model, where we find good agreement with numerically exact calculations. We also discuss future directions of improvement for our approach with a view to improving accuracy and efficiency.
Adiabatic cooling processes in frustrated magnetic systems with pyrochlore structure
Jurčišinová, E.; Jurčišin, M.
2017-11-01
We investigate in detail the process of adiabatic cooling in the framework of the exactly solvable antiferromagnetic spin-1/2 Ising model in the presence of the external magnetic field on an approximate lattice with pyrochlore structure. The behavior of the entropy of the model is studied and exact values of the residual entropies of all ground states are found. The temperature variation of the system under adiabatic (de)magnetization is investigated and the central role of the macroscopically degenerated ground states in cooling processes is explicitly demonstrated. It is shown that the model parameter space of the studied geometrically frustrated system is divided into five disjunct regions with qualitatively different processes of the adiabatic cooling. The effectiveness of the adiabatic (de)magnetization cooling in the studied model is compared to the corresponding processes in paramagnetic salts. It is shown that the processes of the adiabatic cooling in the antiferromagnetic frustrated systems are much more effective especially in nonzero external magnetic fields. It means that the frustrated magnetic materials with pyrochlore structure can be considered as very promising refrigerants mainly in the situations with nonzero final values of the magnetic field.
Studies in Chaotic adiabatic dynamics
International Nuclear Information System (INIS)
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the open-quotes goodnessclose quotes of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees)
An Adiabatic Phase-Matching Accelerator
Energy Technology Data Exchange (ETDEWEB)
Lemery, Francois [DESY; Floettmann, Klaus [DESY; Piot, Philippe [Northern Illinois U.; Kaertner, Franz X. [Hamburg U.; Assmann, Ralph [DESY
2017-12-22
We present a general concept to accelerate non-relativistic charged particles. Our concept employs an adiabatically-tapered dielectric-lined waveguide which supports accelerating phase velocities for synchronous acceleration. We propose an ansatz for the transient field equations, show it satisfies Maxwell's equations under an adiabatic approximation and find excellent agreement with a finite-difference time-domain computer simulation. The fields were implemented into the particle-tracking program {\\sc astra} and we present beam dynamics results for an accelerating field with a 1-mm-wavelength and peak electric field of 100~MV/m. The numerical simulations indicate that a $\\sim 200$-keV electron beam can be accelerated to an energy of $\\sim10$~MeV over $\\sim 10$~cm. The novel scheme is also found to form electron beams with parameters of interest to a wide range of applications including, e.g., future advanced accelerators, and ultra-fast electron diffraction.
Ion Motion in the Adiabatic Focuser
International Nuclear Information System (INIS)
Henestroza, E.; Sessler, A.M.; Yu, S.S.
2006-01-01
In this paper we numerically study the effect of ion motion in an adiabatic focuser, motivated by a recent suggestion that ion motion in an adiabatic focuser might be significant and even preclude operation of the focuser as previously envisioned. It is shown that despite ion motion the adiabatic focuser should work as well as originally envisioned
Adiabatic quantum pumping and charge quantization
International Nuclear Information System (INIS)
Kashcheyevs, V; Aharony, A.; Entin-Wohlmanl, O.
2004-01-01
Full Text:Modern techniques for coherent manipulation of electrons at the nano scale (electrostatic gating, surface acoustic waves) allow for studies of the adiabatic quantum pumping effect - a directed current induced by a slowly varying external perturbation. Scattering theory of pumping predicts transfer of an almost integer number of electrons per cycle if instantaneous transmission is determined by a sequence of resonances. We show that this quantization can be explained in terms of loading/unloading quasi-bound virtual states, and derive a tool for analyzing quantized pumping induced by a general potential. This theory is applied to a simple model of pumping due to surface acoustic waves. The results reproduce all the qualitative features observed in actual experiments
Adiabatic equilibrium models for direct containment heating
International Nuclear Information System (INIS)
Pilch, M.; Allen, M.D.
1991-01-01
Probabilistic risk assessment (PRA) studies are being extended to include a wider spectrum of reactor plants than was considered in NUREG-1150. There is a need for simple direct containment heating (DCH) models that can be used for screening studies aimed at identifying potentially significant contributors to overall risk in individual nuclear power plants. This paper presents two adiabatic equilibrium models suitable for the task. The first, a single-cell model, places a true upper bound on DCH loads. This upper bound, however, often far exceeds reasonable expectations of containment loads based on CONTAIN calculations and experiment observations. In this paper, a two cell model is developed that captures the major mitigating feature of containment compartmentalization, thus providing more reasonable estimates of the containment load
Quantum Adiabatic Optimization and Combinatorial Landscapes
Smelyanskiy, V. N.; Knysh, S.; Morris, R. D.
2003-01-01
In this paper we analyze the performance of the Quantum Adiabatic Evolution (QAE) algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, gamma = M / N. We introduce a set of macroscopic parameters (landscapes) and put forward an ansatz of universality for random bit flips. We then formulate the problem of finding the smallest eigenvalue and the excitation gap as a statistical mechanics problem. We use the so-called annealing approximation with a refinement that a finite set of macroscopic variables (verses only energy) is used, and are able to show the existence of a dynamic threshold gamma = gammad, beyond which QAE should take an exponentially long time to find a solution. We compare the results for extended and simplified sets of landscapes and provide numerical evidence in support of our universality ansatz.
Quantum tunneling in the adiabatic Dicke model
International Nuclear Information System (INIS)
Chen Gang; Chen Zidong; Liang Jiuqing
2007-01-01
The Dicke model describes N two-level atoms interacting with a single-mode bosonic field and exhibits a second-order phase transition from the normal to the superradiant phase. The energy levels are not degenerate in the normal phase but have degeneracy in the superradiant phase, where quantum tunneling occurs. By means of the Born-Oppenheimer approximation and the instanton method in quantum field theory, the tunneling splitting, inversely proportional to the tunneling rate for the adiabatic Dicke model, in the superradiant phase can be evaluated explicitly. It is shown that the tunneling splitting vanishes as exp(-N) for large N, whereas for small N it disappears as √(N)/exp(N). The dependence of the tunneling splitting on the relevant parameters, especially on the atom-field coupling strength, is also discussed
Adiabatic theorem and spectral concentration
International Nuclear Information System (INIS)
Nenciu, G.
1981-01-01
The spectral concentration of arbitrary order, for the Stark effect is proved to exist for a large class of Hamiltonians appearing in nonrelativistic and relativistic quantum mechanics. The results are consequences of an abstract theorem about the spectral concentration for self-ad oint operators. A general form of the adiabatic theorem of quantum mechanics, generalizing an earlier result of the author as well as some results of Lenard, is also proved [ru
Plasma heating by adiabatic compression
International Nuclear Information System (INIS)
Ellis, R.A. Jr.
1972-01-01
These two lectures will cover the following three topics: (i) The application of adiabatic compression to toroidal devices is reviewed. The special case of adiabatic compression in tokamaks is considered in more detail, including a discussion of the equilibrium, scaling laws, and heating effects. (ii) The ATC (Adiabatic Toroidal Compressor) device which was completed in May 1972, is described in detail. Compression of a tokamak plasma across a static toroidal field is studied in this device. The device is designed to produce a pre-compression plasma with a major radius of 17 cm, toroidal field of 20 kG, and current of 90 kA. The compression leads to a plasma with major radius of 38 cm and minor radius of 10 cm. Scaling laws imply a density increase of a factor 6, temperature increase of a factor 3, and current increase of a factor 2.4. An additional feature of ATC is that it is a large tokamak which operates without a copper shell. (iii) Data which show that the expected MHD behavior is largely observed is presented and discussed. (U.S.)
Fermi-Dirac gas of atoms in a box with low adiabatic invariant
International Nuclear Information System (INIS)
Vlad, V.I.; Inonescu-Pallas, N.
2004-06-01
Quantum degenerate Fermi-Dirac gas of atoms, confined in a cubic box, shows an energy spectrum, which is discrete and strongly dependent on the atomic mass number, A at , box geometry and temperature, for low product of A at and the adiabatic invariant, TV 1/3 , i.e. on γ = A at TV 1/3 . The present study compares the total number of particles and the total energy obtained by summing up the contributions of a finite number of states, defined by the values of γ, to the widespread approximations of the corresponding integrals. The sums show simple calculation algorithms and more precise results for a large interval of values of γ. A new accurate analytic formula for the chemical potential of the Fermi-Dirac quantum gas is also given. (author)
Radial plasma profile and neutron yield in an adiabatic trap with fast atom injection
International Nuclear Information System (INIS)
Panov, D.A.
1988-01-01
Radial profiles of ion densities depending on two dimensionless parameters, which values are determined by the trap, plasma and injected beam parameters are found in dimensionless units for a plasma generated by fast atom injection in an adiabatic trap. The calculated profiles are used for determining the neutron yield. Simple approximated dimensional relations permitting to estimate quickly neutron yield, required injection power, flux of charge exchange atoms on the wall around the plasma in a wide energy range of injected atoms, trap field modulud, injection angle, trap radius and length are determined. The energetic efficiency of neutron production is estimated and it is shown that it grows with the injection energy. 7 refs.; 7 figs
International Nuclear Information System (INIS)
Staśkiewicz, B.; Okrasiński, W.
2012-01-01
We propose a simple analytical form of the vapor–liquid equilibrium curve near the critical point for Lennard-Jones fluids. Coexistence densities curves and vapor pressure have been determined using the Van der Waals and Dieterici equation of state. In described method the Bernoulli differential equations, critical exponent theory and some type of Maxwell's criterion have been used. Presented approach has not yet been used to determine analytical form of phase curves as done in this Letter. Lennard-Jones fluids have been considered for analysis. Comparison with experimental data is done. The accuracy of the method is described. -- Highlights: ► We propose a new analytical way to determine the VLE curve. ► Simple, mathematically straightforward form of phase curves is presented. ► Comparison with experimental data is discussed. ► The accuracy of the method has been confirmed.
Adiabatic invariants of the extended KdV equation
Energy Technology Data Exchange (ETDEWEB)
Karczewska, Anna [Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Rozmej, Piotr, E-mail: p.rozmej@if.uz.zgora.pl [Institute of Physics, Faculty of Physics and Astronomy, University of Zielona Góra, Szafrana 4a, 65-246 Zielona Góra (Poland); Infeld, Eryk [National Centre for Nuclear Research, Hoża 69, 00-681 Warszawa (Poland); Rowlands, George [Department of Physics, University of Warwick, Coventry, CV4 7A (United Kingdom)
2017-01-30
When the Euler equations for shallow water are taken to the next order, beyond KdV, momentum and energy are no longer exact invariants. (The only one is mass.) However, adiabatic invariants (AI) can be found. When the KdV expansion parameters are zero, exact invariants are recovered. Existence of adiabatic invariants results from general theory of near-identity transformations (NIT) which allow us to transform higher order nonintegrable equations to asymptotically equivalent (when small parameters tend to zero) integrable form. Here we present a direct method of calculations of adiabatic invariants. It does not need a transformation to a moving reference frame nor performing a near-identity transformation. Numerical tests show that deviations of AI from constant values are indeed small. - Highlights: • We suggest a new and simple method for calculating adiabatic invariants of second order wave equations. • It is easy to use and we hope that it will be useful if published. • Interesting numerics included.
Digitized adiabatic quantum computing with a superconducting circuit.
Barends, R; Shabani, A; Lamata, L; Kelly, J; Mezzacapo, A; Las Heras, U; Babbush, R; Fowler, A G; Campbell, B; Chen, Yu; Chen, Z; Chiaro, B; Dunsworth, A; Jeffrey, E; Lucero, E; Megrant, A; Mutus, J Y; Neeley, M; Neill, C; O'Malley, P J J; Quintana, C; Roushan, P; Sank, D; Vainsencher, A; Wenner, J; White, T C; Solano, E; Neven, H; Martinis, John M
2016-06-09
Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.
Bhowmick, Amiya Ranjan; Bandyopadhyay, Subhadip; Rana, Sourav; Bhattacharya, Sabyasachi
2016-01-01
The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. Copyright © 2015 Elsevier Inc. All rights reserved.
Adiabatic Wankel type rotary engine
Kamo, R.; Badgley, P.; Doup, D.
1988-01-01
This SBIR Phase program accomplished the objective of advancing the technology of the Wankel type rotary engine for aircraft applications through the use of adiabatic engine technology. Based on the results of this program, technology is in place to provide a rotor and side and intermediate housings with thermal barrier coatings. A detailed cycle analysis of the NASA 1007R Direct Injection Stratified Charge (DISC) rotary engine was performed which concluded that applying thermal barrier coatings to the rotor should be successful and that it was unlikely that the rotor housing could be successfully run with thermal barrier coatings as the thermal stresses were extensive.
Beyond the random phase approximation
DEFF Research Database (Denmark)
Olsen, Thomas; Thygesen, Kristian S.
2013-01-01
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for ab initio calculations of electronic correlation energies in solids and molecules. The method is an extension of the random phase approximation (RPA) derived from time-dependent density...... functional theory and the adiabatic connection fluctuation-dissipation theorem and contains no fitted parameters. The new kernel is shown to preserve the accurate description of dispersive interactions from RPA while significantly improving the description of short-range correlation in molecules, insulators......, and metals. For molecular atomization energies, the rALDA is a factor of 7 better than RPA and a factor of 4 better than the Perdew-Burke-Ernzerhof (PBE) functional when compared to experiments, and a factor of 3 (1.5) better than RPA (PBE) for cohesive energies of solids. For transition metals...
Coherent states, quantum gravity, and the Born-Oppenheimer approximation. I. General considerations
International Nuclear Information System (INIS)
Stottmeister, Alexander; Thiemann, Thomas
2016-01-01
This article, as the first of three, aims at establishing the (time-dependent) Born-Oppenheimer approximation, in the sense of space adiabatic perturbation theory, for quantum systems constructed by techniques of the loop quantum gravity framework, especially the canonical formulation of the latter. The analysis presented here fits into a rather general framework and offers a solution to the problem of applying the usual Born-Oppenheimer ansatz for molecular (or structurally analogous) systems to more general quantum systems (e.g., spin-orbit models) by means of space adiabatic perturbation theory. The proposed solution is applied to a simple, finite dimensional model of interacting spin systems, which serves as a non-trivial, minimal model of the aforesaid problem. Furthermore, it is explained how the content of this article and its companion affect the possible extraction of quantum field theory on curved spacetime from loop quantum gravity (including matter fields).
Adiabatic Shear Bands in Simple and Dipolar Viscoplastic Materials
1991-08-01
d Engineering Mechanics. University of Missouri-Holla. Holla. MO 65401-0249. C S.A Mace -r. Germam .Maxirr. Cork. - DrucK GmbH Carl-i -0&sset7«v...iaxirn Gorki - Druck GmoH Car:- -Ossietzk^ -Str 30 11 7400 Auenöurs I _LL 1+ Xf . . M „ .,Mqon ACTA MECHANICA Acta Mechamca 86, .31—.1...points 13, 14, 15 and 17 becomes clear from the results plotted in Fig. 3d . The plots of the temperature rise at other points con- sidered are not
Adiabatic translation factors in slow ion-atom collisions
International Nuclear Information System (INIS)
Vaaben, J.; Taulbjerg, K.
1981-01-01
The general properties of translation factors in slow atomic collisions are discussed. It is emphasised that an acceptable form of translation factors must be conceptually consistent with the basic underlying assumption of the molecular model; i.e. translation factors must relax adiabatically at intermediate and small internuclear separations. A simple physical argument is applied to derive a general parameter-free expression for the translation factor pertinent to an electron in a two-centre Coulomb field. Within the present approach the adiabatic translation factor is considered to be a property of the two-centre field independently of the molecular state under consideration. The generalisation to many-electron systems is therefore readily made. (author)
Adiabatic theory of Wannier threshold laws and ionization cross sections
International Nuclear Information System (INIS)
Macek, J.H.; Ovchinnikov, S.Y.
1994-01-01
Adiabatic energy eigenvalues of H 2 + are computed for complex values of the internuclear distance R. The infinite number of bound-state eigenenergies are represented by a function ε(R) that is single valued on a multisheeted Riemann surface. A region is found where ε(R) and the corresponding eigenfunctions exhibit harmonic-oscillator structure characteristic of electron motion on a potential saddle. The Schroedinger equation is solved in the adiabatic approximation along a path in the complex R plane to compute ionization cross sections. The cross section thus obtained joins the Wannier threshold region with the keV energy region, but the exponent near the ionization threshold disagrees with well-accepted values. Accepted values are obtained when a lowest-order diabatic correction is employed, indicating that adiabatic approximations do not give the correct zero velocity limit for ionization cross sections. Semiclassical eigenvalues for general top-of-barrier motion are given and the theory is applied to the ionization of atomic hydrogen by electron impact. The theory with a first diabatic correction gives the Wannier threshold law even for this case
Adiabatic theory of nonlinear electron cyclotron resonance heating
International Nuclear Information System (INIS)
Kotel'nikov, I.A.; Stupakov, G.V.
1989-01-01
Plasma heating at electron frequency by an ordinary wave propagating at right angle to unidirectional magnetic field is treated. Injected microwave power is assumed to be so large that relativistic change of electron gyrofrequency during one flight thorugh the wave beam is much greater than inverse time of flight. The electron motion in the wave field is described using Hamiltonian formalism in adiabatic approximation. It is shown that energy coupling from the wave to electrons is due to a bifurcation of electron trajectory which results in a jumpm of the adiabatic invariant. The probability of bifurcational transition from one trajectory to another is calculated analytically and is used for the estimation of the beam power absorbed in plasma. 6 refs.; 2 figs
Adiabatic compression of elongated field-reversed configurations
Energy Technology Data Exchange (ETDEWEB)
Spencer, R.L.; Tuszewski, M.; Linford, R.K.
1982-01-01
The simplest model of plasma dynamics is the adiabatic model. In this model the plasma is assumed to be in MHD equilibrium at each instant of time. The equilibria are connected by the requirement that they all have the same entropy per unit flux, i.e., the equilibria form a sequence generated by adiabatic changes. The standard way of computing such a sequence of equilibria was developed by Grad, but its practical use requires a fairly complicated code. It would be helpful if approximately the same results could be gotten either with a much simpler code or by analytical techniques. In Sec. II a one-dimensional equilibrium code is described and its results are checked against a two-dimensional equilibrium code; in Sec. III an even simpler analytic calculation is presented.
PIPER Continuous Adiabatic Demagnetization Refrigerator
Kimball, Mark O.; Shirron, Peter J.; Canavan, Edgar R.; James, Bryan L.; Sampson, Michael A.; Letmate, Richard V.
2017-01-01
We report upon the development and testing of a 4-stage adiabatic demagnetization refrigerator (ADR) capable of continuous cooling at 0.100 Kelvin. This cooler is being built to cool the detector array aboard NASA's Primordial Inflation Polarization Explorer (PIPER) observatory. The goal of this balloon mission is to measure the primordial gravitational waves that should exist if the theory of cosmological inflation is correct. At altitude, the ADR will hold the array of transition-edge sensors at 100 mK continuously while periodically rejecting heat to a 1.2 K pumped helium bath. During testing on ground, the array is held at the same temperature but heat is rejected to a 4.2 K helium bath indicating the flexibility in this coolers design.
Adiabaticity and gravity theory independent conservation laws for cosmological perturbations
Romano, Antonio Enea; Mooij, Sander; Sasaki, Misao
2016-04-01
We carefully study the implications of adiabaticity for the behavior of cosmological perturbations. There are essentially three similar but different definitions of non-adiabaticity: one is appropriate for a thermodynamic fluid δPnad, another is for a general matter field δPc,nad, and the last one is valid only on superhorizon scales. The first two definitions coincide if cs2 = cw2 where cs is the propagation speed of the perturbation, while cw2 = P ˙ / ρ ˙ . Assuming the adiabaticity in the general sense, δPc,nad = 0, we derive a relation between the lapse function in the comoving slicing Ac and δPnad valid for arbitrary matter field in any theory of gravity, by using only momentum conservation. The relation implies that as long as cs ≠cw, the uniform density, comoving and the proper-time slicings coincide approximately for any gravity theory and for any matter field if δPnad = 0 approximately. In the case of general relativity this gives the equivalence between the comoving curvature perturbation Rc and the uniform density curvature perturbation ζ on superhorizon scales, and their conservation. This is realized on superhorizon scales in standard slow-roll inflation. We then consider an example in which cw =cs, where δPnad = δPc,nad = 0 exactly, but the equivalence between Rc and ζ no longer holds. Namely we consider the so-called ultra slow-roll inflation. In this case both Rc and ζ are not conserved. In particular, as for ζ, we find that it is crucial to take into account the next-to-leading order term in ζ's spatial gradient expansion to show its non-conservation, even on superhorizon scales. This is an example of the fact that adiabaticity (in the thermodynamic sense) is not always enough to ensure the conservation of Rc or ζ.
An adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems
International Nuclear Information System (INIS)
Baranger, M.; Veneroni, M.
1977-11-01
It is shown how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and one starts from the time-dependent Hartree-Fock equation. To this, the adiabatic approximation is added, and the energy in powers of an adiabatic parameter is expanded, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The adiabatic equations of motion are derived in different ways and their analogy with classical mechanics is stressed. The role of the adiabatic hypothesis and its range of validity, are analyzed in detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given and the moment of inertia under rotation is that of Thouless and Valatin
Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation
Bastero-Gil, Mar; Berera, Arjun; Ramos, Rudnei O.; Rosa, João G.
2018-02-01
We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.
Fast fracture: an adiabatic restriction on thermally activated crack propagation
Energy Technology Data Exchange (ETDEWEB)
Burns, S.J.
1978-01-01
Slow, isothermal, crack propagation is widely suspected to be rate controlled by thermally activated plastic deformation in the crack tip region. Adiabatic conditions are generally established in the fracture modified material at the tip of a crack during fast fracture. The temperature of this material is not the temperature of the specimen and is generally not measured during fast fracture. Thus, a complete thermodynamic description of adiabatic crack propagation data can not be made. When the slow, isothermal, crack propagation mechanisms are assumed to be operative during adiabatic crack propagation then certain predictions can be made. For example: the changes in the driving force due to temperature and rate are always in the opposite sense; there is no minimum in the driving force versus crack velocity without a change in mechanism; the temperature rise in the crack tip fracture modified material is determined mainly by the activation enthalpy for crack propagation; the interpretation of fast fracture structural steel data from simple plastic models is suspect since these materials have dissimilar isothermal temperature dependencies.
Narrow-line laser cooling by adiabatic transfer
Norcia, Matthew A.; Cline, Julia R. K.; Bartolotta, John P.; Holland, Murray J.; Thompson, James K.
2018-02-01
We propose and demonstrate a novel laser cooling mechanism applicable to particles with narrow-linewidth optical transitions. By sweeping the frequency of counter-propagating laser beams in a sawtooth manner, we cause adiabatic transfer back and forth between the ground state and a long-lived optically excited state. The time-ordering of these adiabatic transfers is determined by Doppler shifts, which ensures that the associated photon recoils are in the opposite direction to the particle’s motion. This ultimately leads to a robust cooling mechanism capable of exerting large forces via a weak transition and with reduced reliance on spontaneous emission. We present a simple intuitive model for the resulting frictional force, and directly demonstrate its efficacy for increasing the total phase-space density of an atomic ensemble. We rely on both simulation and experimental studies using the 7.5 kHz linewidth 1S0 to 3P1 transition in 88Sr. The reduced reliance on spontaneous emission may allow this adiabatic sweep method to be a useful tool for cooling particles that lack closed cycling transitions, such as molecules.
Energy consumption for shortcuts to adiabaticity
Torrontegui, E.; Lizuain, I.; González-Resines, S.; Tobalina, A.; Ruschhaupt, A.; Kosloff, R.; Muga, J. G.
2017-08-01
Shortcuts to adiabaticity let a system reach the results of a slow adiabatic process in a shorter time. We propose to quantify the "energy cost" of the shortcut by the energy consumption of the system enlarged by including the control device. A mechanical model where the dynamics of the system and control device can be explicitly described illustrates that a broad range of possible values for the consumption is possible, including zero (above the adiabatic energy increment) when friction is negligible and the energy given away as negative power is stored and reused by perfect regenerative braking.
Quantum entangling power of adiabatically connected Hamiltonians
International Nuclear Information System (INIS)
Hamma, Alioscia; Zanardi, Paolo
2004-01-01
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bipartite quantum state space. When the different Hamiltonians in the family fall in the same adiabatic class, one can manipulate entanglement by moving through energy eigenstates corresponding to different values of the control parameters. We introduce an associated notion of adiabatic entangling power. This novel measure is analyzed for general dxd quantum systems, and specific two-qubit examples are studied
Non-Adiabatic Molecular Dynamics Methods for Materials Discovery
Energy Technology Data Exchange (ETDEWEB)
Furche, Filipp [Univ. of California, Irvine, CA (United States); Parker, Shane M. [Univ. of California, Irvine, CA (United States); Muuronen, Mikko J. [Univ. of California, Irvine, CA (United States); Roy, Saswata [Univ. of California, Irvine, CA (United States)
2017-04-04
The flow of radiative energy in light-driven materials such as photosensitizer dyes or photocatalysts is governed by non-adiabatic transitions between electronic states and cannot be described within the Born-Oppenheimer approximation commonly used in electronic structure theory. The non-adiabatic molecular dynamics (NAMD) methods based on Tully surface hopping and time-dependent density functional theory developed in this project have greatly extended the range of molecular materials that can be tackled by NAMD simulations. New algorithms to compute molecular excited state and response properties efficiently were developed. Fundamental limitations of common non-linear response methods were discovered and characterized. Methods for accurate computations of vibronic spectra of materials such as black absorbers were developed and applied. It was shown that open-shell TDDFT methods capture bond breaking in NAMD simulations, a longstanding challenge for single-reference molecular dynamics simulations. The methods developed in this project were applied to study the photodissociation of acetaldehyde and revealed that non-adiabatic effects are experimentally observable in fragment kinetic energy distributions. Finally, the project enabled the first detailed NAMD simulations of photocatalytic water oxidation by titania nanoclusters, uncovering the mechanism of this fundamentally important reaction for fuel generation and storage.
Thermoelectric Effects under Adiabatic Conditions
Directory of Open Access Journals (Sweden)
George Levy
2013-10-01
Full Text Available This paper investigates not fully explained voltage offsets observed by several researchers during the measurement of the Seebeck coefficient of high Z materials. These offsets, traditionally attributed to faulty laboratory procedures, have proven to have an irreducible component that cannot be fully eliminated in spite of careful laboratory procedures. In fact, these offsets are commonly observed and routinely subtracted out of commercially available Seebeck measurement systems. This paper offers a possible explanation based on the spontaneous formation of an adiabatic temperature gradient in the presence of a force field. The diffusion-diffusion heat transport mechanism is formulated and applied to predict two new thermoelectric effects. The first is the existence of a temperature gradient across a potential barrier in a semiconductor and the second is the Onsager reciprocal of the first, that is, the presence of a measureable voltage that arises across a junction when the temperature gradient is forced to zero by a thermal clamp. Suggested future research includes strategies for utilizing the new thermoelectric effects.
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
International Nuclear Information System (INIS)
Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery
2015-01-01
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Symmetry of the Adiabatic Condition in the Piston Problem
Anacleto, Joaquim; Ferreira, J. M.
2011-01-01
This study addresses a controversial issue in the adiabatic piston problem, namely that of the piston being adiabatic when it is fixed but no longer so when it can move freely. It is shown that this apparent contradiction arises from the usual definition of adiabatic condition. The issue is addressed here by requiring the adiabatic condition to be…
Adiabatic invariants in stellar dynamics. 2: Gravitational shocking
Weinberg, Martin D.
1994-01-01
A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.
Correction for adiabatic effects in lethe calculated instantaneous gas consumption of scuba dives
Schellart, Nico A. M.; Le Péchon, Jean-Claude
2015-01-01
Introduction: In scuba-diving practice, instantaneous gas consumption is generally calculated from the fall in cylinder pressure without considering the effects of water temperature (heat transfer) and adiabatic processes. We aimed to develop a simple but precise method for calculating the
Assessment of total efficiency in adiabatic engines
Mitianiec, W.
2016-09-01
The paper presents influence of ceramic coating in all surfaces of the combustion chamber of SI four-stroke engine on working parameters mainly on heat balance and total efficiency. Three cases of engine were considered: standard without ceramic coating, fully adiabatic combustion chamber and engine with different thickness of ceramic coating. Consideration of adiabatic or semi-adiabatic engine was connected with mathematical modelling of heat transfer from the cylinder gas to the cooling medium. This model takes into account changeable convection coefficient based on the experimental formulas of Woschni, heat conductivity of multi-layer walls and also small effect of radiation in SI engines. The simulation model was elaborated with full heat transfer to the cooling medium and unsteady gas flow in the engine intake and exhaust systems. The computer program taking into account 0D model of engine processes in the cylinder and 1D model of gas flow was elaborated for determination of many basic engine thermodynamic parameters for Suzuki DR-Z400S 400 cc SI engine. The paper presents calculation results of influence of the ceramic coating thickness on indicated pressure, specific fuel consumption, cooling and exhaust heat losses. Next it were presented comparisons of effective power, heat losses in the cooling and exhaust systems, total efficiency in function of engine rotational speed and also comparison of temperature inside the cylinder for standard, semi-adiabatic and full adiabatic engine. On the basis of the achieved results it was found higher total efficiency of adiabatic engines at 2500 rpm from 27% for standard engine to 37% for full adiabatic engine.
Adiabatic process reversibility: microscopic and macroscopic views
International Nuclear Information System (INIS)
Anacleto, Joaquim; Pereira, Mario G
2009-01-01
The reversibility of adiabatic processes was recently addressed by two publications. In the first (Miranda 2008 Eur. J. Phys. 29 937-43), an equation was derived relating the initial and final volumes and temperatures for adiabatic expansions of an ideal gas, using a microscopic approach. In that relation the parameter r accounts for the process reversibility, ranging between 0 and 1, which corresponds to the free and reversible expansion, respectively. In the second (Anacleto and Pereira 2009 Eur. J. Phys. 30 177-83), the authors have shown that thermodynamics can effectively and efficiently be used to obtain the general law for adiabatic processes carried out by an ideal gas, including compressions, for which r≥1. The present work integrates and extends the aforementioned studies, providing thus further insights into the analysis of the adiabatic process. It is shown that Miranda's work is wholly valid for compressions. In addition, it is demonstrated that the adiabatic reversibility coefficient given in terms of the piston velocity and the root mean square velocity of the gas particles is equivalent to the macroscopic description, given just by the quotient between surroundings and system pressure values. (letters and comments)
Energy Technology Data Exchange (ETDEWEB)
Benabbas, Abdelkrim; Salna, Bridget; Sage, J. Timothy; Champion, Paul M., E-mail: champ@neu.edu [Department of Physics and Center for Interdisciplinary Research on Complex Systems,Northeastern University, Boston, Massachusetts 02115 (United States)
2015-03-21
Analytical models describing the temperature dependence of the deep tunneling rate, useful for proton, hydrogen, or hydride transfer in proteins, are developed and compared. Electronically adiabatic and non-adiabatic expressions are presented where the donor-acceptor (D-A) motion is treated either as a quantized vibration or as a classical “gating” distribution. We stress the importance of fitting experimental data on an absolute scale in the electronically adiabatic limit, which normally applies to these reactions, and find that vibrationally enhanced deep tunneling takes place on sub-ns timescales at room temperature for typical H-bonding distances. As noted previously, a small room temperature kinetic isotope effect (KIE) does not eliminate deep tunneling as a major transport channel. The quantum approach focuses on the vibrational sub-space composed of the D-A and hydrogen atom motions, where hydrogen bonding and protein restoring forces quantize the D-A vibration. A Duschinsky rotation is mandated between the normal modes of the reactant and product states and the rotation angle depends on the tunneling particle mass. This tunnel-mass dependent rotation contributes substantially to the KIE and its temperature dependence. The effect of the Duschinsky rotation is solved exactly to find the rate in the electronically non-adiabatic limit and compared to the Born-Oppenheimer (B-O) approximation approach. The B-O approximation is employed to find the rate in the electronically adiabatic limit, where we explore both harmonic and quartic double-well potentials for the hydrogen atom bound states. Both the electronically adiabatic and non-adiabatic rates are found to diverge at high temperature unless the proton coupling includes the often neglected quadratic term in the D-A displacement from equilibrium. A new expression is presented for the electronically adiabatic tunnel rate in the classical limit for D-A motion that should be useful to experimentalists working
Adiabatic quantum search algorithm for structured problems
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size
Experimental study on the adiabatic shear bands
International Nuclear Information System (INIS)
Affouard, J.
1984-07-01
Four martensitic steels (Z50CDV5 steel, 28CND8 steel, 35NCDV16 steel and 4340 steel) with different hardness between 190 and 600 Hsub(B) (Brinell hardness), have been studied by means of dynamic compressive tests on split Hopkinson pressure bar. Microscopic observations show that the fracture are associated to the development of adiabatic shear bands (except 4340 steel with 190 Hsub(B) hardness). By means of tests for which the deformation is stopped at predetermined levels, the measurement of shear and hardness inside the band and the matrix indicates the chronology of this phenomenon: first the localization of shear, followed by the formation of adiabatic shear band and ultimatly crack initiation and propagation. These results correlated with few simulations by finite elements have permitted to suggest two mecanisms of deformation leading to the formation of adiabatic shear bands in this specific test [fr
Adiabatic supernova expansion into the circumstellar medium
International Nuclear Information System (INIS)
Band, D.L.; Liang, E.P.
1987-01-01
We perform one dimensional numerical simulations with a Lagrangian hydrodynamics code of the adiabatic expansion of a supernova into the surrounding medium. The early expansion follows Chevalier's analytic self-similar solution until the reverse shock reaches the ejecta core. We follow the expansion as it evolves towards the adiabatic blast wave phase. Some memory of the earlier phases of expansion is retained in the interior even when the outer regions expand as a blast wave. We find the results are sensitive to the initial configuration of the ejecta and to the placement of gridpoints. 6 refs., 2 figs
Collapse and equilibrium of rotating, adiabatic clouds
International Nuclear Information System (INIS)
Boss, A.P.
1980-01-01
A numerical hydrodynamics computer code has been used to follow the collapse and establishment of equilibrium of adiabatic gas clouds restricted to axial symmetry. The clouds are initially uniform in density and rotation, with adiabatic exponents γ=5/3 and 7/5. The numerical technique allows, for the first time, a direct comparison to be made between the dynamic collapse and approach to equilibrium of unconstrained clouds on the one hand, and the results for incompressible, uniformly rotating equilibrium clouds, and the equilibrium structures of differentially rotating polytropes, on the other hand
Superconducting system for adiabatic quantum computing
Energy Technology Data Exchange (ETDEWEB)
Corato, V [Dipartimento di Ingegneria dell' Informazione, Second University of Naples, 81031 Aversa (Italy); Roscilde, T [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484 (Canada); Ruggiero, B [Istituto di Cibernetica ' E.Caianiello' del CNR, I-80078, Pozzuoli (Italy); Granata, C [Istituto di Cibernetica ' E.Caianiello' del CNR, I-80078, Pozzuoli (Italy); Silvestrini, P [Dipartimento di Ingegneria dell' Informazione, Second University of Naples, 81031 Aversa (Italy)
2006-06-01
We study the Hamiltonian of a system of inductively coupled flux qubits, which has been theoretically proposed for adiabatic quantum computation to handle NP problems. We study the evolution of a basic structure consisting of three coupled rf-SQUIDs upon tuning the external flux bias, and we show that the adiabatic nature of the evolution is guaranteed by the presence of the single-SQUID gap. We further propose a scheme and the first realization of an experimental device suitable for verifying the theoretical results.
International Nuclear Information System (INIS)
Villars, F.
1975-01-01
The objective of the work is to draw attention to the essential equivalence of the two apparently quite distinct ways of describing nuclear collective dyanmics, the adiabatic time-dependent Hartree-Fock method (ADTHF) on the one hand, and the Generator Coordinate (GC) method on the other hand. To demonstrate this relation, an analysis of the simplest case, in which collective motion is described by a single collective para- meter q(t) is presented. In the ATDHF approach, two self-consistency conditions are obtained; the resultant expressions for the collective potential and kinetic energies represent a special case of the more general results of Baranger and Veneroni. In the G.C. approach to the same system (with the same collective parameter q), the narrow overlap approximation must be made, as the counterpart of the adiabatic approximation in the TDHF method. In its conventional form, the G.C. method leads to a different expression for the collective kinetic energy. It is shown however, that a simple generalization of the G.C.-wave function leads to corrections determined by a variational principle. In leading order, the corrected expression for the collective kinetic energy is identical with the TDHF result In both cases, the collective inertia is determined by a self-consistent cranking formula
Perturbation methods and closure approximations in nonlinear systems
International Nuclear Information System (INIS)
Dubin, D.H.E.
1984-01-01
In the first section of this thesis, Hamiltonian theories of guiding center and gyro-center motion are developed using modern symplectic methods and Lie transformations. Littlejohn's techniques, combined with the theory of resonant interaction and island overlap, are used to explore the problem of adiabatic invariance and onset of stochasticity. As an example, the breakdown of invariance due to resonance between drift motion and gyromotion in a tokamak is considered. A Hamiltonian is developed for motion in a straight magnetic field with electrostatic perturbations in the gyrokinetic ordering, from which nonlinear gyrokinetic equations are constructed which have the property of phase-space preservation, useful for computer simulation. Energy invariants are found and various limits of the equations are considered. In the second section, statistical closure theories are applied to simple dynamical systems. The logistic map is used as an example because of its universal properties and simple quadratic nonlinearity. The first closure considered is the direct interaction approximation of Kraichnan, which is found to fail when applied to the logistic map because it cannot approximate the bounded support of the map's equilibrium distribution. By imposing a periodically constraint on a Langevin form of the DIA a new stable closure is developed
Inertial parameters in the interacting boson fermion approximation
International Nuclear Information System (INIS)
Dukelsky, J.; Lima, C.
1986-06-01
The Hartree-Bose-Fermi and the adiabatic approximations are used to derive analytic formulas for the moment of inertia and the decoupling parameter of the interacting boson fermion approximation for deformed systems. These formulas are applied to the SU(3) dynamical symmetry, obtaining perfect agreement with the exact results. (Authors) [pt
CERN. Geneva
2015-01-01
Most physics results at the LHC end in a likelihood ratio test. This includes discovery and exclusion for searches as well as mass, cross-section, and coupling measurements. The use of Machine Learning (multivariate) algorithms in HEP is mainly restricted to searches, which can be reduced to classification between two fixed distributions: signal vs. background. I will show how we can extend the use of ML classifiers to distributions parameterized by physical quantities like masses and couplings as well as nuisance parameters associated to systematic uncertainties. This allows for one to approximate the likelihood ratio while still using a high dimensional feature vector for the data. Both the MEM and ABC approaches mentioned above aim to provide inference on model parameters (like cross-sections, masses, couplings, etc.). ABC is fundamentally tied Bayesian inference and focuses on the “likelihood free” setting where only a simulator is available and one cannot directly compute the likelihood for the dat...
Schmidt, Wolfgang M
1980-01-01
"In 1970, at the U. of Colorado, the author delivered a course of lectures on his famous generalization, then just established, relating to Roth's theorem on rational approxi- mations to algebraic numbers. The present volume is an ex- panded and up-dated version of the original mimeographed notes on the course. As an introduction to the author's own remarkable achievements relating to the Thue-Siegel-Roth theory, the text can hardly be bettered and the tract can already be regarded as a classic in its field."(Bull.LMS) "Schmidt's work on approximations by algebraic numbers belongs to the deepest and most satisfactory parts of number theory. These notes give the best accessible way to learn the subject. ... this book is highly recommended." (Mededelingen van het Wiskundig Genootschap)
Pulsed adiabatic structure and complete population transfer
International Nuclear Information System (INIS)
Shore, B.W.
1992-10-01
Population can be transferred between atomic or molecular energy states in a variety of ways. The basic idea of adiabatic transfer, discussed in many textbooks, is as follows. One begins with an atom that is in some single energy state (an eigenstate of an initial Hamiltonian). This energy state is one of many possible states, known variously as the unperturbed states or basis states or diabatic states. Next one begins to change the Hamiltonian very slowly. The changes may occur in either the diagonal elements (the basis state energies) or in the off-diagonal elements (interactions between basis states). If there are off-diagonal elements then the Hamiltonian will no longer commute with the original one. Because the Hamiltonian is no longer the one that was used to define the original basis states, it will cause these states to become mixed. However, if the change is sufficiently slow, the system can remain in a single eigenstate of the changing Hamiltonian -- an adiabatic state, composed of a combination of basis states. Finally, at some later time, one examines the system once again in the original basis. One finds that the population has undergone a change, and now resides in a different unperturbed state. One has produced population transfer. There are many illustrative examples of adiabatic passage, both theory and experiment. The author mentions briefly two common examples, inelastic collisions between atoms, and the static Stark effect in Rydberg atoms, before continuing with the main objective, a discussion of adiabatic passage induced by laser pulses
Post-adiabatic analysis of atomic collisions
International Nuclear Information System (INIS)
Klar, H.; Fano, U.
1976-01-01
The coupling between adiabatic channels can be partially transformed away. The transformation need not induce any transition between channnels; but it correlates the radial wave functions and their gradients with the channel functions and it depresses the lower effective potentials, as the energy increases, in accordance with empirical evidence
Connection between adiabaticity and the mirror mode
International Nuclear Information System (INIS)
Cohen, R.H.
1976-01-01
The size of magnetic moment jumps of a particle in a long, thin equilibrium magnetic mirror field is shown to be related to the complex zeroes of the mirror mode parameter B + 4πdP/sub perpendicular//dB. A consequence is that adiabaticity places a lower limit on β than does the mirror mode
FRW-type cosmologies with adiabatic matter creation
International Nuclear Information System (INIS)
Lima, J.A.; Germano, A.S.; Abramo, L.R.
1996-01-01
Some properties of cosmological models with matter creation are investigated in the framework of the Friedmann-Robertson-Walker line element. For adiabatic matter creation, as developed by Prigogine and co-workers, we derive a simple expression relating the particle number density n and energy density ρ which holds regardless of the matter creation rate. The conditions to generate inflation are discussed and by considering the natural phenomenological matter creation rate ψ=3βnH, where β is a pure number of the order of unity and H is the Hubble parameter, a minimally modified hot big-bang model is proposed. The dynamic properties of such models can be deduced from the standard ones simply by replacing the adiabatic index γ of the equation of state by an effective parameter γ * =γ(1-β). The thermodynamic behavior is determined and it is also shown that ages large enough to agree with observations are obtained even given the high values of H suggested by recent measurements. copyright 1996 The American Physical Society
Geometric approximation algorithms
Har-Peled, Sariel
2011-01-01
Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.
Adiabatic burst evaporation from bicontinuous nanoporous membranes
Ichilmann, Sachar; Rücker, Kerstin; Haase, Markus; Enke, Dirk
2015-01-01
Evaporation of volatile liquids from nanoporous media with bicontinuous morphology and pore diameters of a few 10 nm is an ubiquitous process. For example, such drying processes occur during syntheses of nanoporous materials by sol–gel chemistry or by spinodal decomposition in the presence of solvents as well as during solution impregnation of nanoporous hosts with functional guests. It is commonly assumed that drying is endothermic and driven by non-equilibrium partial pressures of the evaporating species in the gas phase. We show that nearly half of the liquid evaporates in an adiabatic mode involving burst-like liquid-to-gas conversions. During single adiabatic burst evaporation events liquid volumes of up to 107 μm3 are converted to gas. The adiabatic liquid-to-gas conversions occur if air invasion fronts get unstable because of the built-up of high capillary pressures. Adiabatic evaporation bursts propagate avalanche-like through the nanopore systems until the air invasion fronts have reached new stable configurations. Adiabatic cavitation bursts thus compete with Haines jumps involving air invasion front relaxation by local liquid flow without enhanced mass transport out of the nanoporous medium and prevail if the mean pore diameter is in the range of a few 10 nm. The results reported here may help optimize membrane preparation via solvent-based approaches, solution-loading of nanopore systems with guest materials as well as routine use of nanoporous membranes with bicontinuous morphology and may contribute to better understanding of adsorption/desorption processes in nanoporous media. PMID:25926406
Energy Technology Data Exchange (ETDEWEB)
Battmann, A. [Marburg Univ. (Germany). Abt. fuer Strahlendiagnostik; Dieckmann, K.; Resch, A.; Poetter, R. [Allgemeines Krankenhaus, Wien (Austria). Universitaetsklinik Strahlentherapie und Strahlenbiologie; Battmann, A. [Giessen Univ. (Germany). Zentrum fuer Pathologie
2001-03-01
Background: The importance of the size of the primary tumor in lymphomas and its size after treatment is still uncertain. Assuming a prognostic relevance, an assessment of tumor volume before and after induction of chemotherapy has been performed in the pediatric Hodgkin's disease study (HD-90). Since an exact CT-scan-based volumetric tumor assessment is time-consuming and in some centers not possible, the tumor volume is often estimated based on simple geometric approximations. Aim of this study was the development of an easy to apply and nearly exact model of volume estimation compared to CT-scan-based tumor volume measurements. Material and Methods: thirty computed tomographies (CT) of mediastinal Hodgkin lymphomas of children aged 5 to 16 years have been examined. The CT scans were digitalized using a CCD camera combined with a frame grabber. Applying the Global Lab image software, the true tumor volume was determined excluding local organs, which did not belong to the lymphoma. Subsequently, volumes were assessed using simple geometric models (block, ellipsoid, octaeder) by using the maximum diameters of the tumor. The differences between the volume of the geometric models and the true volume, based on the CT scan evaluation, were compared. Results: the maximum diameters of a tumor can be used to calculate its volume based on simple geometric models. The model 'block' overestimates the volume by 89 to 268%. The model 'ellipsoid' overestimates the volume on average by 29%. The model 'octaeder' underestimates the volume on average by 18%. A division of the block volume by 2.3 approximated the geometric closest to the true volume: the average volume was overestimated by 2% in tumors with a volume larger than 20 ml. No model was sufficient to approximate tumors with a volume of less than 20 ml. Conclusions: for the estimation of tumor volumes in mediastinal Hodgkin lumphomas exceeding 20 ml, the formula 'block /2.3&apos
Adiabatic Hamiltonian deformation, linear response theory, and nonequilibrium molecular dynamics
International Nuclear Information System (INIS)
Hoover, W.G.
1980-01-01
Although Hamiltonians of various kinds have previously been used to derive Green-Kubo relations for the transport coefficients, the particular choice described is uniquely related to thermodynamics. This nonequilibrium Hamiltonian formulation of fluid flow provides pedagogically simple routes to nonequilibrium fluxes and distribution functions, to theoretical understanding of long-time effects, and to new numerical methods for simulating systems far from equilibrium. The same methods are now being applied to solid-phase problems. At the relatively high frequencies used in the viscous fluid calculations described, solids typically behave elastically. Lower frequencies lead to the formation of dislocations and other defects, making it possible to study plastic flow. A property of the nonequilibrium equations of motion which might be profitably explored is their effective irreversibility. Because only a few particles are necessary to generate irreversible behavior, simulations using adiabatic deformations of the kind described here could perhaps elucidate the instability in the equations of motion responsible for irreversibility
Adiabatic pumping solutions in global AdS
Energy Technology Data Exchange (ETDEWEB)
Carracedo, Pablo [Meteo-Galicia,Santiago de Compostela E-15782 (Spain); Mas, Javier; Musso, Daniele; Serantes, Alexandre [Departamento de Física de Partículas, Universidade de Santiago de Compostela,Santiago de Compostela E-15782 (Spain); Instituto Galego de Física de Altas Enerxías (IGFAE),Santiago de Compostela E-15782 (Spain)
2017-05-26
We construct a family of very simple stationary solutions to gravity coupled to a massless scalar field in global AdS. They involve a constantly rising source for the scalar field at the boundary and thereby we name them pumping solutions. We construct them numerically in D=4. They are regular and, generically, have negative mass. We perform a study of linear and nonlinear stability and find both stable and unstable branches. In the latter case, solutions belonging to different sub-branches can either decay to black holes or to limiting cycles. This observation motivates the search for non-stationary exactly time-periodic solutions which we actually construct. We clarify the role of pumping solutions in the context of quasistatic adiabatic quenches. In D=3 the pumping solutions can be related to other previously known solutions, like magnetic or translationally-breaking backgrounds. From this we derive an analytic expression.
Non-adiabatic perturbations in multi-component perfect fluids
Energy Technology Data Exchange (ETDEWEB)
Koshelev, N.A., E-mail: koshna71@inbox.ru [Ulyanovsk State University, Leo Tolstoy str 42, 432970 (Russian Federation)
2011-04-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models.
Non-adiabatic perturbations in multi-component perfect fluids
International Nuclear Information System (INIS)
Koshelev, N.A.
2011-01-01
The evolution of non-adiabatic perturbations in models with multiple coupled perfect fluids with non-adiabatic sound speed is considered. Instead of splitting the entropy perturbation into relative and intrinsic parts, we introduce a set of symmetric quantities, which also govern the non-adiabatic pressure perturbation in models with energy transfer. We write the gauge invariant equations for the variables that determine on a large scale the non-adiabatic pressure perturbation and the rate of changes of the comoving curvature perturbation. The analysis of evolution of the non-adiabatic pressure perturbation has been made for several particular models
Diskoseismology: Probing accretion disks. I - Trapped adiabatic oscillations
Nowak, Michael A.; Wagoner, Robert V.
1991-01-01
The normal modes of acoustic oscillations within thin accretion disks which are terminated by an innermost stable orbit around a slowly rotating black hole or weakly magnetized compact neutron star are analyzed. The dominant relativistic effects which allow modes to be trapped within the inner region of the disk are approximated via a modified Newtonian potential. A general formalism is developed for investigating the adiabatic oscillations of arbitrary unperturbed disk models. The generic behavior is explored by way of an expansion of the Lagrangian displacement about the plane of symmetry and by assuming separable solutions with the same radial wavelength for the horizontal and vertical perturbations. The lowest eigenfrequencies and eigenfunctions of a particular set of radial and quadrupole modes which have minimum motion normal for the plane are obtained. These modes correspond to the standard dispersion relation of disk theory.
Hydrodynamic stability of inverted annular flow in an adiabatic simulation
International Nuclear Information System (INIS)
De Jarlais, G.; Ishii, M.; Linehan, J.
1986-01-01
Inverted annular flow was simulated adiabatically with turbulent water jets, issuing downward from large aspect ratio nozzles, enclosed in gas annuli. Velocities, diameters, and gas species were varied, and core jet length, shape, breakup mode, and dispersed core droplet sizes were recorded at approximately 750 data points. Inverted annular flow destabilization led to inverted slug flow at low relative velocities, and to dispersed droplet flow, core breakup length correlations were developed by extending work on free liquid jets to include this coaxial, jet disintegration phenomenon. The results show length dependence upon D/sub J/, Re/sub J/, We/sub J/, α, and We/sub G/,rel. Correlations for core shape, breakup mechanisms, and dispersed core droplet size were also developed, by extending the results of free jet stability, roll wave entrainment, and churn turbulent droplet stability studies
Adiabatic Quantum Optimization for Associative Memory Recall
Directory of Open Access Journals (Sweden)
Hadayat eSeddiqi
2014-12-01
Full Text Available Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO. Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Adiabatic Quantum Optimization for Associative Memory Recall
Seddiqi, Hadayat; Humble, Travis
2014-12-01
Hopfield networks are a variant of associative memory that recall patterns stored in the couplings of an Ising model. Stored memories are conventionally accessed as fixed points in the network dynamics that correspond to energetic minima of the spin state. We show that memories stored in a Hopfield network may also be recalled by energy minimization using adiabatic quantum optimization (AQO). Numerical simulations of the underlying quantum dynamics allow us to quantify AQO recall accuracy with respect to the number of stored memories and noise in the input key. We investigate AQO performance with respect to how memories are stored in the Ising model according to different learning rules. Our results demonstrate that AQO recall accuracy varies strongly with learning rule, a behavior that is attributed to differences in energy landscapes. Consequently, learning rules offer a family of methods for programming adiabatic quantum optimization that we expect to be useful for characterizing AQO performance.
Adiabatic Theorem for Quantum Spin Systems
Bachmann, S.; De Roeck, W.; Fraas, M.
2017-08-01
The first proof of the quantum adiabatic theorem was given as early as 1928. Today, this theorem is increasingly applied in a many-body context, e.g., in quantum annealing and in studies of topological properties of matter. In this setup, the rate of variation ɛ of local terms is indeed small compared to the gap, but the rate of variation of the total, extensive Hamiltonian, is not. Therefore, applications to many-body systems are not covered by the proofs and arguments in the literature. In this Letter, we prove a version of the adiabatic theorem for gapped ground states of interacting quantum spin systems, under assumptions that remain valid in the thermodynamic limit. As an application, we give a mathematical proof of Kubo's linear response formula for a broad class of gapped interacting systems. We predict that the density of nonadiabatic excitations is exponentially small in the driving rate and the scaling of the exponent depends on the dimension.
Adiabatic invariance with first integrals of motion
Adib, Artur B.
2002-10-01
The construction of a microthermodynamic formalism for isolated systems based on the concept of adiabatic invariance is an old but seldom appreciated effort in the literature, dating back at least to P. Hertz [Ann. Phys. (Leipzig) 33, 225 (1910)]. An apparently independent extension of such formalism for systems bearing additional first integrals of motion was recently proposed by Hans H. Rugh [Phys. Rev. E 64, 055101 (2001)], establishing the concept of adiabatic invariance even in such singular cases. After some remarks in connection with the formalism pioneered by Hertz, it will be suggested that such an extension can incidentally explain the success of a dynamical method for computing the entropy of classical interacting fluids, at least in some potential applications where the presence of additional first integrals cannot be ignored.
Ramsey numbers and adiabatic quantum computing.
Gaitan, Frank; Clark, Lane
2012-01-06
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.
Trapped Ion Quantum Computation by Adiabatic Passage
International Nuclear Information System (INIS)
Feng Xuni; Wu Chunfeng; Lai, C. H.; Oh, C. H.
2008-01-01
We propose a new universal quantum computation scheme for trapped ions in thermal motion via the technique of adiabatic passage, which incorporates the advantages of both the adiabatic passage and the model of trapped ions in thermal motion. Our scheme is immune from the decoherence due to spontaneous emission from excited states as the system in our scheme evolves along a dark state. In our scheme the vibrational degrees of freedom are not required to be cooled to their ground states because they are only virtually excited. It is shown that the fidelity of the resultant gate operation is still high even when the magnitude of the effective Rabi frequency moderately deviates from the desired value.
Change of adiabatic invariant near the separatrix
International Nuclear Information System (INIS)
Bulanov, S.V.
1995-10-01
The properties of particle motion in the vicinity of the separatrix in a phase plane are investigated. The change of adiabatic invariant value due to the separatrix crossing is evaluated as a function of a perturbation parameter magnitude and a phase of a particle for time dependent Hamiltonians. It is demonstrated that the change of adiabatic invariant value near the separatrix birth is much larger than that in the case of the separatrix crossing near the saddle point in a phase plane. The conditions of a stochastic regime to appear around the separatrix are found. The results are applied to study the longitudinal invariant behaviour of charged particles near singular lines of the magnetic field. (author). 22 refs, 9 figs
Adiabatic graph-state quantum computation
International Nuclear Information System (INIS)
Antonio, B; Anders, J; Markham, D
2014-01-01
Measurement-based quantum computation (MBQC) and holonomic quantum computation (HQC) are two very different computational methods. The computation in MBQC is driven by adaptive measurements executed in a particular order on a large entangled state. In contrast in HQC the system starts in the ground subspace of a Hamiltonian which is slowly changed such that a transformation occurs within the subspace. Following the approach of Bacon and Flammia, we show that any MBQC on a graph state with generalized flow (gflow) can be converted into an adiabatically driven holonomic computation, which we call adiabatic graph-state quantum computation (AGQC). We then investigate how properties of AGQC relate to the properties of MBQC, such as computational depth. We identify a trade-off that can be made between the number of adiabatic steps in AGQC and the norm of H-dot as well as the degree of H, in analogy to the trade-off between the number of measurements and classical post-processing seen in MBQC. Finally the effects of performing AGQC with orderings that differ from standard MBQC are investigated. (paper)
Random matrix model of adiabatic quantum computing
International Nuclear Information System (INIS)
Mitchell, David R.; Adami, Christoph; Lue, Waynn; Williams, Colin P.
2005-01-01
We present an analysis of the quantum adiabatic algorithm for solving hard instances of 3-SAT (an NP-complete problem) in terms of random matrix theory (RMT). We determine the global regularity of the spectral fluctuations of the instantaneous Hamiltonians encountered during the interpolation between the starting Hamiltonians and the ones whose ground states encode the solutions to the computational problems of interest. At each interpolation point, we quantify the degree of regularity of the average spectral distribution via its Brody parameter, a measure that distinguishes regular (i.e., Poissonian) from chaotic (i.e., Wigner-type) distributions of normalized nearest-neighbor spacings. We find that for hard problem instances - i.e., those having a critical ratio of clauses to variables - the spectral fluctuations typically become irregular across a contiguous region of the interpolation parameter, while the spectrum is regular for easy instances. Within the hard region, RMT may be applied to obtain a mathematical model of the probability of avoided level crossings and concomitant failure rate of the adiabatic algorithm due to nonadiabatic Landau-Zener-type transitions. Our model predicts that if the interpolation is performed at a uniform rate, the average failure rate of the quantum adiabatic algorithm, when averaged over hard problem instances, scales exponentially with increasing problem size
International Nuclear Information System (INIS)
Sundararajan, Pranesh A.; Hughes, Scott A.; Khanna, Gaurav; Drasco, Steve
2008-01-01
This is the second in a series of papers whose aim is to generate adiabatic gravitational waveforms from the inspiral of stellar-mass compact objects into massive black holes. In earlier work, we presented an accurate (2+1)D finite-difference time-domain code to solve the Teukolsky equation, which evolves curvature perturbations near rotating (Kerr) black holes. The key new ingredient there was a simple but accurate model of the singular source term based on a discrete representation of the Dirac-delta function and its derivatives. Our earlier work was intended as a proof of concept, using simple circular, equatorial geodesic orbits as a test bed. Such a source is effectively static, in that the smaller body remains at the same coordinate radius and orbital inclination over an orbit. (It of course moves through axial angle, but we separate that degree of freedom from the problem. Our numerical grid has only radial, polar, and time coordinates.) We now extend the time-domain code so that it can accommodate dynamic sources that move on a variety of physically interesting world lines. We validate the code with extensive comparison to frequency-domain waveforms for cases in which the source moves along generic (inclined and eccentric) bound geodesic orbits. We also demonstrate the ability of the time-domain code to accommodate sources moving on interesting nongeodesic worldlines. We do this by computing the waveform produced by a test mass following a kludged inspiral trajectory, made of bound geodesic segments driven toward merger by an approximate radiation loss formula.
Adiabatic radio-frequency potentials for the coherent manipulation of matter waves
DEFF Research Database (Denmark)
Lesanovsky, Igor; Schumm, Thorsten; Hofferberth, S.
2006-01-01
Adiabatic dressed state potentials are created when magnetic substates of trapped atoms are coupled by a radio-frequency field. We discuss their theoretical foundations and point out fundamental advantages over potentials purely based on static fields. The enhanced flexibility enables one...... to implement numerous configurations, including double wells, Mach-Zehnder, and Sagnac interferometers which even allows for internal state-dependent atom manipulation. These can be realized using simple and highly integrated wire geometries on atom chips....
Quasi-adiabatic motion of energetic particles in a dipole magnetic field
International Nuclear Information System (INIS)
Il'in, V.D.; Kuznetsov, S.N.; Yushkov, B.Yu.
1992-01-01
A moving coordinate system for a dipole magnetic field, in which reversible variations of magnetic moment for the range of obvious violations of adiabatic conditions are absent, and the description of magnetic moment violations is relatively simple, is considered. Constructing of a coordinate system, features of the central trajectory, determining its motion, the application range, the main application field and consequences are discussed. 11 refs.; 3 figs
Three-neutrino oscillations in matter: Analytical results in the adiabatic approximaton
International Nuclear Information System (INIS)
Petcov, S.T.; Toshev, S.
1987-01-01
Analytical expressions for the probabilities of the transitions between different neutrino flavours in matter in the case of three lepton families and small vacuum mixing angles are obtained in the adiabatic approximation. A brief discussion of the characteristic features of the Mikheyev-Smirnov-Wolfenstein effect in the system of the three neutrino flavours ν e , ν μ and ν τ is also given. (orig.)
Accuracy versus run time in an adiabatic quantum search
International Nuclear Information System (INIS)
Rezakhani, A. T.; Pimachev, A. K.; Lidar, D. A.
2010-01-01
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance yet is often poorly understood. We study the dynamics of a continuous time, adiabatic quantum search algorithm and find rigorous results relating the accuracy and the run time. Proceeding with estimates, we show that under fairly general circumstances the adiabatic algorithmic error exhibits a behavior with two discernible regimes: The error decreases exponentially for short times and then decreases polynomially for longer times. We show that the well-known quadratic speedup over classical search is associated only with the exponential error regime. We illustrate the results through examples of evolution paths derived by minimization of the adiabatic error. We also discuss specific strategies for controlling the adiabatic error and run time.
Decoherence in a scalable adiabatic quantum computer
International Nuclear Information System (INIS)
Ashhab, S.; Johansson, J. R.; Nori, Franco
2006-01-01
We consider the effects of decoherence on Landau-Zener crossings encountered in a large-scale adiabatic-quantum-computing setup. We analyze the dependence of the success probability--i.e., the probability for the system to end up in its new ground state--on the noise amplitude and correlation time. We determine the optimal sweep rate that is required to maximize the success probability. We then discuss the scaling of decoherence effects with increasing system size. We find that those effects can be important for large systems, even if they are small for each of the small building blocks
Phase avalanches in near-adiabatic evolutions
International Nuclear Information System (INIS)
Vertesi, T.; Englman, R.
2006-01-01
In the course of slow, nearly adiabatic motion of a system, relative changes in the slowness can cause abrupt and high magnitude phase changes, ''phase avalanches,'' superimposed on the ordinary geometric phases. The generality of this effect is examined for arbitrary Hamiltonians and multicomponent (>2) wave packets and is found to be connected (through the Blaschke term in the theory of analytic signals) to amplitude zeros in the lower half of the complex time plane. Motion on a nonmaximal circle on the Poincare-sphere suppresses the effect. A spectroscopic transition experiment can independently verify the phase-avalanche magnitudes
On adiabatic perturbations in the ekpyrotic scenario
International Nuclear Information System (INIS)
Linde, A.; Mukhanov, V.; Vikman, A.
2010-01-01
In a recent paper, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in Khoury are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario
International Nuclear Information System (INIS)
El Sawi, M.
1983-07-01
A simple approach employing properties of solutions of differential equations is adopted to derive an appropriate extension of the WKBJ method. Some of the earlier techniques that are commonly in use are unified, whereby the general approximate solution to a second-order homogeneous linear differential equation is presented in a standard form that is valid for all orders. In comparison to other methods, the present one is shown to be leading in the order of iteration, and thus possibly has the ability of accelerating the convergence of the solution. The method is also extended for the solution of inhomogeneous equations. (author)
The relaxation time approximation
International Nuclear Information System (INIS)
Gairola, R.P.; Indu, B.D.
1991-01-01
A plausible approximation has been made to estimate the relaxation time from a knowledge of the transition probability of phonons from one state (r vector, q vector) to other state (r' vector, q' vector), as a result of collision. The relaxation time, thus obtained, shows a strong dependence on temperature and weak dependence on the wave vector. In view of this dependence, relaxation time has been expressed in terms of a temperature Taylor's series in the first Brillouin zone. Consequently, a simple model for estimating the thermal conductivity is suggested. the calculations become much easier than the Callaway model. (author). 14 refs
Polynomial approximation on polytopes
Totik, Vilmos
2014-01-01
Polynomial approximation on convex polytopes in \\mathbf{R}^d is considered in uniform and L^p-norms. For an appropriate modulus of smoothness matching direct and converse estimates are proven. In the L^p-case so called strong direct and converse results are also verified. The equivalence of the moduli of smoothness with an appropriate K-functional follows as a consequence. The results solve a problem that was left open since the mid 1980s when some of the present findings were established for special, so-called simple polytopes.
WKB approximation in atomic physics
International Nuclear Information System (INIS)
Karnakov, Boris Mikhailovich
2013-01-01
Provides extensive coverage of the Wentzel-Kramers-Brillouin approximation and its applications. Presented as a sequence of problems with highly detailed solutions. Gives a concise introduction for calculating Rydberg states, potential barriers and quasistationary systems. This book has evolved from lectures devoted to applications of the Wentzel-Kramers-Brillouin- (WKB or quasi-classical) approximation and of the method of 1/N -expansion for solving various problems in atomic and nuclear physics. The intent of this book is to help students and investigators in this field to extend their knowledge of these important calculation methods in quantum mechanics. Much material is contained herein that is not to be found elsewhere. WKB approximation, while constituting a fundamental area in atomic physics, has not been the focus of many books. A novel method has been adopted for the presentation of the subject matter, the material is presented as a succession of problems, followed by a detailed way of solving them. The methods introduced are then used to calculate Rydberg states in atomic systems and to evaluate potential barriers and quasistationary states. Finally, adiabatic transition and ionization of quantum systems are covered.
Adiabatic and non-adiabatic electron oscillations in a static electric field
International Nuclear Information System (INIS)
Wahlberg, C.
1977-03-01
The influence of a static electric field on the oscillations of a one-dimensional stream of electrons is investigated. In the weak field limit the oscillations are adiabatic and mode coupling negligible, but becomes significant if the field is tronger. The latter effect is believed to be of importance for the stability of e.g. potential double layers
Adiabatic evolution of decoherence-free subspaces and its shortcuts
Wu, S. L.; Huang, X. L.; Li, H.; Yi, X. X.
2017-10-01
The adiabatic theorem and shortcuts to adiabaticity for time-dependent open quantum systems are explored in this paper. Starting from the definition of dynamical stable decoherence-free subspace, we show that, under a compact adiabatic condition, the quantum state remains in the time-dependent decoherence-free subspace with an extremely high purity, even though the dynamics of the open quantum system may not be adiabatic. The adiabatic condition mentioned here in the adiabatic theorem for open systems is very similar to that for closed quantum systems, except that the operators required to change slowly are the Lindblad operators. We also show that the adiabatic evolution of decoherence-free subspaces depends on the existence of instantaneous decoherence-free subspaces, which requires that the Hamiltonian of open quantum systems be engineered according to the incoherent control protocol. In addition, shortcuts to adiabaticity for adiabatic decoherence-free subspaces are also presented based on the transitionless quantum driving method. Finally, we provide an example that consists of a two-level system coupled to a broadband squeezed vacuum field to show our theory. Our approach employs Markovian master equations and the theory can apply to finite-dimensional quantum open systems.
Quantum Adiabatic Algorithms and Large Spin Tunnelling
Boulatov, A.; Smelyanskiy, V. N.
2003-01-01
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.
Directory of Open Access Journals (Sweden)
Jeong Ryeol Choi
2015-01-01
Full Text Available An adiabatic invariant, which is a conserved quantity, is useful for studying quantum and classical properties of dynamical systems. Adiabatic invariants for time-dependent superconducting qubit-oscillator systems and resonators are investigated using the Liouville-von Neumann equation. At first, we derive an invariant for a simple superconducting qubit-oscillator through the introduction of its reduced Hamiltonian. Afterwards, an adiabatic invariant for a nanomechanical resonator linearly interfaced with a superconducting circuit, via a coupling with a time-dependent strength, is evaluated using the technique of unitary transformation. The accuracy of conservation for such invariant quantities is represented in detail. Based on the results of our developments in this paper, perturbation theory is applicable to the research of quantum characteristics of more complicated qubit systems that are described by a time-dependent Hamiltonian involving nonlinear terms.
High-fidelity adiabatic inversion of a {sup 31}P electron spin qubit in natural silicon
Energy Technology Data Exchange (ETDEWEB)
Laucht, Arne, E-mail: a.laucht@unsw.edu.au; Kalra, Rachpon; Muhonen, Juha T.; Dehollain, Juan P.; Mohiyaddin, Fahd A.; Hudson, Fay; Dzurak, Andrew S.; Morello, Andrea [Centre for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, University of New South Wales, Sydney, New South Wales 2052 (Australia); McCallum, Jeffrey C.; Jamieson, David N. [Centre for Quantum Computation and Communication Technology, School of Physics, University of Melbourne, Melbourne, Victoria 3010 (Australia)
2014-03-03
The main limitation to the high-fidelity quantum control of spins in semiconductors is the presence of strongly fluctuating fields arising from the nuclear spin bath of the host material. We demonstrate here a substantial improvement in single-qubit inversion fidelities for an electron spin qubit bound to a {sup 31}P atom in natural silicon, by applying adiabatic sweeps instead of narrow-band pulses. We achieve an inversion fidelity of 97%, and we observe signatures in the spin resonance spectra and the spin coherence time that are consistent with the presence of an additional exchange-coupled donor. This work highlights the effectiveness of simple adiabatic inversion techniques for spin control in fluctuating environments.
Zero-point energy, tunnelling, and vibrational adiabaticity in the Mu + H2 reaction
Mielke, Steven L.; Garrett, Bruce C.; Fleming, Donald G.; Truhlar, Donald G.
2015-01-01
Isotopic substitution of muonium for hydrogen provides an unparalleled opportunity to deepen our understanding of quantum mass effects on chemical reactions. A recent topical review in this journal of the thermal and vibrationally state-selected reaction of Mu with H2 raises a number of issues that are addressed here. We show that some earlier quantum mechanical calculations of the Mu + H2 reaction, which are highlighted in this review, and which have been used to benchmark approximate methods, are in error by as much as 19% in the low-temperature limit. We demonstrate that an approximate treatment of the Born-Oppenheimer diagonal correction that was used in some recent studies is not valid for treating the vibrationally state-selected reaction. We also discuss why vibrationally adiabatic potentials that neglect bend zero-point energy are not a useful analytical tool for understanding reaction rates, and why vibrationally non-adiabatic transitions cannot be understood by considering tunnelling through vibrationally adiabatic potentials. Finally, we present calculations on a hierarchical family of potential energy surfaces to assess the sensitivity of rate constants to the quality of the potential surface.
Rotational excitation of H2O by para-H2 from an adiabatically reduced dimensional potential.
Scribano, Yohann; Faure, Alexandre; Lauvergnat, David
2012-03-07
Cross sections and rate coefficients for low lying rotational transitions in H(2)O colliding with para-hydrogen pH(2) are computed using an adiabatic approximation which reduces the dimensional dynamics from a 5D to a 3D problem. Calculations have been performed at the close-coupling level using the recent potential of Valiron et al. [J. Chem. Phys. 129, 134306 (2008)]. A good agreement is found between the reduced adiabatic calculations and the 5D exact calculations, with an impressive time saving and memory gain. This adiabatic reduction of dimensionality seems very promising for scattering studies involving the excitation of a heavy target molecule by a light molecular projectile. © 2012 American Institute of Physics
Dependence of adiabatic population transfer on pulse profile
Indian Academy of Sciences (India)
Control of population transfer by rapid adiabatic passage has been an established technique wherein the exact amplitude profile of the shaped pulse is considered to be insignificant. We study the effect of ultrafast shaped pulses for two-level systems, by density-matrix approach. However, we find that adiabaticity depends ...
Kinetic Theory Derivation of the Adiabatic Law for Ideal Gases.
Sobel, Michael I.
1980-01-01
Discusses how the adiabatic law for ideal gases can be derived from the assumption of a Maxwell-Boltzmann (or any other) distribution of velocities--in contrast to the usual derivations from thermodynamics alone, and the higher-order effect that leads to one-body viscosity. An elementary derivation of the adiabatic law is given. (Author/DS)
Teleportation of an Unknown Atomic State via Adiabatic Passage
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We propose a scheme for teleporting an unknown atomic state via adiabatic passage. Taking advantage of adiabatic passage, the atom has no probability of being excited and thus the atomic spontaneous emission is suppressed.We also show that the fidelity can reach 1 under certain condition.
Adiabatic Compression Sensitivity of AF-M315E
2015-07-01
Brand for their technical expertise and guidance. He also wishes to thank Mr. Stephen McKim from NASA Goddard Space Flight Center for his assistance...Wilson, D. B., and Stoltzfus, J. M. "Adiabatic Compression of Oxygen: Real Fluid Temperatures," 2000. 10Ismail, I. M. K., and Hawkins , T. W. "Adiabatic
Constraints on the Adiabatic Temperature Change in Magnetocaloric Materials
DEFF Research Database (Denmark)
Nielsen, Kaspar Kirstein; Bahl, Christian Robert Haffenden; Smith, Anders
2010-01-01
The thermodynamics of the magnetocaloric effect implies constraints on the allowed variation in the adiabatic temperature change for a magnetocaloric material. An inequality for the derivative of the adiabatic temperature change with respect to temperature is derived for both first- and second...
Diophantine approximation and badly approximable sets
DEFF Research Database (Denmark)
Kristensen, S.; Thorn, R.; Velani, S.
2006-01-01
. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...
Derivation of an adiabatic time-dependent Hartree-Fock formalism from a variational principle
International Nuclear Information System (INIS)
Brink, D.M.; Giannoni, M.J.; Veneroni, M.
1975-10-01
A derivation of the adiabatic time-dependent Hartree-Fock formalism is given, which is based on a variational principle analogous to Hamilton's principle in classical mechanics. The method leads to a Hamiltonian for collective motion which separates into a potential and a kinetic energy and gives mass and potential parameters in terms of the nucleon-nucleon interaction. The adiabatic approximation assumes slow motion but not small amplitudes and can therefore describe anharmonic effects. The RPA is a limiting case where both amplitudes and velocities are small. The variational approach provides a consistent way of extracting coordinated and momenta from the density matrix and of obtaining equations of motion when particular trial forms for this density matrix are chosen. One such choice leads to Thouless-Valatin formula. An other choice leads to irrotational hydrodynamics [fr
Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures
International Nuclear Information System (INIS)
Sevastianov, L. A.; Egorov, A. A.; Sevastyanov, A. L.
2013-01-01
Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell’s equations is made to obey “inclined” boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of “entanglement” of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lüneburg lens.
An adiabatic spectroscopic investigation of the CsRb system in ground and numerous excited states
Souissi, Hanen; Jellali, Soulef; Maha, Chaieb; Habli, Héla; Oujia, Brahim; Gadéa, Florent Xavier
2017-10-01
Via ab-initio approximations, we investigate the electronic and structural features of the CsRb molecule. Adiabatic potential energy curves of 261,3Σ+, 181,3Π and 61,3Δ electronic states with their derived spectroscopic constants as well as vibrational levels spacing have been carried out and well explained. Our approach is founded on an Effective Core Potential (ECP) describing the valence electrons of the system. Using a large Gaussian basis set, the full valence Configuration Interaction can be applied easily on the two-effective valence electrons of the CsRb system. Furthermore, a detailed analysis of the electric dipolar properties has been made through the investigation of both permanent and transition dipole moments (PDM and TDM). It is significant that the ionic character connected with electron transfer that is linked to Cs+ Rb- state has been clearly illustrated in the adiabatic permanent dipole moment.
Tichauer, Kenneth M.; Osswald, Christian R.; Dosmar, Emily; Guthrie, Micah J.; Hones, Logan; Sinha, Lagnojita; Xu, Xiaochun; Mieler, William F.; St. Lawrence, Keith; Kang-Mieler, Jennifer J.
2015-06-01
Clinical symptoms of diabetic retinopathy are not detectable until damage to the retina reaches an irreversible stage, at least by today's treatment standards. As a result, there is a push to develop new, "sub-clinical" methods of predicting the onset of diabetic retinopathy before the onset of irreversible damage. With diabetic retinopathy being associated with the accumulation of long-term mild damage to the retinal vasculature, retinal blood vessel permeability has been proposed as a key parameter for detecting preclinical stages of retinopathy. In this study, a kinetic modeling approach used to quantify vascular permeability in dynamic contrast-enhanced medical imaging was evaluated in noise simulations and then applied to retinal videoangiography data in a diabetic rat for the first time to determine the potential for this approach to be employed clinically as an early indicator of diabetic retinopathy. Experimental levels of noise were found to introduce errors of less than 15% in estimates of blood flow and extraction fraction (a marker of vascular permeability), and fitting of rat retinal fluorescein angiography data provided stable maps of both parameters.
Adiabatic/diabatic polarization beam splitter
Energy Technology Data Exchange (ETDEWEB)
DeRose, Christopher; Cai, Hong
2017-09-12
The various presented herein relate to an on-chip polarization beam splitter (PBS), which is adiabatic for the transverse magnetic (TM) mode and diabatic for the transverse electric (TE) mode. The PBS comprises a through waveguide and a cross waveguide, wherein an electromagnetic beam comprising TE mode and TM mode components is applied to an input port of the through waveguide. The PBS can be utilized to separate the TE mode component from the TM mode component, wherein the TE mode component exits the PBS via an output port of the through waveguide, and the TM mode component exits the PBS via an output port of the cross waveguide. The PBS has a structure that is tolerant to manufacturing variations and exhibits high polarization extinction ratios over a wide bandwidth.
Design of ternary clocked adiabatic static random access memory
International Nuclear Information System (INIS)
Wang Pengjun; Mei Fengna
2011-01-01
Based on multi-valued logic, adiabatic circuits and the structure of ternary static random access memory (SRAM), a design scheme of a novel ternary clocked adiabatic SRAM is presented. The scheme adopts bootstrapped NMOS transistors, and an address decoder, a storage cell and a sense amplifier are charged and discharged in the adiabatic way, so the charges stored in the large switch capacitance of word lines, bit lines and the address decoder can be effectively restored to achieve energy recovery during reading and writing of ternary signals. The PSPICE simulation results indicate that the ternary clocked adiabatic SRAM has a correct logic function and low power consumption. Compared with ternary conventional SRAM, the average power consumption of the ternary adiabatic SRAM saves up to 68% in the same conditions. (semiconductor integrated circuits)
Generalized shortcuts to adiabaticity and enhanced robustness against decoherence
Santos, Alan C.; Sarandy, Marcelo S.
2018-01-01
Shortcuts to adiabaticity provide a general approach to mimic adiabatic quantum processes via arbitrarily fast evolutions in Hilbert space. For these counter-diabatic evolutions, higher speed comes at higher energy cost. Here, the counter-diabatic theory is employed as a minimal energy demanding scheme for speeding up adiabatic tasks. As a by-product, we show that this approach can be used to obtain infinite classes of transitionless models, including time-independent Hamiltonians under certain conditions over the eigenstates of the original Hamiltonian. We apply these results to investigate shortcuts to adiabaticity in decohering environments by introducing the requirement of a fixed energy resource. In this scenario, we show that generalized transitionless evolutions can be more robust against decoherence than their adiabatic counterparts. We illustrate this enhanced robustness both for the Landau-Zener model and for quantum gate Hamiltonians.
Adiabatic logic future trend and system level perspective
Teichmann, Philip
2012-01-01
Adiabatic logic is a potential successor for static CMOS circuit design when it comes to ultra-low-power energy consumption. Future development like the evolutionary shrinking of the minimum feature size as well as revolutionary novel transistor concepts will change the gate level savings gained by adiabatic logic. In addition, the impact of worsening degradation effects has to be considered in the design of adiabatic circuits. The impact of the technology trends on the figures of merit of adiabatic logic, energy saving potential and optimum operating frequency, are investigated, as well as degradation related issues. Adiabatic logic benefits from future devices, is not susceptible to Hot Carrier Injection, and shows less impact of Bias Temperature Instability than static CMOS circuits. Major interest also lies on the efficient generation of the applied power-clock signal. This oscillating power supply can be used to save energy in short idle times by disconnecting circuits. An efficient way to generate the p...
Design of ternary clocked adiabatic static random access memory
Pengjun, Wang; Fengna, Mei
2011-10-01
Based on multi-valued logic, adiabatic circuits and the structure of ternary static random access memory (SRAM), a design scheme of a novel ternary clocked adiabatic SRAM is presented. The scheme adopts bootstrapped NMOS transistors, and an address decoder, a storage cell and a sense amplifier are charged and discharged in the adiabatic way, so the charges stored in the large switch capacitance of word lines, bit lines and the address decoder can be effectively restored to achieve energy recovery during reading and writing of ternary signals. The PSPICE simulation results indicate that the ternary clocked adiabatic SRAM has a correct logic function and low power consumption. Compared with ternary conventional SRAM, the average power consumption of the ternary adiabatic SRAM saves up to 68% in the same conditions.
Adiabatic Rearrangement of Hollow PV Towers
Directory of Open Access Journals (Sweden)
Eric A Hendricks
2010-10-01
Full Text Available Diabatic heating from deep moist convection in the hurricane eyewall produces a towering annular structure of elevated potential vorticity (PV. This structure has been referred to as a hollow PV tower. The sign reversal of the radial gradient of PV satisfies the Charney-Stern necessary condition for combined barotropic-baroclinic instability. For thin enough annular structures, small perturbations grow exponentially, extract energy from the mean flow, and lead to hollow tower breakdown, with significant vortex structural and intensity change. The three-dimensional adiabatic rearrangements of two prototypical hurricane-like hollow PV towers (one thick and one thin are examined in an idealized framework. For both hollow towers, dynamic instability causes air parcels with high PV to be mixed into the eye preferentially at lower levels, where unstable PV wave growth rates are the largest. Little or no mixing is found to occur at upper levels. The mixing at lower and middle levels is most rapid for the breakdown of the thin hollow tower, consistent with previous barotropic results. For both hollow towers, this advective rearrangement of PV affects the tropical cyclone structure and intensity in a number of ways. First, the minimum central pressure and maximum azimuthal mean velocity simultaneously decrease, consistent with previous barotropic results. Secondly, isosurfaces of absolute angular momentum preferentially shift inward at low levels, implying an adiabatic mechanism by which hurricane eyewall tilt can form. Thirdly, a PV bridge, similar to that previously found in full-physics hurricane simulations, develops as a result of mixing at the isentropic levels where unstable PV waves grow most rapidly. Finally, the balanced mass field resulting from the PV rearrangement is warmer in the eye between 900 and 700 hPa. The location of this warming is consistent with observed warm anomalies in the eye, indicating that in certain instances the hurricane
International Nuclear Information System (INIS)
Buechner, J.M.
1989-01-01
For a number of problems in the Plasma Astrophysics it is necessary to know the laws, which govern the non adiabatic charged particle dynamics in strongly curves magnetic field reversals. These are, e.q., the kinetic theory of the microscopic and macroscopicstability of current sheets in collionless plasma, of microturbulence, causing anomalous resistivity and dissipating currents, the problem of spontaneous reconnection, the formation of non Maxwellian distribution functions, particle acceleration and the use of particles as a diagnostic tool ('tracers'). To find such laws we derived from the differential equations of motion discrete mappings. These mappings allow an investigation of the motion after the break down of the adiabaticity of the magnetic moment. (author). 32 refs.; 5 figs.; 1 tab
Adiabatic time-dependent Hartree-Fock theory of collective motion in finite systems
International Nuclear Information System (INIS)
Baranger, M.; Veneroni, M.
1978-01-01
We show how to derive the parameters of a phenomenological collective model from a microscopic theory. The microscopic theory is Hartree-Fock, and we start from the time-dependent Hartree-Fock equation. To this we add the adiabatic approximation, which results in a collective kinetic energy quadratic in the velocities, with coefficients depending on the coordinates, as in the phenomenological models. The crucial step is the decomposition of the single-particle density matrix p in the form exp(i/sub chi/) rho/sub omicron/exp(-i/sub chi/), where rho/sub omicron/ represents a time-even Slater determinant and plays the role of coordinate. Then chi plays the role of momentum, and the adiabatic assumption is that chi is small. The energy is expanded in powers of chi, the zeroth-order being the collective potential energy. The analogy with classical mechanics is stressed and studied. The same adiabatic equations of motion are derived in three different ways (directly, from the Lagrangian, from the Hamiltonian), thus proving the consistency of the theory. The dynamical equation is not necessary for writing the energy or for the subsequent quantization which leads to a Schroedinger equation, but it must be used to check the validity of various approximation schemes, particularly to reduce the problem to a few degrees of freedom. The role of the adiabatic hypothesis, its definition, and range of validity, are analyzed in great detail. It assumes slow motion, but not small amplitude, and is therefore suitable for large-amplitude collective motion. The RPA is obtained as the limiting case where the amplitude is also small. The translational mass is correctly given, and the moment of inertia under rotation is that of Thouless and Valatin. For a quadrupole two-body force, the Baranger-Kumar formalism is recovered. The self-consistency brings additional terms to the Inglis cranking formula. Comparison is also made with generator coordinate methods
Quantum theory of NMR adiabatic pulses and their applications
International Nuclear Information System (INIS)
Ke, Y.
1993-01-01
Recently explosive developments of in vivo NMR spectroscopy (NMRS) and imaging (NMRI) in biological and medical sciences have resulted in the establishment of NMR as one of the most advanced major technique in life sciences. These developments have created huge demands for a variety of NMR adiabatic pulses with play a very important role in NMR experiments in vivo. In order to develop new NMR adiabatic pulses, a rigorous systematical quantum theory for this kind of pulses is greatly needed. Providing such a theory is one of the important goals of this dissertation. Quantum density matrix theory and product operator method have been used throughout this dissertation. Another goal, which is the major goal of this thesis research, is to use the quantum theory as a guide to develop new NMR adiabatic pulses and their applications. To fill this goal, a technique to construct a new type of adiabatic pulses, narrow band selective adiabatic pulses, has been invented, which is described through the example of constructing an adiabatic DANTE inversion pulse. This new adiabatic pulse is the first narrow band selective adiabatic pulses: Adiabatic homonuclear and heteronuclear spectral editing sequences. Unique to the first pulse sequence is a B 1 -field filter which is built by using two non-refocusing adiabatic full passage pulses to refocus the wanted signal and dephase unwanted signals. This extra filter greatly enhance the editing efficiency. Unlike commonly used heteronuclear spectral editing sequences which depend on the polarization transfer or spectral subtraction by phase cycling techniques, the second pulse sequences accomplishes the editing of heteronuclear J-coupled signals based on the fact that this sequence is transparent to the uncoupled spins and is equivalent a 90 degrees excitation pulse to the heteronuclear J-coupled spins. Experimental results have confirmed the ability of spectral editing with these two new sequences
Evolution of f{sub NL} to the adiabatic limit
Energy Technology Data Exchange (ETDEWEB)
Elliston, Joseph; Mulryne, David J.; Tavakol, Reza [School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS (United Kingdom); Seery, David, E-mail: J.Elliston@qmul.ac.uk, E-mail: D.Mulryne@qmul.ac.uk, E-mail: D.Seery@sussex.ac.uk, E-mail: R.Tavakol@qmul.ac.uk [Astronomy Centre, University of Sussex, Falmer, Brighton BN1 9QH (United Kingdom)
2011-11-01
We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay — the {sup a}diabatic limit{sup .} We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of f{sub NL} to be large. Other examples can be constructed using a waterfall field to terminate inflation while f{sub NL} is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak f{sub NL}.
Evolution of fNL to the adiabatic limit
Elliston, Joseph; Mulryne, David J.; Seery, David; Tavakol, Reza
2011-11-01
We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay — the "adiabatic limit". We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of fNL to be large. Other examples can be constructed using a waterfall field to terminate inflation while fNL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak fNL.
Asteroseismology of white dwarf stars. I - Adiabatic results
Energy Technology Data Exchange (ETDEWEB)
Bradley, P.A.; Winget, D.E. (Texas, University (USA) McDonald Observatory, Austin (USA))
1991-02-01
A preliminary investigation of the asteroseismological properties of chemically stratified evolutionary DA and DB white dwarf models is reported. The period and kinetic energy distributions for nonradial g-modes of spherical harmonic indices l = 1-3 are computed in the adiabatic approximation, and the effects of varying the total stellar masss and the surface layer masses on the pulsation properties are studied using an extensive grid of models. Significant resonant mode trapping due to chemical stratification is found. Modes trapped in the outer layers have much lower kinetic energies; these minima also show up as minima in the period spacing between modes of consecutive radial overtone k. Mode trapping occurs at the same or nearly the same value of k for different l-values. Thus, l-values of trapped modes may be identified on the basis of their period ratios. It is shown that observational identification of these period ratios can be used to constrain the mass of the star and its surface layer. 68 refs.
Non-adiabatic perturbations in Ricci dark energy model
International Nuclear Information System (INIS)
Karwan, Khamphee; Thitapura, Thiti
2012-01-01
We show that the non-adiabatic perturbations between Ricci dark energy and matter can grow both on superhorizon and subhorizon scales, and these non-adiabatic perturbations on subhorizon scales can lead to instability in this dark energy model. The rapidly growing non-adiabatic modes on subhorizon scales always occur when the equation of state parameter of dark energy starts to drop towards -1 near the end of matter era, except that the parameter α of Ricci dark energy equals to 1/2. In the case where α = 1/2, the rapidly growing non-adiabatic modes disappear when the perturbations in dark energy and matter are adiabatic initially. However, an adiabaticity between dark energy and matter perturbations at early time implies a non-adiabaticity between matter and radiation, this can influence the ordinary Sachs-Wolfe (OSW) effect. Since the amount of Ricci dark energy is not small during matter domination, the integrated Sachs-Wolfe (ISW) effect is greatly modified by density perturbations of dark energy, leading to a wrong shape of CMB power spectrum. The instability in Ricci dark energy is difficult to be alleviated if the effects of coupling between baryon and photon on dark energy perturbations are included
Pre-History Of The Concepts Underlying Stimulated Raman Adiabatic Passage (STIRAP)
International Nuclear Information System (INIS)
Shore, B.W.
2013-01-01
This tutorial review discusses some of the work that preceded development, twenty-five years ago, of the stimulated Raman adiabatic passage (STIRAP) technique, now widely used in the controlled coherent dynamics of three-state systems, noting how the use of time-dependent adiabatically-evolving population-trapping dark states made possible the robust and highly-efficient population transfer between quantum states that first popularized STIRAP. Preceding the history discussion is a tutorial definition of STIRAP and its necessary and sufficient ingredients — understanding that has led to applications well beyond those of the original quantum systems. This review also discusses the relationship between STIRAP and two related procedures: chirped Raman adiabatic passage (RCAP or CHIRAP) and electromagnetically induced transparency (EIT) with slow and captured light. It concludes with a brief discussion of ways in which contemporary STIRAP has extended the original concept and enlarged the definition, beyond that of simple quantum systems to classical macroscopic devices. Appendices offer further details. The presentation emphasizes theory but with illustrations of experimental results. (author)
International Nuclear Information System (INIS)
Saul, Lukas; Wurz, Peter; Kallenbach, Reinald
2009-01-01
Interstellar neutral gas enters the inner heliosphere where it is ionized and becomes the pickup ion population of the solar wind. It is often assumed that this population will subsequently cool adiabatically, like an expanding ideal gas due, to the divergent flow of the solar wind. Here, we report the first independent measure of the effective adiabatic cooling index in the inner heliosphere from SOHO CELIAS measurements of singly charged helium taken during times of perpendicular interplanetary magnetic field. We use a simple adiabatic transport model of interstellar pickup helium ions, valid for the upwind region of the inner heliosphere. The time averaged velocity spectrum of helium pickup ions measured by CELIAS/CTOF is fit to this model with a single free parameter which indicates an effective cooling rate with a power-law index of γ = 1.35 ± 0.2. While this average is consistent with the 'ideal-gas' assumption of γ = 1.5, the analysis indicates that such an assumption will not apply in general, and that due to observational constraints further measurements are necessary to constrain the cooling process. Implications are discussed for understanding the transport processes in the inner heliosphere and improving this measurement technique.
Approximate Bayesian computation.
Directory of Open Access Journals (Sweden)
Mikael Sunnåker
Full Text Available Approximate Bayesian computation (ABC constitutes a class of computational methods rooted in Bayesian statistics. In all model-based statistical inference, the likelihood function is of central importance, since it expresses the probability of the observed data under a particular statistical model, and thus quantifies the support data lend to particular values of parameters and to choices among different models. For simple models, an analytical formula for the likelihood function can typically be derived. However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate. ABC methods bypass the evaluation of the likelihood function. In this way, ABC methods widen the realm of models for which statistical inference can be considered. ABC methods are mathematically well-founded, but they inevitably make assumptions and approximations whose impact needs to be carefully assessed. Furthermore, the wider application domain of ABC exacerbates the challenges of parameter estimation and model selection. ABC has rapidly gained popularity over the last years and in particular for the analysis of complex problems arising in biological sciences (e.g., in population genetics, ecology, epidemiology, and systems biology.
Are the reactions of quinones on graphite adiabatic?
International Nuclear Information System (INIS)
Luque, N.B.; Schmickler, W.
2013-01-01
Outer sphere electron transfer reactions on pure metal electrodes are often adiabatic and hence independent of the electrode material. Since it is not clear, whether adiabatic electron transfer can also occur on a semi-metal like graphite, we have re-investigated experimental data presented in a recent communication by Nissim et al. [Chemical Communications 48 (2012) 3294] on the reactions of quinones on graphite. We have supplemented their work by DFT calculations and conclude, that these reactions are indeed adiabatic. This contradicts the assertion of Nissim et al. that the rates are proportional to the density of states at the Fermi level
Adiabatic quantum algorithm for search engine ranking.
Garnerone, Silvano; Zanardi, Paolo; Lidar, Daniel A
2012-06-08
We propose an adiabatic quantum algorithm for generating a quantum pure state encoding of the PageRank vector, the most widely used tool in ranking the relative importance of internet pages. We present extensive numerical simulations which provide evidence that this algorithm can prepare the quantum PageRank state in a time which, on average, scales polylogarithmically in the number of web pages. We argue that the main topological feature of the underlying web graph allowing for such a scaling is the out-degree distribution. The top-ranked log(n) entries of the quantum PageRank state can then be estimated with a polynomial quantum speed-up. Moreover, the quantum PageRank state can be used in "q-sampling" protocols for testing properties of distributions, which require exponentially fewer measurements than all classical schemes designed for the same task. This can be used to decide whether to run a classical update of the PageRank.
Adiabatic liquid piston compressed air energy storage
Energy Technology Data Exchange (ETDEWEB)
Petersen, Tage [Danish Technological Institute, Aarhus (Denmark); Elmegaard, B. [Technical Univ. of Denmark. DTU Mechanical Engineering, Kgs. Lyngby (Denmark); Schroeder Pedersen, A. [Technical Univ. of Denmark. DTU Energy Conversion, Risoe Campus, Roskilde (Denmark)
2013-01-15
This project investigates the potential of a Compressed Air Energy Storage system (CAES system). CAES systems are used to store mechanical energy in the form of compressed air. The systems use electricity to drive the compressor at times of low electricity demand with the purpose of converting the mechanical energy into electricity at times of high electricity demand. Two such systems are currently in operation; one in Germany (Huntorf) and one in the USA (Macintosh, Alabama). In both cases, an underground cavern is used as a pressure vessel for the storage of the compressed air. Both systems are in the range of 100 MW electrical power output with several hours of production stored as compressed air. In this range, enormous volumes are required, which make underground caverns the only economical way to design the pressure vessel. Both systems use axial turbine compressors to compress air when charging the system. The compression leads to a significant increase in temperature, and the heat generated is dumped into the ambient. This energy loss results in a low efficiency of the system, and when expanding the air, the expansion leads to a temperature drop reducing the mechanical output of the expansion turbines. To overcome this, fuel is burned to heat up the air prior to expansion. The fuel consumption causes a significant cost for the storage. Several suggestions have been made to store compression heat for later use during expansion and thereby avoid the use of fuel (so called Adiabatic CAES units), but no such units are in operation at present. The CAES system investigated in this project uses a different approach to avoid compression heat loss. The system uses a pre-compressed pressure vessel full of air. A liquid is pumped into the bottom of the vessel when charging and the same liquid is withdrawn through a turbine when discharging. In this case, the liquid works effectively as a piston compressing the gas in the vessel, hence the name ''Adiabatic
Spatial non-adiabatic passage using geometric phases
Energy Technology Data Exchange (ETDEWEB)
Benseny, Albert; Busch, Thomas [Okinawa Institute of Science and Technology Graduate University, Quantum Systems Unit, Okinawa (Japan); Kiely, Anthony; Ruschhaupt, Andreas [University College Cork, Department of Physics, Cork (Ireland); Zhang, Yongping [Okinawa Institute of Science and Technology Graduate University, Quantum Systems Unit, Okinawa (Japan); Shanghai University, Department of Physics, Shanghai (China)
2017-12-15
Quantum technologies based on adiabatic techniques can be highly effective, but often at the cost of being very slow. Here we introduce a set of experimentally realistic, non-adiabatic protocols for spatial state preparation, which yield the same fidelity as their adiabatic counterparts, but on fast timescales. In particular, we consider a charged particle in a system of three tunnel-coupled quantum wells, where the presence of a magnetic field can induce a geometric phase during the tunnelling processes. We show that this leads to the appearance of complex tunnelling amplitudes and allows for the implementation of spatial non-adiabatic passage. We demonstrate the ability of such a system to transport a particle between two different wells and to generate a delocalised superposition between the three traps with high fidelity in short times. (orig.)
On the adiabatic theorem in quantum statistical mechanics
International Nuclear Information System (INIS)
Narnhofer, H.; Thirring, W.
1982-01-01
We show that with suitable assumptions the equilibrium states are exactly the states invariant under adiabatic local perturbations. The relevance of this fact to the problem of ergodicity is discussed. (Author)
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians
Bringewatt, Jacob; Dorland, William; Jordan, Stephen P.; Mink, Alan
2018-02-01
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real non-negative amplitudes and thus for whom destructive interference is not manifest. This raises the question of whether classical Monte Carlo algorithms can efficiently simulate quantum adiabatic optimization with stoquastic Hamiltonians. Recent results have given counterexamples in which path-integral and diffusion Monte Carlo fail to do so. However, most adiabatic optimization algorithms, such as for solving MAX-k -SAT problems, use k -local Hamiltonians, whereas our previous counterexample for diffusion Monte Carlo involved n -body interactions. Here we present a 6-local counterexample which demonstrates that even for these local Hamiltonians there are cases where diffusion Monte Carlo cannot efficiently simulate quantum adiabatic optimization. Furthermore, we perform empirical testing of diffusion Monte Carlo on a standard well-studied class of permutation-symmetric tunneling problems and similarly find large advantages for quantum optimization over diffusion Monte Carlo.
Adiabatic rotation, quantum search, and preparation of superposition states
International Nuclear Information System (INIS)
Siu, M. Stewart
2007-01-01
We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied 'straight line' adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev's toric code state, the cluster state of the measurement-based computation model, and the history state used in the adiabatic simulation of a quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the standard adiabatic algorithm
Virial theorem and the Born-Oppenheimer approximation at different orders of perturbation
International Nuclear Information System (INIS)
Olivier, Gabriel; Weislinger, Edmond
1977-01-01
The link between the virial theorem and the adiabatic approximation is studied for a few orders of perturbation. It is shown that the total energy of the system is distributed between the mean values of kinetic and potential energy of the nuclei and the electrons in each order of perturbation. No static approximation connected with the Hellmann-Feynman theorem is made [fr
On Adiabatic Processes at the Elementary Particle Level
A, Michaud
2016-01-01
Analysis of adiabatic processes at the elementary particle level and of the manner in which they correlate with the principle of conservation of energy, the principle of least action and entropy. Analysis of the initial and irreversible adiabatic acceleration sequence of newly created elementary particles and its relation to these principles. Exploration of the consequences if this first initial acceleration sequence is not subject to the principle of conservation.
RFDR with Adiabatic Inversion Pulses: Application to Internuclear Distance Measurements
International Nuclear Information System (INIS)
Leppert, Joerg; Ohlenschlaeger, Oliver; Goerlach, Matthias; Ramachandran, Ramadurai
2004-01-01
In the context of the structural characterisation of biomolecular systems via MAS solid state NMR, the potential utility of homonuclear dipolar recoupling with adiabatic inversion pulses has been assessed via numerical simulations and experimental measurements. The results obtained suggest that it is possible to obtain reliable estimates of internuclear distances via an analysis of the initial cross-peak intensity buildup curves generated from two-dimensional adiabatic inversion pulse driven longitudinal magnetisation exchange experiments
International Nuclear Information System (INIS)
Gheisari, R.; Eskandari, M. R.
2006-01-01
Meta-stable symmetric ions ppμ * and ddμ * are formed in the collisions of the excited muonic atoms with the hydrogen isotopes. By dissociation of them, the muon transfers from 2s to 1s via the new channels. Considering the quantum electrodynamics field and employing the new wave functions, the matrix elements are simply integrated. In this method using the adiabatic representations, the photo-decay widths for the some of ppμ * and ddμ * states are variationally calculated. The decay rates for X-ray productions of the similar states are approximately same.
Approximate Implicitization Using Linear Algebra
Directory of Open Access Journals (Sweden)
Oliver J. D. Barrowclough
2012-01-01
Full Text Available We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD systems. We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms. We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms. We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
Weighted approximation with varying weight
Totik, Vilmos
1994-01-01
A new construction is given for approximating a logarithmic potential by a discrete one. This yields a new approach to approximation with weighted polynomials of the form w"n"(" "= uppercase)P"n"(" "= uppercase). The new technique settles several open problems, and it leads to a simple proof for the strong asymptotics on some L p(uppercase) extremal problems on the real line with exponential weights, which, for the case p=2, are equivalent to power- type asymptotics for the leading coefficients of the corresponding orthogonal polynomials. The method is also modified toyield (in a sense) uniformly good approximation on the whole support. This allows one to deduce strong asymptotics in some L p(uppercase) extremal problems with varying weights. Applications are given, relating to fast decreasing polynomials, asymptotic behavior of orthogonal polynomials and multipoint Pade approximation. The approach is potential-theoretic, but the text is self-contained.
Approximate reasoning in physical systems
International Nuclear Information System (INIS)
Mutihac, R.
1991-01-01
The theory of fuzzy sets provides excellent ground to deal with fuzzy observations (uncertain or imprecise signals, wavelengths, temperatures,etc.) fuzzy functions (spectra and depth profiles) and fuzzy logic and approximate reasoning. First, the basic ideas of fuzzy set theory are briefly presented. Secondly, stress is put on application of simple fuzzy set operations for matching candidate reference spectra of a spectral library to an unknown sample spectrum (e.g. IR spectroscopy). Thirdly, approximate reasoning is applied to infer an unknown property from information available in a database (e.g. crystal systems). Finally, multi-dimensional fuzzy reasoning techniques are suggested. (Author)
Perturbation to Unified Symmetry and Adiabatic Invariants for Relativistic Hamilton Systems
International Nuclear Information System (INIS)
Zhang Mingjiang; Fang Jianhui; Lu Kai; Pang Ting; Lin Peng
2009-01-01
Based on the concept of adiabatic invariant, the perturbation to unified symmetry and adiabatic invariants for relativistic Hamilton systems are studied. The definition of the perturbation to unified symmetry for the system is presented, and the criterion of the perturbation to unified symmetry is given. Meanwhile, the Noether adiabatic invariants, the generalized Hojman adiabatic invariants, and the Mei adiabatic invariants for the perturbed system are obtained. (general)
Fast-forward of quantum adiabatic dynamics in electro-magnetic field
Masuda, Shumpei; Nakamura, Katsuhiro
2010-01-01
We show a method to accelerate quantum adiabatic dynamics of wavefunctions under electro-magnetic field by developing the previous theory (Masuda & Nakamura 2008 and 2010). Firstly we investigate the orbital dynamics of a charged particle. We derive the driving field which accelerates quantum adiabatic dynamics in order to obtain the final adiabatic states except for the spatially uniform phase such as the adiabatic phase in any desired short time. Fast-forward of adiabatic squeezing and tran...
Graybill, George
2007-01-01
Just how simple are simple machines? With our ready-to-use resource, they are simple to teach and easy to learn! Chocked full of information and activities, we begin with a look at force, motion and work, and examples of simple machines in daily life are given. With this background, we move on to different kinds of simple machines including: Levers, Inclined Planes, Wedges, Screws, Pulleys, and Wheels and Axles. An exploration of some compound machines follows, such as the can opener. Our resource is a real time-saver as all the reading passages, student activities are provided. Presented in s
Boehler, R.
1982-07-01
The adiabats of olivine, magnesium oxide, and quartz were measured up to 50kbar and 1000 K. An end-loaded piston-cylinder apparatus with an in situ pressure gauge and a very fine thermocouple was used to measure (∂T/∂P)s during adiabatic compression. A power law between (∂T/∂P)s and compression yields values of the power n = -∂ ln (∂T/∂P)s/∂ ln ρ that agree with previous results from salts, metals, and fluids. Assuming constant values for n, the adiabtic gradient for an olivine upper mantle and a magnesium oxide lower mantle was calculated. The results agree well with some previous theoretical estimates. The volume dependence of the Grüneisen parameter γ was calculated from the thermodynamic equation ∂ ln γ/∂ ln ρ = ∂B/∂P - n, where B is the isothermal bulk modulus. γ is found to a good approximation to be proportional to volume. Table 6 is available with entire article on microfiche. Order from American Geophysical Union, 2000 Florida Avenue, N.W., Washington, D.C. 20009. Document J82-002; $1.00. Payment must accompany order.
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Li, Guo-Ping; Zu, Xiao-Tao [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Pu, Jin [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); China West Normal University, College of Physics and Space Science, Nanchong (China); Jiang, Qing-Quan [China West Normal University, College of Physics and Space Science, Nanchong (China)
2017-05-15
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painleve) of coordinates as well as in different gravity frames, the adiabatic invariant I{sub adia} = circular integral p{sub i}dq{sub i} introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area. (orig.)
Quantum tunneling, adiabatic invariance and black hole spectroscopy
Li, Guo-Ping; Pu, Jin; Jiang, Qing-Quan; Zu, Xiao-Tao
2017-05-01
In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang-Han's proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant I_adia = \\oint p_i dq_i introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang-Han's proposal reasonably in more general gravity frames (including Einstein's gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.
Adiabatic condition and the quantum hitting time of Markov chains
International Nuclear Information System (INIS)
Krovi, Hari; Ozols, Maris; Roland, Jeremie
2010-01-01
We present an adiabatic quantum algorithm for the abstract problem of searching marked vertices in a graph, or spatial search. Given a random walk (or Markov chain) P on a graph with a set of unknown marked vertices, one can define a related absorbing walk P ' where outgoing transitions from marked vertices are replaced by self-loops. We build a Hamiltonian H(s) from the interpolated Markov chain P(s)=(1-s)P+sP ' and use it in an adiabatic quantum algorithm to drive an initial superposition over all vertices to a superposition over marked vertices. The adiabatic condition implies that, for any reversible Markov chain and any set of marked vertices, the running time of the adiabatic algorithm is given by the square root of the classical hitting time. This algorithm therefore demonstrates a novel connection between the adiabatic condition and the classical notion of hitting time of a random walk. It also significantly extends the scope of previous quantum algorithms for this problem, which could only obtain a full quadratic speedup for state-transitive reversible Markov chains with a unique marked vertex.
Shortcuts to adiabaticity in cutting a spin chain
Energy Technology Data Exchange (ETDEWEB)
Ren, Feng-Hua [Department of Physics, Ocean University of China, Qingdao 266100 (China); School of Computer Engineering, Qingdao Technological University, Qingdao 266033 (China); Wang, Zhao-Ming, E-mail: mingmoon78@126.com [Department of Physics, Ocean University of China, Qingdao 266100 (China); Gu, Yong-Jian, E-mail: yjgu@ouc.edu.cn [Department of Physics, Ocean University of China, Qingdao 266100 (China)
2017-01-15
“Shortcuts to adiabaticity” represents a strategy for accelerating a quantum adiabatic process, is useful for preparing or manipulating a quantum state. In this paper, we investigate the adiabaticity in the dynamics of an XY spin chain. During the process of cutting one long chain into two short chains, a “shortcut” can be obtained by applying a sequence of external pulses. The fidelity which measures the adiabaticity can be dramatically enhanced by increasing the pulse strength or pulse duration time. This reliability can be kept for different types of pulses, such as random pulse time interval or random strength. The free choice of the pulse can be explained by the adiabatic representation of the Hamiltonian, and it shows that the control effects are determined by the integral of the control function in the time domain. - Highlights: • “Shortcuts to adiabaticity” is proposed by applying external pulses. • The adiabaticity can be accelerated by increasing pulse strength or duration time. • Control effects are determined by the integral of the control function with respect to time.
Energy Technology Data Exchange (ETDEWEB)
Paredes, C.; Trueba, M.
2014-07-01
The CRDA accident in BWR plants was analysed historically in situations of stop cold and stop hot with adiabatic methods, to have considered these situations the more limiting for this type of event. The proposed analysis is done with the two methodologies in order to show that this accident is effectively limiting how much lower is the power, as well as the conservatism of the adiabatic approximation. (Author)
Approximation properties of haplotype tagging
Directory of Open Access Journals (Sweden)
Dreiseitl Stephan
2006-01-01
Full Text Available Abstract Background Single nucleotide polymorphisms (SNPs are locations at which the genomic sequences of population members differ. Since these differences are known to follow patterns, disease association studies are facilitated by identifying SNPs that allow the unique identification of such patterns. This process, known as haplotype tagging, is formulated as a combinatorial optimization problem and analyzed in terms of complexity and approximation properties. Results It is shown that the tagging problem is NP-hard but approximable within 1 + ln((n2 - n/2 for n haplotypes but not approximable within (1 - ε ln(n/2 for any ε > 0 unless NP ⊂ DTIME(nlog log n. A simple, very easily implementable algorithm that exhibits the above upper bound on solution quality is presented. This algorithm has running time O((2m - p + 1 ≤ O(m(n2 - n/2 where p ≤ min(n, m for n haplotypes of size m. As we show that the approximation bound is asymptotically tight, the algorithm presented is optimal with respect to this asymptotic bound. Conclusion The haplotype tagging problem is hard, but approachable with a fast, practical, and surprisingly simple algorithm that cannot be significantly improved upon on a single processor machine. Hence, significant improvement in computatational efforts expended can only be expected if the computational effort is distributed and done in parallel.
Compact beam splitters in coupled waveguides using shortcuts to adiabaticity
Chen, Xi; Wen, Rui-Dan; Shi, Jie-Long; Tseng, Shuo-Yen
2018-04-01
There are various works on adiabatic (three) waveguide coupler devices but most are focused on the quantum optical analogies and the physics itself. We successfully apply shortcuts to adiabaticity techniques to the coupled waveguide system with a suitable length for integrated optics devices. Especially, the counter-diabatic driving protocol followed by unitary transformation overcomes the previously unrealistic implemention, and is used to design feasible and robust 1 × 2 and 1 × 3 beam splitters for symmetric and asymmetric three waveguide couplers. Numerical simulations with the beam propagation method demonstrate that these shortcut designs for beam splitters are shorter than the adiabatic ones, and also have a better tolerance than parallel waveguides resonant beam splitters with respect to spacing errors and wavelength variation.
Adiabatic passage and ensemble control of quantum systems
International Nuclear Information System (INIS)
Leghtas, Z; Sarlette, A; Rouchon, P
2011-01-01
This paper considers population transfer between eigenstates of a finite quantum ladder controlled by a classical electric field. Using an appropriate change of variables, we show that this setting can be set in the framework of adiabatic passage, which is known to facilitate ensemble control of quantum systems. Building on this insight, we present a mathematical proof of robustness for a control protocol-chirped pulse-practised by experimentalists to drive an ensemble of quantum systems from the ground state to the most excited state. We then propose new adiabatic control protocols using a single chirped and amplitude-shaped pulse, to robustly perform any permutation of eigenstate populations, on an ensemble of systems with unknown coupling strengths. These adiabatic control protocols are illustrated by simulations on a four-level ladder.
Adiabatic Expansion of Electron Gas in a Magnetic Nozzle
Takahashi, Kazunori; Charles, Christine; Boswell, Rod; Ando, Akira
2018-01-01
A specially constructed experiment shows the near perfect adiabatic expansion of an ideal electron gas resulting in a polytropic index greater than 1.4, approaching the adiabatic value of 5 /3 , when removing electric fields from the system, while the polytropic index close to unity is observed when the electrons are trapped by the electric fields. The measurements were made on collisionless electrons in an argon plasma expanding in a magnetic nozzle. The collision lengths of all electron collision processes are greater than the scale length of the expansion, meaning the system cannot be in thermodynamic equilibrium, yet thermodynamic concepts can be used, with caution, in explaining the results. In particular, a Lorentz force, created by inhomogeneities in the radial plasma density, does work on the expanding magnetic field, reducing the internal energy of the electron gas that behaves as an adiabatically expanding ideal gas.
A design study of non-adiabatic electron guns
International Nuclear Information System (INIS)
Barroso, J.J.; Stellati, C.
1994-01-01
The design of a non-adiabatic gun capable of producing a 10 A, 50 KeV high-quality laminar electron beam is reported. In contrast to the magnetron injection gun with a conical cathode, where the beam is generated initially with a transverse velocity component, in the non-adiabatic gun electrons are extracted in a direction parallel to the axial guide magnetic field. The beam electrons acquire cyclotron motion as result of non-adiabatic processes in a strong non uniform electric field across the modulation anode. Such an extraction method gives rise to favourable features that are explored throughout the work. An extensive numerical simulation study has also been done to minimize velocity and energy spreads. (author). 3 refs, 5 figs, 1 tab
Collective modes in simple melts: Transition from soft spheres to the hard sphere limit.
Khrapak, Sergey; Klumov, Boris; Couëdel, Lénaïc
2017-08-11
We study collective modes in a classical system of particles with repulsive inverse-power-law (IPL) interactions in the fluid phase, near the fluid-solid coexistence (IPL melts). The IPL exponent is varied from n = 10 to n = 100 to mimic the transition from moderately soft to hard-sphere-like interactions. We compare the longitudinal dispersion relations obtained using molecular dynamic (MD) simulations with those calculated using the quasi-crystalline approximation (QCA) and find that this simple theoretical approach becomes grossly inaccurate for [Formula: see text]. Similarly, conventional expressions for high-frequency (instantaneous) elastic moduli, predicting their divergence as n increases, are meaningless in this regime. Relations of the longitudinal and transverse elastic velocities of the QCA model to the adiabatic sound velocity, measured in MD simulations, are discussed for the regime where QCA is applicable. Two potentially useful freezing indicators for classical particle systems with steep repulsive interactions are discussed.
Appearance of gauge structure in simple dynamical systems
Wilczek, F.; Zee, A.
1984-01-01
By generalizing a construction of Berry and Simon, it is shown that non-Abelian gauge fields arise in the adiabatic development of simple quantum mechanical systems. Characteristics of the gauge fields are related to energy splittings, which may be observable in real systems. Similar phenomena are found for suitable classical systems.
International Nuclear Information System (INIS)
Ginsburg, C.A.
1980-01-01
In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)
High beta lasing in micropillar cavities with adiabatic layer design
DEFF Research Database (Denmark)
Lermer, M.; Gregersen, Niels; Lorke, M.
2013-01-01
We report on lasing in optically pumped adiabatic micropillar cavities, based on the AlAs/GaAs material system. A detailed study of the threshold pump power and the spontaneous emission β factor in the lasing regime for different diameters dc is presented. We demonstrate a reduction of the thresh...... of the threshold pump power by over 2 orders of magnitude from dc = 2.25 μm down to 0.95 μm. Lasing with β factors exceeding 0.5 shows that adiabatic micropillars are operating deeply in the cavity quantum electrodynamics regime....
Adiabatic theory of ionization of atoms by intense laser pulses
International Nuclear Information System (INIS)
Tolstikhin, Oleg I; Morishita, Toru; Watanabe, Shinichi
2009-01-01
As a first step towards the adiabatic theory of ionization of atoms by intense laser pulses, here we consider the simplest one-dimensional zero-range potential model. The asymptotic solution to the time-dependent Schroedinger equation in the adiabatic regime is obtained and the photoelectron spectrum is calculated. The factorization formula for the photoelectron spectrum in the back-rescattering region, first suggested by Morishita et al. [Phys. Rev. Lett. 100, 013903 (2008)] on the basis of ab initio calculations, is derived analytically.
On the adiabatic theorem when eigenvalues dive into the continuum
DEFF Research Database (Denmark)
Cornean, Decebal Horia; Jensen, Arne; Knörr, Hans Konrad
2018-01-01
We consider a reduced two-channel model of an atom consisting of a quantum dot coupled to an open scattering channel described by a three-dimensional Laplacian. We are interested in the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial...... in the adiabatic limit. At the end of the paper, we present a short outlook on how our method may be extended to cover other classes of Hamiltonians; details will be given elsewhere....
Approximation algorithms for guarding holey polygons ...
African Journals Online (AJOL)
Guarding edges of polygons is a version of art gallery problem.The goal is finding the minimum number of guards to cover the edges of a polygon. This problem is NP-hard, and to our knowledge there are approximation algorithms just for simple polygons. In this paper we present two approximation algorithms for guarding ...
Sparse approximation with bases
2015-01-01
This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications. The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...
... Han M, Partin AW. Simple prostatectomy: open and robot-assisted laparoscopic approaches. In: Wein AJ, Kavoussi LR, ... M. is also a founding member of Hi-Ethics and subscribes to the principles of the Health ...
International Nuclear Information System (INIS)
Ohlsson, D.
1978-08-01
Previous stability theories concerning electrostatic current and magnetic curvature driven modes in cold plasma mantle boundary layers are generalized. In particular the commonly used adiabatic approximation is relaxed. In the general theory presented important new effects associated with heat conduction, ionization and ohmic heating are found. In combination with viscosity and resistivity these effects introduce additional stabilizing as well as destabilizing effects. Furthermore the present theory typically predicts similar stability properties as the adiabatic theory in the limit |d(1nT)/d(1nn)| >1 the general theory predicts less favourable stability properties. One may speculate that these conclusions also apply to more general types of electrostatic modes associated with density and temperature gradients in cold plasma mantel boundary layers. (author)
Study of doubly excited states of H- and He in the coupled-channel hypersperical adiabatic approach
International Nuclear Information System (INIS)
Abrashkevich, A.G.; Abrashkevich, D.G.; Vinitskij, S.I.; Kaschiev, M.S.; Puzynin, I.V.
1989-01-01
Doubly excited states (DES) of H - and He are investigated within the coupled-channel hyperspherical adiabatic (HSA) approach. Influence of the angular and radial electron correlations on the rate of convergence of the values of the potential curves and matrix elements of radial coupling is studied numerically. The scheme based on molecular classification of the HSA basis states is used for the classification of DES. The results of the multichannel calculations of 1 S e and 1 P 0 DES of H - and He below the second threshold are presented. The obtained results are compared with other calculations and experiment. The region of applicability of the adiabatic approximation is discussed. 75 refs.; 10 tabs
Energy Technology Data Exchange (ETDEWEB)
Taioli, Simone [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Department of Physics, University of Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (Italy); Department of Chemistry, University of Bologna, Bologna (Italy); Garberoglio, Giovanni [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Simonucci, Stefano [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (Italy); Department of Physics, University of Camerino, Camerino (Italy); Beccara, Silvio a [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Department of Physics, University of Trento, Trento (Italy); Aversa, Lucrezia [Institute of Materials for Electronics and Magnetism, IMEM-CNR, Trento (Italy); Nardi, Marco [Institute of Materials for Electronics and Magnetism, IMEM-CNR, Trento (Italy); Institut fuer Physik, Humboldt-Universitaet zu Berlin, Berlin (Germany); Verucchi, Roberto [Institute of Materials for Electronics and Magnetism, FBK-CNR, Trento (Italy); Iannotta, Salvatore [Institute of Materials for Electronics and Magnetism, IMEM-CNR, Parma (Italy); Dapor, Maurizio [Interdisciplinary Laboratory for Computational Science, FBK-Center for Materials and Microsystems and University of Trento, Trento (Italy); Department of Materials Engineering and Industrial Technologies, University of Trento, Trento (Italy); Istituto Nazionale di Fisica Nucleare, Sezione di Padova (Italy); and others
2013-01-28
In this work, we investigate the processes leading to the room-temperature growth of silicon carbide thin films by supersonic molecular beam epitaxy technique. We present experimental data showing that the collision of fullerene on a silicon surface induces strong chemical-physical perturbations and, for sufficient velocity, disruption of molecular bonds, and cage breaking with formation of nanostructures with different stoichiometric character. We show that in these out-of-equilibrium conditions, it is necessary to go beyond the standard implementations of density functional theory, as ab initio methods based on the Born-Oppenheimer approximation fail to capture the excited-state dynamics. In particular, we analyse the Si-C{sub 60} collision within the non-adiabatic nuclear dynamics framework, where stochastic hops occur between adiabatic surfaces calculated with time-dependent density functional theory. This theoretical description of the C{sub 60} impact on the Si surface is in good agreement with our experimental findings.
International Nuclear Information System (INIS)
Ponce, W.A.; Zepeda, A.
1987-08-01
We present the results obtained from our systematic search of a simple Lie group that unifies weak and electromagnetic interactions in a single truly unified theory. We work with fractionally charged quarks, and allow for particles and antiparticles to belong to the same irreducible representation. We found that models based on SU(6), SU(7), SU(8) and SU(10) are viable candidates for simple unification. (author). 23 refs
Approximate symmetries of Hamiltonians
Chubb, Christopher T.; Flammia, Steven T.
2017-08-01
We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.
Adiabatic compression and radiative compression of magnetic fields
International Nuclear Information System (INIS)
Woods, C.H.
1980-01-01
Flux is conserved during mechanical compression of magnetic fields for both nonrelativistic and relativistic compressors. However, the relativistic compressor generates radiation, which can carry up to twice the energy content of the magnetic field compressed adiabatically. The radiation may be either confined or allowed to escape
Non - Adiabaticity and Novel Isotope Effect in the Doped Cuprates
International Nuclear Information System (INIS)
Kresin, V.; WOLF, S. A.
1995-01-01
This paper reports a novel isotope effect which is due to a strong non-adiabaticity that manifests itself in the dependence of the carrier concentration on the isotopic mass. The critical temperature in turn depends on the carrier concentration giving rise to a unique and non-phononic isotope shift. (author)
Non-adiabatic rotational excitation of dipolar molecule under the ...
Indian Academy of Sciences (India)
J. Chem. Sci. Vol. 125, No. 5, September 2013, pp. 1213–1221. c Indian Academy of Sciences. ... The rotational wave packets of LiCl molecule excited non-adiabatically by half cycle pulse. (HCP) is .... pared to the intensities required for the ionization of ..... out and with delayed ultrashort HCP at different initial pulse dura-.
Adiabatic and diabatic aerosol transport to the Jungfraujoch
Energy Technology Data Exchange (ETDEWEB)
Lugauer, M.; Baltensperger, U.; Furger, M.; Jost, D.T.; Schwikowski, M.; Gaeggeler, H.W. [Paul Scherrer Inst. (PSI), Villigen (Switzerland)
1997-09-01
Synoptic scale vertical motion, here detected by the geopotential height of the 500 hPa surface, mainly accounts for the aerosol transport to the Jungfraujoch in winter. In summer, diabatic convection provides the dominant vertical transport mechanism. Nevertheless, synoptic scale adiabatic motion still determines whether diabatic convection can develop. (author) 2 figs., 2 refs.
Monte Carlo Simulation of Adiabatic Cooling and Nuclear Magnetism
DEFF Research Database (Denmark)
Lindgård, Per-Anker; Viertiö, H. E.; Mouritsen, Ole G.
1988-01-01
in experimental studies of nuclear magnetism using adiabatic demagnetization methods. It is found that, although fluctuations reduce the transition temperatures by 40%, the isentropes are reduced by less than 10% relative to those calculated by mean-field theory. The dynamics of the ordering process following...
Probing Entanglement in Adiabatic Quantum Optimization with Trapped Ions
Directory of Open Access Journals (Sweden)
Philipp eHauke
2015-04-01
Full Text Available Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.
Building an adiabatic quantum computer simulation in the classroom
Rodríguez-Laguna, Javier; Santalla, Silvia N.
2018-05-01
We present a didactic introduction to adiabatic quantum computation (AQC) via the explicit construction of a classical simulator of quantum computers. This constitutes a suitable route to introduce several important concepts for advanced undergraduates in physics: quantum many-body systems, quantum phase transitions, disordered systems, spin-glasses, and computational complexity theory.
Adiabatic CMB perturbations in pre-big bang string cosmology
DEFF Research Database (Denmark)
Enqvist, Kari; Sloth, Martin Snoager
2001-01-01
We consider the pre-big bang scenario with a massive axion field which starts to dominate energy density when oscillating in an instanton-induced potential and subsequently reheats the universe as it decays into photons, thus creating adiabatic CMB perturbations. We find that the fluctuations...
Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition
International Nuclear Information System (INIS)
Qian Shangwu; Gu Zhiyu
2005-01-01
There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the general time-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.
Approximating distributions from moments
Pawula, R. F.
1987-11-01
A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.
CONTRIBUTIONS TO RATIONAL APPROXIMATION,
Some of the key results of linear Chebyshev approximation theory are extended to generalized rational functions. Prominent among these is Haar’s...linear theorem which yields necessary and sufficient conditions for uniqueness. Some new results in the classic field of rational function Chebyshev...Furthermore a Weierstrass type theorem is proven for rational Chebyshev approximation. A characterization theorem for rational trigonometric Chebyshev approximation in terms of sign alternation is developed. (Author)
Approximation techniques for engineers
Komzsik, Louis
2006-01-01
Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.
Quantum tunneling beyond semiclassical approximation
International Nuclear Information System (INIS)
Banerjee, Rabin; Majhi, Bibhas Ranjan
2008-01-01
Hawking radiation as tunneling by Hamilton-Jacobi method beyond semiclassical approximation is analysed. We compute all quantum corrections in the single particle action revealing that these are proportional to the usual semiclassical contribution. We show that a simple choice of the proportionality constants reproduces the one loop back reaction effect in the spacetime, found by conformal field theory methods, which modifies the Hawking temperature of the black hole. Using the law of black hole mechanics we give the corrections to the Bekenstein-Hawking area law following from the modified Hawking temperature. Some examples are explicitly worked out.
Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures
Energy Technology Data Exchange (ETDEWEB)
Sevastianov, L. A., E-mail: sevast@sci.pfu.edu.ru [Peoples' Friendship University of Russia (Russian Federation); Egorov, A. A. [Russian Academy of Sciences, Prokhorov General Physics Institute (Russian Federation); Sevastyanov, A. L. [Peoples' Friendship University of Russia (Russian Federation)
2013-02-15
Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell's equations is made to obey 'inclined' boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of 'entanglement' of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lueneburg lens.
Chaos induced by quantum effect due to breakdown of the Born-Oppenheimer adiabaticity
International Nuclear Information System (INIS)
Fujisaki, Hiroshi; Takatsuka, Kazuo
2001-01-01
Chaos in the multimode nonadiabatic system constructed by Heller [J. Chem. Phys. >92, 1718 (1990)], which consists of two diabatic two-dimensional harmonic potentials with the Condon coupling, is studied. A thorough investigation is carried out by scanning the magnitudes of the Condon coupling and the Duschinsky angle. To elucidate mechanisms that can cause chaos in this quantum system, the statistical properties of the energy levels and eigenfunctions of the system are investigated. We find an evidence in terms of the nearest-neighbor spacing distribution of energy levels and other measures that a certain class of chaos is purely induced by the nonadiabatic interaction due to breakdown of the Born-Oppenheimer approximation. Since the nonadiabatic transition can induce repeated bifurcation and merging of a wave packet around the region of quasicrossing between two potential surfaces, and since this interaction does not have a counterpart in the lower adiabatic system, the present chaos deserves being called 'nonadiabatic chaos.' Another type of chaos in a nonadiabatic system was previously identified [D. M. Leitner et al., J. Chem. Phys. >104, 434 (1996)] that reflects the inherent chaos of a corresponding adiabatic potential. We present a comparative study to establish the similarity and difference between these kinds of chaos
Expectation Consistent Approximate Inference
DEFF Research Database (Denmark)
Opper, Manfred; Winther, Ole
2005-01-01
We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability dis...
Ordered cones and approximation
Keimel, Klaus
1992-01-01
This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.
International Nuclear Information System (INIS)
Bazhin, M.A.; Fedosenko, G.Eh.; Shiryaeva, N.M.; Mal'ko, M.V.
1986-01-01
It is shown that adiabatic non-equilibrium chemically reacting gas flow with energy exchange in a variable cross-section channel may be subdivided into five possible types: 1) quasi-equilibrium flow; 2) flow in the linear region of deviation from equilibrium state; 3) quasi-frozen flow; 4) flow in the linear region of deviation from frozen state; 5) non-equilibrium flow. Criteria of quasi-equilibrium and quazi-frozen flows, including factors of external action of chemically reacting gas on flow, allow to obtain simple but sufficiently reliable approximate method of calculation of flow parameters. The considered method for solving the problem of chemically reacting nitrogen tetroxide in the variable cross-section channel with energy exchange can be used for evaluation of chemical reaction kinetics on the flow parameter in the stages of axial-flow and radial-flow turbines and in another practical problems
A Controlled-Phase Gate via Adiabatic Rydberg Dressing of Neutral Atoms
Keating, Tyler; Deutsch, Ivan; Cook, Robert; Biederman, Grant; Jau, Yuan-Yu
2014-05-01
The dipole blockade effect between Rydberg atoms is a promising tool for quantum information processing in neutral atoms. So far, most efforts to perform a quantum logic gate with this effect have used resonant laser pulses to excite the atoms, which makes the system particularly susceptible to decoherence through thermal motional effects. We explore an alternative scheme in which the atomic ground states are adiabatically ``dressed'' by turning on an off-resonant laser. We analyze the implementation of a CPHASE gate using this mechanism and find that fidelities of >99% should be possible with current technology, owing primarily to the suppression of motional errors. We also discuss how such a scheme could be generalized to perform more complicated, multi-qubit gates; in particular, a simple generalization would allow us to perform a Toffoli gate in a single step.
Approximate and renormgroup symmetries
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H. [Blekinge Institute of Technology, Karlskrona (Sweden). Dept. of Mathematics Science; Kovalev, Vladimir F. [Russian Academy of Sciences, Moscow (Russian Federation). Inst. of Mathematical Modeling
2009-07-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximate and renormgroup symmetries
International Nuclear Information System (INIS)
Ibragimov, Nail H.; Kovalev, Vladimir F.
2009-01-01
''Approximate and Renormgroup Symmetries'' deals with approximate transformation groups, symmetries of integro-differential equations and renormgroup symmetries. It includes a concise and self-contained introduction to basic concepts and methods of Lie group analysis, and provides an easy-to-follow introduction to the theory of approximate transformation groups and symmetries of integro-differential equations. The book is designed for specialists in nonlinear physics - mathematicians and non-mathematicians - interested in methods of applied group analysis for investigating nonlinear problems in physical science and engineering. (orig.)
Approximations of Fuzzy Systems
Directory of Open Access Journals (Sweden)
Vinai K. Singh
2013-03-01
Full Text Available A fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. Such results can be viewed as an existence of optimal fuzzy systems. Li-Xin Wang discussed a similar problem using Gaussian membership function and Stone-Weierstrass Theorem. He established that fuzzy systems, with product inference, centroid defuzzification and Gaussian functions are capable of approximating any real continuous function on a compact set to arbitrary accuracy. In this paper we study a similar approximation problem by using exponential membership functions
Potvin, Guy
2015-10-01
We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.
International Nuclear Information System (INIS)
Knobloch, A.F.
1980-01-01
A simplified cost approximation for INTOR parameter sets in a narrow parameter range is shown. Plausible constraints permit the evaluation of the consequences of parameter variations on overall cost. (orig.) [de
Gautschi, Walter; Rassias, Themistocles M
2011-01-01
Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg
Rebolini, Elisa; Teale, Andrew M.; Helgaker, Trygve; Savin, Andreas; Toulouse, Julien
2018-06-01
A Görling-Levy (GL)-based perturbation theory along the range-separated adiabatic connection is assessed for the calculation of electronic excitation energies. In comparison with the Rayleigh-Schrödinger (RS)-based perturbation theory this GL-based perturbation theory keeps the ground-state density constant at each order and thus gives the correct ionisation energy at each order. Excitation energies up to first order in the perturbation have been calculated numerically for the helium and beryllium atoms and the hydrogen molecule without introducing any density-functional approximations. In comparison with the RS-based perturbation theory, the present GL-based perturbation theory gives much more accurate excitation energies for Rydberg states but similar excitation energies for valence states.
Manipulation of ultracold atoms in dressed adiabatic radio-frequency potentials
DEFF Research Database (Denmark)
Lesanovsky, Igor; Hofferberth, S.; Schmiedmayer, Jörg
2006-01-01
We explore properties of atoms whose magnetic hyperfine sublevels are coupled by an external magnetic radio frequency (rf) field. We perform a thorough theoretical analysis of this driven system and present a number of systematic approximations which eventually give rise to dressed adiabatic radio...... frequency potentials. The predictions of this analytical investigation are compared to numerically exact results obtained by a wave packet propagation. We outline the versatility and flexibility of this class of potentials and demonstrate their potential use to build atom optical elements such as double...... wells, interferometers, and ringtraps. Moreover, we perform simulations of interference experiments carried out in rf induced double-well potentials. We discuss how the nature of the atom-field coupling mechanism gives rise to a decrease of the interference contrast....
International Nuclear Information System (INIS)
Abdolsalami, M.; Abdolsalami, F.; Gonzalez, H.R.
1994-01-01
We have implemented nonlocal exchange effects rigorously in the first-order nondegenerate adiabatic (FONDA) theory. This implementation requires solving integrodifferential equations that involve double integrals. Separable and model exchange approximations that simplify the inclusion of exchange in the scattering calculations have been previously implemented in the FONDA theory. The discrepancy between the exact exchange FONDA cross sections and the separable and model exchange results suggests that one needs to include exchange rigorously to obtain accurate results over a wide range of energies. Specifically, a difference of up to 30% is observed between the exact and separable exchange FONDA cross sections at near-threshold energies. At higher energies the FONDA results from the rigorous and model exchange implementations disagree by as much as 10%
Experimental study of inverted-annular-flow hydrodynamics utilizing an adiabatic simulation
International Nuclear Information System (INIS)
De Jarlais, G.
1983-03-01
In experiments, inverted annular flow was simulated adiabatically with turbulent water jets, issuing downward from long aspect nozzles, enclosed in gas annuli. Velocities, diameters, and gas species were varied, and core jet length, shape, break-up mode, and dispersed-core droplet sizes were recorded at approximately 750 data points. Inverted annular flow was observed to develop into inverted slug flow at low relative velocities, and into dispersed droplet flow at high relative velocities. For both of the above transitions from inverted annular flow, correlations for core jet length were developed by extending work done on free liquid jets to include this new, coaxial, jet disintegration phenomenon. Jet break-up length is correlated as a function of jet diameter, jet Reynolds number, jet Weber number, void fraction, and gas Weber number. Correlations for core shape, break-up mechanisms and dispersed core droplet size for the case of transition to inverted slug flow were developed
Discrete Bose-Einstein systems in a box with low adiabatic invariant
International Nuclear Information System (INIS)
Vlad, V.I.; Ionescu-Pallas, N.
2002-03-01
The Bose-Einstein energy spectrum of a quantum gas, confined in a (cubic) box, is discrete and strongly dependent on the box geometry and temperature, for low product of the atomic mass number, A at and the adiabatic invariant, TV 2/3 , i.e. on γ=A at TV 2/3 . Even within the approximation of noninteracting particles in the gas, the calculation of the thermodynamic properties of Bose-Einstein systems turns out to be a difficult mathematical problem. It is solved in the textbooks and most papers by approximating the sums by integrals. The present study compares the total number of particles and the total energy obtained by summing up the exact contributions of the eigenvalues and their weights, for defined values of γ, to the results of the approximate integrals. Then, the passage from sums to integrals is done in a more rigorous manner and better analytical approximations are found. The corrected thermodynamic functions depend on γ. The critical temperature is corrected also in order to describe more accurately the discrete Bose-Einstein systems and their onset of the phase transition. (author)
Approximate kernel competitive learning.
Wu, Jian-Sheng; Zheng, Wei-Shi; Lai, Jian-Huang
2015-03-01
Kernel competitive learning has been successfully used to achieve robust clustering. However, kernel competitive learning (KCL) is not scalable for large scale data processing, because (1) it has to calculate and store the full kernel matrix that is too large to be calculated and kept in the memory and (2) it cannot be computed in parallel. In this paper we develop a framework of approximate kernel competitive learning for processing large scale dataset. The proposed framework consists of two parts. First, it derives an approximate kernel competitive learning (AKCL), which learns kernel competitive learning in a subspace via sampling. We provide solid theoretical analysis on why the proposed approximation modelling would work for kernel competitive learning, and furthermore, we show that the computational complexity of AKCL is largely reduced. Second, we propose a pseudo-parallelled approximate kernel competitive learning (PAKCL) based on a set-based kernel competitive learning strategy, which overcomes the obstacle of using parallel programming in kernel competitive learning and significantly accelerates the approximate kernel competitive learning for large scale clustering. The empirical evaluation on publicly available datasets shows that the proposed AKCL and PAKCL can perform comparably as KCL, with a large reduction on computational cost. Also, the proposed methods achieve more effective clustering performance in terms of clustering precision against related approximate clustering approaches. Copyright © 2014 Elsevier Ltd. All rights reserved.
Adiabatic theorem for the time-dependent wave operator
International Nuclear Information System (INIS)
Viennot, David; Jolicard, Georges; Killingbeck, John P.; Perrin, Marie-Yvonne
2005-01-01
The application of time-dependent wave operator theory to the development of a quantum adiabatic perturbation theory is treated both theoretically and numerically, with emphasis on the description of field-matter interactions which involve short laser pulses. It is first shown that the adiabatic limit of the time-dependent wave operator corresponds to a succession of instantaneous static Bloch wave operators. Wave operator theory is then shown to be compatible with the two-time Floquet theory of light-matter interaction, thus allowing the application of Floquet theory to cases which require the use of a degenerate active space. A numerical study of some problems shows that the perturbation strength associated with nonadiabatic processes can be reduced by using multidimensional active spaces and illustrates the capacity of the wave operator approach to produce a quasiadiabatic treatment of a nominally nonadiabatic Floquet dynamical system
Adiabatic instability in coupled dark energy/dark matter models
International Nuclear Information System (INIS)
Bean, Rachel; Flanagan, Eanna E.; Trodden, Mark
2008-01-01
We consider theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the Universe. Such theories can possess an adiabatic regime in which the quintessence field always sits at the minimum of its effective potential, which is set by the local dark matter density. We show that if the coupling strength is much larger than gravitational, then the adiabatic regime is always subject to an instability. The instability, which can also be thought of as a type of Jeans instability, is characterized by a negative sound speed squared of an effective coupled dark matter/dark energy fluid, and results in the exponential growth of small scale modes. We discuss the role of the instability in specific coupled cold dark matter and mass varying neutrino models of dark energy and clarify for these theories the regimes in which the instability can be evaded due to nonadiabaticity or weak coupling.
An adiabatic matching device for the Orsay linear positron accelerator
International Nuclear Information System (INIS)
Chehab, R.; Le Meur, G.; Mouton, B.; Renard, M.
1983-03-01
An adiabatically tapered solenoidal magnetic field is used to match positron beam source emittance to accelerating section acceptance. Such a matching system improves the accepted energy band which has been accurately computed and compared with analytical determination. The tapered field is provided by stacked pancakes and solenoids of various radii; total lens length is about 0.75m. The adiabatic matching system took place of a quarter wave transformer system and has been in operation for two years. Positron conversion ratio is 3.3% for a 1 GeV incident beam and presents a factor of nearly two of improvement for the positron yield. Energy bandwidth of positron beam has also been increased by a factor of nearly 2.5; the output positron beam energy is of 1.2 GeV
Adiabatic pair creation in heavy-ion and laser fields
International Nuclear Information System (INIS)
Pickl, P.; Durr, D.
2008-01-01
The planned generation of lasers and heavy-ion colliders renews the hope to see electron-positron pair creation in strong classical fields. This old prediction is usually referred to as spontaneous pair creation. We observe that both heavy-ion collisions and pair creation in strong laser fields, are instances of the theory of adiabatic pair creation. We shall present the theory, thereby correcting earlier results. We give the momentum distribution of created pairs in overcritical fields. We discuss carefully the proposed experimental verifications and conclude that pure laser-based experiments are highly questionable. We propose a new experiment, joining laser fields and heavy ions, which may be feasible with present-day technology and which may indeed verify the theoretical prediction of adiabatic pair creation. Our presentation relies on recent rigorous works in mathematical physics. (authors)
Perturbative treatment of possible failures in the adiabatic theorem
International Nuclear Information System (INIS)
Vertesi, T.; Englman, R.
2005-01-01
Complete text of publication follows. The adiabatic theorem (AT) is one of the oldest and basic results in quantum physics, and has been in widespread use ever since. The theorem concerns the evolution of systems subject to slowly varying Hamiltonians. Roughly, its content is that a system prepared in an instantaneous eigenstate of a time-dependent Hamiltonian H(t) will remain close to an instantaneous eigenstate at later times, provided the Hamiltonian changes sufficiently slowly. The role of the AT in the study of slowly varying quantum mechanical systems spans a vast array of fields and applications. In a recent application the adiabatic geometric phases have been proposed to perform various quantum computational tasks on a naturally fault-tolerant way. Additional interest has arisen in adiabatic processes in connection with the concept of adiabatic quantum computing, where the solution to a problem is encoded in the (unknown) ground state of a (known) Hamiltonian. The evolution of the quantum state is governed by a time-dependent Hamiltonian H(t), starting with an initial Hamiltonian H i with a known ground state and slowly (adiabatically) evolving to the final Hamiltonian H f with the unknown ground state, e.g., H(t) = (1 - t/T )H i + (t/T )H f , (1) where 0 ≤ t/T ≤ 1 and T controls the rate at which H(t) varies. Since the ground state of the system is very robust against external perturbations and decoherence, this scheme offers many advantages compared to the conventional quantum circuit model of quantum computation. The achievable speed-up of adiabatic quantum algorithms (compared to classical methods) depends on the value of the run-time T. The standard AT yields a general criterion to estimate the necessary run-time T, however recently Marzlin and Sanders have claimed that an inconsistency does exist for a particular class of Hamiltonians, so that the condition for the estimate of T may do not hold. Marzlin and Sanders start with a time
Adiabatic tapered optical fiber fabrication in two step etching
Chenari, Z.; Latifi, H.; Ghamari, S.; Hashemi, R. S.; Doroodmand, F.
2016-01-01
A two-step etching method using HF acid and Buffered HF is proposed to fabricate adiabatic biconical optical fiber tapers. Due to the fact that the etching rate in second step is almost 3 times slower than the previous droplet etching method, terminating the fabrication process is controllable enough to achieve a desirable fiber diameter. By monitoring transmitted spectrum, final diameter and adiabaticity of tapers are deduced. Tapers with losses about 0.3 dB in air and 4.2 dB in water are produced. The biconical fiber taper fabricated using this method is used to excite whispering gallery modes (WGMs) on a microsphere surface in an aquatic environment. So that they are suitable to be used in applications like WGM biosensors.
Adiabatic pipelining: a key to ternary computing with quantum dots
Pečar, P.; Ramšak, A.; Zimic, N.; Mraz, M.; Lebar Bajec, I.
2008-12-01
The quantum-dot cellular automaton (QCA), a processing platform based on interacting quantum dots, was introduced by Lent in the mid-1990s. What followed was an exhilarating period with the development of the line, the functionally complete set of logic functions, as well as more complex processing structures, however all in the realm of binary logic. Regardless of these achievements, it has to be acknowledged that the use of binary logic is in computing systems mainly the end result of the technological limitations, which the designers had to cope with in the early days of their design. The first advancement of QCAs to multi-valued (ternary) processing was performed by Lebar Bajec et al, with the argument that processing platforms of the future should not disregard the clear advantages of multi-valued logic. Some of the elementary ternary QCAs, necessary for the construction of more complex processing entities, however, lead to a remarkable increase in size when compared to their binary counterparts. This somewhat negates the advantages gained by entering the ternary computing domain. As it turned out, even the binary QCA had its initial hiccups, which have been solved by the introduction of adiabatic switching and the application of adiabatic pipeline approaches. We present here a study that introduces adiabatic switching into the ternary QCA and employs the adiabatic pipeline approach to successfully solve the issues of elementary ternary QCAs. What is more, the ternary QCAs presented here are sizewise comparable to binary QCAs. This in our view might serve towards their faster adoption.
Adiabatic pipelining: a key to ternary computing with quantum dots
International Nuclear Information System (INIS)
Pecar, P; Zimic, N; Mraz, M; Lebar Bajec, I; Ramsak, A
2008-01-01
The quantum-dot cellular automaton (QCA), a processing platform based on interacting quantum dots, was introduced by Lent in the mid-1990s. What followed was an exhilarating period with the development of the line, the functionally complete set of logic functions, as well as more complex processing structures, however all in the realm of binary logic. Regardless of these achievements, it has to be acknowledged that the use of binary logic is in computing systems mainly the end result of the technological limitations, which the designers had to cope with in the early days of their design. The first advancement of QCAs to multi-valued (ternary) processing was performed by Lebar Bajec et al, with the argument that processing platforms of the future should not disregard the clear advantages of multi-valued logic. Some of the elementary ternary QCAs, necessary for the construction of more complex processing entities, however, lead to a remarkable increase in size when compared to their binary counterparts. This somewhat negates the advantages gained by entering the ternary computing domain. As it turned out, even the binary QCA had its initial hiccups, which have been solved by the introduction of adiabatic switching and the application of adiabatic pipeline approaches. We present here a study that introduces adiabatic switching into the ternary QCA and employs the adiabatic pipeline approach to successfully solve the issues of elementary ternary QCAs. What is more, the ternary QCAs presented here are sizewise comparable to binary QCAs. This in our view might serve towards their faster adoption.
Adiabatic pipelining: a key to ternary computing with quantum dots.
Pečar, P; Ramšak, A; Zimic, N; Mraz, M; Lebar Bajec, I
2008-12-10
The quantum-dot cellular automaton (QCA), a processing platform based on interacting quantum dots, was introduced by Lent in the mid-1990s. What followed was an exhilarating period with the development of the line, the functionally complete set of logic functions, as well as more complex processing structures, however all in the realm of binary logic. Regardless of these achievements, it has to be acknowledged that the use of binary logic is in computing systems mainly the end result of the technological limitations, which the designers had to cope with in the early days of their design. The first advancement of QCAs to multi-valued (ternary) processing was performed by Lebar Bajec et al, with the argument that processing platforms of the future should not disregard the clear advantages of multi-valued logic. Some of the elementary ternary QCAs, necessary for the construction of more complex processing entities, however, lead to a remarkable increase in size when compared to their binary counterparts. This somewhat negates the advantages gained by entering the ternary computing domain. As it turned out, even the binary QCA had its initial hiccups, which have been solved by the introduction of adiabatic switching and the application of adiabatic pipeline approaches. We present here a study that introduces adiabatic switching into the ternary QCA and employs the adiabatic pipeline approach to successfully solve the issues of elementary ternary QCAs. What is more, the ternary QCAs presented here are sizewise comparable to binary QCAs. This in our view might serve towards their faster adoption.
Adame, J.; Warzel, S.
2015-11-01
In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM.
International Nuclear Information System (INIS)
Adame, J.; Warzel, S.
2015-01-01
In this note, we use ideas of Farhi et al. [Int. J. Quantum. Inf. 6, 503 (2008) and Quantum Inf. Comput. 11, 840 (2011)] who link a lower bound on the run time of their quantum adiabatic search algorithm to an upper bound on the energy gap above the ground-state of the generators of this algorithm. We apply these ideas to the quantum random energy model (QREM). Our main result is a simple proof of the conjectured exponential vanishing of the energy gap of the QREM
Thermal reservoir sizing for adiabatic compressed air energy storage
Energy Technology Data Exchange (ETDEWEB)
Kere, Amelie; Goetz, Vincent; Py, Xavier; Olives, Regis; Sadiki, Najim [Perpignan Univ. (France). PROMES CNRS UPR 8521; Mercier-Allart, Eric [EDF R et D, Chatou (France)
2012-07-01
Despite the operation of the two existing industrial facilities to McIntosh (Alabama), and for more than thirty years, Huntorf (Germany), electricity storage in the form of compressed air in underground cavern (CAES) has not seen the development that was expected in the 80s. The efficiency of this form of storage was with the first generation CAES, less than 50%. The evolving context technique can significantly alter this situation. The new generation so-called Adiabatic CAES (A-CAES) is to retrieve the heat produced by the compression via thermal storage, thus eliminating the necessity of gas to burn and would allow consideration efficiency overall energy of the order of 70%. To date, there is no existing installation of A-CAES. Many studies describe the principal and the general working mode of storage systems by adiabatic compression of air. So, efficiencies of different configurations of adiabatic compression process were analyzed. The aim of this paper is to simulate and analyze the performances of a thermal storage reservoir integrated in the system and adapted to the working conditions of a CAES.
Quantum trajectories for time-dependent adiabatic master equations
Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.
2018-02-01
We describe a quantum trajectories technique for the unraveling of the quantum adiabatic master equation in Lindblad form. By evolving a complex state vector of dimension N instead of a complex density matrix of dimension N2, simulations of larger system sizes become feasible. The cost of running many trajectories, which is required to recover the master equation evolution, can be minimized by running the trajectories in parallel, making this method suitable for high performance computing clusters. In general, the trajectories method can provide up to a factor N advantage over directly solving the master equation. In special cases where only the expectation values of certain observables are desired, an advantage of up to a factor N2 is possible. We test the method by demonstrating agreement with direct solution of the quantum adiabatic master equation for 8-qubit quantum annealing examples. We also apply the quantum trajectories method to a 16-qubit example originally introduced to demonstrate the role of tunneling in quantum annealing, which is significantly more time consuming to solve directly using the master equation. The quantum trajectories method provides insight into individual quantum jump trajectories and their statistics, thus shedding light on open system quantum adiabatic evolution beyond the master equation.
Lahiri, B. B.; Ranoo, Surojit; Philip, John
2017-11-01
Magnetic fluid hyperthermia (MFH) is becoming a viable cancer treatment methodology where the alternating magnetic field induced heating of magnetic fluid is utilized for ablating the cancerous cells or making them more susceptible to the conventional treatments. The heating efficiency in MFH is quantified in terms of specific absorption rate (SAR), which is defined as the heating power generated per unit mass. In majority of the experimental studies, SAR is evaluated from the temperature rise curves, obtained under non-adiabatic experimental conditions, which is prone to various thermodynamic uncertainties. A proper understanding of the experimental uncertainties and its remedies is a prerequisite for obtaining accurate and reproducible SAR. Here, we study the thermodynamic uncertainties associated with peripheral heating, delayed heating, heat loss from the sample and spatial variation in the temperature profile within the sample. Using first order approximations, an adiabatic reconstruction protocol for the measured temperature rise curves is developed for SAR estimation, which is found to be in good agreement with those obtained from the computationally intense slope corrected method. Our experimental findings clearly show that the peripheral and delayed heating are due to radiation heat transfer from the heating coils and slower response time of the sensor, respectively. Our results suggest that the peripheral heating is linearly proportional to the sample area to volume ratio and coil temperature. It is also observed that peripheral heating decreases in presence of a non-magnetic insulating shielding. The delayed heating is found to contribute up to ~25% uncertainties in SAR values. As the SAR values are very sensitive to the initial slope determination method, explicit mention of the range of linear regression analysis is appropriate to reproduce the results. The effect of sample volume to area ratio on linear heat loss rate is systematically studied and the
International Nuclear Information System (INIS)
Lahiri, B B; Ranoo, Surojit; Philip, John
2017-01-01
Magnetic fluid hyperthermia (MFH) is becoming a viable cancer treatment methodology where the alternating magnetic field induced heating of magnetic fluid is utilized for ablating the cancerous cells or making them more susceptible to the conventional treatments. The heating efficiency in MFH is quantified in terms of specific absorption rate (SAR), which is defined as the heating power generated per unit mass. In majority of the experimental studies, SAR is evaluated from the temperature rise curves, obtained under non-adiabatic experimental conditions, which is prone to various thermodynamic uncertainties. A proper understanding of the experimental uncertainties and its remedies is a prerequisite for obtaining accurate and reproducible SAR. Here, we study the thermodynamic uncertainties associated with peripheral heating, delayed heating, heat loss from the sample and spatial variation in the temperature profile within the sample. Using first order approximations, an adiabatic reconstruction protocol for the measured temperature rise curves is developed for SAR estimation, which is found to be in good agreement with those obtained from the computationally intense slope corrected method. Our experimental findings clearly show that the peripheral and delayed heating are due to radiation heat transfer from the heating coils and slower response time of the sensor, respectively. Our results suggest that the peripheral heating is linearly proportional to the sample area to volume ratio and coil temperature. It is also observed that peripheral heating decreases in presence of a non-magnetic insulating shielding. The delayed heating is found to contribute up to ∼25% uncertainties in SAR values. As the SAR values are very sensitive to the initial slope determination method, explicit mention of the range of linear regression analysis is appropriate to reproduce the results. The effect of sample volume to area ratio on linear heat loss rate is systematically studied and
On Covering Approximation Subspaces
Directory of Open Access Journals (Sweden)
Xun Ge
2009-06-01
Full Text Available Let (U';C' be a subspace of a covering approximation space (U;C and X⊂U'. In this paper, we show that and B'(X⊂B(X∩U'. Also, iff (U;C has Property Multiplication. Furthermore, some connections between outer (resp. inner definable subsets in (U;C and outer (resp. inner definable subsets in (U';C' are established. These results answer a question on covering approximation subspace posed by J. Li, and are helpful to obtain further applications of Pawlak rough set theory in pattern recognition and artificial intelligence.
Directory of Open Access Journals (Sweden)
Lacroix D.
2010-03-01
Full Text Available Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238U [1]. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn’t seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238U and 239U for an excitation energy of 2.3 MeV above the barrier [2–4]. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.
International Nuclear Information System (INIS)
Bernard, R.; Goutte, H.; Gogny, D.; Dubray, N.; Lacroix, D.
2009-01-01
Among the different theoretical approaches able to describe fission, microscopic ones can help us in the understanding of this process, as they have the advantage of describing the nuclear structure and the dynamics in a consistent manner. The sole input of the calculations is the nucleon-nucleon interaction. Such a microscopic time-dependent and quantum mechanical formalism has already been used, based on the Gaussian Overlap Approximation of the Generator Coordinate Method with the adiabatic approximation, to analyze the collective dynamics of low-energy fission in 238 U. However, at higher energies, a few MeV above the barrier, the adiabatic approximation doesn't seem valid anymore. Indeed, manifestations of proton pair breaking have been observed in 238 U and 239 U for an excitation energy of 2.3 MeV above the barrier. Taking the intrinsic excitations into account during the fission process will enable us to determine the coupling between collective and intrinsic degrees of freedom, in particular from saddle to scission. Guidelines of the new formalism under development are presented and some preliminary results on overlaps between non excited and excited states are discussed.
On Convex Quadratic Approximation
den Hertog, D.; de Klerk, E.; Roos, J.
2000-01-01
In this paper we prove the counterintuitive result that the quadratic least squares approximation of a multivariate convex function in a finite set of points is not necessarily convex, even though it is convex for a univariate convex function. This result has many consequences both for the field of
Prestack wavefield approximations
Alkhalifah, Tariq
2013-01-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
DEFF Research Database (Denmark)
Madsen, Rasmus Elsborg
2005-01-01
The Dirichlet compound multinomial (DCM), which has recently been shown to be well suited for modeling for word burstiness in documents, is here investigated. A number of conceptual explanations that account for these recent results, are provided. An exponential family approximation of the DCM...
Approximation by Cylinder Surfaces
DEFF Research Database (Denmark)
Randrup, Thomas
1997-01-01
We present a new method for approximation of a given surface by a cylinder surface. It is a constructive geometric method, leading to a monorail representation of the cylinder surface. By use of a weighted Gaussian image of the given surface, we determine a projection plane. In the orthogonal...
Prestack wavefield approximations
Alkhalifah, Tariq
2013-09-01
The double-square-root (DSR) relation offers a platform to perform prestack imaging using an extended single wavefield that honors the geometrical configuration between sources, receivers, and the image point, or in other words, prestack wavefields. Extrapolating such wavefields, nevertheless, suffers from limitations. Chief among them is the singularity associated with horizontally propagating waves. I have devised highly accurate approximations free of such singularities which are highly accurate. Specifically, I use Padé expansions with denominators given by a power series that is an order lower than that of the numerator, and thus, introduce a free variable to balance the series order and normalize the singularity. For the higher-order Padé approximation, the errors are negligible. Additional simplifications, like recasting the DSR formula as a function of scattering angle, allow for a singularity free form that is useful for constant-angle-gather imaging. A dynamic form of this DSR formula can be supported by kinematic evaluations of the scattering angle to provide efficient prestack wavefield construction. Applying a similar approximation to the dip angle yields an efficient 1D wave equation with the scattering and dip angles extracted from, for example, DSR ray tracing. Application to the complex Marmousi data set demonstrates that these approximations, although they may provide less than optimal results, allow for efficient and flexible implementations. © 2013 Society of Exploration Geophysicists.
International Nuclear Information System (INIS)
Lyons, L.R.; Williams, D.J.
1976-01-01
Explorer 45 observations of ring current protons mirroring near the equator, 1--800 keV, are presented at constant first adiabatic invariant μ throughout the period of the December 17, 1971, geomagnetic storm. To obtain μ, simultaneous magnetic field and particle observations are used. Particle deceleration in response to the storm time magnetic field decrease causes ring current measurements viewed at constant energy to underestimate the storm time increase in proton intensities at energies approximately-less-than200 keV. This adiabatic deceleration also accounts for the large flux decreases observed at energies approximately-greater-than200 keV during the storm, in contradiction with previous results (Soraas and Davis, 1968) obtained using a model for the storm time magnetic field
Tkatchenko, Alexandre; Ambrosetti, Alberto; DiStasio, Robert A.
2013-02-01
Interatomic pairwise methods are currently among the most popular and accurate ways to include dispersion energy in density functional theory calculations. However, when applied to more than two atoms, these methods are still frequently perceived to be based on ad hoc assumptions, rather than a rigorous derivation from quantum mechanics. Starting from the adiabatic connection fluctuation-dissipation (ACFD) theorem, an exact expression for the electronic exchange-correlation energy, we demonstrate that the pairwise interatomic dispersion energy for an arbitrary collection of isotropic polarizable dipoles emerges from the second-order expansion of the ACFD formula upon invoking the random-phase approximation (RPA) or the full-potential approximation. Moreover, for a system of quantum harmonic oscillators coupled through a dipole-dipole potential, we prove the equivalence between the full interaction energy obtained from the Hamiltonian diagonalization and the ACFD-RPA correlation energy. This property makes the Hamiltonian diagonalization an efficient method for the calculation of the many-body dispersion energy. In addition, we show that the switching function used to damp the dispersion interaction at short distances arises from a short-range screened Coulomb potential, whose role is to account for the spatial spread of the individual atomic dipole moments. By using the ACFD formula, we gain a deeper understanding of the approximations made in the interatomic pairwise approaches, providing a powerful formalism for further development of accurate and efficient methods for the calculation of the dispersion energy.
Adiabatic perturbation theory for atoms and molecules in the low-frequency regime.
Martiskainen, Hanna; Moiseyev, Nimrod
2017-12-14
There is an increasing interest in the photoinduced dynamics in the low frequency, ω, regime. The multiphoton absorptions by molecules in strong laser fields depend on the polarization of the laser and on the molecular structure. The unique properties of the interaction of atoms and molecules with lasers in the low-frequency regime imply new concepts and directions in strong-field light-matter interactions. Here we represent a perturbational approach for the calculations of the quasi-energy spectrum in the low-frequency regime, which avoids the construction of the Floquet operator with extremely large number of Floquet channels. The zero-order Hamiltonian in our perturbational approach is the adiabatic Hamiltonian where the atoms/molecules are exposed to a dc electric field rather than to ac-field. This is in the spirit of the first step in the Corkum three-step model. The second-order perturbation correction terms are obtained when iℏω∂∂τ serves as a perturbation and τ is a dimensionless variable. The second-order adiabatic perturbation scheme is found to be an excellent approach for calculating the ac-field Floquet solutions in our test case studies of a simple one-dimensional time-periodic model Hamiltonian. It is straightforward to implement the perturbation approach presented here for calculating atomic and molecular energy shifts (positions) due to the interaction with low-frequency ac-fields using high-level electronic structure methods. This is enabled since standard quantum chemistry packages allow the calculations of atomic and molecular energy shifts due to the interaction with dc-fields. In addition to the shift of the energy positions, the energy widths (inverse lifetimes) can be obtained at the same level of theory. These energy shifts are functions of the laser parameters (low frequency, intensity, and polarization).
Correlated mixture between adiabatic and isocurvature fluctuations and recent CMB observations
International Nuclear Information System (INIS)
Andrade, Ana Paula A.; Wuensche, Carlos Alexandre; Ribeiro, Andre Luis Batista
2005-01-01
This work presents a reduced χ ν 2 test to search for non-Gaussian signals in the cosmic microwave background radiation (CMBR) TT power spectrum of recent CMBR data, Wilkinson Anisotropy Microwave Probe, Arcminute Cosmology Bolometer Array Receiver, and Cosmic Background Imager data sets, assuming a mixed density field including adiabatic and isocurvature fluctuations. We assume a skew positive mixed model with adiabatic inflation perturbations plus additional isocurvature perturbations possibly produced by topological defects. The joint probability distribution used in this context is a weighted combination of Gaussian and non-Gaussian random fields. Results from simulations of CMBR temperature for the mixed field show a distinct signature in CMB power spectrum for very small deviations (∼0.1%) from a pure Gaussian field, and can be used as a direct test for the nature of primordial fluctuations. A reduced χ ν 2 test applied on the most recent CMBR observations reveals that an isocurvature fluctuations field is not ruled out and indeed permits a very good description for a flat geometry Λ-CDM Universe, χ 930 2 ∼1.5, rather than the simple inflationary standard model with χ 930 2 ∼2.3. This result may looks is particular discrepant with the reduced χ 2 of 1.07 obtained with the same model in Spergel et al. [Astrophys. J. 148, 175 (2003)] for temperature only, however, our work is restricted to a region of the parameter space that does not include the best fit model for TT only of Spergel et al.
Tension and Approximation in Poetic Translation
Al-Shabab, Omar A. S.; Baka, Farida H.
2015-01-01
Simple observation reveals that each language and each culture enjoys specific linguistic features and rhetorical traditions. In poetry translation difference and the resultant linguistic tension create a gap between Source Language and Target language, a gap that needs to be bridged by creating an approximation processed through the translator's…
An improved saddlepoint approximation.
Gillespie, Colin S; Renshaw, Eric
2007-08-01
Given a set of third- or higher-order moments, not only is the saddlepoint approximation the only realistic 'family-free' technique available for constructing an associated probability distribution, but it is 'optimal' in the sense that it is based on the highly efficient numerical method of steepest descents. However, it suffers from the problem of not always yielding full support, and whilst [S. Wang, General saddlepoint approximations in the bootstrap, Prob. Stat. Lett. 27 (1992) 61.] neat scaling approach provides a solution to this hurdle, it leads to potentially inaccurate and aberrant results. We therefore propose several new ways of surmounting such difficulties, including: extending the inversion of the cumulant generating function to second-order; selecting an appropriate probability structure for higher-order cumulants (the standard moment closure procedure takes them to be zero); and, making subtle changes to the target cumulants and then optimising via the simplex algorithm.
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2011-01-01
Most prestack traveltime relations we tend work with are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multi-focusing or double square-root (DSR) and the common reflection stack (CRS) equations. Using the DSR equation, I analyze the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I derive expansion based solutions of this eikonal based on polynomial expansions in terms of the reflection and dip angles in a generally inhomogenous background medium. These approximate solutions are free of singularities and can be used to estimate travetimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. A Marmousi example demonstrates the usefulness of the approach. © 2011 Society of Exploration Geophysicists.
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Li, Chen; Requist, Ryan; Gross, E. K. U.
2018-02-01
We perform model calculations for a stretched LiF molecule, demonstrating that nonadiabatic charge transfer effects can be accurately and seamlessly described within a density functional framework. In alkali halides like LiF, there is an abrupt change in the ground state electronic distribution due to an electron transfer at a critical bond length R = Rc, where an avoided crossing of the lowest adiabatic potential energy surfaces calls the validity of the Born-Oppenheimer approximation into doubt. Modeling the R-dependent electronic structure of LiF within a two-site Hubbard model, we find that nonadiabatic electron-nuclear coupling produces a sizable elongation of the critical Rc by 0.5 bohr. This effect is very accurately captured by a simple and rigorously derived correction, with an M-1 prefactor, to the exchange-correlation potential in density functional theory, M = reduced nuclear mass. Since this nonadiabatic term depends on gradients of the nuclear wave function and conditional electronic density, ∇Rχ(R) and ∇Rn(r, R), it couples the Kohn-Sham equations at neighboring R points. Motivated by an observed localization of nonadiabatic effects in nuclear configuration space, we propose a local conditional density approximation—an approximation that reduces the search for nonadiabatic density functionals to the search for a single function y(n).
Approximate Bayesian recursive estimation
Czech Academy of Sciences Publication Activity Database
Kárný, Miroslav
2014-01-01
Roč. 285, č. 1 (2014), s. 100-111 ISSN 0020-0255 R&D Projects: GA ČR GA13-13502S Institutional support: RVO:67985556 Keywords : Approximate parameter estimation * Bayesian recursive estimation * Kullback–Leibler divergence * Forgetting Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 4.038, year: 2014 http://library.utia.cas.cz/separaty/2014/AS/karny-0425539.pdf
Approximating Preemptive Stochastic Scheduling
Megow Nicole; Vredeveld Tjark
2009-01-01
We present constant approximative policies for preemptive stochastic scheduling. We derive policies with a guaranteed performance ratio of 2 for scheduling jobs with release dates on identical parallel machines subject to minimizing the sum of weighted completion times. Our policies as well as their analysis apply also to the recently introduced more general model of stochastic online scheduling. The performance guarantee we give matches the best result known for the corresponding determinist...
Optimization and approximation
Pedregal, Pablo
2017-01-01
This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.
International Nuclear Information System (INIS)
Graefe, E. M.; Korsch, H. J.; Witthaut, D.
2006-01-01
We investigate the dynamics of a Bose-Einstein condensate in a triple-well trap in a three-level approximation. The interatomic interactions are taken into account in a mean-field approximation (Gross-Pitaevskii equation), leading to a nonlinear three-level model. Additional eigenstates emerge due to the nonlinearity, depending on the system parameters. Adiabaticity breaks down if such a nonlinear eigenstate disappears when the parameters are varied. The dynamical implications of this loss of adiabaticity are analyzed for two important special cases: A three-level Landau-Zener model and the stimulated Raman adiabatic passage (STIRAP) scheme. We discuss the emergence of looped levels for an equal-slope Landau-Zener model. The Zener tunneling probability does not tend to zero in the adiabatic limit and shows pronounced oscillations as a function of the velocity of the parameter variation. Furthermore we generalize the STIRAP scheme for adiabatic coherent population transfer between atomic states to the nonlinear case. It is shown that STIRAP breaks down if the nonlinearity exceeds the detuning
Adiabatic quantum computing with spin qubits hosted by molecules.
Yamamoto, Satoru; Nakazawa, Shigeaki; Sugisaki, Kenji; Sato, Kazunobu; Toyota, Kazuo; Shiomi, Daisuke; Takui, Takeji
2015-01-28
A molecular spin quantum computer (MSQC) requires electron spin qubits, which pulse-based electron spin/magnetic resonance (ESR/MR) techniques can afford to manipulate for implementing quantum gate operations in open shell molecular entities. Importantly, nuclear spins, which are topologically connected, particularly in organic molecular spin systems, are client qubits, while electron spins play a role of bus qubits. Here, we introduce the implementation for an adiabatic quantum algorithm, suggesting the possible utilization of molecular spins with optimized spin structures for MSQCs. We exemplify the utilization of an adiabatic factorization problem of 21, compared with the corresponding nuclear magnetic resonance (NMR) case. Two molecular spins are selected: one is a molecular spin composed of three exchange-coupled electrons as electron-only qubits and the other an electron-bus qubit with two client nuclear spin qubits. Their electronic spin structures are well characterized in terms of the quantum mechanical behaviour in the spin Hamiltonian. The implementation of adiabatic quantum computing/computation (AQC) has, for the first time, been achieved by establishing ESR/MR pulse sequences for effective spin Hamiltonians in a fully controlled manner of spin manipulation. The conquered pulse sequences have been compared with the NMR experiments and shown much faster CPU times corresponding to the interaction strength between the spins. Significant differences are shown in rotational operations and pulse intervals for ESR/MR operations. As a result, we suggest the advantages and possible utilization of the time-evolution based AQC approach for molecular spin quantum computers and molecular spin quantum simulators underlain by sophisticated ESR/MR pulsed spin technology.
Simulating a topological transition in a superconducting phase qubit by fast adiabatic trajectories
Wang, Tenghui; Zhang, Zhenxing; Xiang, Liang; Gong, Zhihao; Wu, Jianlan; Yin, Yi
2018-04-01
The significance of topological phases has been widely recognized in the community of condensed matter physics. The well controllable quantum systems provide an artificial platform to probe and engineer various topological phases. The adiabatic trajectory of a quantum state describes the change of the bulk Bloch eigenstates with the momentum, and this adiabatic simulation method is however practically limited due to quantum dissipation. Here we apply the "shortcut to adiabaticity" (STA) protocol to realize fast adiabatic evolutions in the system of a superconducting phase qubit. The resulting fast adiabatic trajectories illustrate the change of the bulk Bloch eigenstates in the Su-Schrieffer-Heeger (SSH) model. A sharp transition is experimentally determined for the topological invariant of a winding number. Our experiment helps identify the topological Chern number of a two-dimensional toy model, suggesting the applicability of the fast adiabatic simulation method for topological systems.
International Nuclear Information System (INIS)
Aleshin, V.S.
1980-01-01
Presented are calculated dependences for adiabatic compressibility, isoentropy coefficient and thermodynamic sound velocity of a two-phase media with homogeneous disperse structure being in a state of equilibrium. The character of the change of the values mentioned for vapor water media at the change of vapor mass composition in the mixture from zero to 1 is shown. Comparison of the calculated data as to dependences obtained with the experimental ones for critical regimes of vapor-water flow outflow through short and long cylindrical channels with sharp entrance rims. The calculation error does not exceed approximately 12%. Analysis of the results obtained showed that at outflow through short channels of metastable vapor liquid flow the main characteristics, like at outflow through long channels, are determined by the pressure in the exit cross section, mass vapor content and specific volume of the mixture, which are calculated with account for real overheating of the liquid to the exit cross section. At critical regime of outflow through the very long channels, when one can not neglect hydraulic resistance in the channel and the process is not isoentropic, the pressure and mass vapor content in the exit cross section also unambiguously determine the value of adiabatic compressibility of two-phase media, sound velocity and isoentropy coefficient in the cross section. Conclusion is made that the dependences obtained can be used with sufficient for practical purposes accuracy when solving different engineering problems, as well as for the calculations of the mixture consumption at flow of the reactor contours NAI with WWR
Adiabatic quantum computation and quantum annealing theory and practice
McGeoch, Catherine C
2014-01-01
Adiabatic quantum computation (AQC) is an alternative to the better-known gate model of quantum computation. The two models are polynomially equivalent, but otherwise quite dissimilar: one property that distinguishes AQC from the gate model is its analog nature. Quantum annealing (QA) describes a type of heuristic search algorithm that can be implemented to run in the ``native instruction set'''' of an AQC platform. D-Wave Systems Inc. manufactures {quantum annealing processor chips} that exploit quantum properties to realize QA computations in hardware. The chips form the centerpiece of a nov
η Condensate of Fermionic Atom Pairs via Adiabatic State Preparation
International Nuclear Information System (INIS)
Kantian, A.; Daley, A. J.; Zoller, P.
2010-01-01
We discuss how an η condensate, corresponding to an exact excited eigenstate of the Fermi-Hubbard model, can be produced with cold atoms in an optical lattice. Using time-dependent density matrix renormalization group methods, we analyze a state preparation scheme beginning from a band insulator state in an optical superlattice. This state can act as an important test case, both for adiabatic preparation methods and the implementation of the many-body Hamiltonian, and measurements on the final state can be used to help detect associated errors.
Stimulated Raman adiabatic passage in Tm3+:YAG
International Nuclear Information System (INIS)
Alexander, A. L.; Lauro, R.; Louchet, A.; Chaneliere, T.; Le Goueet, J. L.
2008-01-01
We report on the experimental demonstration of stimulated Raman adiabatic passage in a Tm 3+ :YAG crystal. Tm 3+ :YAG is a promising material for use in quantum information processing applications, but as yet there are few experimental investigations of coherent Raman processes in this material. We investigate the effect of inhomogeneous broadening and Rabi frequency on the transfer efficiency and the width of the two-photon spectrum. Simulations of the complete Tm 3+ :YAG system are presented along with the corresponding experimental results
Non-adiabatic pumping in an oscillating-piston model
Chuchem, Maya; Dittrich, Thomas; Cohen, Doron
2012-05-01
We consider the prototypical "piston pump" operating on a ring, where a circulating current is induced by means of an AC driving. This can be regarded as a generalized Fermi-Ulam model, incorporating a finite-height moving wall (piston) and non-trivial topology (ring). The amount of particles transported per cycle is determined by a layered structure of phase space. Each layer is characterized by a different drift velocity. We discuss the differences compared with the adiabatic and Boltzmann pictures, and highlight the significance of the "diabatic" contribution that might lead to a counter-stirring effect.
Adiabatic regularization of power spectra in nonminimally coupled chaotic inflation
Energy Technology Data Exchange (ETDEWEB)
Alinea, Allan L., E-mail: alinea@het.phys.sci.osaka-u.ac.jp [Department of Physics, Osaka University, Toyonaka, Osaka 560-0043 (Japan)
2016-10-01
We investigate the effect of adiabatic regularization on both the tensor- and scalar-perturbation power spectra in nonminimally coupled chaotic inflation. Similar to that of the minimally coupled general single-field inflation, we find that the subtraction term is suppressed by an exponentially decaying factor involving the number of e -folds. By following the subtraction term long enough beyond horizon crossing, the regularized power spectrum tends to the ''bare'' power spectrum. This study justifies the use of the unregularized (''bare'') power spectrum in standard calculations.
Adiabatic resonant oscillations of solar neutrinos in three generations
International Nuclear Information System (INIS)
Kim, C.W.; Sze, W.K.
1987-01-01
The Mikheyev-Smirnov-Wolfenstein model of resonant solar-neutrino oscillations is discussed for three generations of leptons. Assuming adiabatic transitions, bounds for the μ- and e-neutrinos mass-squared difference Δ/sub 21,0/ are obtained as a function of the e-μ mixing angle theta 1 . The allowed region in the Δ/sub 21,0/-theta 1 plot that would solve the solar-neutrino problem is shown to be substantially larger than that of the two-generation case. In particular, the difference between the two- and three-generation cases becomes significant for theta 1 larger than --20 0
Non-adiabatic study of the Kepler subgiant KIC 6442183
Directory of Open Access Journals (Sweden)
Grosjean M.
2015-01-01
Full Text Available Thanks to the precision of Kepler observations, [3] were able to measure the linewidth and amplitude of individual modes (including mixed modes in several subgiant power spectra. We perform a forward modelling of a Kepler subgiant based on surface properties and observed frequencies. Non-adiabatic computations including a time- dependent treatment of convection give the lifetimes of radial and non-radial modes. Next, combining the lifetimes and inertias with a stochastic excitation model gives the amplitudes of the modes. We can now directly compare theoretical and observed linewidths and amplitudes of mixed-modes to obtain new constraints on our theoretical models.
Quasi-adiabatic Switching for Metal-Island Quantum-dot Cellular Automata
Toth, Geza; Lent, Craig S.
2000-01-01
Recent experiments have demonstrated a working cell suitable for implementing the Quantum-dot Cellular Automata (QCA) paradigm. These experiments have been performed using metal island clusters. The most promising approach to QCA operation involves quasi-adiabatically switching the cells. This has been analyzed extensively in gated semiconductor cells. Here we present a metal island cell structure that makes quasi-adiabatic switching possible. We show how this permits quasi-adiabatic clocking...
Cyclic approximation to stasis
Directory of Open Access Journals (Sweden)
Stewart D. Johnson
2009-06-01
Full Text Available Neighborhoods of points in $mathbb{R}^n$ where a positive linear combination of $C^1$ vector fields sum to zero contain, generically, cyclic trajectories that switch between the vector fields. Such points are called stasis points, and the approximating switching cycle can be chosen so that the timing of the switches exactly matches the positive linear weighting. In the case of two vector fields, the stasis points form one-dimensional $C^1$ manifolds containing nearby families of two-cycles. The generic case of two flows in $mathbb{R}^3$ can be diffeomorphed to a standard form with cubic curves as trajectories.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Dynamic and Thermodynamic Properties of a CA Engine with Non-Instantaneous Adiabats
Directory of Open Access Journals (Sweden)
Ricardo T. Paéz-Hernández
2017-11-01
Full Text Available This paper presents an analysis of a Curzon and Alhborn thermal engine model where both internal irreversibilities and non-instantaneous adiabatic branches are considered, operating with maximum ecological function and maximum power output regimes. Its thermodynamic properties are shown, and an analysis of its local dynamic stability is performed. The results derived are compared throughout the work with the results obtained previously for a case in which the adiabatic branches were assumed as instantaneous. The results indicate a better performance for thermodynamic properties in the model with instantaneous adiabatic branches, whereas there is an improvement in robustness in the case where non-instantaneous adiabatic branches are considered.
Non-adiabatic effect on Laughlin's argument of the quantum Hall effect
International Nuclear Information System (INIS)
Maruyama, I; Hatsugai, Y
2009-01-01
We have numerically studied a non-adiabatic charge transport in the quantum Hall system pumped by a magnetic flux, as one of the simplest theoretical realizations of non-adiabatic Thouless pumping. In the adiabatic limit, a pumped charge is quantized, known as Laughlin's argument in a cylindrical lattice. In a uniform electric field, we obtained a formula connecting quantized pumping in the adiabatic limit and no-pumping in the sudden limit. The intermediate region between the two limits is determined by the Landau gap. A randomness or impurity effect is also discussed.
Estimation of the adiabatic energy limit versus beta in Baseball II
International Nuclear Information System (INIS)
Foote, J.H.
1976-01-01
Several estimates of the adiabatic energy limit versus beta in Baseball II are summarized, and the calculational methods used to obtain them are described. Some estimates are based on analytic expressions; for others, particle orbits are calculated, magnetic-moment jumps are inspected, and adiabatic limits then derived. The results are sensitive to the assumed variation of the combined vacuum-plus-plasma magnetic field. The calculated adiabatic energy limit falls rapidly with beta, even for a gradual magnetic-field variation. If we assume a sharp depression in the axial profile of the combined magnetic field for a finite-beta plasma, the adiabatic limit can be further markedly reduced
Magnetic reconnection under anisotropic magnetohydrodynamic approximation
International Nuclear Information System (INIS)
Hirabayashi, K.; Hoshino, M.
2013-01-01
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observations. Our results showed that once magnetic reconnection takes place, a firehose-sense (p ∥ >p ⊥ ) pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with those in an isotropic MHD. In spite of the weakness of the shocks, however, the resultant reconnection rate is 10%–30% higher than that in an isotropic case. This result implies that the slow shock does not necessarily play an important role in the energy conversion in the reconnection system and is consistent with the satellite observation in the Earth's magnetosphere
Explicitly solvable complex Chebyshev approximation problems related to sine polynomials
Freund, Roland
1989-01-01
Explicitly solvable real Chebyshev approximation problems on the unit interval are typically characterized by simple error curves. A similar principle is presented for complex approximation problems with error curves induced by sine polynomials. As an application, some new explicit formulae for complex best approximations are derived.
On Love's approximation for fluid-filled elastic tubes
International Nuclear Information System (INIS)
Caroli, E.; Mainardi, F.
1980-01-01
A simple procedure is set up to introduce Love's approximation for wave propagation in thin-walled fluid-filled elastic tubes. The dispersion relation for linear waves and the radial profile for fluid pressure are determined in this approximation. It is shown that the Love approximation is valid in the low-frequency regime. (author)
Optimization using quantum mechanics: quantum annealing through adiabatic evolution
International Nuclear Information System (INIS)
Santoro, Giuseppe E; Tosatti, Erio
2006-01-01
We review here some recent work in the field of quantum annealing, alias adiabatic quantum computation. The idea of quantum annealing is to perform optimization by a quantum adiabatic evolution which tracks the ground state of a suitable time-dependent Hamiltonian, where 'ℎ' is slowly switched off. We illustrate several applications of quantum annealing strategies, starting from textbook toy-models-double-well potentials and other one-dimensional examples, with and without disorder. These examples display in a clear way the crucial differences between classical and quantum annealing. We then discuss applications of quantum annealing to challenging hard optimization problems, such as the random Ising model, the travelling salesman problem and Boolean satisfiability problems. The techniques used to implement quantum annealing are either deterministic Schroedinger's evolutions, for the toy models, or path-integral Monte Carlo and Green's function Monte Carlo approaches, for the hard optimization problems. The crucial role played by disorder and the associated non-trivial Landau-Zener tunnelling phenomena is discussed and emphasized. (topical review)
Adiabatic Processes Realized with a Trapped Brownian Particle
Martínez, Ignacio A.; Roldán, Édgar; Dinis, Luis; Petrov, Dmitri; Rica, Raúl A.
2015-03-01
The ability to implement adiabatic processes in the mesoscale is of key importance in the study of artificial or biological micro- and nanoengines. Microadiabatic processes have been elusive to experimental implementation due to the difficulty in isolating Brownian particles from their fluctuating environment. Here we report on the experimental realization of a microscopic quasistatic adiabatic process employing a trapped Brownian particle. We circumvent the complete isolation of the Brownian particle by designing a protocol where both characteristic volume and temperature of the system are changed in such a way that the entropy of the system is conserved along the process. We compare the protocols that follow from either the overdamped or underdamped descriptions, demonstrating that the latter is mandatory in order to obtain a vanishing average heat flux to the particle. We provide analytical expressions for the distributions of the fluctuating heat and entropy and verify them experimentally. Our protocols could serve to implement the first microscopic engine that is able to attain the fundamental limit for the efficiency set by Carnot.
Adiabatic invariants in stellar dynamics, 3: Application to globular cluster evolution
Weinberg, Martin D.
1994-01-01
The previous two companion papers demonstrate that slowly varying perturbations may not result in adiabatic cutoffs and provide a formalism for computing the long-term effects of time-dependent perturbations on stellar systems. Here, the theory is implemented in a Fokker-Planck code and a suite of runs illustrating the effects of shock heating on globular cluster evolution are described. Shock heating alone results in considerable mass loss for clusters with R(sub g) less than or approximately 8 kpc: a concentration c = 1.5 cluster with R(sub g) kpc loses up to 95% of its initial mass in 15 Gyr. Only those with concentration c greater than or approximately 1.3 survive disk shocks inside of this radius. Other effects, such as mass loss by stellar evolution, will decrease this survival bound. Loss of the initial halo together with mass segregation leads to mass spectral indices, x, which may be considerably larger than their initial values.
Energy Technology Data Exchange (ETDEWEB)
Castro, A., E-mail: acastro@bifi.es [Institute for Biocomputation and Physics of Complex Systems (BIFI) and Zaragoza Scientific Center for Advanced Modelling (ZCAM), University of Zaragoza, 50018 Zaragoza (Spain); Isla, M. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47005 Valladolid (Spain); Martinez, Jose I. [Departamento de Fisica Teorica de la Materia Condensada, Universidad Autonoma de Madrid, ES-28049 Madrid (Spain); Alonso, J.A. [Departamento de Fisica Teorica, Atomica y Optica, Universidad de Valladolid, 47005 Valladolid (Spain)
2012-05-03
Graphical abstract: Two trajectories for the collision of a proton with the Lithium tetramer. On the left, the proton is scattered away, and a Li{sub 2} molecule plus two isolated Lithium atoms result. On the right, the proton is captured and a LiH molecule is created. Highlights: Black-Right-Pointing-Pointer Scattering of a proton with Lithium clusters described from first principles. Black-Right-Pointing-Pointer Description based on non-adiabatic molecular dynamics. Black-Right-Pointing-Pointer The electronic structure is described with time-dependent density-functional theory. Black-Right-Pointing-Pointer The method allows to discern reaction channels depending on initial parameters. - Abstract: We have employed non-adiabatic molecular dynamics based on time-dependent density-functional theory to characterize the scattering behavior of a proton with the Li{sub 4} cluster. This technique assumes a classical approximation for the nuclei, effectively coupled to the quantum electronic system. This time-dependent theoretical framework accounts, by construction, for possible charge transfer and ionization processes, as well as electronic excitations, which may play a role in the non-adiabatic regime. We have varied the incidence angles in order to analyze the possible reaction patterns. The initial proton kinetic energy of 10 eV is sufficiently high to induce non-adiabatic effects. For all the incidence angles considered the proton is scattered away, except in one interesting case in which one of the Lithium atoms captures it, forming a LiH molecule. This theoretical formalism proves to be a powerful, effective and predictive tool for the analysis of non-adiabatic processes at the nanoscale.
The random phase approximation
International Nuclear Information System (INIS)
Schuck, P.
1985-01-01
RPA is the adequate theory to describe vibrations of the nucleus of very small amplitudes. These vibrations can either be forced by an external electromagnetic field or can be eigenmodes of the nucleus. In a one dimensional analogue the potential corresponding to such eigenmodes of very small amplitude should be rather stiff otherwise the motion risks to be a large amplitude one and to enter a region where the approximation is not valid. This means that nuclei which are supposedly well described by RPA must have a very stable groundstate configuration (must e.g. be very stiff against deformation). This is usually the case for doubly magic nuclei or close to magic nuclei which are in the middle of proton and neutron shells which develop a very stable groundstate deformation; we take the deformation as an example but there are many other possible degrees of freedom as, for example, compression modes, isovector degrees of freedom, spin degrees of freedom, and many more
The quasilocalized charge approximation
International Nuclear Information System (INIS)
Kalman, G J; Golden, K I; Donko, Z; Hartmann, P
2005-01-01
The quasilocalized charge approximation (QLCA) has been used for some time as a formalism for the calculation of the dielectric response and for determining the collective mode dispersion in strongly coupled Coulomb and Yukawa liquids. The approach is based on a microscopic model in which the charges are quasilocalized on a short-time scale in local potential fluctuations. We review the conceptual basis and theoretical structure of the QLC approach and together with recent results from molecular dynamics simulations that corroborate and quantify the theoretical concepts. We also summarize the major applications of the QLCA to various physical systems, combined with the corresponding results of the molecular dynamics simulations and point out the general agreement and instances of disagreement between the two
International Nuclear Information System (INIS)
Ruschhaupt, A.; Muga, J. G.
2006-01-01
We present a generalized two-level scheme for an 'atom diode', namely, a laser device that lets a two-level ground-state atom pass in one direction, say from left to right, but not in the opposite direction. The laser field is composed of two lateral state-selective mirror regions and a central pumping region. We demonstrate the robustness of the scheme and propose a physical realization. It is shown that the inclusion of a counterintuitive laser field blocking the excited atoms on the left side of the device is essential for a perfect diode effect. The reason for this, the diodic behavior, and the robustness may be understood with an adiabatic approximation. The conditions to break down the approximation, which imply also the diode failure, are analyzed
Xie, Changjian; Malbon, Christopher L; Yarkony, David R; Guo, Hua
2017-07-28
The incorporation of the geometric phase in single-state adiabatic dynamics near a conical intersection (CI) seam has so far been restricted to molecular systems with high symmetry or simple model Hamiltonians. This is due to the fact that the ab initio determined derivative coupling (DC) in a multi-dimensional space is not curl-free, thus making its line integral path dependent. In a recent work [C. L. Malbon et al., J. Chem. Phys. 145, 234111 (2016)], we proposed a new and general approach based on an ab initio determined diabatic representation consisting of only two electronic states, in which the DC is completely removable, so that its line integral is path independent in the simply connected domains that exclude the CI seam. Then with the CIs included, the line integral of the single-valued DC can be used to construct the complex geometry-dependent phase needed to exactly eliminate the double-valued character of the real-valued adiabatic electronic wavefunction. This geometry-dependent phase gives rise to a vector potential which, when included in the adiabatic representation, rigorously accounts for the geometric phase in a system with an arbitrary locus of the CI seam and an arbitrary number of internal coordinates. In this work, we demonstrate this approach in a three-dimensional treatment of the tunneling facilitated dissociation of the S 1 state of phenol, which is affected by a C s symmetry allowed but otherwise accidental seam of CI. Here, since the space is three-dimensional rather than two-dimensional, the seam is a curve rather than a point. The nodal structure of the ground state vibronic wavefunction is shown to map out the seam of CI.
Approximate quantum Markov chains
Sutter, David
2018-01-01
This book is an introduction to quantum Markov chains and explains how this concept is connected to the question of how well a lost quantum mechanical system can be recovered from a correlated subsystem. To achieve this goal, we strengthen the data-processing inequality such that it reveals a statement about the reconstruction of lost information. The main difficulty in order to understand the behavior of quantum Markov chains arises from the fact that quantum mechanical operators do not commute in general. As a result we start by explaining two techniques of how to deal with non-commuting matrices: the spectral pinching method and complex interpolation theory. Once the reader is familiar with these techniques a novel inequality is presented that extends the celebrated Golden-Thompson inequality to arbitrarily many matrices. This inequality is the key ingredient in understanding approximate quantum Markov chains and it answers a question from matrix analysis that was open since 1973, i.e., if Lieb's triple ma...
Prestack traveltime approximations
Alkhalifah, Tariq Ali
2012-05-01
Many of the explicit prestack traveltime relations used in practice are based on homogeneous (or semi-homogenous, possibly effective) media approximations. This includes the multifocusing, based on the double square-root (DSR) equation, and the common reflection stack (CRS) approaches. Using the DSR equation, I constructed the associated eikonal form in the general source-receiver domain. Like its wave-equation counterpart, it suffers from a critical singularity for horizontally traveling waves. As a result, I recasted the eikonal in terms of the reflection angle, and thus, derived expansion based solutions of this eikonal in terms of the difference between the source and receiver velocities in a generally inhomogenous background medium. The zero-order term solution, corresponding to ignoring the lateral velocity variation in estimating the prestack part, is free of singularities and can be used to estimate traveltimes for small to moderate offsets (or reflection angles) in a generally inhomogeneous medium. The higher-order terms include limitations for horizontally traveling waves, however, we can readily enforce stability constraints to avoid such singularities. In fact, another expansion over reflection angle can help us avoid these singularities by requiring the source and receiver velocities to be different. On the other hand, expansions in terms of reflection angles result in singularity free equations. For a homogenous background medium, as a test, the solutions are reasonably accurate to large reflection and dip angles. A Marmousi example demonstrated the usefulness and versatility of the formulation. © 2012 Society of Exploration Geophysicists.
Dzyaloshinskii-Moriya interactions and adiabatic magnetization dynamics in molecular magnets
De Raedt, H; Miyashita, S; Michielsen, K; Machida, M
A microscopic model of the molecular magnet V-15 is used to study mechanisms for the adiabatic change of the magnetization in time-dependent magnetic fields. The effects of the Dzyaloshinskii-Moriya interaction, the most plausible source for the energy-level repulsions that lead to adiabatic changes
Properties of a two stage adiabatic demagnetization refrigerator
International Nuclear Information System (INIS)
Fukuda, H; Ueda, S; Arai, R; Numazawa, T; Li, J; Saito, A T; Nakagome, H
2015-01-01
Currently, many space missions using cryogenic temperatures are being planned. In particular, high resolution sensors such as Transition Edge Sensors need very low temperatures, below 100 mK. It is well known that the adiabatic demagnetization refrigerator (ADR) is one of most useful tools for producing ultra-low temperatures in space because it is gravity independent. We studied a continuous ADR system consisting of 4 stages and demonstrated it could provide continuous temperatures around 100 mK. However, there was some heat leakage from the power leads which resulted in reduced cooling power. Our efforts to upgrade our ADR system are presented. We show the effect of using the HTS power leads and discuss a cascaded Carnot cycle consisting of 2 ADR units. (paper)
Adiabatic quantum-flux-parametron cell library adopting minimalist design
Energy Technology Data Exchange (ETDEWEB)
Takeuchi, Naoki, E-mail: takeuchi-naoki-kx@ynu.jp [Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501 (Japan); Yamanashi, Yuki; Yoshikawa, Nobuyuki [Institute of Advanced Sciences, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501 (Japan); Department of Electrical and Computer Engineering, Yokohama National University, 79-5 Tokiwadai, Hodogaya, Yokohama 240-8501 (Japan)
2015-05-07
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits.
Adiabatic photo-steering theory in topological insulators
Inoue, Jun-ichi
2014-12-01
Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane-Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed.
Adiabatic surface thermometer for improved production braze quality
International Nuclear Information System (INIS)
Dittbenner, G.R.
1975-01-01
An adiabatic surface thermometer was developed to control automatically the critical temperature-time cycle of a production vacuum-brazing process. Investigations revealed that optimum braze-joint strength required precise control of the brazing temperature. Spot-welded thermocouples could not be used because the spot welds cause surface damage. This thermometer touches the surface and uses a differential thermocouple and heater to measure surface temperature without heat flow, thereby eliminating large errors caused by conduction losses common to conventional spring-loaded thermocouples. Temperatures in air or vacuum are measured to 800 0 C with errors less than 5 0 C. This thermometer has minimized the rejection of production parts, resulting in a cost saving to the U. S. Energy Research and Development Administration
Novel latch for adiabatic quantum-flux-parametron logic
International Nuclear Information System (INIS)
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki; Ortlepp, Thomas
2014-01-01
We herein propose the quantum-flux-latch (QFL) as a novel latch for adiabatic quantum-flux-parametron (AQFP) logic. A QFL is very compact and compatible with AQFP logic gates and can be read out in one clock cycle. Simulation results revealed that the QFL operates at 5 GHz with wide parameter margins of more than ±22%. The calculated energy dissipation was only ∼0.1 aJ/bit, which yields a small energy delay product of 20 aJ·ps. We also designed shift registers using QFLs to demonstrate more complex circuits with QFLs. Finally, we experimentally demonstrated correct operations of the QFL and a 1-bit shift register (a D flip-flop)
Hydroxylamine nitrate self-catalytic kinetics study with adiabatic calorimetry
Energy Technology Data Exchange (ETDEWEB)
Liu Lijun [Mary Kay O' Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A and M University System, College Station, TX 77843-3122 (United States); Wei Chunyang [BASF Corporation, Wyandotte, MI 48192 (United States); Guo Yuyan; Rogers, William J. [Mary Kay O' Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A and M University System, College Station, TX 77843-3122 (United States); Sam Mannan, M. [Mary Kay O' Connor Process Safety Center, Artie McFerrin Department of Chemical Engineering, Texas A and M University System, College Station, TX 77843-3122 (United States)], E-mail: mannan@tamu.edu
2009-03-15
Hydroxylamine nitrate (HAN) is an important member of the hydroxylamine compound family with applications that include equipment decontamination in the nuclear industry and aqueous or solid propellants. Due to its instability and autocatalytic behavior, HAN has been involved in several incidents at the Hanford and Savannah River Site (SRS) [Technical Report on Hydroxylamine Nitrate, US Department of Energy, 1998]. Much research has been conducted on HAN in different areas, such as combustion mechanism, decomposition mechanism, and runaway behavior. However, the autocatalytic decomposition behavior of HAN at runaway stage has not been fully addressed due to its highly exothermic and rapid decomposition behavior. This work is focused on extracting HAN autocatalytic kinetics and analyzing HAN critical behavior from adiabatic calorimetry measurements. A lumped autocatalytic kinetic model for HAN and associated model parameters are determined. Also the storage and handling critical conditions of diluted HAN solution without metal presence are quantified.
Adiabatic Cooling for Rovibrational Spectroscopy of Molecular Ions
DEFF Research Database (Denmark)
Fisher, Karin
2017-01-01
The field of cold molecular ions is a fast growing one, with applications in high resolution spectroscopy and metrology, the search for time variations of fundamental constants, cold chemistry and collisions, and quantum information processing, to name a few. The study of single molecular ions...... is attractive as it enables one to push the limits of spectroscopic accuracy. Non-destructive spectroscopic detection of molecular ions can be achieved by co-trapping with an easier to detect atomic ion. The ion chain has coupled motion, and transitions which change both the internal and motional states...... to the measured heating rates, almost perfectly fitting existing heating rate theory. Further, the same model successfully predicted the heating rates of the in-phase mode of a two-ion crystal, indicating that we can use it to predict the heating rates in experiments on molecule-atom chains. Adiabatic cooling...
Ohmic ignition of Neo-Alcator tokamak with adiabatic compression
International Nuclear Information System (INIS)
Inoue, Nobuyuki; Ogawa, Yuichi
1992-01-01
Ohmic ignition condition on axis of the DT tokamak plasma heated by minor radius and major radius adiabatic compression is studied assuming parabolic profiles for plasma parameters, elliptic plasma cross section, and Neo-Alcator confinement scaling. It is noticeable that magnetic compression reduces the necessary total plasma current for Ohmic ignition device. Typically in compact ignition tokamak of the minor radius of 0.47 m, major radius of 1.5 m and on-axis toroidal field of 20 T, the plasma current of 6.8 MA is sufficient for compression plasma, while that of 11.7 MA is for no compression plasma. Another example with larger major radius is also described. In such a device the large flux swing of Ohmic transformer is available for long burn. Application of magnetic compression saves the flux swing and thereby extends the burn time. (author)
Hydrodynamics of adiabatic inverted annular flow: an experimental study
International Nuclear Information System (INIS)
De Jarlais, G.; Ishii, M.
1983-01-01
For low-quality film boiling in tubes or rod bundles, the flow pattern may consist of a liquid jet-like core surrounded by a vapor annulus, i.e., inverted annular flow. The stability, shape, and break-up mechanisms of this liquid core must be understood in order to model correctly this regime and to develop appropriate interfacial transfer correlations. This paper reports on a study in which inverted annular flow was simulated in an adiabatic system. Turbulent water jets, issuing downward from long-aspect nozzles were enclosed within cocurrent gas annuli. Jet-core diameter and velocity, and gas-annulus diameter, velocity, and species were varied, yielding liquid Reynolds numbers up to 33,000, void fractions from 0.29 to 0.95, and relative velocities from near zero to over 80 m/s. Jet-core break-up lengths and secondarily, core break-up mechanisms, were observed visually, using strobe lighting
Adiabatic invariants in stellar dynamics. 1: Basic concepts
Weinberg, Martin D.
1994-01-01
The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.
Adiabatic effective action for vortices in neutral and charged superfluids
International Nuclear Information System (INIS)
Hatsuda, M.; Sato, M.; Yahikozawa, S.; Hatsuda, T.
1996-01-01
Adiabatic effective action for vortices in neutral and charged superfluids at zero temperature are calculated using the topological Landau-Ginzburg theory recently proposed by Hatsuda, Yahikozawa, Ao and Thouless, and vortex dynamics are examined. The Berry phase term arising in the effective action naturally yields the Magnus force in both neutral and charged superfluids. It is shown that in neutral superfluid there is only one degree of freedom, namely the center of vorticities, and the vortex energy is proportional to the sum of all vorticities so that it is finite only for the vanishing total vorticity of the system. On the other hand the effective mass and the vortex energy for a vortex in charged superfluids are defined individually as expected. The effects of the vortex core on these quantities are also estimated. The possible depinning scenario which is governed by the Magnus force and the inertial mass is also discussed
Hydroxylamine nitrate self-catalytic kinetics study with adiabatic calorimetry
International Nuclear Information System (INIS)
Liu Lijun; Wei Chunyang; Guo Yuyan; Rogers, William J.; Sam Mannan, M.
2009-01-01
Hydroxylamine nitrate (HAN) is an important member of the hydroxylamine compound family with applications that include equipment decontamination in the nuclear industry and aqueous or solid propellants. Due to its instability and autocatalytic behavior, HAN has been involved in several incidents at the Hanford and Savannah River Site (SRS) [Technical Report on Hydroxylamine Nitrate, US Department of Energy, 1998]. Much research has been conducted on HAN in different areas, such as combustion mechanism, decomposition mechanism, and runaway behavior. However, the autocatalytic decomposition behavior of HAN at runaway stage has not been fully addressed due to its highly exothermic and rapid decomposition behavior. This work is focused on extracting HAN autocatalytic kinetics and analyzing HAN critical behavior from adiabatic calorimetry measurements. A lumped autocatalytic kinetic model for HAN and associated model parameters are determined. Also the storage and handling critical conditions of diluted HAN solution without metal presence are quantified
Standing shocks in adiabatic black hole accretion of rotating matter
International Nuclear Information System (INIS)
Abramowicz, M.A.; Chakrabarti, S.K.
1988-08-01
We present all the solutions for stationary, axially symmetric, transonic, adiabatic flows with polytropic, rotating fluid configurations of small transverse thickness, in an arbitrarily chosen potential. Special attention is paid to the formation of the standing shocks in the case of black hole accretion and winds. We point out the possibility of three types of shocks depending upon three extreme physical conditions at the shocks. These are: Rankine-Hugoniot shocks, isentropic compression waves, and isothermal shocks. We write down the shock conditions for these three cases and discuss briefly the physical situations under which these shocks may form. A complete discussion on the properties of these shocks will be presented elsewhere. (author). 21 refs, 4 figs
Adiabatic quantum-flux-parametron cell library adopting minimalist design
International Nuclear Information System (INIS)
Takeuchi, Naoki; Yamanashi, Yuki; Yoshikawa, Nobuyuki
2015-01-01
We herein build an adiabatic quantum-flux-parametron (AQFP) cell library adopting minimalist design and a symmetric layout. In the proposed minimalist design, every logic cell is designed by arraying four types of building block cells: buffer, NOT, constant, and branch cells. Therefore, minimalist design enables us to effectively build and customize an AQFP cell library. The symmetric layout reduces unwanted parasitic magnetic coupling and ensures a large mutual inductance in an output transformer, which enables very long wiring between logic cells. We design and fabricate several logic circuits using the minimal AQFP cell library so as to test logic cells in the library. Moreover, we experimentally investigate the maximum wiring length between logic cells. Finally, we present an experimental demonstration of an 8-bit carry look-ahead adder designed using the minimal AQFP cell library and demonstrate that the proposed cell library is sufficiently robust to realize large-scale digital circuits
Solving Simple Kinetics without Integrals
de la Pen~a, Lisandro Herna´ndez
2016-01-01
The solution of simple kinetic equations is analyzed without referencing any topic from differential equations or integral calculus. Guided by the physical meaning of the rate equation, a systematic procedure is used to generate an approximate solution that converges uniformly to the exact solution in the case of zero, first, and second order…
Adiabatic motion of charged dust grains in rotating magnetospheres
International Nuclear Information System (INIS)
Northrop, T.G.; Hill, J.R.
1983-01-01
Dust grains in the ring systems and rapidly rotating magnetospheres of the outer planets such as Jupiter and Saturn may be sufficiently charged that the magnetic and electric forces on them are comparable with the gravitational force. The adiabatic theory of charged particle motion has previously been applied to electrons and atomic size particles. But it is also applicable to these charged dust grains in the micrometer and smaller size range. We derive here the guiding center equation of motion, drift velocity, and parallel equation of motion for these grains in a rotating magnetosphere. The effects of periodic grain charge-discharge have not been treated previously and have been included in this analysis. Grain charge is affected by the surrounding plasma properties and by the grain plasma velocity (among other factors), both of which may vary over the gyrocircle. The resulting charge-discharge process at the gyrofrequency destroys the invariance of the magnetic moment and causes a grain to move radially. The magnetic moment may increase or decrease, depending on the gyrophase of the charge variation. If it decreases, the motion is always toward synchronous radius for an equatorial grain. But the orbit becomes circular before the grain reaches synchronous radius, a conclusion that follows from an exact constant of the motion. This circularization can be viewed as a consequence of the gradual reduction in the magnetic moment. This circularization also suggests that dust grains leaving Io could not reach the region of the Jovian ring, but several effects could change that conclusion. Excellent qualitative and quantitative agreement is obtained between adiabatic theory and detailed numerical orbit integrations
Observational tests of non-adiabatic Chaplygin gas
Energy Technology Data Exchange (ETDEWEB)
Carneiro, S.; Pigozzo, C., E-mail: saulo.carneiro@pq.cnpq.br, E-mail: cpigozzo@ufba.br [Instituto de Física, Universidade Federal da Bahia, Campus de Ondina, Salvador, BA 40210-340 (Brazil)
2014-10-01
In a previous paper [1] it was shown that any dark sector model can be mapped into a non-adiabatic fluid formed by two interacting components, one with zero pressure and the other with equation-of-state parameter ω = -1. It was also shown that the latter does not cluster and, hence, the former is identified as the observed clustering matter. This guarantees that the dark matter power spectrum does not suffer from oscillations or instabilities. It applies in particular to the generalised Chaplygin gas, which was shown to be equivalent to interacting models at both background and perturbation levels. In the present paper we test the non-adiabatic Chaplygin gas against the Hubble diagram of type Ia supernovae, the position of the first acoustic peak in the anisotropy spectrum of the cosmic microwave background and the linear power spectrum of large scale structures. We consider two different compilations of SNe Ia, namely the Constitution and SDSS samples, both calibrated with the MLCS2k2 fitter, and for the power spectrum we use the 2dFGRS catalogue. The model parameters to be adjusted are the present Hubble parameter, the present matter density and the Chaplygin gas parameter α. The joint analysis best fit gives α ≈ - 0.5, which corresponds to a constant-rate energy flux from dark energy to dark matter, with the dark energy density decaying linearly with the Hubble parameter. The ΛCDM model, equivalent to α = 0, stands outside the 3σ confidence interval.
Thermodynamic study of ibuprofen by adiabatic calorimetry and thermal analysis
International Nuclear Information System (INIS)
Xu Fen; Sun Lixian; Tan Zhicheng; Liang Jianguo; Li Ruilian
2004-01-01
Molar heat capacities of ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 400 K. The polynomial functions of C p,m (J K -1 mol -1 ) versus T were established on the heat capacity measurements by means of the least fitting square method. The functions are as follows: for solid ibuprofen, at the temperature range of 79.105 K≤T≤333.297 K, C p,m =144.27+77.046X+3.5171X 2 +10.925X 3 +11.224X 4 , where X=(T-206.201)/127.096; for liquid ibuprofen, at the temperature range of 353.406 K≤T≤378.785 K, C p,m =325.79+8.9696X-1.6073X 2 -1.5145X 3 , where X=(T-366.095)/12.690. A fusion transition at T=348.02 K was found from the C p -T curve. The molar enthalpy and entropy of the fusion transition were determined to be 26.65 kJ mol -1 and 76.58 J mol -1 K -1 , respectively. The thermodynamic functions on the base of the reference temperature of 298.15 K, (H T -H 298.15 ) and (S T -S 298.15 ), were derived. Thermal characteristic of ibuprofen was studied by thermo-gravimetric analysis (TG-DTG) and differential scanning calorimeter (DSC). The temperature of fusion, the molar enthalpy and entropy of fusion obtained by DSC were well consistent with those obtained by adiabatic calorimeter. The evaporation process of ibuprofen was investigated further by TG and DTG, and the activation energy of the evaporation process was determined to be 80.3±1.4 kJ mol -1
Simple and reusable fibre-to-chip interconnect with adjustable coupling eficiency
Heideman, Rene; Lambeck, Paul; Parriaux, Olivier M.; Kley, Ernst-Bernhard
1997-01-01
A simple, efficient and reusable fiber-to-chip interconnect is presented. The interconnect is based on a V-groove (wet- chemically etched) in silicon, combined with a loose-mode Si3N4-channel waveguide. The loose-mode waveguide is adiabatically tapered to the integrated optical (sensor) circuitry.
Thin-wall approximation in vacuum decay: A lemma
Brown, Adam R.
2018-05-01
The "thin-wall approximation" gives a simple estimate of the decay rate of an unstable quantum field. Unfortunately, the approximation is uncontrolled. In this paper I show that there are actually two different thin-wall approximations and that they bracket the true decay rate: I prove that one is an upper bound and the other a lower bound. In the thin-wall limit, the two approximations converge. In the presence of gravity, a generalization of this lemma provides a simple sufficient condition for nonperturbative vacuum instability.
DEFF Research Database (Denmark)
Frimurer, Thomas M.; Günther, Peter H.; Sørensen, Morten Dahl
1999-01-01
adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)......adiabatic mapping, conformational change, essentialdynamics, free energy simulations, Kunitz type inhibitor *ga3(VI)...
Self-similar factor approximants
International Nuclear Information System (INIS)
Gluzman, S.; Yukalov, V.I.; Sornette, D.
2003-01-01
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties
International Nuclear Information System (INIS)
Tessier, Michael J.; Floros, Michael C.; Bouzidi, Laziz; Narine, Suresh S.
2016-01-01
Adiabatic compressed air energy storage is an emerging energy storage technology with excellent power and storage capacities. Currently, efficiencies are approximately 70%, in part due to the issue of heat loss during the compression stage. An exergy analysis is presented on a novel adiabatic compressed air energy storage system design utilizing a cascade of PCMs (phase change materials) for waste heat storage and recovery. The melting temperatures and enthalpies of the PCMs were optimized for this system and were shown to be dependent on the number of PCMs, the number of compression stages, and the maximum compression ratio. Efficiencies of storage and recovery using this approach are predicted to be as high as 85%, a 15% increase over current designs which do not incorporate PCMs. - Highlights: • A compressed air energy storage plant using phase change materials is proposed. • Increasing number of phase change materials increases roundtrip exergy efficiency. • A thermodynamic model allows melting points and latent heats required to be predicted.
Faulkner, Ty; Miller, Isaac; Raston, Paul L.
2018-01-01
We report high-resolution infrared spectra of OCS isotopologues embedded in helium nanodroplets that were recorded with a newly built spectrometer. For the normal isotopologue, we observed the relatively weak third bending overtone band, in addition to new high J transitions in the C-O stretching fundamental, which has previously been investigated by diode laser spectroscopy [S. Grebenev et al., J. Chem. Phys. 112, 4485 (2000)]. Similar to the gas phase, the overtone band is (only) 45 cm-1 higher in energy than the fundamental, and this leads to additional broadening due to rapid vibrational relaxation that is accompanied by the creation of real/virtual phonon excitations. We also observed spectra in the C-O stretching fundamental for several minor isotopologues of OCS, including 18OCS, O13CS, and OC33S, in addition to some new peaks for OC34S. A rovibrational analysis allowed for determination of the moment of inertia of helium (ΔIHe) that couples to the rotation of OCS for each isotopologue. In the context of the adiabatic following approximation, the helium density structure that follows the rotation of OCS should essentially remain unchanged between the isotopologues, i.e., there should be no dependence of ΔIHe on the gas phase moment of inertia of OCS (IG). While this behavior was expected for the "heavy" OCS rotor investigated here, we instead found an approximately linear 1:1 relation between ΔIHe and IG, which suggests partial breakdown of the adiabatic following approximation, making OCS the heaviest molecule for which evidence for this effect has been obtained.
Approximate reflection coefficients for a thin VTI layer
Hao, Qi; Stovas, Alexey
2017-01-01
We present an approximate method to derive simple expressions for the reflection coefficients of P- and SV-waves for a thin transversely isotropic layer with a vertical symmetry axis (VTI) embedded in a homogeneous VTI background. The layer
Diffusive Wave Approximation to the Shallow Water Equations: Computational Approach
Collier, Nathan; Radwan, Hany; Dalcin, Lisandro; Calo, Victor M.
2011-01-01
We discuss the use of time adaptivity applied to the one dimensional diffusive wave approximation to the shallow water equations. A simple and computationally economical error estimator is discussed which enables time-step size adaptivity
Structural Influence on Excited State Dynamics in Simple Amines
DEFF Research Database (Denmark)
Klein, Liv Bærenholdt
experiments with calculations, provides new insight into the nature of the internal conversion processes that mediate the dynamical evolution between Rydberg states, and how structural variations in simple amine system have a large impact on the non-adiabatic processes. The experimental method of choice...... is femtosecond time-resolved photoelectron velocity map imaging (VMI), which is a newtechnique in the Copenhagen lab. The design, building and implementation of the VMI spectrometer has been a very substantial part of the thesis work. This techniques oers enhanced information content in the form of ecient...... and sensitive collection of photoelectron spectra. In particular, the angleresolved data available from the VMI approach provides highly detailed mechanistic insight about the relaxation pathways. One striking novel nding is that for tertiary amines, the critical factor driving the non-adiabatic dynamics...
International Conference Approximation Theory XV
Schumaker, Larry
2017-01-01
These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...
Quantum-classical dynamics of scattering processes in adiabatic and diabatic representations
International Nuclear Information System (INIS)
Puzari, Panchanan; Sarkar, Biplab; Adhikari, Satrajit
2004-01-01
We demonstrate the workability of a TDDVR based [J. Chem. Phys. 118, 5302 (2003)], novel quantum-classical approach, for simulating scattering processes on a quasi-Jahn-Teller model [J. Chem. Phys. 105, 9141 (1996)] surface. The formulation introduces a set of DVR grid points defined by the Hermite part of the basis set in each dimension and allows the movement of grid points around the central trajectory. With enough trajectories (grid points), the method converges to the exact quantum formulation whereas with only one grid point, we recover the conventional molecular dynamics approach. The time-dependent Schroedinger equation and classical equations of motion are solved self-consistently and electronic transitions are allowed anywhere in the configuration space among any number of coupled states. Quantum-classical calculations are performed on diabatic surfaces (two and three) to reveal the effects of symmetry on inelastic and reactive state-to-state transition probabilities, along with calculations on an adiabatic surface with ordinary Born-Oppenheimer approximation. Excellent agreement between TDDVR and DVR results is obtained in both the representations
A model for the interfacial shear in vertical, adiabatic, annular-mist flow
International Nuclear Information System (INIS)
Cappiello, M.W.
1992-01-01
A model is developed for the interfacial shear in upward, vertical, adiabatic, annular-mist flow. The model accounts for the momentum of both the droplet and film components and is applicable to the two-fluid approximation. Three computer programs are developed to evaluate the sensitivity of the droplet drag coefficient on the droplet velocity calculation, to solve the two-fluid set of equations by iteration, and to evaluate the required film friction factor from the data. The results of the sensitivity calculation show that a constant drag coefficient of 0.44 for the droplet is sufficient for estimating the droplet velocity over a typical range of gas velocities. Several film friction factor correlations from the literature were tested against the existing data of Hossfeld and Barathan. It was found that a modified effective roughness correlation proposed by Wallis performs the best overall in predicting the data for both small- and large-diameter pipes. The Electrical Power Research Institute drift-flux correlation and the Barathan correlation consistently underpredict the data. The use of the Henstock and Hanratty correlation predicts an incorrect trend. A new correlation is developed that better predicts the data over the entire range of gas injection rates. 17 refs
Adiabatic sweep pulses for earth's field NMR with a surface coil
Conradi, Mark S.; Altobelli, Stephen A.; Sowko, Nicholas J.; Conradi, Susan H.; Fukushima, Eiichi
2018-03-01
Adiabatic NMR sweep pulses are described for inversion and excitation in very low magnetic fields B0 and with broad distribution of excitation field amplitude B1. Two aspects distinguish the low field case: (1) when B1 is comparable to or greater than B0, the rotating field approximation fails and (2) inversion sweeps cannot extend to values well below the Larmor frequency because they would approach or pass through zero frequency. Three approaches to inversion are described. The first is a conventional tangent frequency sweep down to the Larmor frequency, a 180° phase shift, and a sweep back up to the starting frequency. The other two are combined frequency and amplitude sweeps covering a narrower frequency range; one is a symmetric sweep from above to below the Larmor frequency and the other uses a smooth decrease of B1 immediately before and after the 180° phase shift. These two AM/FM sweeps show excellent inversion efficiencies over a wide range of B1, a factor of 30 or more. We also demonstrate an excitation sweep that works well in the presence of the same wide range of B1. We show that the primary effect of the counter-rotating field (i.e., at low B0) is that the magnetization suffers large, periodic deviations from where it would be at large B0. Thus, successful sweep pulses must avoid any sharp features in the amplitude, phase, or frequency.
Two-level system in spin baths: Non-adiabatic dynamics and heat transport
Segal, Dvira
2014-04-01
We study the non-adiabatic dynamics of a two-state subsystem in a bath of independent spins using the non-interacting blip approximation, and derive an exact analytic expression for the relevant memory kernel. We show that in the thermodynamic limit, when the subsystem-bath coupling is diluted (uniformly) over many (infinite) degrees of freedom, our expression reduces to known results, corresponding to the harmonic bath with an effective, temperature-dependent, spectral density function. We then proceed and study the heat current characteristics in the out-of-equilibrium spin-spin-bath model, with a two-state subsystem bridging two thermal spin-baths of different temperatures. We compare the behavior of this model to the case of a spin connecting boson baths, and demonstrate pronounced qualitative differences between the two models. Specifically, we focus on the development of the thermal diode effect, and show that the spin-spin-bath model cannot support it at weak (subsystem-bath) coupling, while in the intermediate-strong coupling regime its rectifying performance outplays the spin-boson model.
Two-level system in spin baths: Non-adiabatic dynamics and heat transport
Energy Technology Data Exchange (ETDEWEB)
Segal, Dvira [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George St., Toronto, Ontario M5S 3H6 (Canada)
2014-04-28
We study the non-adiabatic dynamics of a two-state subsystem in a bath of independent spins using the non-interacting blip approximation, and derive an exact analytic expression for the relevant memory kernel. We show that in the thermodynamic limit, when the subsystem-bath coupling is diluted (uniformly) over many (infinite) degrees of freedom, our expression reduces to known results, corresponding to the harmonic bath with an effective, temperature-dependent, spectral density function. We then proceed and study the heat current characteristics in the out-of-equilibrium spin-spin-bath model, with a two-state subsystem bridging two thermal spin-baths of different temperatures. We compare the behavior of this model to the case of a spin connecting boson baths, and demonstrate pronounced qualitative differences between the two models. Specifically, we focus on the development of the thermal diode effect, and show that the spin-spin-bath model cannot support it at weak (subsystem-bath) coupling, while in the intermediate-strong coupling regime its rectifying performance outplays the spin-boson model.
Recent developments in trapping and manipulation of atoms with adiabatic potentials
Garraway, Barry M.; Perrin, Hélène
2016-09-01
A combination of static and oscillating magnetic fields can be used to ‘dress’ atoms with radio-frequency (RF), or microwave, radiation. The spatial variation of these fields can be used to create an enormous variety of traps for ultra-cold atoms and quantum gases. This article reviews the type and character of these adiabatic traps and the applications which include atom interferometry and the study of low-dimensional quantum systems. We introduce the main concepts of magnetic traps leading to adiabatic dressed traps. The concept of adiabaticity is discussed in the context of the Landau-Zener model. The first bubble trap experiment is reviewed together with the method used for loading it. Experiments based on atom chips show the production of double wells and ring traps. Dressed atom traps can be evaporatively cooled with an additional RF field, and a weak RF field can be used to probe the spectroscopy of the adiabatic potentials. Several approaches to ring traps formed from adiabatic potentials are discussed, including those based on atom chips, time-averaged adiabatic potentials and induction methods. Several proposals for adiabatic lattices with dressed atoms are also reviewed.
Energy Technology Data Exchange (ETDEWEB)
Graham, Peter W.; /Stanford U., ITP; Horn, Bart; Kachru, Shamit; /Stanford U., ITP /SLAC; Rajendran, Surjeet; /Johns Hopkins U. /Stanford U., ITP; Torroba, Gonzalo; /Stanford U., ITP /SLAC
2011-12-14
We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k = +1, and are supported by a negative cosmological term and matter with -1 < w < -1 = 3. In the case of moderate bounces (where the ratio of the maximal scale factor a{sub +} to the minimal scale factor a{sub -} is {Omicron}(1)), the solutions are shown to be classically stable and cycle through an infinite set of bounces. For more extreme cases with large a{sub +} = a{sub -}, the solutions can still oscillate many times before classical instabilities take them out of the regime of validity of our approximations. In this regime, quantum particle production also leads eventually to a departure from the realm of validity of semiclassical general relativity, likely yielding a singular crunch. We briefly discuss possible applications of these models to realistic cosmology.
The effect of adiabatic and conducting wall boundary conditions on LES of a thermal mixing tee
International Nuclear Information System (INIS)
Howard, Richard J.A.; Pasutto, Thomas
2009-01-01
In this paper preliminary LES simulations are carried out of the FATHERINO mixing T junction experiment. In this experiment 80degC hot water enters a lateral steel pipe which has a diameter of D=0.054m, at a speed of 1.04m/s and meets 5degC cold water which enters a perpendicular steel pipe branch that also has a diameter D=0.054m but this time at a lower speed of 0.26m/s. The modelling of the steel pipe walls is tested by comparing adiabatic and 1D conducting wall boundary conditions. The numerical grid used contains approximately 440,000 hexahedral elements. The near wall refinement is not sufficient to resolve the near wall boundary layer (y + approx. = 32) and a standard logarithmic boundary condition is used. A method known as the synthetic eddy method is used to generate the turbulent flow at the pipe inlets. Three different LES models are used (Smagorinsky, dynamic Smagorinsky and wale) to resolve the subgrid turbulent motion beyond the wall grid. An additional test is carried out where no subgrid model is used with only the wall modelling being applied. The results show that the wale model generates much less resolved turbulence than the other cases and this model shows virtually no difference between the two methods of wall thermal modelling. The dynamic Smagorinsky model shows that, downstream of the mixing T, the lower wall remains at a lower temperature for longer when the adiabatic boundary condition is applied. The Smagorinsky model is found to produce the highest level of resolved temperature fluctuation. For this model the 1D thermal modelling approach increases the unsteadiness of both the velocity and temperature fields at the onset of the mixing and in the middle of the pipe downstream of the T junction. However near the lower wall the 1D thermal modelling approach tends to reduce the unsteadiness. The case with no subgrid modelling shows higher levels of turbulence kinetic energy but lower levels of temperature fluctuation than the cases with
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-01
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Hierarchical low-rank approximation for high dimensional approximation
Nouy, Anthony
2016-01-07
Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.
Thermodynamic study of ibuprofen by adiabatic calorimetry and thermal analysis
Energy Technology Data Exchange (ETDEWEB)
Xu Fen; Sun Lixian; Tan Zhicheng; Liang Jianguo; Li Ruilian
2004-03-23
Molar heat capacities of ibuprofen were precisely measured with a small sample precision automated adiabatic calorimeter over the temperature range from 80 to 400 K. The polynomial functions of C{sub p,m} (J K{sup -1} mol{sup -1}) versus T were established on the heat capacity measurements by means of the least fitting square method. The functions are as follows: for solid ibuprofen, at the temperature range of 79.105 K{<=}T{<=}333.297 K, C{sub p,m}=144.27+77.046X+3.5171X{sup 2}+10.925X{sup 3}+11.224X{sup 4}, where X=(T-206.201)/127.096; for liquid ibuprofen, at the temperature range of 353.406 K{<=}T{<=}378.785 K, C{sub p,m}=325.79+8.9696X-1.6073X{sup 2}-1.5145X{sup 3}, where X=(T-366.095)/12.690. A fusion transition at T=348.02 K was found from the C{sub p}-T curve. The molar enthalpy and entropy of the fusion transition were determined to be 26.65 kJ mol{sup -1} and 76.58 J mol{sup -1} K{sup -1}, respectively. The thermodynamic functions on the base of the reference temperature of 298.15 K, (H{sub T}-H{sub 298.15}) and (S{sub T}-S{sub 298.15}), were derived. Thermal characteristic of ibuprofen was studied by thermo-gravimetric analysis (TG-DTG) and differential scanning calorimeter (DSC). The temperature of fusion, the molar enthalpy and entropy of fusion obtained by DSC were well consistent with those obtained by adiabatic calorimeter. The evaporation process of ibuprofen was investigated further by TG and DTG, and the activation energy of the evaporation process was determined to be 80.3{+-}1.4 kJ mol{sup -1}.
Dimova, E.; Steflekova, V.; Karatodorov, S.; Kyoseva, E.
2018-03-01
We propose a way of achieving efficient and robust second-harmonic generation. The technique proposed is similar to the adiabatic population transfer in a two-state quantum system with crossing energies. If the phase mismatching changes slowly, e.g., due to a temperature gradient along the crystal, and makes the phase match for second-harmonic generation to occur, then the energy would be converted adiabatically to the second harmonic. As an adiabatic technique, the second-harmonic generation scheme presented is stable to variations in the crystal parameters, as well as in the input light, crystal length, input intensity, wavelength and angle of incidence.
Connection between optimal control theory and adiabatic-passage techniques in quantum systems
Assémat, E.; Sugny, D.
2012-08-01
This work explores the relationship between optimal control theory and adiabatic passage techniques in quantum systems. The study is based on a geometric analysis of the Hamiltonian dynamics constructed from Pontryagin's maximum principle. In a three-level quantum system, we show that the stimulated Raman adiabatic passage technique can be associated to a peculiar Hamiltonian singularity. One deduces that the adiabatic pulse is solution of the optimal control problem only for a specific cost functional. This analysis is extended to the case of a four-level quantum system.
Adiabatic transfer of energy fluctuations between membranes inside an optical cavity
Garg, Devender; Chauhan, Anil K.; Biswas, Asoka
2017-08-01
A scheme is presented for the adiabatic transfer of average fluctuations in the phonon number between two membranes in an optical cavity. We show that by driving the cavity modes with external time-delayed pulses, one can obtain an effect analogous to stimulated Raman adiabatic passage in the atomic systems. The adiabatic transfer of fluctuations from one membrane to the other is attained through a "dark" mode, which is robust against decay of the mediating cavity mode. The results are supported with analytical and numerical calculations with experimentally feasible parameters.
Directory of Open Access Journals (Sweden)
Peter Keefe
2004-03-01
Full Text Available Abstract: The nature of the thermodynamic behavior of Type I superconductor particles, having a cross section less than the Ginzburg-Landau temperature dependent coherence length is discussed for magnetic field induced adiabatic phase transitions from the superconductive state to the normal state. Argument is advanced supporting the view that when the adiabatic magneto-caloric process is applied to particles, the phase transition is characterized by a decrease in entropy in violation of traditional formulations of the Second Law, evidenced by attainment of a final process temperature below that which would result from an adiabatic magneto-caloric process applied to bulk dimensioned specimens.
Topological structures of adiabatic phase for multi-level quantum systems
International Nuclear Information System (INIS)
Liu Zhengxin; Zhou Xiaoting; Liu Xin; Liu Xiongjun; Chen Jingling
2007-01-01
The topological properties of adiabatic gauge fields for multi-level (three-level in particular) quantum systems are studied in detail. Similar to the result that the adiabatic gauge field for SU(2) systems (e.g. two-level quantum system or angular momentum systems, etc) has a monopole structure, the curvature 2-forms of the adiabatic holonomies for SU(3) three-level and SU(3) eight-level quantum systems are shown to have monopole-like (for all levels) or instanton-like (for the degenerate levels) structures
Dynamics of unwinding of a simple entaglement
Wiegel, F.W.; Michels, J.P.J.
1987-01-01
The dynamics of unwinding of a simple entanglement is studied in two ways, firstly using an optimal path approximation in the Rouse model and secondly by simulating the movement of a more realistic model using Brownian molecular dynamics
When is the Anelastic Approximation a Valid Model for Compressible Convection?
Alboussiere, T.; Curbelo, J.; Labrosse, S.; Ricard, Y. R.; Dubuffet, F.
2017-12-01
Compressible convection is ubiquitous in large natural systems such Planetary atmospheres, stellar and planetary interiors. Its modelling is notoriously more difficult than the case when the Boussinesq approximation applies. One reason for that difficulty has been put forward by Ogura and Phillips (1961): the compressible equations generate sound waves with very short time scales which need to be resolved. This is why they introduced an anelastic model, based on an expansion of the solution around an isentropic hydrostatic profile. How accurate is that anelastic model? What are the conditions for its validity? To answer these questions, we have developed a numerical model for the full set of compressible equations and compared its solutions with those of the corresponding anelastic model. We considered a simple rectangular 2D Rayleigh-Bénard configuration and decided to restrict the analysis to infinite Prandtl numbers. This choice is valid for convection in the mantles of rocky planets, but more importantly lead to a zero Mach number. So we got rid of the question of the interference of acoustic waves with convection. In that simplified context, we used the entropy balances (that of the full set of equations and that of the anelastic model) to investigate the differences between exact and anelastic solutions. We found that the validity of the anelastic model is dictated by two conditions: first, the superadiabatic temperature difference must be small compared with the adiabatic temperature difference (as expected) ɛ = Δ TSA / delta Ta << 1, and secondly that the product of ɛ with the Nusselt number must be small.
Forms of Approximate Radiation Transport
Brunner, G
2002-01-01
Photon radiation transport is described by the Boltzmann equation. Because this equation is difficult to solve, many different approximate forms have been implemented in computer codes. Several of the most common approximations are reviewed, and test problems illustrate the characteristics of each of the approximations. This document is designed as a tutorial so that code users can make an educated choice about which form of approximate radiation transport to use for their particular simulation.
Energy Technology Data Exchange (ETDEWEB)
Martínez-Mesa, Aliezer [Departmento de Física Teórica, Universidad de la Habana, San Lázaro y L, La Habana 10400 (Cuba); Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm (Germany); Saalfrank, Peter [Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm (Germany)
2015-05-21
Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the “curse of dimensionality” encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influence of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0{sup +}) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given.
Approximation by planar elastic curves
DEFF Research Database (Denmark)
Brander, David; Gravesen, Jens; Nørbjerg, Toke Bjerge
2016-01-01
We give an algorithm for approximating a given plane curve segment by a planar elastic curve. The method depends on an analytic representation of the space of elastic curve segments, together with a geometric method for obtaining a good initial guess for the approximating curve. A gradient......-driven optimization is then used to find the approximating elastic curve....
Energy Technology Data Exchange (ETDEWEB)
Milovich, J. L., E-mail: milovich1@llnl.gov; Robey, H. F.; Clark, D. S.; Baker, K. L.; Casey, D. T.; Cerjan, C.; Field, J.; MacPhee, A. G.; Pak, A.; Patel, P. K.; Peterson, J. L.; Smalyuk, V. A.; Weber, C. R. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States)
2015-12-15
Experimental results from indirectly driven ignition implosions during the National Ignition Campaign (NIC) [M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013)] achieved a record compression of the central deuterium-tritium fuel layer with measured areal densities up to 1.2 g/cm{sup 2}, but with significantly lower total neutron yields (between 1.5 × 10{sup 14} and 5.5 × 10{sup 14}) than predicted, approximately 10% of the 2D simulated yield. An order of magnitude improvement in the neutron yield was subsequently obtained in the “high-foot” experiments [O. A. Hurricane et al., Nature 506, 343 (2014)]. However, this yield was obtained at the expense of fuel compression due to deliberately higher fuel adiabat. In this paper, the design of an adiabat-shaped implosion is presented, in which the laser pulse is tailored to achieve similar resistance to ablation-front instability growth, but with a low fuel adiabat to achieve high compression. Comparison with measured performance shows a factor of 3–10× improvement in the neutron yield (>40% of predicted simulated yield) over similar NIC implosions, while maintaining a reasonable fuel compression of >1 g/cm{sup 2}. Extension of these designs to higher laser power and energy is discussed to further explore the trade-off between increased implosion velocity and the deleterious effects of hydrodynamic instabilities.
Zero-range approximation for two-component boson systems
International Nuclear Information System (INIS)
Sogo, T.; Fedorov, D.V.; Jensen, A.S.
2005-01-01
The hyperspherical adiabatic expansion method is combined with the zero-range approximation to derive angular Faddeev-like equations for two-component boson systems. The angular eigenvalues are solutions to a transcendental equation obtained as a vanishing determinant of a 3 x 3 matrix. The eigenfunctions are linear combinations of Jacobi functions of argument proportional to the distance between pairs of particles. We investigate numerically the influence of two-body correlations on the eigenvalue spectrum, the eigenfunctions and the effective hyperradial potential. Correlations decrease or increase the distance between pairs for effectively attractive or repulsive interactions, respectively. New structures appear for non-identical components. Fingerprints can be found in the nodal structure of the density distributions of the condensates. (author)
Bond charge approximation for valence electron density in elemental semiconductors
International Nuclear Information System (INIS)
Bashenov, V.K.; Gorbachov, V.E.; Marvakov, D.I.
1985-07-01
The spatial valence electron distribution in silicon and diamond is calculated in adiabatic bond charge approximation at zero temperature when bond charges have the Gaussian shape and their tensor character is taken into account. An agreement between theory and experiment has been achieved. For this purpose Xia's ionic pseudopotentials and Schulze-Unger's dielectric function are used. By two additional parameters Asub(B) and Zsub(B)sup(') we describe the spatial extent of the bond charge and local-field corrections, respectively. The parameter Zsub(B)sup(') accounts for the ratio between the Coulomb and exchange correlation interactions of the valence electrons and its silicon and diamond values have different signs. (author)
Theory of magnetohydrodynamic waves: The WKB approximation revisited
International Nuclear Information System (INIS)
Barnes, A.
1992-01-01
Past treatments of the eikonal or WKB theory of the propagation of magnetohydrodynamics waves have assumed a strictly isentropic background. IF in fact there is a gradient in the background entropy, then in second order in the WKB ordering, adiabatic fluctuations (in the Lagrangian sense) are not strictly isentropic in the Eulerian sense. This means that in the second order of the WKB expansion, which determines the variation of wave amplitude along rays, the violation of isentropy must be accounted for. The present paper revisits the derivation of the WKB approximation for small-amplitude magnetohydrodynamic waves, allowing for possible spatial variation of the background entropy. The equation of variation of wave amplitude is rederived; it is a bilinear equation which, it turns out, can be recast in the action conservation form. It is shown that this action conservation equation is in fact equivalent to the action conservation law obtained from Lagrangian treatments
Quasi-fractional approximation to the Bessel functions
International Nuclear Information System (INIS)
Guerrero, P.M.L.
1989-01-01
In this paper the authors presents a simple Quasi-Fractional Approximation for Bessel Functions J ν (x), (- 1 ≤ ν < 0.5). This has been obtained by extending a method published which uses simultaneously power series and asymptotic expansions. Both functions, exact and approximated, coincide in at least two digits for positive x, and ν between - 1 and 0,4
Comparison of approximate methods for multiple scattering in high-energy collisions. II
International Nuclear Information System (INIS)
Nolan, A.M.; Tobocman, W.; Werby, M.F.
1976-01-01
The scattering in one dimension of a particle by a target of N like particles in a bound state has been studied. The exact result for the transmission probability has been compared with the predictions of the Glauber theory, the Watson optical potential model, and the adiabatic (or fixed scatterer) approximation. The approximate methods optical potential model is second best. The Watson method is found to work better when the kinematics suggested by Foldy and Walecka are used rather than that suggested by Watson, that is to say, when the two-body of the nucleon-nucleon reduced mass
Joubert-Doriol, Loïc; Izmaylov, Artur F.
2018-03-01
A new methodology of simulating nonadiabatic dynamics using frozen-width Gaussian wavepackets within the moving crude adiabatic representation with the on-the-fly evaluation of electronic structure is presented. The main feature of the new approach is the elimination of any global or local model representation of electronic potential energy surfaces; instead, the electron-nuclear interaction is treated explicitly using the Gaussian integration. As a result, the new scheme does not introduce any uncontrolled approximations. The employed variational principle ensures the energy conservation and leaves the number of electronic and nuclear basis functions as the only parameter determining the accuracy. To assess performance of the approach, a model with two electronic and two nuclear spacial degrees of freedom containing conical intersections between potential energy surfaces has been considered. Dynamical features associated with nonadiabatic transitions and nontrivial geometric (or Berry) phases were successfully reproduced within a limited basis expansion.
Diabatic and adiabatic representations for atomic collision processes
International Nuclear Information System (INIS)
Delos, J.B.; Thorson, W.R.
1979-01-01
A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity-dependent couplings in slow collisions, including the effects of electron-translation factors (ETF's). We compare the couplings arising from atomic representations and atomic ETF's with those arising from molecular representations and ''switching function'' ETF's. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then show that an acceptable general definition of a diabatic representation is provided by the condition P+A=0, where P is the usual nonadiabatic coupling matrix and A represents corrections to it arising from electron translation factors (ETF's). Two distinct types of diabatic representation result, depending on the definition taken for A. States that undergo no deformation are called F diabatic; those that have no velocity-dependent couplings are called M diabatic. Finally, we discuss the properties of representations that are partially diabatic and partially adiabatic, and we give some rules for the construction of representations that should be nearly optimal for describing many types of collision processes
Adiabatic photo-steering theory in topological insulators
International Nuclear Information System (INIS)
Inoue, Jun-ichi
2014-01-01
Feasible external control of material properties is a crucial issue in condensed matter physics. A new approach to achieving this aim, named adiabatic photo-steering, is reviewed. The core principle of this scheme is that several material constants are effectively turned into externally tunable variables by irradiation of monochromatic laser light. Two-dimensional topological insulators are selected as the optimal systems that exhibit a prominent change in their properties following the application of this method. Two specific examples of photo-steered quantum phenomena, which reflect topological aspects of the electronic systems at hand, are presented. One is the integer quantum Hall effect described by the Haldane model, and the other is the quantum spin Hall effect described by the Kane–Mele model. The topological quantities associated with these phenomena are the conventional Chern number and spin Chern number, respectively. A recent interesting idea, time-reversal symmetry breaking via a temporary periodic external stimulation, is also discussed. (focus issue review)
Hot-electron nanoscopy using adiabatic compression of surface plasmons
Giugni, Andrea
2013-10-20
Surface plasmon polaritons are a central concept in nanoplasmonics and have been exploited to develop ultrasensitive chemical detection platforms, as well as imaging and spectroscopic techniques at the nanoscale. Surface plasmons can decay to form highly energetic (or hot) electrons in a process that is usually thought to be parasitic for applications, because it limits the lifetime and propagation length of surface plasmons and therefore has an adverse influence on the functionality of nanoplasmonic devices. Recently, however, it has been shown that hot electrons produced by surface plasmon decay can be harnessed to produce useful work in photodetection, catalysis and solar energy conversion. Nevertheless, the surface-plasmon-to-hot-electron conversion efficiency has been below 1% in all cases. Here we show that adiabatic focusing of surface plasmons on a Schottky diode-terminated tapered tip of nanoscale dimensions allows for a plasmon-to-hot-electron conversion efficiency of ∼30%. We further demonstrate that, with such high efficiency, hot electrons can be used for a new nanoscopy technique based on an atomic force microscopy set-up. We show that this hot-electron nanoscopy preserves the chemical sensitivity of the scanned surface and has a spatial resolution below 50 nm, with margins for improvement.
Development of a semi-adiabatic isoperibol solution calorimeter.
Venkata Krishnan, R; Jogeswararao, G; Parthasarathy, R; Premalatha, S; Prabhakar Rao, J; Gunasekaran, G; Ananthasivan, K
2014-12-01
A semi-adiabatic isoperibol solution calorimeter has been indigenously developed. The measurement system comprises modules for sensitive temperature measurement probe, signal processing, data collection, and joule calibration. The sensitivity of the temperature measurement module was enhanced by using a sensitive thermistor coupled with a lock-in amplifier based signal processor. A microcontroller coordinates the operation and control of these modules. The latter in turn is controlled through personal computer (PC) based custom made software developed with LabView. An innovative summing amplifier concept was used to cancel out the base resistance of the thermistor. The latter was placed in the dewar. The temperature calibration was carried out with a standard platinum resistance (PT100) sensor coupled with an 8½ digit multimeter. The water equivalent of this calorimeter was determined by using electrical calibration with the joule calibrator. The experimentally measured values of the quantum of heat were validated by measuring heats of dissolution of pure KCl (for endotherm) and tris (hydroxyl methyl) amino-methane (for exotherm). The uncertainity in the measurements was found to be within ±3%.
Development of a semi-adiabatic isoperibol solution calorimeter
International Nuclear Information System (INIS)
Venkata Krishnan, R.; Jogeswararao, G.; Parthasarathy, R.; Premalatha, S.; Prabhakar Rao, J.; Gunasekaran, G.; Ananthasivan, K.
2014-01-01
A semi-adiabatic isoperibol solution calorimeter has been indigenously developed. The measurement system comprises modules for sensitive temperature measurement probe, signal processing, data collection, and joule calibration. The sensitivity of the temperature measurement module was enhanced by using a sensitive thermistor coupled with a lock-in amplifier based signal processor. A microcontroller coordinates the operation and control of these modules. The latter in turn is controlled through personal computer (PC) based custom made software developed with LabView. An innovative summing amplifier concept was used to cancel out the base resistance of the thermistor. The latter was placed in the dewar. The temperature calibration was carried out with a standard platinum resistance (PT100) sensor coupled with an 8½ digit multimeter. The water equivalent of this calorimeter was determined by using electrical calibration with the joule calibrator. The experimentally measured values of the quantum of heat were validated by measuring heats of dissolution of pure KCl (for endotherm) and tris (hydroxyl methyl) amino-methane (for exotherm). The uncertainity in the measurements was found to be within ±3%
Kinetic theory of plasma adiabatic major radius compression in tokamaks
International Nuclear Information System (INIS)
Gorelenkova, M.V.; Gorelenkov, N.N.; Azizov, E.A.; Romannikov, A.N.; Herrmann, H.W.
1998-01-01
In order to understand the individual charged particle behavior as well as plasma macroparameters (temperature, density, etc.) during the adiabatic major radius compression (R-compression) in a tokamak, a kinetic approach is used. The perpendicular electric field from the Ohm close-quote s law at zero resistivity is made use of in order to describe particle motion during the R-compression. Expressions for both passing and trapped particle energy and pitch angle change are derived for a plasma with high aspect ratio and circular magnetic surfaces. The particle behavior near the passing trapped boundary during the compression is studied to simulate the compression-induced collisional losses of alpha particles. Qualitative agreement is obtained with the alphas loss measurements in deuterium-tritium (D-T) experiments in the Tokamak Fusion Test Reactor (TFTR) [World Survey of Activities in Controlled Fusion Research [Nucl. Fusion special supplement (1991)] (International Atomic Energy Agency, Vienna, 1991)]. The plasma macroparameters evolution at the R-compression is calculated by solving the gyroaveraged drift kinetic equation. copyright 1998 American Institute of Physics
Hot-electron nanoscopy using adiabatic compression of surface plasmons
Giugni, Andrea; Torre, Bruno; Toma, Andrea; Francardi, Marco; Malerba, Mario; Alabastri, Alessandro; Proietti Zaccaria, Remo; Stockman, Mark Mark; Di Fabrizio, Enzo M.
2013-01-01
Surface plasmon polaritons are a central concept in nanoplasmonics and have been exploited to develop ultrasensitive chemical detection platforms, as well as imaging and spectroscopic techniques at the nanoscale. Surface plasmons can decay to form highly energetic (or hot) electrons in a process that is usually thought to be parasitic for applications, because it limits the lifetime and propagation length of surface plasmons and therefore has an adverse influence on the functionality of nanoplasmonic devices. Recently, however, it has been shown that hot electrons produced by surface plasmon decay can be harnessed to produce useful work in photodetection, catalysis and solar energy conversion. Nevertheless, the surface-plasmon-to-hot-electron conversion efficiency has been below 1% in all cases. Here we show that adiabatic focusing of surface plasmons on a Schottky diode-terminated tapered tip of nanoscale dimensions allows for a plasmon-to-hot-electron conversion efficiency of ∼30%. We further demonstrate that, with such high efficiency, hot electrons can be used for a new nanoscopy technique based on an atomic force microscopy set-up. We show that this hot-electron nanoscopy preserves the chemical sensitivity of the scanned surface and has a spatial resolution below 50 nm, with margins for improvement.
Salt pill design and fabrication for adiabatic demagnetization refrigerators
Shirron, Peter J.; McCammon, Dan
2014-07-01
The performance of an adiabatic demagnetization refrigerator (ADR) is critically dependent on the design and construction of the salt pills that produce cooling. In most cases, the primary goal is to obtain the largest cooling capacity at the low temperature end of the operating range. The realizable cooling capacity depends on a number of factors, including refrigerant mass, and how efficiently it absorbs heat from the various instrument loads. The design and optimization of “salt pills” for ADR systems depend not only on the mechanical, chemical and thermal properties of the refrigerant, but also on the range of heat fluxes that the salt pill must accommodate. Despite the fairly wide variety of refrigerants available, those used at very low temperature tend to be hydrated salts that require a dedicated thermal bus and must be hermetically sealed, while those used at higher temperature - greater than about 0.5 K - tend to be single- or poly-crystals that have much simpler requirements for thermal and mechanical packaging. This paper presents a summary of strategies and techniques for designing, optimizing and fabricating salt pills for both low- and mid-temperature applications.
Theoretical analysis of consecutive reactions in adiabatic stirred tank reactors
International Nuclear Information System (INIS)
Jo, Byung Wook; Kim, Sun Il; Hong, Won Hae; Cha, Wol Suk; Kim, Soong Pyung; Kim, Jung Gyu
1990-01-01
By mathematical model for the case of the consecutive first-order exothermic reaction in an adiabatic CSTR, the effects of the system parameter i. e. relative residence time, heat of reaction and thermal sensitivity of reaction rate constant, on the concentration profile of the intermediate product of a consecutive reaction were obtained as follows. For fixed values of the ratio of the reaction rate constants t 1 / t 2 , the ratio of the correponding system parameter α where α>1 and the sensitivities of the reaction rate constants S1 and S2, the maximum value of the intermediate production dimensionless concentration increases with increase in the values of the relative energy parameter E1 and E2 and it decreases with a decrease in E1 and E2. For fixed values of the ratio of the reaction rate constants t 1 / t 2 , the ratio of the corresponding system parameter α where α 1 and t 2 and it increases with a decrease in S1 and S2. For fixed values of the ratio of the reaction rate constants t 1 / t 2 , the ratio of the corresponding system parameters α where α=1 and the relative energy parameters E1 and E2, the maximum value of the intermediate product dimensionless is constant with either increase or decrease in the sensitivities of the reaction rate constants S1 and S2. (Author)
Intermittent strong transport of the quasi-adiabatic plasma state.
Kim, Chang-Bae; An, Chan-Yong; Min, Byunghoon
2018-06-05
The dynamics of the fluctuating electrostatic potential and the plasma density couched in the resistive-drift model at nearly adiabatic state are simulated. The linear modes are unstable if the phase difference between the potential and the density are positive. Exponential growth of the random small perturbations slows down due to the nonlinear E × B flows that work in two ways. They regulate the strength of the fluctuations by transferring the energy from the energy-producing scale to neighboring scales and reduce the cross phase at the same time. During quasi-steady relaxation sporadic appearance of very strong turbulent particle flux is observed that is characterized by the flat energy spectrum and the broad secondary peak in the mesoscale of the order of the gyro-radius. Such boost of the transport is found to be caused by presence of relatively large cross phase as the E × B flows are not effective in cancelling out the cross phase.
Numerical simulation and experimental validation of coiled adiabatic capillary tubes
Energy Technology Data Exchange (ETDEWEB)
Garcia-Valladares, O. [Centro de Investigacion en Energia, Universidad Nacional Autonoma de Mexico (UNAM), Apdo. Postal 34, 62580 Temixco, Morelos (Mexico)
2007-04-15
The objective of this study is to extend and validate the model developed and presented in previous works [O. Garcia-Valladares, C.D. Perez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: mathematical formulation and numerical model, Applied Thermal Engineering 22 (2) (2002) 173-182; O. Garcia-Valladares, C.D. Perez-Segarra, A. Oliva, Numerical simulation of capillary tube expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: experimental validation and parametric studies, Applied Thermal Engineering 22 (4) (2002) 379-391] to coiled adiabatic capillary tube expansion devices working with pure and mixed refrigerants. The discretized governing equations are coupled using an implicit step by step method. A special treatment has been implemented in order to consider transitions (subcooled liquid region, metastable liquid region, metastable two-phase region and equilibrium two-phase region). All the flow variables (enthalpies, temperatures, pressures, vapor qualities, velocities, heat fluxes, etc.) together with the thermophysical properties are evaluated at each point of the grid in which the domain is discretized. The numerical model allows analysis of aspects such as geometry, type of fluid (pure substances and mixtures), critical or non-critical flow conditions, metastable regions, and transient aspects. Comparison of the numerical simulation with a wide range of experimental data presented in the technical literature will be shown in the present article in order to validate the model developed. (author)
The effect of freestream turbulence on film cooling adiabatic effectiveness
International Nuclear Information System (INIS)
Mayhew, James E.; Baughn, James W.; Byerley, Aaron R.
2003-01-01
The film-cooling performance of a flat plate in the presence of low and high freestream turbulence is investigated using liquid crystal thermography. This paper contributes high-resolution color images that clearly show how the freestream turbulence spreads the cooling air around a larger area of the film-cooled surface. Distributions of the adiabatic effectiveness are determined over the film-cooled surface of the flat plate using the hue method and image processing. Three blowing rates are investigated for a model with three straight holes spaced three diameters apart, with density ratio near unity. High freestream turbulence is shown to increase the area-averaged effectiveness at high blowing rates, but decrease it at low blowing rates. At low blowing ratio, freestream turbulence clearly reduces the coverage area of the cooling air due to increased mixing with the main flow. However, at high blowing ratio, when much of the jet has lifted off in the low turbulence case, high freestream turbulence turns its increased mixing into an asset, entraining some of the coolant that penetrates into the main flow and mixing it with the air near the surface
Effect of hole imperfection on adiabatic film cooling effectiveness
International Nuclear Information System (INIS)
Jovanovic, M.B.; Lange, H.C.; Steenhoven, A.A. van
2008-01-01
The influence of a discrete imperfection on film cooling is studied by means of thermochromic liquid crystals measurements of the adiabatic film cooling effectiveness. As a benchmark, the effect of a jet ejected through a perfect hole is used. The film cooling effectiveness achieved with an imperfect hole is compared to the benchmark. A half torus plays the role of the discrete imperfection. The influence of the presence of the imperfection, its position and the turbulence intensity of the free stream are analyzed. The measurement data are depicted as two-dimensional plots but also as integral values. It is found that the imperfection, placed one diameter from the hole leading edge, deteriorates the effectiveness at moderate velocity ratios. Under the same conditions, the same imperfection fixed at the hole exit improves the effectiveness. At the velocity ratio of 1.50, the exit imperfection improves the integral effectiveness relatively for more than two times. The turbulence intensity and imperfections placed deeper in the hole do not have a significant influence
Adiabatic theory in regions of strong field gradients. [in magnetosphere
Whipple, E. C.; Northrop, T. G.; Birmingham, T. J.
1986-01-01
The theory for the generalized first invariant for adiabatic motion of charged particles in regions where there are large gradients in magnetic or electric fields is developed. The general condition for an invariant to exist in such regions is that the potential well in which the particle oscillates change its shape slowly as the particle drifts. It is shown how the Kruskal (1962) procedure can be applied to obtain expressions for the invariant and for drift velocities that are asymptotic in a smallness parameter epsilon. The procedure is illustrated by obtaining the invariant and drift velocities for particles traversing a perpendicular shock, and the generalized invariant is compared with the magnetic moment, and the drift orbits with the actual orbits, for a particular case. In contrast to the magnetic moment, the generalized first invariant is better for large gyroradii (large kinetic energies) than for small gyroradii. Expressions for the invariant when an electrostatic potential jump is imposed across the perpendicular shock, and when the particle traverses a rotational shear layer with a small normal component of the magnetic field are given.
Development of a semi-adiabatic isoperibol solution calorimeter
Energy Technology Data Exchange (ETDEWEB)
Venkata Krishnan, R.; Jogeswararao, G.; Parthasarathy, R.; Premalatha, S.; Prabhakar Rao, J.; Gunasekaran, G.; Ananthasivan, K., E-mail: asivan@igcar.gov.in [Chemistry Group, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamilnadu (India)
2014-12-15
A semi-adiabatic isoperibol solution calorimeter has been indigenously developed. The measurement system comprises modules for sensitive temperature measurement probe, signal processing, data collection, and joule calibration. The sensitivity of the temperature measurement module was enhanced by using a sensitive thermistor coupled with a lock-in amplifier based signal processor. A microcontroller coordinates the operation and control of these modules. The latter in turn is controlled through personal computer (PC) based custom made software developed with LabView. An innovative summing amplifier concept was used to cancel out the base resistance of the thermistor. The latter was placed in the dewar. The temperature calibration was carried out with a standard platinum resistance (PT100) sensor coupled with an 8½ digit multimeter. The water equivalent of this calorimeter was determined by using electrical calibration with the joule calibrator. The experimentally measured values of the quantum of heat were validated by measuring heats of dissolution of pure KCl (for endotherm) and tris (hydroxyl methyl) amino-methane (for exotherm). The uncertainity in the measurements was found to be within ±3%.
Salt Pill Design and Fabrication for Adiabatic Demagnetization Refrigerators
Shirron, Peter J.; Mccammon, Dan
2014-01-01
The performance of an adiabatic demagnetization refrigerator (ADR) is critically dependent on the design and construction of the salt pills that produce cooling. In most cases, the primary goal is to obtain the largest cooling capacity at the low temperature end of the operating range. The realizable cooling capacity depends on a number of factors, including refrigerant mass, and how efficiently it absorbs heat from the various instrument loads. The design and optimization of "salt pills" for ADR systems depend not only on the mechanical, chemical and thermal properties of the refrigerant, but also on the range of heat fluxes that the salt pill must accommodate. Despite the fairly wide variety of refrigerants available, those used at very low temperature tend to be hydrated salts that require a dedicated thermal bus and must be hermetically sealed, while those used at higher temperature - greater than about 0.5 K - tend to be single-- or poly--crystals that have much simpler requirements for thermal and mechanical packaging. This paper presents a summary of strategies and techniques for designing, optimizing and fabricating salt pills for both low-- and mid--temperature applications.
Stimulated Raman adiabatic passage in physics, chemistry, and beyond
Vitanov, Nikolay V.; Rangelov, Andon A.; Shore, Bruce W.; Bergmann, Klaas
2017-01-01
The technique of stimulated Raman adiabatic passage (STIRAP), which allows efficient and selective population transfer between quantum states without suffering loss due to spontaneous emission, was introduced in 1990 by Gaubatz et al.. Since then STIRAP has emerged as an enabling methodology with widespread successful applications in many fields of physics, chemistry, and beyond. This article reviews the many applications of STIRAP emphasizing the developments since 2001, the time when the last major review on the topic was written (Vitanov, Fleischhauer et al.). A brief introduction into the theory of STIRAP and the early applications for population transfer within three-level systems is followed by the discussion of several extensions to multilevel systems, including multistate chains and tripod systems. The main emphasis is on the wide range of applications in atomic and molecular physics (including atom optics, cavity quantum electrodynamics, formation of ultracold molecules, etc.), quantum information (including single- and two-qubit gates, entangled-state preparation, etc.), solid-state physics (including processes in doped crystals, nitrogen-vacancy centers, superconducting circuits, semiconductor quantum dots and wells), and even some applications in classical physics (including waveguide optics, polarization optics, frequency conversion, etc.). Promising new prospects for STIRAP are also presented (including processes in optomechanics, precision experiments, detection of parity violation in molecules, spectroscopy of core-nonpenetrating Rydberg states, population transfer with x-ray pulses, etc.).
Approximate Bayesian evaluations of measurement uncertainty
Possolo, Antonio; Bodnar, Olha
2018-04-01
The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty. This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand. The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists. We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.
Exact constants in approximation theory
Korneichuk, N
1991-01-01
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are base
International Conference Approximation Theory XIV
Schumaker, Larry
2014-01-01
This volume developed from papers presented at the international conference Approximation Theory XIV, held April 7–10, 2013 in San Antonio, Texas. The proceedings contains surveys by invited speakers, covering topics such as splines on non-tensor-product meshes, Wachspress and mean value coordinates, curvelets and shearlets, barycentric interpolation, and polynomial approximation on spheres and balls. Other contributed papers address a variety of current topics in approximation theory, including eigenvalue sequences of positive integral operators, image registration, and support vector machines. This book will be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
International Nuclear Information System (INIS)
Yang, Y.; Tan, G.Y.; Chen, P.X.; Zhang, Q.M.
2012-01-01
The adiabatic shear susceptibility of 2195 aluminum–lithium alloy was investigated by means of split Hopkinson pressure bar. The stress collapse in true stress–true strain curves and true stress–time curves was observed. The adiabatic shear susceptibility of different aging statuses and strain rate were discussed by means of metallography observation. The critical strain, stress collapse time and formation energy of adiabatic shear bands were compared. The results show that different aging statuses and strain rate have significant influences on adiabatic shear behaviors of 2195 aluminum–lithium alloy. The peak-aged specimen has the highest adiabatic shearing susceptibility, while the under-aged specimen has the least adiabatic shear susceptibility. The susceptibility of adiabatic shearing increases with the increases of strain rate.
Energy Technology Data Exchange (ETDEWEB)
Yang, Y. [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); State Key Laboratory of Explosion Science and Technology, Beijing 100081 (China); Tan, G.Y., E-mail: yangyanggroup@163.com [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); Chen, P.X. [School of Materials Science and Engineering, Central South University, Changsha 410083, Hunan (China); Zhang, Q.M. [State Key Laboratory of Explosion Science and Technology, Beijing 100081 (China)
2012-06-01
The adiabatic shear susceptibility of 2195 aluminum-lithium alloy was investigated by means of split Hopkinson pressure bar. The stress collapse in true stress-true strain curves and true stress-time curves was observed. The adiabatic shear susceptibility of different aging statuses and strain rate were discussed by means of metallography observation. The critical strain, stress collapse time and formation energy of adiabatic shear bands were compared. The results show that different aging statuses and strain rate have significant influences on adiabatic shear behaviors of 2195 aluminum-lithium alloy. The peak-aged specimen has the highest adiabatic shearing susceptibility, while the under-aged specimen has the least adiabatic shear susceptibility. The susceptibility of adiabatic shearing increases with the increases of strain rate.
Group C∗-algebras without the completely bounded approximation property
DEFF Research Database (Denmark)
Haagerup, U.
2016-01-01
It is proved that: (1) The Fourier algebra A(G) of a simple Lie group G of real rank at least 2 with finite center does not have a multiplier bounded approximate unit. (2) The reduced C∗-algebra C∗ r of any lattice in a non-compact simple Lie group of real rank at least 2 with finite center does...... not have the completely bounded approximation property. Hence, the results obtained by de Canniere and the author for SOe (n, 1), n ≥ 2, and by Cowling for SU(n, 1) do not generalize to simple Lie groups of real rank at least 2. © 2016 Heldermann Verlag....
Adiabatic Low-Pass J Filters for Artifact Suppression in Heteronuclear NMR
DEFF Research Database (Denmark)
Meier, Sebastian; Benie, Andrew J; Duus, Jens Øllgaard
2009-01-01
NMR artifact purging: Modern NMR experiments depend on efficient coherence transfer pathways for their sensitivity and on suppression of undesired pathways leading to artifacts for their spectral clarity. A novel robust adiabatic element suppresses hard-to-get-at artifacts....
Development of Adiabatic Doppler Feedback Model in 3D space time analysis Code ARCH
International Nuclear Information System (INIS)
Dwivedi, D.K.; Gupta, Anurag
2015-01-01
Integrated 3D space-time neutron kinetics with thermal-hydraulic feedback code system is being developed for transient analysis of Compact High Temperature Reactor (CHTR) and Advanced Heavy Water Reactor (AHWR). ARCH (code for Analysis of Reactor transients in Cartesian and Hexagon geometries) has been developed with IQS module for efficient 3D space time analysis. Recently, an adiabatic Doppler (fuel temperature) feedback module has been incorporated in this ARCH-IQS version of tile code. In the adiabatic model of fuel temperature feedback, the transfer of the excess heat from the fuel to the coolant during transient is neglected. The viability of Doppler feedback in ARCH-IQS with adiabatic heating has been checked with AER benchmark (Dyn002). Analyses of anticipated transient without scram (ATWS) case in CHTR as well as in AHWR have been performed with adiabatic fuel temperature feedback. The methodology and results have been presented in this paper. (author)
Development of a model for dimethyl ether non-adiabatic reactors to improve methanol conversion
Energy Technology Data Exchange (ETDEWEB)
Nasrollahi, Fatemeh [University of Tehran, Tehran (Iran, Islamic Republic of); Bakeri, Gholamreza; Rahimnejad, Mostafa [Babol Noshirvani University of Technology, Babol (Iran, Islamic Republic of); Ismail, Ahmad Fauzi [Universiti Teknologi Malaysia, Skudai (Malaysia); Imanian, Mahdi [Mohajer Technical University, Isfahan (Iran, Islamic Republic of)
2013-10-15
The modeling of adiabatic and non-adiabatic reactors, using three cooling mediums in the shell side of a shell and tube reactor in cocurrent and countercurrent flow regimes has been conducted. The cooling mediums used in this research are saturated water and methanol feed gas to a reactor which is preheated in the shell side and a special type of oil. The results of adiabatic reactor modeling show good compatibility with the data received from a commercial plant. The results of non-adiabatic reactor modeling showed that more methanol conversion can be achieved in a lower length of reactor, even though in some cases the maximum temperature in the tube side of the reactor is more than the deactivation temperature of the catalyst.
Simulation of adiabatic thermal beams in a periodic solenoidal magnetic focusing field
Directory of Open Access Journals (Sweden)
T. J. Barton
2012-12-01
Full Text Available Self-consistent particle-in-cell simulations are performed to verify earlier theoretical predictions of adiabatic thermal beams in a periodic solenoidal magnetic focusing field [K. R. Samokhvalova, J. Zhou, and C. Chen, Phys. Plasmas 14, 103102 (2007PHPAEN1070-664X10.1063/1.2779281; J. Zhou, K. R. Samokhvalova, and C. Chen, Phys. Plasmas 15, 023102 (2008PHPAEN1070-664X10.1063/1.2837891]. In particular, results are obtained for adiabatic thermal beams that do not rotate in the Larmor frame. For such beams, the theoretical predictions of the rms beam envelope, the conservations of the rms thermal emittances, the adiabatic equation of state, and the Debye length are verified in the simulations. Furthermore, the adiabatic thermal beam is found be stable in the parameter regime where the simulations are performed.
Evidence for the adiabatic invariance of the black hole horizon area
Mayo, Avraham E.
1998-01-01
Some examples in support of the conjecture that the horizon area of a near equilibrium black hole is an adiabatic invariant are described. These clarify somewhat the conditions under which the conjecture would be true.
NVU perspective on simple liquids’ quasiuniversality
DEFF Research Database (Denmark)
Dyre, J. C.
2013-01-01
The last half-century of research into the structure, dynamics, and thermodynamics of simple liquids has revealed a number of approximate universalities. This paper argues that simple liquids' reduced-coordinate constant-potential-energy hypersurfaces constitute a quasiuniversal family of compact...
A simple approach to nonlinear oscillators
International Nuclear Information System (INIS)
Ren Zhongfu; He Jihuan
2009-01-01
A very simple and effective approach to nonlinear oscillators is suggested. Anyone with basic knowledge of advanced calculus can apply the method to finding approximately the amplitude-frequency relationship of a nonlinear oscillator. Some examples are given to illustrate its extremely simple solution procedure and an acceptable accuracy of the obtained solutions.
Non-adiabatic transition of the fissioning nucleus at scission: the time scale
International Nuclear Information System (INIS)
Carjan, N.; Rizea, M.
2012-01-01
The sudden approximation has been recently used to calculate the microscopic scission-properties during low-energy fission of 236 U. In this approach the scission process, i.e., the transition from two fragments connected by a thin neck to two separated fragments was considered to happen suddenly. The approach is stationary (the time evolution is not explicitly treated) and it only involves the two sets of neutron eigenstates for the two nuclear configurations considered: just before scission (α i ) and immediately after scission (α f ). The purpose of the present paper is to go beyond this mathematical approximation considering the real physical situation in which the above mentioned transition takes place in a time interval ΔT ≠ 0. For this we need to follow the evolution from α i to αf of all occupied neutron states by solving numerically the two-dimensional time-dependent Schroedinger equation with time-dependent potential. Calculations are performed for mass divisions from A L = 70 to A L = 118 (A L being the light fragment mass) taking into account all the neutron states (Ω = 1/2, 3/2,..., 11/2) that are bound in 236 U at α i . The diabatic-dissipative dynamics of the neck rupture is very complicated and its exact duration is un-known. ΔT is therefore taken as parameter having values from 0.25 x 10 -22 to 6 x 10 -22 sec. The resulting scission neutron multiplicities - sc and primary fragments' excitation energies E sc * are compared with those obtained in the frame of the sudden approximation (that corresponds to ΔT = 0). As expected, shorter is the transition time more excited are the fragments and more neutrons are emitted, the sudden approximation being an upper limit. For ΔT = 10 -22 sec, which is a realistic value, the time dependent results are 20% below this limit. For transition times longer than 5 x 10 -22 sec the adiabatic limit is reached: no scission neutrons are emitted anymore and the excitation energy at α f is negligible. The
Keefe, Peter
2004-01-01
Abstract: The nature of the thermodynamic behavior of Type I superconductor particles, having a cross section less than the Ginzburg-Landau temperature dependent coherence length is discussed for magnetic field induced adiabatic phase transitions from the superconductive state to the normal state. Argument is advanced supporting the view that when the adiabatic magneto-caloric process is applied to particles, the phase transition is characterized by a decrease in entropy in violation of tradi...
Deng, Jiawen; Wang, Qing-hai; Liu, Zhihao; Hanggi, Peter; Gong, Jiangbin
2013-01-01
Under a general framework, shortcuts to adiabatic processes are shown to be possible in classical systems. We then study the distribution function of the work done on a small system initially prepared at thermal equilibrium. It is found that the work fluctuations can be significantly reduced via shortcuts to adiabatic processes. For example, in the classical case probabilities of having very large or almost zero work values are suppressed. In the quantum case negative work may be totally remo...
Energy Technology Data Exchange (ETDEWEB)
Todorov, N S [Low Temperature Department of the Institute of Solid State Physics of the Bulgarian Academy of Sciences, Sofia
1981-04-01
It is shown that the nonstationary Schroedinger equation does not satisfy a well-known adiabatical principle in thermodynamics. A ''renormalization procedure'' based on the possible existence of a time-irreversible basic evolution equation is proposed with the help of which one comes to agreement in a variety of specific cases of an adiabatic inclusion of a perturbing potential. The ideology of the present article rests essentially on the ideology of the preceding articles, in particular article I.
Energy Technology Data Exchange (ETDEWEB)
Todorov, N S
1981-04-01
It is shown that the nonstationary Schroedinger equation does not satisfy a well-known adiabatical principle in thermodynamics. A ''renormalization procedure'' based on the possible existence of a time-irreversible basic evolution equation is proposed with the help of which one comes to agreement in a variety of specific cases of an adiabatic inclusion of a perturbing potential. The ideology of the present article IV rests essentially on the ideology of the preceding articles, in particular article I.
... Solitary Kidney Your Kidneys & How They Work Simple Kidney Cysts What are simple kidney cysts? Simple kidney cysts are abnormal, fluid-filled ... that form in the kidneys. What are the kidneys and what do they do? The kidneys are ...
Study of some approximation schemes in the spin-boson problem
International Nuclear Information System (INIS)
Kenkre, V.M.; Giuggioli, L.
2004-01-01
Some approximation schemes used in the description of the evolution of the spin-boson system are studied through numerical and analytic methods. Among the procedures investigated are semiclassical approximations and the memory function approach. An infinitely large number of semiclassical approximations are discussed. Their two extreme limits are shown to be characterized, respectively, by effective energy mismatch and effective intersite transfer. The validity of the two limits is explored by explicit numerical calculations for important regions in parameter space, and it is shown that they can provide good descriptions in the so-called adiabatic and anti-adiabatic regimes, respectively. The memory function approach, which provides an excellent approximation scheme for a certain range of parameters, is shown to be connected to other approaches such as the non-interacting blip approximation. New results are derived from the memory approach in semiclassical contexts. Comments are made on thermal effects in the spin-boson problem, the discrete non-linear Schroedinger equation, and connections to the areas of dynamic localization, and quantum control
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
Energy Technology Data Exchange (ETDEWEB)
Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B. [Research Department of Biomedical Engineering, Institute of Electrical Engineering, Chinese Academy of Science, Beijing 100190 (China); Qin, G., E-mail: wangjunfang@mail.iee.ac.cn, E-mail: qingang@hit.edu.cn [School of Science, Harbin Institute of Technology, Shenzhen 518055 (China)
2017-08-20
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
International Nuclear Information System (INIS)
Kanungo, Jitendra; Dasgupta, S.
2014-01-01
We analyze the energy performance of a complete adiabatic circuit/system including the Power Clock Generator (PCG) at the 90 nm CMOS technology node. The energy performance in terms of the conversion efficiency of the PCG is extensively carried out under the variations of supply voltage, process corner and the driver transistor's width. We propose an energy-efficient singe cycle control circuit based on the two-stage comparator for the synchronous charge recovery sinusoidal power clock generator (PCG). The proposed PCG is used to drive the 4-bit adiabatic Ripple Carry Adder (RCA) and their simulation results are compared with the adiabatic RCA driven by the reported PCG. We have also simulated the logically equivalent static CMOS RCA circuit to compare the energy saving of adiabatic and non-adiabatic logic circuits. In the clock frequency range from 25 MHz to 1GHz, the proposed PCG gives a maximum conversion efficiency of 56.48%. This research work shows how the design of an efficient PCG increases the energy saving of adiabatic logic. (semiconductor integrated circuits)
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
Wang, J. F.; Qin, G.; Ma, Q. M.; Song, T.; Yuan, S. B.
2017-08-01
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
Perpendicular Diffusion Coefficient of Comic Rays: The Presence of Weak Adiabatic Focusing
International Nuclear Information System (INIS)
Wang, J. F.; Ma, Q. M.; Song, T.; Yuan, S. B.; Qin, G.
2017-01-01
The influence of adiabatic focusing on particle diffusion is an important topic in astrophysics and plasma physics. In the past, several authors have explored the influence of along-field adiabatic focusing on the parallel diffusion of charged energetic particles. In this paper, using the unified nonlinear transport theory developed by Shalchi and the method of He and Schlickeiser, we derive a new nonlinear perpendicular diffusion coefficient for a non-uniform background magnetic field. This formula demonstrates that the particle perpendicular diffusion coefficient is modified by along-field adiabatic focusing. For isotropic pitch-angle scattering and the weak adiabatic focusing limit, the derived perpendicular diffusion coefficient is independent of the sign of adiabatic focusing characteristic length. For the two-component model, we simplify the perpendicular diffusion coefficient up to the second order of the power series of the adiabatic focusing characteristic quantity. We find that the first-order modifying factor is equal to zero and that the sign of the second order is determined by the energy of the particles.
General background conditions for K-bounce and adiabaticity
Energy Technology Data Exchange (ETDEWEB)
Romano, Antonio Enea [University of Crete, Department of Physics, Heraklion (Greece); Kyoto University, Yukawa Institute for Theoretical Physics, Kyoto (Japan); Universidad de Antioquia, Instituto de Fisica, A.A.1226, Medellin (Colombia)
2017-03-15
We study the background conditions for a bounce uniquely driven by a single scalar field model with a generalized kinetic term K(X), without any additional matter field. At the background level we impose the existence of two turning points where the derivative of the Hubble parameter H changes sign and of a bounce point where the Hubble parameter vanishes. We find the conditions for K(X) and the potential which ensure the above requirements. We then give the examples of two models constructed according to these conditions. One is based on a quadratic K(X), and the other on a K(X) which is avoiding divergences of the second time derivative of the scalar field, which may otherwise occur. An appropriate choice of the initial conditions can lead to a sequence of consecutive bounces, or oscillations of H. In the region where these models have a constant potential they are adiabatic on any scale and because of this they may not conserve curvature perturbations on super-horizon scales. While at the perturbation level one class of models is free from ghosts and singularities of the classical equations of motion, in general gradient instabilities are present around the bounce time, because the sign of the squared speed of sound is opposite to the sign of the time derivative of H. We discuss how this kind of instabilities could be avoided by modifying the Lagrangian by introducing Galilean terms in order to prevent a negative squared speed of sound around the bounce. (orig.)
General background conditions for K-bounce and adiabaticity
International Nuclear Information System (INIS)
Romano, Antonio Enea
2017-01-01
We study the background conditions for a bounce uniquely driven by a single scalar field model with a generalized kinetic term K(X), without any additional matter field. At the background level we impose the existence of two turning points where the derivative of the Hubble parameter H changes sign and of a bounce point where the Hubble parameter vanishes. We find the conditions for K(X) and the potential which ensure the above requirements. We then give the examples of two models constructed according to these conditions. One is based on a quadratic K(X), and the other on a K(X) which is avoiding divergences of the second time derivative of the scalar field, which may otherwise occur. An appropriate choice of the initial conditions can lead to a sequence of consecutive bounces, or oscillations of H. In the region where these models have a constant potential they are adiabatic on any scale and because of this they may not conserve curvature perturbations on super-horizon scales. While at the perturbation level one class of models is free from ghosts and singularities of the classical equations of motion, in general gradient instabilities are present around the bounce time, because the sign of the squared speed of sound is opposite to the sign of the time derivative of H. We discuss how this kind of instabilities could be avoided by modifying the Lagrangian by introducing Galilean terms in order to prevent a negative squared speed of sound around the bounce. (orig.)
On adiabatic pair potentials of highly charged colloid particles
Sogami, Ikuo S.
2018-03-01
Generalizing the Debye-Hückel formalism, we develop a new mean field theory for adiabatic pair potentials of highly charged particles in colloid dispersions. The unoccupied volume and the osmotic pressure are the key concepts to describe the chemical and thermodynamical equilibrium of the gas of small ions in the outside region of all of the colloid particles. To define the proper thermodynamic quantities, it is postulated to take an ensemble averaging with respect to the particle configurations in the integrals for their densities consisting of the electric potential satisfying a set of equations that are derived by linearizing the Poisson-Boltzmann equation. With the Fourier integral representation of the electric potential, we calculate first the internal electric energy of the system from which the Helmholtz free energy is obtained through the Legendre transformation. Then, the Gibbs free energy is calculated using both ways of the Legendre transformation with respect to the unoccupied volume and the summation of chemical potentials. The thermodynamic functions provide three types of pair potentials, all of which are inversely proportional to the fraction of the unoccupied volume. At the limit when the fraction factor reduces to unity, the Helmholtz pair potential turns exactly into the well known Derjaguin-Landau-Verwey-Overbeek repulsive potential. The Gibbs pair potential possessing a medium-range strong repulsive part and a long-range weak attractive tail can explain the Schulze-Hardy rule for coagulation in combination with the van der Waals-London potential and describes a rich variety of phenomena of phase transitions observed in the dilute dispersions of highly charged particles.
Classical molecular dynamics simulation of electronically non-adiabatic processes.
Miller, William H; Cotton, Stephen J
2016-12-22
Both classical and quantum mechanics (as well as hybrids thereof, i.e., semiclassical approaches) find widespread use in simulating dynamical processes in molecular systems. For large chemical systems, however, which involve potential energy surfaces (PES) of general/arbitrary form, it is usually the case that only classical molecular dynamics (MD) approaches are feasible, and their use is thus ubiquitous nowadays, at least for chemical processes involving dynamics on a single PES (i.e., within a single Born-Oppenheimer electronic state). This paper reviews recent developments in an approach which extends standard classical MD methods to the treatment of electronically non-adiabatic processes, i.e., those that involve transitions between different electronic states. The approach treats nuclear and electronic degrees of freedom (DOF) equivalently (i.e., by classical mechanics, thereby retaining the simplicity of standard MD), and provides "quantization" of the electronic states through a symmetrical quasi-classical (SQC) windowing model. The approach is seen to be capable of treating extreme regimes of strong and weak coupling between the electronic states, as well as accurately describing coherence effects in the electronic DOF (including the de-coherence of such effects caused by coupling to the nuclear DOF). A survey of recent applications is presented to illustrate the performance of the approach. Also described is a newly developed variation on the original SQC model (found universally superior to the original) and a general extension of the SQC model to obtain the full electronic density matrix (at no additional cost/complexity).
Some results in Diophantine approximation
DEFF Research Database (Denmark)
Pedersen, Steffen Højris
the basic concepts on which the papers build. Among other it introduces metric Diophantine approximation, Mahler’s approach on algebraic approximation, the Hausdorff measure, and properties of the formal Laurent series over Fq. The introduction ends with a discussion on Mahler’s problem when considered......This thesis consists of three papers in Diophantine approximation, a subbranch of number theory. Preceding these papers is an introduction to various aspects of Diophantine approximation and formal Laurent series over Fq and a summary of each of the three papers. The introduction introduces...
Limitations of shallow nets approximation.
Lin, Shao-Bo
2017-10-01
In this paper, we aim at analyzing the approximation abilities of shallow networks in reproducing kernel Hilbert spaces (RKHSs). We prove that there is a probability measure such that the achievable lower bound for approximating by shallow nets can be realized for all functions in balls of reproducing kernel Hilbert space with high probability, which is different with the classical minimax approximation error estimates. This result together with the existing approximation results for deep nets shows the limitations for shallow nets and provides a theoretical explanation on why deep nets perform better than shallow nets. Copyright © 2017 Elsevier Ltd. All rights reserved.
SAM revisited: uniform semiclassical approximation with absorption
International Nuclear Information System (INIS)
Hussein, M.S.; Pato, M.P.
1986-01-01
The uniform semiclassical approximation is modified to take into account strong absorption. The resulting theory, very similar to the one developed by Frahn and Gross is used to discuss heavy-ion elastic scattering at intermediate energies. The theory permits a reasonably unambiguos separation of refractive and diffractive effects. The systems 12 C+ 12 C and 12 C+ 16 O, which seem to exhibit a remnant of a nuclear rainbow at E=20 Mev/N, are analysed with theory which is built directly on a model for the S-matrix. Simple relations between the fit S-matrix and the underlying complex potential are derived. (Author) [pt
Multi-compartment linear noise approximation
International Nuclear Information System (INIS)
Challenger, Joseph D; McKane, Alan J; Pahle, Jürgen
2012-01-01
The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented. (paper)
High energy approximations in quantum field theory
International Nuclear Information System (INIS)
Orzalesi, C.A.
1975-01-01
New theoretical methods in hadron physics based on a high-energy perturbation theory are discussed. The approximated solutions to quantum field theory obtained by this method appear to be sufficiently simple and rich in structure to encourage hadron dynamics studies. Operator eikonal form for field - theoretic Green's functions is derived and discussion is held on how the eikonal perturbation theory is to be renormalized. This method is extended to massive quantum electrodynamics of scalar charged bosons. Possible developments and applications of this theory are given [pt
Analytical Ballistic Trajectories with Approximately Linear Drag
Directory of Open Access Journals (Sweden)
Giliam J. P. de Carpentier
2014-01-01
Full Text Available This paper introduces a practical analytical approximation of projectile trajectories in 2D and 3D roughly based on a linear drag model and explores a variety of different planning algorithms for these trajectories. Although the trajectories are only approximate, they still capture many of the characteristics of a real projectile in free fall under the influence of an invariant wind, gravitational pull, and terminal velocity, while the required math for these trajectories and planners is still simple enough to efficiently run on almost all modern hardware devices. Together, these properties make the proposed approach particularly useful for real-time applications where accuracy and performance need to be carefully balanced, such as in computer games.
Analysing organic transistors based on interface approximation
International Nuclear Information System (INIS)
Akiyama, Yuto; Mori, Takehiko
2014-01-01
Temperature-dependent characteristics of organic transistors are analysed thoroughly using interface approximation. In contrast to amorphous silicon transistors, it is characteristic of organic transistors that the accumulation layer is concentrated on the first monolayer, and it is appropriate to consider interface charge rather than band bending. On the basis of this model, observed characteristics of hexamethylenetetrathiafulvalene (HMTTF) and dibenzotetrathiafulvalene (DBTTF) transistors with various surface treatments are analysed, and the trap distribution is extracted. In turn, starting from a simple exponential distribution, we can reproduce the temperature-dependent transistor characteristics as well as the gate voltage dependence of the activation energy, so we can investigate various aspects of organic transistors self-consistently under the interface approximation. Small deviation from such an ideal transistor operation is discussed assuming the presence of an energetically discrete trap level, which leads to a hump in the transfer characteristics. The contact resistance is estimated by measuring the transfer characteristics up to the linear region
Adiabatic energization in the ring current and its relation to other source and loss terms
Liemohn, M. W.; Kozyra, J. U.; Clauer, C. R.; Khazanov, G. V.; Thomsen, M. F.
2002-04-01
The influence of adiabatic energization and deenergization effects, caused by particle drift in radial distance, on ring current growth rates and loss lifetimes is investigated. Growth and loss rates from simulation results of four storms (5 June 1991, 15 May 1997, 19 October 1998, and 25 September 1998) are examined and compared against the y component of the solar wind electric field (Ey,sw). Energy change rates with and without the inclusion of adiabatic energy changes are considered to isolate the influence of this mechanism in governing changes of ring current strength. It is found that the influence of adiabatic drift effects on the energy change rates is very large when energization and deenergization are considered separately as gain and loss mechanisms, often about an order of magnitude larger than all other source or loss terms combined. This is true not only during storm times, when the open drift path configuration of the hot ions dominates the physics of the ring current, but also during quiet times, when the small oscillation in L of the closed trajectories creates a large source and loss of energy each drift orbit. However, the net energy change from adiabatic drift is often smaller than other source and loss processes, especially during quiet times. Energization from adiabatic drift dominates ring current growth only during portions of the main phase of storms. Furthermore, the net-adiabatic energization is often positive, because some particles are lost in the inner magnetosphere before they can adiabatically deenergize. It is shown that the inclusion of only this net-adiabatic drift effect in the total source rate or loss lifetime (depending on the sign of the net-adiabatic energization) best matches the observed source and loss values from empirical Dst predictor methods (that is, for consistency, these values should be compared between the calculation methods). While adiabatic deenergization dominates the loss timescales for all Ey,sw values
Spherical Approximation on Unit Sphere
Directory of Open Access Journals (Sweden)
Eman Samir Bhaya
2018-01-01
Full Text Available In this paper we introduce a Jackson type theorem for functions in LP spaces on sphere And study on best approximation of functions in spaces defined on unit sphere. our central problem is to describe the approximation behavior of functions in spaces for by modulus of smoothness of functions.
Approximate circuits for increased reliability
Hamlet, Jason R.; Mayo, Jackson R.
2015-08-18
Embodiments of the invention describe a Boolean circuit having a voter circuit and a plurality of approximate circuits each based, at least in part, on a reference circuit. The approximate circuits are each to generate one or more output signals based on values of received input signals. The voter circuit is to receive the one or more output signals generated by each of the approximate circuits, and is to output one or more signals corresponding to a majority value of the received signals. At least some of the approximate circuits are to generate an output value different than the reference circuit for one or more input signal values; however, for each possible input signal value, the majority values of the one or more output signals generated by the approximate circuits and received by the voter circuit correspond to output signal result values of the reference circuit.
Cosmological Simulations with Scale-Free Initial Conditions. I. Adiabatic Hydrodynamics
International Nuclear Information System (INIS)
Owen, J.M.; Weinberg, D.H.; Evrard, A.E.; Hernquist, L.; Katz, N.
1998-01-01
We analyze hierarchical structure formation based on scale-free initial conditions in an Einstein endash de Sitter universe, including a baryonic component with Ω bary = 0.05. We present three independent, smoothed particle hydrodynamics (SPH) simulations, performed at two resolutions (32 3 and 64 3 dark matter and baryonic particles) and with two different SPH codes (TreeSPH and P3MSPH). Each simulation is based on identical initial conditions, which consist of Gaussian-distributed initial density fluctuations that have a power spectrum P(k) ∝ k -1 . The baryonic material is modeled as an ideal gas subject only to shock heating and adiabatic heating and cooling; radiative cooling and photoionization heating are not included. The evolution is expected to be self-similar in time, and under certain restrictions we identify the expected scalings for many properties of the distribution of collapsed objects in all three realizations. The distributions of dark matter masses, baryon masses, and mass- and emission-weighted temperatures scale quite reliably. However, the density estimates in the central regions of these structures are determined by the degree of numerical resolution. As a result, mean gas densities and Bremsstrahlung luminosities obey the expected scalings only when calculated within a limited dynamic range in density contrast. The temperatures and luminosities of the groups show tight correlations with the baryon masses, which we find can be well represented by power laws. The Press-Schechter (PS) approximation predicts the distribution of group dark matter and baryon masses fairly well, though it tends to overestimate the baryon masses. Combining the PS mass distribution with the measured relations for T(M) and L(M) predicts the temperature and luminosity distributions fairly accurately, though there are some discrepancies at high temperatures/luminosities. In general the three simulations agree well for the properties of resolved groups, where a group
Rabli, Djamal; McCarroll, Ronald
2018-02-01
This review surveys the different theoretical approaches, used to describe inelastic and rearrangement processes in collisions involving atoms and ions. For a range of energies from a few meV up to about 1 keV, the adiabatic representation is expected to be valid and under these conditions, inelastic and rearrangement processes take place via a network of avoided crossings of the potential energy curves of the collision system. In general, such avoided crossings are finite in number. The non-adiabatic coupling, due to the breakdown of the Born-Oppenheimer separation of the electronic and nuclear variables, depends on the ratio of the electron mass to the nuclear mass terms in the total Hamiltonian. By limiting terms in the total Hamiltonian correct to first order in the electron to nuclear mass ratio, a system of reaction coordinates is found which allows for a correct description of both inelastic channels. The connection between the use of reaction coordinates in the quantum description and the electron translation factors of the impact parameter approach is established. A major result is that only when reaction coordinates are used, is it possible to introduce the notion of a minimal basis set. Such a set must include all avoided crossings including both radial coupling and long range Coriolis coupling. But, only when reactive coordinates are used, can such a basis set be considered as complete. In particular when the centre of nuclear mass is used as centre of coordinates, rather than the correct reaction coordinates, it is shown that erroneous results are obtained. A few results to illustrate this important point are presented: one concerning a simple two-state Landau-Zener type avoided crossing, the other concerning a network of multiple crossings in a typical electron capture process involving a highly charged ion with a neutral atom.
Approximating the physical inner product of loop quantum cosmology
International Nuclear Information System (INIS)
Bahr, Benjamin; Thiemann, Thomas
2007-01-01
In this paper, we investigate the possibility of approximating the physical inner product of constrained quantum theories. In particular, we calculate the physical inner product of a simple cosmological model in two ways: firstly, we compute it analytically via a trick; secondly, we use the complexifier coherent states to approximate the physical inner product defined by the master constraint of the system. We find that the approximation is able to recover the analytic solution of the problem, which consolidates hopes that coherent states will help to approximate solutions of more complicated theories, like loop quantum gravity
Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.
Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E
2018-06-01
An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.
Approximate analytic theory of the multijunction grill
International Nuclear Information System (INIS)
Hurtak, O.; Preinhaelter, J.
1991-03-01
An approximate analytic theory of the general multijunction grill is developed. Omitting the evanescent modes in the subsidiary waveguides both at the junction and at the grill mouth and neglecting multiple wave reflection, simple formulae are derived for the reflection coefficient, the amplitudes of the incident and reflected waves and the spectral power density. These quantities are expressed through the basic grill parameters (the electric length of the structure and phase shift between adjacent waveguides) and two sets of reflection coefficients describing wave reflections in the subsidiary waveguides at the junction and at the plasma. Approximate expressions for these coefficients are also given. The results are compared with a numerical solution of two specific examples; they were shown to be useful for the optimization and design of multijunction grills.For the JET structure it is shown that, in the case of a dense plasma,many results can be obtained from the simple formulae for a two-waveguide multijunction grill. (author) 12 figs., 12 refs
The efficiency of Flory approximation
International Nuclear Information System (INIS)
Obukhov, S.P.
1984-01-01
The Flory approximation for the self-avoiding chain problem is compared with a conventional perturbation theory expansion. While in perturbation theory each term is averaged over the unperturbed set of configurations, the Flory approximation is equivalent to the perturbation theory with the averaging over the stretched set of configurations. This imposes restrictions on the integration domain in higher order terms and they can be treated self-consistently. The accuracy δν/ν of Flory approximation for self-avoiding chain problems is estimated to be 2-5% for 1 < d < 4. (orig.)
Adiabatic theory of Wannier threshold laws and ionization cross sections
International Nuclear Information System (INIS)
Macek, J.H.; Ovchinnikov, S.Yu.
1994-01-01
The Wannier threshold law for three-particle fragmentation is reviewed. By integrating the Schroedinger equation along a path where the reaction coordinate R is complex, anharmonic corrections to the simple power law are obtained. These corrections are found to be non-analytic in the energy E, in contrast to the expected analytic dependence upon E
Adiabatic theory of Wannier threshold laws and ionization cross sections
International Nuclear Information System (INIS)
Macek, J.H.; Ovchinnikov, S.Y.
1995-01-01
The Wannier threshold law for three-particle fragmentation is reviewed. By integrating the Schroedinger equation along a path where the reaction coordinate R is complex, anharmonic corrections to the simple power law are obtained. These corrections are found to be non-analytic in the energy E, in contrast to the expected analytic dependence upon E. copyright 1995 American Institute of Physics
Rollout sampling approximate policy iteration
Dimitrakakis, C.; Lagoudakis, M.G.
2008-01-01
Several researchers have recently investigated the connection between reinforcement learning and classification. We are motivated by proposals of approximate policy iteration schemes without value functions, which focus on policy representation using classifiers and address policy learning as a
Framework for sequential approximate optimization
Jacobs, J.H.; Etman, L.F.P.; Keulen, van F.; Rooda, J.E.
2004-01-01
An object-oriented framework for Sequential Approximate Optimization (SAO) isproposed. The framework aims to provide an open environment for thespecification and implementation of SAO strategies. The framework is based onthe Python programming language and contains a toolbox of Python
Babajanova, Gulmira; Matrasulov, Jasur; Nakamura, Katsuhiro
2018-04-01
With use of the scheme of fast forward which realizes quasistatic or adiabatic dynamics in shortened timescale, we investigate a thermally isolated ideal quantum gas confined in a rapidly dilating one-dimensional (1D) cavity with the time-dependent size L =L (t ) . In the fast-forward variants of equation of states, i.e., Bernoulli's formula and Poisson's adiabatic equation, the force or 1D analog of pressure can be expressed as a function of the velocity (L ˙) and acceleration (L ̈) of L besides rapidly changing state variables like effective temperature (T ) and L itself. The force is now a sum of nonadiabatic (NAD) and adiabatic contributions with the former caused by particles moving synchronously with kinetics of L and the latter by ideal bulk particles insensitive to such a kinetics. The ratio of NAD and adiabatic contributions does not depend on the particle number (N ) in the case of the soft-wall confinement, whereas such a ratio is controllable in the case of hard-wall confinement. We also reveal the condition when the NAD contribution overwhelms the adiabatic one and thoroughly changes the standard form of the equilibrium equation of states.
Energy Technology Data Exchange (ETDEWEB)
Patrick, Christopher E., E-mail: chripa@fysik.dtu.dk; Thygesen, Kristian S., E-mail: thygesen@fysik.dtu.dk [Center for Atomic-Scale Materials Design (CAMD), Department of Physics, Technical University of Denmark, DK—2800 Kongens Lyngby (Denmark)
2015-09-14
We present calculations of the correlation energies of crystalline solids and isolated systems within the adiabatic-connection fluctuation-dissipation formulation of density-functional theory. We perform a quantitative comparison of a set of model exchange-correlation kernels originally derived for the homogeneous electron gas (HEG), including the recently introduced renormalized adiabatic local-density approximation (rALDA) and also kernels which (a) satisfy known exact limits of the HEG, (b) carry a frequency dependence, or (c) display a 1/k{sup 2} divergence for small wavevectors. After generalizing the kernels to inhomogeneous systems through a reciprocal-space averaging procedure, we calculate the lattice constants and bulk moduli of a test set of 10 solids consisting of tetrahedrally bonded semiconductors (C, Si, SiC), ionic compounds (MgO, LiCl, LiF), and metals (Al, Na, Cu, Pd). We also consider the atomization energy of the H{sub 2} molecule. We compare the results calculated with different kernels to those obtained from the random-phase approximation (RPA) and to experimental measurements. We demonstrate that the model kernels correct the RPA’s tendency to overestimate the magnitude of the correlation energy whilst maintaining a high-accuracy description of structural properties.
Green-Ampt approximations: A comprehensive analysis
Ali, Shakir; Islam, Adlul; Mishra, P. K.; Sikka, Alok K.
2016-04-01
Green-Ampt (GA) model and its modifications are widely used for simulating infiltration process. Several explicit approximate solutions to the implicit GA model have been developed with varying degree of accuracy. In this study, performance of nine explicit approximations to the GA model is compared with the implicit GA model using the published data for broad range of soil classes and infiltration time. The explicit GA models considered are Li et al. (1976) (LI), Stone et al. (1994) (ST), Salvucci and Entekhabi (1994) (SE), Parlange et al. (2002) (PA), Barry et al. (2005) (BA), Swamee et al. (2012) (SW), Ali et al. (2013) (AL), Almedeij and Esen (2014) (AE), and Vatankhah (2015) (VA). Six statistical indicators (e.g., percent relative error, maximum absolute percent relative error, average absolute percent relative errors, percent bias, index of agreement, and Nash-Sutcliffe efficiency) and relative computer computation time are used for assessing the model performance. Models are ranked based on the overall performance index (OPI). The BA model is found to be the most accurate followed by the PA and VA models for variety of soil classes and infiltration periods. The AE, SW, SE, and LI model also performed comparatively better. Based on the overall performance index, the explicit models are ranked as BA > PA > VA > LI > AE > SE > SW > ST > AL. Results of this study will be helpful in selection of accurate and simple explicit approximate GA models for solving variety of hydrological problems.
International Nuclear Information System (INIS)
Collins, T.
1985-08-01
A simple criterion governs the beam distortion and/or loss of protons on a fast resonance crossing. Results from numerical integrations are illustrated for simple sextupole, octupole, and 10-pole resonances
Energy Technology Data Exchange (ETDEWEB)
Collins, T.
1985-08-01
A simple criterion governs the beam distortion and/or loss of protons on a fast resonance crossing. Results from numerical integrations are illustrated for simple sextupole, octupole, and 10-pole resonances.
Discovery of functional and approximate functional dependencies in relational databases
Directory of Open Access Journals (Sweden)
Ronald S. King
2003-01-01
Full Text Available This study develops the foundation for a simple, yet efficient method for uncovering functional and approximate functional dependencies in relational databases. The technique is based upon the mathematical theory of partitions defined over a relation's row identifiers. Using a levelwise algorithm the minimal non-trivial functional dependencies can be found using computations conducted on integers. Therefore, the required operations on partitions are both simple and fast. Additionally, the row identifiers provide the added advantage of nominally identifying the exceptions to approximate functional dependencies, which can be used effectively in practical data mining applications.
Nuclear Hartree-Fock approximation testing and other related approximations
International Nuclear Information System (INIS)
Cohenca, J.M.
1970-01-01
Hartree-Fock, and Tamm-Dancoff approximations are tested for angular momentum of even-even nuclei. Wave functions, energy levels and momenta are comparatively evaluated. Quadripole interactions are studied following the Elliott model. Results are applied to Ne 20 [pt
Optimal control of the power adiabatic stroke of an optomechanical heat engine.
Bathaee, M; Bahrampour, A R
2016-08-01
We consider the power adiabatic stroke of the Otto optomechanical heat engine introduced in Phys. Rev. Lett. 112, 150602 (2014)PRLTAO0031-900710.1103/PhysRevLett.112.150602. We derive the maximum extractable work of both optomechanical normal modes in the minimum time while the system experiences quantum friction effects. We show that the total work done by the system in the power adiabatic stroke is optimized by a bang-bang control. The time duration of the power adiabatic stroke is of the order of the inverse of the effective optomechanical-coupling coefficient. The optimal phase-space trajectory of the Otto cycle for both optomechanical normal modes is also obtained.
Predicting the effect of relaxation during frequency-selective adiabatic pulses
Pfaff, Annalise R.; McKee, Cailyn E.; Woelk, Klaus
2017-11-01
Adiabatic half and full passages are invaluable for achieving uniform, B1-insensitive excitation or inversion of macroscopic magnetization across a well-defined range of NMR frequencies. To accomplish narrow frequency ranges with adiabatic pulses (computer-calculated data with experimental results demonstrates that, in non-viscous, small-molecule fluids, it is possible to model magnetization and relaxation by considering standard T1 and T2 relaxation in the traditional rotating frame. The proposed model is aimed at performance optimizations of applications in which these pulses are employed. It differs from previous reports which focused on short high-power adiabatic pulses and relaxation that is governed by dipole-dipole interactions, cross polarization, or chemical exchange.
Aspects of hyperspherical adiabaticity in an atomic-gas Bose-Einstein condensate
International Nuclear Information System (INIS)
Kushibe, Daisuke; Mutou, Masaki; Morishita, Toru; Watanabe, Shinichi; Matsuzawa, Michio
2004-01-01
Excitation of an atomic-gas Bose-Einstein condensate (BEC) in the zeroth-order ground-state channel is studied with the hyperspherical adiabatic method of Bohn et al. [Bohn et al., Phys. Rev. A 58, 584 (1998)] suitably generalized to accommodate the anisotropic trapping potential. The method exploits the system's size as an adiabatic parameter so that the explicit size dependence is immediately conducive to the virial theorem. The oscillation frequencies associated with the monopole (breathing) and quadrupole modes thus emerge naturally and converge to the well-known Thomas-Fermi limits. Analysis of the single-particle density and the projected excitation wave function shows that the excitation in the single hyperspherical ground-state channel merely represents a progressive increase in occupancy of the first excited single-particle state. The work paves the way for applying the adiabatic picture to other BEC phenomena
Inhomogeneous quasi-adiabatic driving of quantum critical dynamics in weakly disordered spin chains
International Nuclear Information System (INIS)
Rams, Marek M; Mohseni, Masoud; Campo, Adolfo del
2016-01-01
We introduce an inhomogeneous protocol to drive a weakly disordered quantum spin chain quasi-adiabatically across a quantum phase transition and minimize the residual energy of the final state. The number of spins that simultaneously reach the critical point is controlled by the length scale in which the magnetic field is modulated, introducing an effective size that favors adiabatic dynamics. The dependence of the residual energy on this length scale and the velocity at which the magnetic field sweeps out the chain is shown to be nonmonotonic. We determine the conditions for an optimal suppression of the residual energy of the final state and show that inhomogeneous driving can outperform conventional adiabatic schemes based on homogeneous control fields by several orders of magnitude. (paper)
Geometry of quantal adiabatic evolution driven by a non-Hermitian Hamiltonian
International Nuclear Information System (INIS)
Wu Zhaoyan; Yu Ting; Zhou Hongwei
1994-01-01
It is shown by using a counter example, which is exactly solvable, that the quantal adiabatic theorem does not generally hold for a non-Hermitian driving Hamiltonian, even if it varies extremely slowly. The condition for the quantal adiabatic theorem to hold for non-Hermitian driving Hamiltonians is given. The adiabatic evolutions driven by a non-Hermitian Hamiltonian provide examples of a new geometric structure, that is the vector bundle in which the inner product of two parallelly transported vectors generally changes. A new geometric concept, the attenuation tensor, is naturally introduced to describe the decay or flourish of the open quantum system. It is constructed in terms of the spectral projector of the Hamiltonian. (orig.)
International Nuclear Information System (INIS)
Peña-Monferrer, C.; Passalacqua, A.; Chiva, S.; Muñoz-Cobo, J.L.
2016-01-01
Highlights: • A population balance equation solved with QMOM approximation is implemented in OpenFOAM. • Available models for interfacial forces and bubble induced turbulence are analyzed. • A vertical pipe flow is simulated for different bubbly flow conditions. • Two-phase flow characteristics in vertical pipes are properly predicted. - Abstract: An Eulerian–Eulerian approach was investigated to model adiabatic bubbly flow with CFD techniques. In the framework of the OpenFOAM"® software, a two-fluid model solver was modified to include a population balance equation, solved with the quadrature method of moments approximation to predict upward bubbly flow in vertical pipes considering the polydisperse nature of two-phase flow. Some progress have been made recently solving population balance equations in OpenFOAM"® and this research aims to extend its application to the case of vertical pipes under different conditions of liquid and gas velocities. In order to test the solver for nuclear applications, interfacial forces and bubble induced turbulence models were included to provide to this solver the capability to correctly predict the behavior of the continuous and disperse phases. Two-phase flow experiments with different superficial velocities of gas and liquid are used to validate the model and its implementation. Radial profiles of void fraction, gas and liquid velocities, Sauter mean diameter and turbulence intensity are compared to the computational results. These results are in satisfactory agreement with the experiments, showing the capability of the solver to predict two-phase flow characteristics.
Common approximations for density operators may lead to imaginary entropy
International Nuclear Information System (INIS)
Lendi, K.; Amaral Junior, M.R. do
1983-01-01
The meaning and validity of usual second order approximations for density operators are illustrated with the help of a simple exactly soluble two-level model in which all relevant quantities can easily be controlled. This leads to exact upper bound error estimates which help to select more precisely permissible correlation times as frequently introduced if stochastic potentials are present. A final consideration of information entropy reveals clearly the limitations of this kind of approximation procedures. (Author) [pt
Approximate Integrals of rf-driven Particle Motion in Magnetic Field
International Nuclear Information System (INIS)
Dodin, I.Y.; Fisch, N.J.
2004-01-01
For a particle moving in nonuniform magnetic field under the action of an rf wave, ponderomotive effects result from rf-driven oscillations nonlinearly coupled with Larmor rotation. Using Lagrangian and Hamiltonian formalism, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. Those are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the magnetic field. Under the assumption of non-resonant interaction of the particle with the rf field, these integrals represent adiabatic invariants of the particle motion