Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
The supersymmetric quantization condition is used to study the wave functions of SWKB equivalent -deformed harmonic oscillator which are obtained by using only the knowledge of bound-state spectra of -deformed harmonic oscillator. We have also studied the nonuniqueness of the obtained interactions by this ...
Schunck, N.; Dobaczewski, J.; Satuła, W.; Bączyk, P.; Dudek, J.; Gao, Y.; Konieczka, M.; Sato, K.; Shi, Y.; Wang, X. B.; Werner, T. R.
2017-07-01
We describe the new version (v2.73y) of the code HFODD which solves the nuclear Skyrme Hartree-Fock or Skyrme Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following new features: (i) full proton-neutron mixing in the particle-hole channel for Skyrme functionals, (ii) the Gogny force in both particle-hole and particle-particle channels, (iii) linear multi-constraint method at finite temperature, (iv) fission toolkit including the constraint on the number of particles in the neck between two fragments, calculation of the interaction energy between fragments, and calculation of the nuclear and Coulomb energy of each fragment, (v) the new version 200d of the code HFBTHO, together with an enhanced interface between HFBTHO and HFODD, (vi) parallel capabilities, significantly extended by adding several restart options for large-scale jobs, (vii) the Lipkin translational energy correction method with pairing, (viii) higher-order Lipkin particle-number corrections, (ix) interface to a program plotting single-particle energies or Routhians, (x) strong-force isospin-symmetry-breaking terms, and (xi) the Augmented Lagrangian Method for calculations with 3D constraints on angular momentum and isospin. Finally, an important bug related to the calculation of the entropy at finite temperature and several other little significant errors of the previous published version were corrected.
First, Second Quantization and Q-Deformed Harmonic Oscillator
Van Ngu, Man; Gia Vinh, Ngo; Lan, Nguyen Tri; Thanh, Luu Thi Kim; Viet, Nguyen Ai
2015-06-01
Relations between the first, the second quantized representations and deform algebra are investigated. In the case of harmonic oscillator, the axiom of first quantization (the commutation relation between coordinate and momentum operators) and the axiom of second quantization (the commutation relation between creation and annihilation operators) are equivalent. We shown that in the case of q-deformed harmonic oscillator, a violence of the axiom of second quantization leads to a violence of the axiom of first quantization, and inverse. Using the coordinate representation, we study fine structures of the vacuum state wave function depend in the deformation parameter q. A comparison with fine structures of Cooper pair of superconductivity in the coordinate representation is also performed.
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
surable quantities for known interparticle forces and confronting them with ex- perimental data. In quantum theory [1], the .... the q-numbers take the form. [k] = sin(βk) sin(β) . (7). It is clear that in both cases [k] → k in the limit q → 1. The Hamiltonian of the q-deformed harmonic oscillator [17] is. Hq = p2 q. 2m. +. 1. 2. mω2Q2 q.
Schunck, N.; Dobaczewski, J.; McDonnell, J.; Satuła, W.; Sheikh, J. A.; Staszczak, A.; Stoitsov, M.; Toivanen, P.
2012-01-01
We describe the new version (v2.49t) of the code HFODD which solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogolyubov (HFB) problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented the following physics features: (i) the isospin mixing and projection, (ii) the finite-temperature formalism for the HFB and HF + BCS methods, (iii) the Lipkin translational energy correction method, (iv) the calculation of the shell correction. A number of specific numerical methods have also been implemented in order to deal with large-scale multi-constraint calculations and hardware limitations: (i) the two-basis method for the HFB method, (ii) the Augmented Lagrangian Method (ALM) for multi-constraint calculations, (iii) the linear constraint method based on the approximation of the RPA matrix for multi-constraint calculations, (iv) an interface with the axial and parity-conserving Skyrme-HFB code HFBTHO, (v) the mixing of the HF or HFB matrix elements instead of the HF fields. Special care has been paid to using the code on massively parallel leadership class computers. For this purpose, the following features are now available with this version: (i) the Message Passing Interface (MPI) framework, (ii) scalable input data routines, (iii) multi-threading via OpenMP pragmas, (iv) parallel diagonalization of the HFB matrix in the simplex-breaking case using the ScaLAPACK library. Finally, several little significant errors of the previous published version were corrected. New version program summaryProgram title:HFODD (v2.49t) Catalogue identifier: ADFL_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFL_v3_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public Licence v3 No. of lines in distributed program, including test data, etc.: 190 614 No. of bytes in distributed program, including test data, etc.: 985 898 Distribution
The quantum harmonic oscillator on a circle and a deformed quantum field theory
International Nuclear Information System (INIS)
Rego-Monteiro, M.A.
2001-05-01
We construct a deformed free quantum field theory with an standard Hilbert space based on a deformed Heisenberg algebra. This deformed algebra is a Heisenberg-type algebra describing the first levels of the quantum harmonic oscillator on a circle of large length L. The successive energy levels of this quantum harmonic oscillator on a circle of large length L are interpreted, similarly to the standard quantum one-dimensional harmonic oscillator on an infinite line, as being obtained by the creation of a quantum particle of frequency w at very high energies. (author)
Sang, Nguyen Anh; Thu Thuy, Do Thi; Loan, Nguyen Thi Ha; Lan, Nguyen Tri; Viet, Nguyen Ai
2017-06-01
Using the simple deformed three-level model (D3L model) proposed in our early work, we study the entanglement problem of composite bosons. Consider three first energy levels are known, we can get two energy separations, and can define the level deformation parameter δ. Using connection between q-deformed harmonic oscillator and Morse-like anharmonic potential, the deform parameter q also can be derived explicitly. Like the Einstein’s theory of special relativity, we introduce the observer e˙ects: out side observer (looking from outside the studying system) and inside observer (looking inside the studying system). Corresponding to those observers, the outside entanglement entropy and inside entanglement entropy will be defined.. Like the case of Foucault pendulum in the problem of Earth rotation, our deformation energy level investigation might be useful in prediction the environment e˙ect outside a confined box.
Harmonic oscillator Green's function
International Nuclear Information System (INIS)
Macek, J.H.; Ovchinnikov, S.Yu.; Khrebtukov, D.B.
2000-01-01
The Green's function for the harmonic oscillator in three dimensions plays an important role in the theory of atomic collisions. One representation of low-energy ion-atom collisions involves harmonic oscillator potentials. A closed-form expression for the harmonic oscillator Green's function, needed to exploit this representation, is derived. This expression is similar to the expression for the Coulomb Green's function obtained by Hostler and Pratt. Calculations of electron distributions for a model system of ion-atom collisions are reported to illustrate the theory.
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
The effective harmonic oscillator is constructed variationally, by taking the trial wave function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational para- eters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar ...
Harmonic oscillator and nuclear pseudospin
International Nuclear Information System (INIS)
Lisboa, Ronai; Malheiro, Manuel; Castro, Antonio S. de; Alberto, Pedro; Fiolhais, Manuel
2004-01-01
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ = S + V or Δ = V - S to zero, analytical solutions for bound states are found. The eingenenergies and their nonrelativistic limits are presented and particular cases are discussed, especially the case Σ = 0, for which pseudospin symmetry is exact
Harmonic oscillator on a lattice
International Nuclear Information System (INIS)
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
New construction of coherent states for generalized harmonic oscillators
International Nuclear Information System (INIS)
El Baz, M.; Hassouni, Y.; Madouri, F.
2001-08-01
A dynamical algebra A q , englobing many of the deformed harmonic oscillator algebras is introduced. One of its special cases is extensively developed. A general method for constructing coherent states related to any algebra of the type A q is discussed. The construction following this method is carried out for the special case. (author)
Harmonic oscillator and nuclear pseudospin
International Nuclear Information System (INIS)
Lisboa, Ronai; Malheiro, Manuel; Castro, Antonio S. de; Alberto, Pedro; Fiolhais, M.
2004-01-01
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonians contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U, linear in r. Setting either Σ=S+V or Δ=V - S to zero, analytical solutions for bound states are found. The eigenenergies and their nonrelativistic limits are present and particular cases are discussed, especially the case Σ=0, for which pseudospin symmetry is exact. (author)
Making space for harmonic oscillators
Energy Technology Data Exchange (ETDEWEB)
Michelotti, Leo; /Fermilab
2004-11-01
If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.
Introduction to classical and quantum harmonic oscillators
Bloch, Sylvan C
2013-01-01
From conch shells to lasers . harmonic oscillators, the timeless scientific phenomenon As intriguing to Galileo as they are to scientists today, harmonic oscillators have provided a simple and compelling paradigm for understanding the complexities that underlie some of nature's and mankind's most fascinating creations. From early string and wind instruments fashioned from bows and seashells to the intense precision of lasers, harmonic oscillators have existed in various forms, as objects of beauty and scientific use. And harmonic oscillation has endured as one of science's most fascinating con
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
... a harmonic oscillator eigenfunction with the centroid and width parameter as variational paraeters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in these studies.
Effective harmonic oscillator description of anharmonic molecular ...
Indian Academy of Sciences (India)
Administrator
function as a harmonic oscillator eigenfunction with the centroid and width parameter as variational para- eters. It is found that the effective harmonic oscillator approximation provides a description of the anharmonic eigenstates very similar to the vibrational self consistent field results. Coriolis coupling is also included in ...
Quantum wormholes and harmonic oscillators
Garay, Luis J.
1993-01-01
The quantum state of a wormhole can be represented by a path integral over all asymptotically Euclidean four-geometries and all matter fields which have prescribed values, the arguments of the wave function, on a three-surface which divides the space time manifold into two disconnected parts. Minisuperspace models which consist of a homogeneous massless scalar field coupled to a Friedmann-Robertson-Walker space time are considered. Once the path integral over the lapse function is performed, the requirement that the space time be asymptotically Euclidean can be accomplished by fixing the asymptotic gravitational momentum in the remaining path integral. It is argued that there does not exist any wave function which corresponds to asymptotic field configurations such that the effective gravitational constant is negative in the asymptotic region. Then, the wormhole wave functions can be written as linear combinations of harmonic oscillator wave functions.
Damping of coupled harmonic oscillators
Dolfo, Gilles; Vigué, Jacques
2018-03-01
When two harmonic oscillators are coupled in the presence of damping, their dynamics exhibit two very different regimes depending on the relative magnitude of the coupling and damping terms At resonance, when the coupling has its largest effect, if the coupling dominates the damping, there is a periodic exchange of energy between the two oscillators while, in the opposite case, the energy transfer from one oscillator to the other one is irreversible. We prove that the border between these two regimes goes through an exceptional point and we briefly explain what is an exceptional point. The present paper is written for undergraduate students, with some knowledge in classical mechanics, but it may also be of interest for graduate students.
Pseudospin symmetry and the relativistic harmonic oscillator
International Nuclear Information System (INIS)
Lisboa, R.; Malheiro, M.; Castro, A.S. de; Alberto, P.; Fiolhais, M.
2004-01-01
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar S and a vector V quadratic potentials in the radial coordinate, as well as a tensor potential U linear in r. Setting either or both combinations Σ=S+V and Δ=V-S to zero, analytical solutions for bound states of the corresponding Dirac equations are found. The eigenenergies and wave functions are presented and particular cases are discussed, devoting a special attention to the nonrelativistic limit and the case Σ=0, for which pseudospin symmetry is exact. We also show that the case U=Δ=0 is the most natural generalization of the nonrelativistic harmonic oscillator. The radial node structure of the Dirac spinor is studied for several combinations of harmonic-oscillator potentials, and that study allows us to explain why nuclear intruder levels cannot be described in the framework of the relativistic harmonic oscillator in the pseudospin limit
Stoitsov, M. V.; Schunck, N.; Kortelainen, M.; Michel, N.; Nam, H.; Olsen, E.; Sarich, J.; Wild, S.
2013-06-01
We describe the new version 2.00d of the code HFBTHO that solves the nuclear Skyrme-Hartree-Fock (HF) or Skyrme-Hartree-Fock-Bogoliubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Program summaryProgram title: HFBTHO v2.00d Catalog identifier: ADUI_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUI_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License version 3 No. of lines in distributed program, including test data, etc.: 167228 No. of bytes in distributed program, including test data, etc.: 2672156 Distribution format: tar.gz Programming language: FORTRAN-95. Computer: Intel Pentium-III, Intel Xeon, AMD-Athlon, AMD-Opteron, Cray XT5, Cray XE6. Operating system: UNIX, LINUX, WindowsXP. RAM: 200 Mwords Word size: 8 bits Classification: 17.22. Does the new version supercede the previous version?: Yes Catalog identifier of previous version: ADUI_v1_0 Journal reference of previous version: Comput. Phys. Comm. 167 (2005) 43 Nature of problem: The solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasi-particle wave functions. In the present implementation, this is achieved by using the single-particle wave functions
Second International Workshop on Harmonic Oscillators
Han, Daesoo (Editor); Wolf, Kurt Bernardo (Editor)
1995-01-01
The Second International Workshop on Harmonic Oscillators was held at the Hotel Hacienda Cocoyoc from March 23 to 25, 1994. The Workshop gathered 67 participants; there were 10 invited lecturers, 30 plenary oral presentations, 15 posters, and plenty of discussion divided into the five sessions of this volume. The Organizing Committee was asked by the chairman of several Mexican funding agencies what exactly was meant by harmonic oscillators, and for what purpose the new research could be useful. Harmonic oscillators - as we explained - is a code name for a family of mathematical models based on the theory of Lie algebras and groups, with applications in a growing range of physical theories and technologies: molecular, atomic, nuclear and particle physics; quantum optics and communication theory.
Laguerre polynomials by a harmonic oscillator
Baykal, Melek; Baykal, Ahmet
2014-09-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators.
Laguerre polynomials by a harmonic oscillator
International Nuclear Information System (INIS)
Baykal, Melek; Baykal, Ahmet
2014-01-01
The study of an isotropic harmonic oscillator, using the factorization method given in Ohanian's textbook on quantum mechanics, is refined and some collateral extensions of the method related to the ladder operators and the associated Laguerre polynomials are presented. In particular, some analytical properties of the associated Laguerre polynomials are derived using the ladder operators. (paper)
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
2Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de. Madrid, Spain. E-mail: bbongio@math.unl.edu.ar; joseluis.torrea@uam.es. MS received 27 September 2005. Abstract. We define the Hermite–Sobolev spaces naturally associated to the harmonic oscillator H = − + |x|2. Structural properties ...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
Abstract. We show that in the case of unknown harmonic oscillator coherent states it is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state.
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
article/fulltext/pram/059/02/0263-0267. Keywords. Cloning; coherent states. Abstract. We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that ...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
We show that in the case of unknown harmonic oscillator coherent statesit is possible to achieve what we call perfect information cloning. By this we mean that it is still possible to make arbitrary number of copies of a state which has exactly the same information content as the original unknown coherent state. By making use ...
Perez, R. Navarro; Schunck, N.; Lasseri, R.-D.; Zhang, C.; Sarich, J.
2017-11-01
We describe the new version 3.00 of the code HFBTHO that solves the nuclear Hartree-Fock (HF) or Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the full Gogny force in both particle-hole and particle-particle channels, (ii) the calculation of the nuclear collective inertia at the perturbative cranking approximation, (iii) the calculation of fission fragment charge, mass and deformations based on the determination of the neck, (iv) the regularization of zero-range pairing forces, (v) the calculation of localization functions, (vi) a MPI interface for large-scale mass table calculations. Program Files doi:http://dx.doi.org/10.17632/c5g2f92by3.1 Licensing provisions: GPL v3 Programming language: FORTRAN-95 Journal reference of previous version: M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, and S. Wild, Comput. Phys. Commun. 184 (2013). Does the new version supersede the previous one: Yes Summary of revisions: 1. the Gogny force in both particle-hole and particle-particle channels was implemented; 2. the nuclear collective inertia at the perturbative cranking approximation was implemented; 3. fission fragment charge, mass and deformations were implemented based on the determination of the position of the neck between nascent fragments; 4. the regularization method of zero-range pairing forces was implemented; 5. the localization functions of the HFB solution were implemented; 6. a MPI interface for large-scale mass table calculations was implemented. Nature of problem:HFBTHO is a physics computer code that is used to model the structure of the nucleus. It is an implementation of the energy density functional (EDF) approach to atomic nuclei, where the energy of the nucleus is obtained by integration over space of some phenomenological energy density, which is itself a functional of the neutron and proton
Pisot q-coherent states quantization of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Gazeau, J.P., E-mail: gazeau@apc.univ-paris7.fr [Laboratoire APC, Univ. Paris Diderot, Sorbonne Paris Cite, 75205 Paris (France); Olmo, M.A. del, E-mail: olmo@fta.uva.es [Departamento de Fisica Teorica and IMEVA, Universidad de Valladolid, E-47005, Valladolid (Spain)
2013-03-15
We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories. - Highlights: Black-Right-Pointing-Pointer Quantized version of the harmonic oscillator (HO) through a q-family of coherent states. Black-Right-Pointing-Pointer For q,0
Deformed numbers are Fibonacci-like integer sequences (1/q a quadratic unit Pisot number). Black-Right-Pointing-Pointer We examine the main physical characteristics of the corresponding quantum oscillator.
Non-singular spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Guardiola, R.
1990-01-01
A perturbative study of a class of non-singular spiked harmonic oscillators defined by the hamiltonian H = d sup(2)/dr sup(2) + r sup(2) + λ/r sup(α) in the domain [0,∞] is carried out, in the two extremes of a weak coupling and a strong coupling regimes. A path has been found to connect both expansions for α near 2. (author)
Introduction to Classical and Quantum Harmonic Oscillators
International Nuclear Information System (INIS)
Latal, H
1997-01-01
As the title aptly states, this book deals with harmonic oscillators of various kinds, from classical mechanical and electrical oscillations up to quantum oscillations. It is written in a lively language, and occasional interspersed anecdotes make the reading of an otherwise mathematically oriented text quite a pleasure. Although the author claims to have written an 'elementary introduction', it is certainly necessary to have a good deal of previous knowledge in physics (mechanics, electrodynamics, quantum theory), electrical engineering and, of course, mathematics in order to follow the general line of his arguments. The book begins with a thorough treatment of classical oscillators (free, damped, forced) that is followed by an elaboration on Fourier analysis. Lagrange and Hamilton formalisms are then introduced before the problem of coupled oscillations is attacked. A chapter on statistical perspectives leads over to the final discussion of quantum oscillations. With the book comes a diskette containing a number of worksheets (Microsoft Excel) that can be used by the reader for instant visualization to get a better qualitative and quantitative understanding of the material. To the reviewer it seems difficult to pinpoint exactly the range of prospective readership of the book. It can certainly not be intended as a textbook for students, but rather as a reference book for teachers of physics or researchers, who want to look up one or other aspect of harmonic oscillations, for which purpose the diskette represents a very valuable tool. (book review)
Coupled harmonic oscillators and their quantum entanglement
Makarov, Dmitry N.
2018-04-01
A system of two coupled quantum harmonic oscillators with the Hamiltonian H ̂=1/2 (1/m1p̂1 2+1/m2p̂2 2+A x12+B x22+C x1x2) can be found in many applications of quantum and nonlinear physics, molecular chemistry, and biophysics. The stationary wave function of such a system is known, but its use for the analysis of quantum entanglement is complicated because of the complexity of computing the Schmidt modes. Moreover, there is no exact analytical solution to the nonstationary Schrodinger equation H ̂Ψ =i ℏ ∂/Ψ ∂ t and Schmidt modes for such a dynamic system. In this paper we find a solution to the nonstationary Schrodinger equation; we also find in an analytical form a solution to the Schmidt mode for both stationary and dynamic problems. On the basis of the Schmidt modes, the quantum entanglement of the system under consideration is analyzed. It is shown that for certain parameters of the system, quantum entanglement can be very large.
Discontinuities in a damped quantum harmonic oscillator
International Nuclear Information System (INIS)
Giraldi, Filippo; Petruccione, Francesco
2012-01-01
The quantum model for a damped harmonic oscillator linearly coupled to a reservoir of continuous frequency modes has been exactly diagonalized either with or without the rotating wave approximation. The exact dynamics, formally described in terms of the coupling function, is analyzed for the Drude model. In this scenario, we focus on a class of couplings recovering the Drude form as a limiting case. The exact time evolution of the expectation values of the position, momentum and number operators are described through Fox H-functions, as well as the correlation function of the reservoir. In correspondence with the critical values of the frequency, discontinuities appear in the long time scale dynamics, arbitrarily slowing down the relaxations of the above observables. This effect allows one to enhance arbitrarily the lifetime of the excitations, giving relevant applications in the study of the quantum domain of opto-mechanical and nano-mechanical resonators. The critical frequency approach constitutes a further method of control in the scenario of environment-induced decoherence via reservoir engineering. (paper)
Harmonic oscillator in quantum rotational spectra: Molecules and nuclei
Pavlichenkov, Igor M.
1995-01-01
The mapping of a rotational dynamics on a harmonic oscillator is considered. The method used for studying the stabilization of the rigid top rotation around the intermediate moment of inertial axix by orbiting particle is described.
A harmonic oscillator having “volleyball damping”
Mickens, R. E.; Oyedeji, K.; Rucker, S. A.
2006-05-01
Volleyball damping corresponds to linear damping up to a certain critical velocity, with zero damping above this value. The dynamics of a linear harmonic oscillator is investigated with this damping mechanism.
Harmonic oscillator in an elastic medium with a spiral dislocation
Maia, A. V. D. M.; Bakke, K.
2018-02-01
We investigate the behaviour of a two-dimensional harmonic oscillator in an elastic medium that possesses a spiral dislocation (an edge dislocation). We show that the Schrödinger equation for harmonic oscillator in the presence of a spiral dislocation can be solved analytically. Further, we discuss the effects of this topological defect on the confinement to a hard-wall confining potential. In both cases, we analyse if the effects of the topology of the spiral dislocation gives rise to an Aharonov-Bohm-type effect for bound states.
Predicting charmonium and bottomonium spectra with a quark harmonic oscillator
Norbury, J. W.; Badavi, F. F.; Townsend, L. W.
1986-01-01
The nonrelativistic quark model is applied to heavy (nonrelativistic) meson (two-body) systems to obtain sufficiently accurate predictions of the spin-averaged mass levels of the charmonium and bottomonium spectra as an example of the three-dimensional harmonic oscillator. The present calculations do not include any spin dependence, but rather, mass values are averaged for different spins. Results for a charmed quark mass value of 1500 MeV/c-squared show that the simple harmonic oscillator model provides good agreement with experimental values for 3P states, and adequate agreement for the 3S1 states.
Local Mechanical Behavior of Steel Exposed to Nonlinear Harmonic Oscillation
Cole, D. P.; Habtour, E. M.; Sano, T.; Fudger, S. J.; Grendahl, S. M.; Dasgupta, Anshuman
2017-01-01
The local mechanical behavior of fatigued steel specimens was probed using nanoindentation. High-carbon steel cantilevers were exposed to nonlinear harmonic oscillation. The indentation modulus on the beam surface and plastic work during indentation decreased as a function of cycles, which was
A simple mechanical model for the isotropic harmonic oscillator
International Nuclear Information System (INIS)
Nita, Gelu M
2010-01-01
A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels.
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
The wave function can then be found easily, by making use of these ladder operators. Glauber proposed standard coherent states for a harmonic oscillator which is the prototype for most of the coherent states [3,4]. The coherent states form a very convenient representation for problems of quantum mechanics and can be ...
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Taking advantage of dynamical invariant operator, we derived quantum mechanical solution of general time-dependent harmonic oscillator. ... The domain part of the email address of all email addresses used by the office of Indian Academy of Sciences, including those of the staff, the journals, various programmes, and ...
A new analytical approximation to the Duffing-harmonic oscillator
International Nuclear Information System (INIS)
Fesanghary, M.; Pirbodaghi, T.; Asghari, M.; Sojoudi, H.
2009-01-01
In this paper, a novel analytical approximation to the nonlinear Duffing-harmonic oscillator is presented. The variational iteration method (VIM) is used to obtain some accurate analytical results for frequency. The accuracy of the results is excellent in the whole range of oscillation amplitude variations.
Coherent states of general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Abstract. By introducing an invariant operator, we obtain exact wave functions for a general time-dependent quadratic harmonic oscillator. The coherent states, both in x- and p-spaces, are calculated. We confirm that the uncertainty product in coherent state is always larger than Η/2 and is equal to the minimum of the ...
The forced harmonic oscillator with damping and thermal effects
International Nuclear Information System (INIS)
Menezes Franca, H. de; Thomaz, M.T.
1984-01-01
Nonperturbative quantum mechanical solutions of the forced harmonic oscillator with radiation reaction damping are obtained from previous analysis based on Stochastic Electrodynamics. The transition to excited states is shown to be to coherent states which follow the classical trajectory. The quantum Wigner distribution in phase space is constructed. All the results are extended to finite temperatures. (Author) [pt
Statistical mechanics of quantum one-dimensional damped harmonic oscillator
International Nuclear Information System (INIS)
Borges, E.N.M.; Borges, O.N.; Ribeiro, L.A.A.
1985-01-01
We calculate the thermal correlation functions of the one-dimensional damped harmonic oscillator in contact with a reservoir, in an exact form by applying Green's function method. In this way the thermal fluctuations are incorporated in the Caldirola-Kanai Hamiltonian
The resonating group method in an harmonic oscillator basis
International Nuclear Information System (INIS)
Silvestre-Brac, B.; Gignoux, C.; Ayant, Y.
1987-05-01
The scattering states for a general many body system is formulated within the resonating group method. The resulting Lippman-Schwinger equation is solved in an harmonic oscillator basis for which a number of advantages are emphasized. The analytical formula giving the free propagator in that basis is fully derived
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
Departamento de Fısica, Facultad de Ciencias, Universidad de Tarapacá, Casilla 7-D,. Arica, Chile. E-mail: cleivas@uta.cl; cleivas2008@live.cl. MS received 18 August 2009; revised 20 October 2009; accepted 27 October 2009. Abstract. The harmonic oscillator in Snyder space is investigated in its classical and quantum ...
Maximal Regularity of the Discrete Harmonic Oscillator Equation
Directory of Open Access Journals (Sweden)
Airton Castro
2009-01-01
Full Text Available We give a representation of the solution for the best approximation of the harmonic oscillator equation formulated in a general Banach space setting, and a characterization of lp-maximal regularity—or well posedness—solely in terms of R-boundedness properties of the resolvent operator involved in the equation.
Two-dimensional generalized harmonic oscillators and their Darboux partners
International Nuclear Information System (INIS)
Schulze-Halberg, Axel
2011-01-01
We construct two-dimensional Darboux partners of the shifted harmonic oscillator potential and of an isotonic oscillator potential belonging to the Smorodinsky–Winternitz class of superintegrable systems. The transformed solutions, their potentials and the corresponding discrete energy spectra are computed in explicit form. (paper)
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
no difficulty to accommodate them. This observation tend to present one of the main difficulties in applying Noether's theorem on the damped harmonic oscillator. Being nonself-adjoint (1) does not satisfy the Helmholtz criterion [4] to have a. Lagrangian representation. However, multiplying (1) by eλt we can convert it to.
On quantum harmonic oscillator being subjected to absolute
Indian Academy of Sciences (India)
In a quantum harmonic oscillator (QHO), the energy of the oscillator increases with increased frequency. In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing ...
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the ...
Free Fall and Harmonic Oscillations: Analyzing Trampoline Jumps
Pendrill, Ann-Marie; Eager, David
2015-01-01
Trampolines can be found in many gardens and also in some playgrounds. They offer an easily accessible vertical motion that includes free fall. In this work, the motion on a trampoline is modelled by assuming a linear relation between force and deflection, giving harmonic oscillations for small amplitudes. An expression for the cycle-time is…
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
The harmonic oscillator in Snyder space is investigated in its classical and quantum versions. The classical trajectory is obtained and the semiclassical quantization from the phase space trajectories is discussed. An effective cut-off to high frequencies is found. The quantum version is developed and an equivalent usual ...
Thermal state of the general time-dependent harmonic oscillator
Indian Academy of Sciences (India)
Harmonic oscillator that has time-dependent mass or frequency may be a good example of time-dependent Hamiltonian systems. Although a large number of dynamical systems have been investigated using approximation and perturbation method in the literature [2,3], we confine our concern to the exact quantum solution ...
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... Phase-space treatment of the driven quantum harmonic oscillator. DIÓGENES CAMPOS1,2,∗. 1Universidad La Gran .... whereas some other treatments deal with the coordi- nate representation of the Schrödinger ...... Im[ +(q,p,t)] a structure of leaves that gradually appears over time and, for the values of (q ...
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
On quantum harmonic oscillator being subjected to absolute potential state. SWAMI NITYAYOGANANDA. Ramakrishna Mission Ashrama, R.K. Beach, Visakhapatnam 530 003, India. E-mail: nityayogananda@gmail.com. MS received 1 May 2015; accepted 6 May 2016; published online 3 December 2016. Abstract.
Quantum theory of damped harmonic oscillator | Antia | Global ...
African Journals Online (AJOL)
The exact solutions of the Schrödinger equation for damped harmonic oscillator with pulsating mass and modified Caldirola-Kanai Hamiltonian are evaluated. We also investigated the case of under-damped for the two models constructed and the results obtained in both cases do not violate Heisenberg uncertainty principle ...
Parametric Resonance in a Time-Dependent Harmonic Oscillator
Directory of Open Access Journals (Sweden)
P. N. Nesterov
2013-01-01
Full Text Available In this paper, we study the phenomenon of appearance of new resonances in a timedependent harmonic oscillator under an oscillatory decreasing force. The studied equation belongs to the class of adiabatic oscillators and arises in connection with the spectral problem for the one-dimensional Schr¨odinger equation with Wigner–von Neumann type potential. We use a specially developed method for asymptotic integration of linear systems of differential equations with oscillatory decreasing coefficients. This method uses the ideas of the averaging method to simplify the initial system. Then we apply Levinson’s fundamental theorem to get the asymptotics for its solutions. Finally, we analyze the features of a parametric resonance phenomenon. The resonant frequencies of perturbation are found and the pointwise type of the parametric resonance phenomenon is established. In conclusion, we construct an example of a time-dependent harmonic oscillator (adiabatic oscillator in which the parametric resonances, mentioned in the paper, may occur.
Controllability in tunable chains of coupled harmonic oscillators
DEFF Research Database (Denmark)
Buchmann, Lukas Filip; Mølmer, Klaus; Petrosyan, David
2018-01-01
any desired Gaussian state requires at most 3 N ( N −1)/2 operations. We illustrate this capability by engineering squeezed pseudo-phonon states—highly nonlocal, strongly correlated states that may result from various nonlinear processes. Tunable chains of coupled harmonic oscillators can......We prove that temporal control of the strengths of springs connecting N harmonic oscillators in a chain provides complete access to all Gaussian states of N −1 collective modes. The proof relies on the construction of a suitable basis of cradle modes for the system. An iterative algorithm to reach...... be implemented by a number of current state-of-the-art experimental platforms, including cold atoms in lattice potentials, arrays of mechanical micro-oscillators, and coupled optical waveguides....
Variational and perturbative schemes for a spiked harmonic oscillator
International Nuclear Information System (INIS)
Aguilera-Navarro, V.C.; Estevez, G.A.; Guardiola, R.
1989-01-01
A variational analysis of the spiked harmonic-oscillator Hamiltonian operator -d 2 /dx 2 + x 2 + l(l+1)/x 2 + λ |x| -α , where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schroedinger equation for the linear harmonic-oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provides accurate approximations for the ground-state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large-coupling pertubative-expansion is carried out and the contributions up to fourth order to the ground-state energy are explicitly evaluated. Numerical results are compared for the special case α=5/2. (author) [pt
Driven damped harmonic oscillator resonance with an Arduino
Goncalves, A. M. B.; Cena, C. R.; Bozano, D. F.
2017-07-01
In this paper we propose a simple experimental apparatus that can be used to show quantitative and qualitative results of resonance in a driven damped harmonic oscillator. The driven oscillation is made by a servo motor, and the oscillation amplitude is measured by an ultrasonic position sensor. Both are controlled by an Arduino board. The frequency of free oscillation measured was campatible with the resonance frequency that was measured.
Coherent and squeezed states for the 3D harmonic oscillator
Mazouz, Amel; Bentaiba, Mustapha; Mahieddine, Ali
2017-01-01
A three-dimensional harmonic oscillator is studied in the context of generalized coherent states. We construct its squeezed states as eigenstates of linear contribution of ladder operators which are associated to the generalized Heisenberg algebra. We study the probability density to show the compression effect on the squeezed states. Our analysis reveals that squeezed states give us some freedom on the precise knowledge of position of the particle while maintaining the Heisenberg uncertainty relation minimum, squeezed states remains squeezed states over time.
An analogue of the Berry phase for simple harmonic oscillators
Suslov, S. K.
2013-03-01
We evaluate a variant of Berry's phase for a ‘missing’ family of the square integrable wavefunctions for the linear harmonic oscillator, which cannot be derived by the separation of variables (in a natural way). Instead, it is obtained by the action of the maximal kinematical invariance group on the standard solutions. A simple closed formula for the phase (in terms of elementary functions) is found here by integration with the help of a computer algebra system.
Rabi oscillation between states of a coupled harmonic oscillator
International Nuclear Information System (INIS)
Park, Tae Jun
2003-01-01
Rabi oscillation between bound states of a single potential is well known. However the corresponding formula between the states of two different potentials has not been obtained yet. In this work, we derive Rabi formula between the states of a coupled harmonic oscillator which may be used as a simple model for the electron transfer. The expression is similar to typical Rabi formula for a single potential. This result may be used to describe transitions between coupled diabatic potential curves
Spectral inverse problem for q-deformed harmonic oscillator
Indian Academy of Sciences (India)
perimental data. In quantum theory [1], the spectral inverse problem consists of determining the interparticle forces from the information obtained more or less di- rectly by experiments. Studies along this line have continued and we are convinced that these will be continued both at sophisticated and pedagogical levels [2].
Energy Technology Data Exchange (ETDEWEB)
Arcos-Olalla, Rafael, E-mail: olalla@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Reyes, Marco A., E-mail: marco@fisica.ugto.mx [Departamento de Física, DCI Campus León, Universidad de Guanajuato, Apdo. Postal E143, 37150 León, Gto. (Mexico); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo. Postal 3-74 Tangamanga, 78231 San Luis Potosí, S.L.P. (Mexico)
2012-10-01
We introduce an alternative factorization of the Hamiltonian of the quantum harmonic oscillator which leads to a two-parameter self-adjoint operator from which the standard harmonic oscillator, the one-parameter oscillators introduced by Mielnik, and the Hermite operator are obtained in certain limits of the parameters. In addition, a single Bernoulli-type parameter factorization, which is different from the one introduced by M.A. Reyes, H.C. Rosu, and M.R. Gutiérrez [Phys. Lett. A 375 (2011) 2145], is briefly discussed in the final part of this work. -- Highlights: ► Factorizations with operators which are not mutually adjoint are presented. ► New two-parameter and one-parameter self-adjoint oscillator operators are introduced. ► Their eigenfunctions are two- and one-parameter deformed Hermite functions.
International Nuclear Information System (INIS)
Lewis, Zachary; Takeuchi, Tatsu
2011-01-01
We analyze the position and momentum uncertainties of the energy eigenstates of the harmonic oscillator in the context of a deformed quantum mechanics, namely, that in which the commutator between the position and momentum operators is given by [x-circumflex,p-circumflex]=i(ℎ/2π)(1+βp-circumflex 2 ). This deformed commutation relation leads to the minimal length uncertainty relation Δx≥((ℎ/2π)/2)(1/Δp+βΔp), which implies that Δx∼1/Δp at small Δp while Δx∼Δp at large Δp. We find that the uncertainties of the energy eigenstates of the normal harmonic oscillator (m>0), derived in L. N. Chang, D. Minic, N. Okamura, and T. Takeuchi, Phys. Rev. D 65, 125027 (2002), only populate the Δx∼1/Δp branch. The other branch, Δx∼Δp, is found to be populated by the energy eigenstates of the 'inverted' harmonic oscillator (m min =(ℎ/2π)√(β)>√(2)[(ℎ/2π) 2 /k|m|] 1/4 . Correspondence with the classical limit is also discussed.
Harmonic oscillator states with integer and non-integer orbital angular momentum
International Nuclear Information System (INIS)
Land, Martin
2011-01-01
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as basis states for representing their respective symmetry groups — O(2), O(1,1), O(3), and O(2,1). The goal of this study is to establish a correspondence between Hilbert space descriptions found by solving the Schrodinger equation in polar coordinates, and Fock space descriptions constructed by expressing the symmetry operators in terms of creation/annihilation operators. We obtain wavefunctions characterized by a principal quantum number, the group Casimir eigenvalue, and one group generator whose eigenvalue is m + s, for integer m and real constant parameter s. For the three groups that contain O(2), the solutions split into two inequivalent representations, one associated with s = 0, from which we recover the familiar description of the oscillator as a product of one-dimensional solutions, and the other with s > 0 (in three dimensions, solutions are found for s = 0 and s = 1/2) whose solutions are non-separable in Cartesian coordinates, and are hence overlooked by the standard Fock space approach. The O(1,1) solutions are singlet states, restricted to zero eigenvalue of the symmetry operator, which represents the boost, not angular momentum. For O(2), a single set of creation and annihilation operators forms a ladder representation for the allowed oscillator states for any s, and the degeneracy of energy states is always finite. However, in three dimensions, the integer and half-integer eigenstates are qualitatively different: the former can be expressed as finite dimensional irreducible tensors under O(3) or O(2,1) while the latter exhibit infinite degeneracy. Creation operators that produce the allowed integer states by acting on the non-degenerate ground state are constructed as irreducible tensor products of the fundamental vector representation. However, the half-integer eigenstates are infinite-dimensional, as expected for the non
Studies on phase and squeezed states of quantum harmonic oscillators
International Nuclear Information System (INIS)
Ma, Xin.
1989-01-01
A fundamental quantum-mechanical problem on the phase of quantum harmonic oscillators, which has remained an enigma for more than sixty years since the first treatment by Dirac, is completely solved. Contrary to the common belief that no Hermitian phase operators can be found to describe the phase properties of a quantum harmonic oscillator, a well-defined Hermitian phase operator with an appropriate classical limit is constructed unambiguously. The approach is different in nature from those of many previous attempts which were more or less based on the idea of polar decomposition of the annihilation operator. The fundamental difference between the quantum phase and the classical phase in spite of their conceptual consistency is pointed out and explained. The eigenvalue spectrum and eigenstates of the phase operator are obtained. Some important properties of the phase operator and phase states are investigated. The rest of this research is devoted to the studies of multimode Gaussian squeezed states of quantum harmonic oscillators. Multimode squeeze operators and rotation operators are defined such that they have extremely similar algebraic properties as those of their single-mode counterparts. It is shown that the introduction of N-mode squeeze operators provides a convenient set of parameters to describe squeezing in multimode Gaussian squeezed states. The disentangling, normal ordering, and some other properties of N-mode squeeze operators are investigated. It is also shown that the time-evolution operator for a general N-mode quadratic Hamiltonian can be conveniently expressed as an operator product containing an N-mode squeeze operator, an N-mode rotation operator, and an N-mode displacement operator
Complex-potential description of the damped harmonic oscillator
International Nuclear Information System (INIS)
Exner, P.
1981-01-01
Multidimensional damped harmonic oscillator is treated by means of a non-selfadjoint Hamiltonian with complex potential. The latter is chosen as V(x)=xx(A-iW)x with positive matrices A, W, By a perturbation-theory argument, the corresponding Hamiltonian H=-1/2Δ+V with the natural domain is shown to be closed and such that Vsub(t)=exp(-iHt) is a continuous contractive semigroup. Explicit integral-operator form of Vsub(t) is found by use of Lie-Trotter formula [ru
Nonlinear analysis of a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2005-01-01
The dynamic equations governing the cross-coupled quadrature harmonic oscillator are derived assuming quasi-sinusoidal operation. This allows for an investigation of the previously reported tradeoff between close-to-carrier phase noise and quadrature precision. The results explain how nonlinearity...... in the coupling transconductances, in conjunction with a finite amplitude relaxation time and de-tuning of the individual oscillators, cause close-to-carrier AM-to-PM noise conversion. A discussion is presented of how the theoretic results translate into design rules for quadrature oscillator ICs. SPECTRE RF...
Elementary derivation of the quantum propagator for the harmonic oscillator
Shao, Jiushu
2016-10-01
Operator algebra techniques are employed to derive the quantum evolution operator for the harmonic oscillator. The derivation begins with the construction of the annihilation and creation operators and the determination of the wave function for the coherent state as well as its time-dependent evolution, and ends with the transformation of the propagator in a mixed position-coherent-state representation to the desired one in configuration space. Throughout the entire procedure, besides elementary operator manipulations, it is only necessary to solve linear differential equations and to calculate Gaussian integrals.
Brownian motion with adhesion: harmonic oscillator with fluctuating mass.
Gitterman, M; Klyatskin, V I
2010-05-01
In contrast to the cases usually studied of a harmonic oscillator subject to a random force (Brownian motion) or having random frequency or random damping, we consider a random mass which corresponds to an oscillator for which the particles of the surrounding medium adhere to it for some (random) time after the collision, thereby changing the oscillator mass. This model, which describes Brownian motion with adhesion, can be useful for the analysis of chemical and biological solutions as well as nanotechnological devices. We consider dichotomous noise and its limiting case, white noise.
The Aerodynamic Behavior of a Harmonically Oscillating Finite Sweptback Wing in Supersonic Flow
National Research Council Canada - National Science Library
Chang, Chieh-Chien
1951-01-01
By an extension of Evvard's "diaphragm" concept outside the wing tip, the present paper presents two approximate methods for calculating the aerodynamic behavior of harmonically oscillating, sweptback...
Dissipative quantum trajectories in complex space: Damped harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Chou, Chia-Chun, E-mail: ccchou@mx.nthu.edu.tw
2016-10-15
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
Exact solution of a quantum forced time-dependent harmonic oscillator
Yeon, Kyu Hwang; George, Thomas F.; Um, Chung IN
1992-01-01
The Schrodinger equation is used to exactly evaluate the propagator, wave function, energy expectation values, uncertainty values, and coherent state for a harmonic oscillator with a time dependent frequency and an external driving time dependent force. These quantities represent the solution of the classical equation of motion for the time dependent harmonic oscillator.
The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach
Lee, Keeyung
2009-01-01
The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…
Fundamental and Harmonic Oscillations in Neighboring Coronal Loops
Li, Hongbo; Liu, Yu; Vai Tam, Kuan
2017-06-01
We present observations of multimode (fundamental and harmonic) oscillations in a loop system, which appear to be simultaneously excited by a GOES C-class flare. Analysis of the periodic oscillations reveals that (1) the primary loop with a period of P a ≈ 4 minutes and a secondary loop with two periods of P a ≈ 4 minutes and P b ≈ 2 minutes are detected simultaneously in closely spaced loop strands; (2) both oscillation components have their peak amplitudes near the loop apex, while in the second loop the low-frequency component P a dominates in a loop segment that is two times larger than the high-frequency component P b ; (3) the harmonic mode P b shows the largest deviation from a sinusoidal loop shape at the loop apex. We conclude that multiple harmonic modes with different displacement profiles can be excited simultaneously even in closely spaced strands, similar to the overtones of a violin string.
High spin rotations of nuclei with the harmonic oscillator potential
International Nuclear Information System (INIS)
Cerkaski, M.; Szymanski, Z.
1978-01-01
Calculations of the nuclear properties at high angular momentum have been performed recently. They are based on the liquid drop model of a nucleus and/or on the assumption of the single particle shell structure of the nucleonic motion. The calculations are usually complicated and involve long computer codes. In this article we shall discuss general trends in fast rotating nuclei in the approximation of the harmonic oscillator potential. We shall see that using the Bohr Mottelson simplified version of the rigorous solution of Valatin one can perform a rather simple analysis of the rotational bands, structure of the yrast line, moments of inertia etc. in the rotating nucleus. While the precision fit to experimental data in actual nuclei is not the purpose of this paper, one can still hope to reach some general understanding within the model of the simple relations resulting in nuclei at high spin. (author)
A method of solving simple harmonic oscillator Schroedinger equation
Maury, Juan Carlos F.
1995-01-01
A usual step in solving totally Schrodinger equation is to try first the case when dimensionless position independent variable w is large. In this case the Harmonic Oscillator equation takes the form (d(exp 2)/dw(exp 2) - w(exp 2))F = 0, and following W.K.B. method, it gives the intermediate corresponding solution F = exp(-w(exp 2)/2), which actually satisfies exactly another equation, (d(exp 2)/dw(exp 2) + 1 - w(exp 2))F = 0. We apply a different method, useful in anharmonic oscillator equations, similar to that of Rampal and Datta, and although it is slightly more complicated however it is also more general and systematic.
Spontaneous decoherence of coupled harmonic oscillators confined in a ring
Gong, ZhiRui; Zhang, ZhenWei; Xu, DaZhi; Zhao, Nan; Sun, ChangPu
2018-04-01
We study the spontaneous decoherence of coupled harmonic oscillators confined in a ring container, where the nearest-neighbor harmonic potentials are taken into consideration. Without any external symmetry-breaking field or surrounding environment, the quantum superposition state prepared in the relative degrees of freedom gradually loses its quantum coherence spontaneously. This spontaneous decoherence is interpreted by the gauge couplings between the center-of-mass and the relative degrees of freedoms, which actually originate from the symmetries of the ring geometry and the corresponding nontrivial boundary conditions. In particular, such spontaneous decoherence does not occur at all at the thermodynamic limit because the nontrivial boundary conditions become the trivial Born-von Karman boundary conditions when the perimeter of the ring container tends to infinity. Our investigation shows that a thermal macroscopic object with certain symmetries has a chance for its quantum properties to degrade even without applying an external symmetry-breaking field or surrounding environment.
Spectral theory of non-commutative harmonic oscillators an introduction
Parmeggiani, Alberto
2010-01-01
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Modeling stock return distributions with a quantum harmonic oscillator
Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.
2017-11-01
We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Torres del Castillo, G.F. [Departamento de Fisica Matematica, Instituto de Ciencias, Universidad Autonoma de Puebla, 72570 Puebla (Mexico); Tepper G, T. [Escuela de Ciencias, Departamento de Fisica y Matematicas, Universidad de Las Americas-Puebla, Santa Catarina Martir, 72820 Cholula, Puebla (Mexico)
2002-07-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Supersymmetry and the constants of motion of the two-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Torres del Castillo, G.F.; Tepper G, T.
2002-01-01
It is shown that the constants of motion of the two-dimensional isotropic harmonic oscillator not related to the rotational invariance of the Hamiltonian can be derived using the ideas of supersymmetric quantum mechanics. (Author)
Study of the phase delay in the amplitude-modulated harmonic oscillator
International Nuclear Information System (INIS)
Krupska, Aldona; Krupski, Marcin
2003-01-01
The delayed response of a damped harmonic oscillator (RLC circuit) to a slow periodic disturbance is presented. This communication is supplementary to the paper published recently (Krupska et al 2001 Eur. J. Phys. 22 133-8)
Meson spectra with a harmonic-oscillator potential in the Klein-Gordon equation
International Nuclear Information System (INIS)
Ram, B.; Halasa, R.
1979-01-01
Meson masses are calculated using a harmonic-oscillator potential in the Klein-Gordon equation, and compared with those from a linear potential. Values of the transmission coefficient are also given for both cases
Exact diagonalization of the D-dimensional spatially confined quantum harmonic oscillator
Directory of Open Access Journals (Sweden)
Kunle Adegoke
2016-01-01
Full Text Available In the existing literature various numerical techniques have been developed to quantize the confined harmonic oscillator in higher dimensions. In obtaining the energy eigenvalues, such methods often involve indirect approaches such as searching for the roots of hypergeometric functions or numerically solving a differential equation. In this paper, however, we derive an explicit matrix representation for the Hamiltonian of a confined quantum harmonic oscillator in higher dimensions, thus facilitating direct diagonalization.
Quantum dynamics of deformed open systems
Isar, A
2002-01-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model using perturbation theory . The coefficient of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is obtained and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation. (author)
SOLUTION OF HARMONIC OSCILLATOR OF NONLINEAR MASTER SCHRÃ–DINGER
Directory of Open Access Journals (Sweden)
T B Prayitno
2012-02-01
Full Text Available We have computed the solution of a nonrelativistic particle motion in a harmonic oscillator potential of the nonlinear master SchrÃ¶dinger equation. The equation itself is based on two classical conservation laws, the Hamilton-Jacobi and the continuity equations. Those two equations give each contribution for the definition of quantum particle. We also prove that the solution canâ€™t be normalized. Â Keywords : harmonic oscillator, nonlinear SchrÃ¶dinger.
Parnis, J. Mark; Thompson, Matthew G. K.
2004-01-01
An introductory undergraduate physical organic chemistry exercise that introduces the harmonic oscillator's use in vibrational spectroscopy is developed. The analysis and modeling exercise begins with the students calculating the stretching modes of common organic molecules with the help of the quantum mechanical harmonic oscillator (QMHO) model.
Barragán-Gil, L. F.; Walser, R.
2018-01-01
A first-order partial differential equation is derived whose solution enables us to find straightforwardly the off-diagonal matrix elements in the position representation of the harmonic oscillator density operator. This approach constitutes an alternative to techniques that require advanced knowledge of mathematical and quantum mechanical results.
On the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
Czech Academy of Sciences Publication Activity Database
Novák, Radek
2015-01-01
Roč. 54, č. 11 (2015), s. 4142-4153 ISSN 0020-7748 R&D Projects: GA ČR(CZ) GA14-06818S Institutional support: RVO:61389005 Keywords : pseudospectrum * harmonic oscillator * imaginary qubic potential * PT-symmetry * semiclassical method Subject RIV: BE - Theoretical Physics Impact factor: 1.041, year: 2015
Experiment on Impulsive Excitation, Resonance, and Fourier Analysis of a Harmonic Oscillator.
Macomber, Hilliard K.
1981-01-01
Describes an electric circuit permitting easy observation and measurement of the response of a damped harmonic oscillator to impulsive excitation. The impulse analysis is carried out and related to experimental observations. The phenomenon of resonance is then interpreted and demonstrated, and through it, contact is made with Fourier analysis.…
Root System of Singular Perturbations of the Harmonic Oscillator Type Operators
Czech Academy of Sciences Publication Activity Database
Mityagin, B.; Siegl, Petr
2016-01-01
Roč. 106, č. 2 (2016), s. 147-167 ISSN 0377-9017 Institutional support: RVO:61389005 Keywords : non-self-adjoint operators * harmonic oscillator * Riesz basis * quadratic forms * singular petentials Subject RIV: BE - Theoretical Physics Impact factor: 1.671, year: 2016
The study of entanglement and teleportation of the harmonic oscillator bipartite coherent states
Directory of Open Access Journals (Sweden)
A Rabeie and
2015-01-01
Full Text Available In this paper, we reproduce the harmonic oscillator bipartite coherent states with imperfect cloning of coherent states. We show that if these entangled coherent states are embedded in a vacuum environment, their entanglement is degraded but not totally lost . Also, the optimal fidelity of these states is worked out for investigating their teleportation
Isar, A.
2004-09-01
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is obtained in the microscopic model, using perturbation theory. The coefficients of the master equation depend on the deformation function. The steady state solution of the equation for the density matrix in the number representation is derived and the equilibrium energy of the deformed harmonic oscillator is calculated in the approximation of small deformation. Note from Publisher: This article contains the abstract and references only.
DEFF Research Database (Denmark)
Nørrelykke, Simon F; Flyvbjerg, Henrik
2011-01-01
The stochastic dynamics of the damped harmonic oscillator in a heat bath is simulated with an algorithm that is exact for time steps of arbitrary size. Exact analytical results are given for correlation functions and power spectra in the form they acquire when computed from experimental time...... to the extent that it is interpreted as a damped harmonic oscillator at finite temperature-such as an AFM cantilever. (iii) Three other models of fundamental interest are limiting cases of the damped harmonic oscillator at finite temperature; it consequently bridges their differences and describes the effects...
Energy Technology Data Exchange (ETDEWEB)
Rosu, H.C., E-mail: hcr@ipicyt.edu.mx [IPICyT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosi, S.L.P. (Mexico); Khmelnytskaya, K.V. [Universidad Autonoma de Queretaro, Centro Universitario, Cerro de las Campanas s/n, C.P. 76010 Santiago de Queretaro, Qro. (Mexico)
2011-09-19
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant shift of the Riccati solution of the classical harmonic oscillator. The mathematical results show that some of these oscillators could be of physical nature. We give the solutions of the obtained second-order differential equations and the values of the shift parameter providing strictly periodic and antiperiodic solutions. We also notice that this simple problem presents parity-time (PT) symmetry. Possible applications are mentioned. -- Highlights: → A particular Riccati solution of the classical harmonic oscillator is shifted by a constant. → Such a solution is used in the factorization brackets to get different equations of motion. → The properties of the parametric oscillators obtained in this way are examined.
Harmonic-oscillator pattern arising from an algebraic approach to chiral symmetry
Buccella, F; Savoy, C A
1972-01-01
The Weinberg equation for the (mass)/sup 2/ operator (Q/sub 5//sup +/, (Q/sub 5//sup +/, m/sup 2/))=0, between meson states, is saturated in a perturbative approach. The generator Z of the mixing operators is completely established as Z=(W*M)/sub z/, where W is the W-spin operator and M is the co-ordinate of the three-dimensional harmonic oscillator. In a perturbative expansion of the (mass)/sup 2/ operator, the lowest term consists of two parts, the harmonic-oscillator energy and a spin-orbit coupling of the form (-1)/sup L+1/(L.S+/sup 1///sub 2 /). The resulting (mass)/sup 2/ consists of families of equispaced linearly rising trajectories. (11 refs).
Non-isospectrality of the generalized Swanson Hamiltonian and harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Midya, Bikashkali; Dube, P P; Roychoudhury, Rajkumar, E-mail: bikash.midya@gmail.com, E-mail: ppdube1@gmail.com, E-mail: raj@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108 (India)
2011-02-11
The generalized Swanson Hamiltonian H{sub GS}=w(a-tilde a-tilde{sup {dagger}}+1/2)+{alpha}{alpha}-tilde{sup 2}+{beta}a-tilde{sup {dagger}}{sup 2} with a-tilde = A(x) d/dx + B(x) can be transformed into an equivalent Hermitian Hamiltonian with the help of a similarity transformation. It is shown that the equivalent Hermitian Hamiltonian can be further transformed into the harmonic oscillator Hamiltonian so long as [a-ilde,a-tilde{sup {dagger}}]=constant. However, the main objective of this communication is to show that though the commutator of a-tilde and a-tilde{sup {dagger}} is constant, the generalized Swanson Hamiltonian is not necessarily isospectral to the harmonic oscillator. The reason for this anomaly is discussed in the framework of position-dependent mass models by choosing A(x) as the inverse square root of the mass function. (fast track communication)
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials, which grow at spatial infinity slower than quadratic, but faster than linear functions, and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with the algebraic growth rate, which increases indefinitely, when the growth rate of perturbations at infinity decrease from the near quadratic to the near linear ones....
Spatial growth of fundamental solutions for certain perturbations of the harmonic oscillator
DEFF Research Database (Denmark)
Jensen, Arne; Yajima, Kenji
2010-01-01
We consider the fundamental solution for the Cauchy problem for perturbations of the harmonic oscillator by time dependent potentials which grow at spatial infinity slower than quadratic but faster than linear functions and whose Hessian matrices have a fixed sign. We prove that the fundamental...... solution at resonant times grows indefinitely at spatial infinity with an algebraic growth rate, which increases indefinitely when the growth rate of perturbations at infinity decreases from the near quadratic to the near linear ones....
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Müller H.
2009-01-01
Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spect...
The adiabatic invariant of the n-degree-of-freedom harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Devaud, M; Bacri, J-C; Hocquet, T [Laboratoire Matiere et Systemes Complexes, Universite Paris 7 and CNRS UMR 7057, 10 rue Alice Domon et Leonie Duquet, 75013 Paris (France); Leroy, V [Laboratoire Ondes et Acoustique, Universite Paris 7 and CNRS UMR 7587, ESPCI, 10 rue Vauquelin, 75005 Paris (France)], E-mail: Thierry.Hocquet@upmc.fr
2008-07-15
In this graduate-level theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with this simplest result: the oscillator's adiabatic invariant is just the sum of all the semiclassical quanta numbers associated with its different eigenmodes.
Directory of Open Access Journals (Sweden)
P. A. Deymier
2016-12-01
Full Text Available We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.
Generalized Lyapunov exponents of the random harmonic oscillator: Cumulant expansion approach
Vallejos, Raúl O.; Anteneodo, Celia
2012-02-01
The cumulant expansion is used to estimate generalized Lyapunov exponents of the random-frequency harmonic oscillator. Three stochastic processes are considered: Gaussian white noise, Ornstein-Uhlenbeck, and Poisson shot noise. In some cases, nontrivial numerical difficulties arise. These are mostly solved by implementing an appropriate importance-sampling Monte Carlo scheme. We analyze the relation between random-frequency oscillators and many-particle systems with pairwise interactions like the Lennard-Jones gas.
Daoud, M.; Jellal, A.; Choubabi, E. B.; El Kinani, E. H.
2011-08-01
We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.
Daoud, M.; Jellal, A.; Choubabi, E. B.; Kinani, E. H. El
2012-01-01
We introduce a special class of truncated Weyl-Heisenberg algebra and discuss the corresponding Hilbertian and analytical representations. Subsequently, we study the effect of a quantum network of beam splitting on coherent states of this nonlinear class of harmonic oscillators. We particularly focus on quantum networks involving one and two beam splitters and examine the degree of bipartite as well as tripartite entanglement using the linear entropy.
A non-orthogonal harmonic-oscillator basis for three-body problems
International Nuclear Information System (INIS)
Agrello, D.A.; Aguilera-Navarro, V.C.; Chacon, E.
1979-01-01
A set of harmonic-oscillator states suitable for the representation of the wave function of the bound states of a system of three identical particles, is presented. As an illustration of the possibilities of the states defined in this paper, they are applied in a variational determination of the lowest symmetric S state of 12 C, in the model of three structureless α particles interacting through the Coulomb force plus a phenomenological two-body force. (author) [pt
Wang, Fei; Nie, Wei; Feng, Xunli; Oh, C. H.
2016-07-01
The correlated emission lasing (CEL) is experimentally demonstrated in harmonic oscillators coupled via a single three-level artificial atom [Phys. Rev. Lett. 115, 223603 (2015), 10.1103/PhysRevLett.115.223603] in which two-mode entanglement only exists in a certain time period when the harmonic oscillators are resonant with the atomic transitions. Here we examine this system and show that it is possible to obtain the steady-state entanglement when the two harmonic oscillators are resonant with Rabi sidebands. Applying dressed atomic states and Bogoliubov-mode transformation, we obtain the analytical results of the variance sum of a pair of Einstein-Podolsky-Rosen (EPR)-like operators. The stable entanglement originates from the dissipation process of the Bogoliubov modes because the atomic system can act as a reservoir in dressed state representation. We also show that the entanglement is robust against the dephasing rates of the superconducing atom, which is expected to have important applications in quantum information processing.
Instrumentation and control of harmonic oscillators via a single-board microprocessor-FPGA device
Picone, Rico A. R.; Davis, Solomon; Devine, Cameron; Garbini, Joseph L.; Sidles, John A.
2017-04-01
We report the development of an instrumentation and control system instantiated on a microprocessor-field programmable gate array (FPGA) device for a harmonic oscillator comprising a portion of a magnetic resonance force microscope. The specific advantages of the system are that it minimizes computation, increases maintainability, and reduces the technical barrier required to enter the experimental field of magnetic resonance force microscopy. Heterodyne digital control and measurement yields computational advantages. A single microprocessor-FPGA device improves system maintainability by using a single programming language. The system presented requires significantly less technical expertise to instantiate than the instrumentation of previous systems, yet integrity of performance is retained and demonstrated with experimental data.
International Nuclear Information System (INIS)
Young, T. D.; Armiento, R.
2010-01-01
A Schroedinger eigenvalue problem is solved for the 2D quantum simple harmonic oscillator using a finite element discretization of real space within which elements are adaptively spatially refined. We compare two competing methods of adaptively discretizing the real-space grid on which computations are performed without modifying the standard polynomial basis-set traditionally used in finite element interpolations; namely, (i) an application of the Kelly error estimator, and (ii) a refinement based on the local potential level. When the performance of these methods are compared to standard uniform global refinement, we find that they significantly improve the total time spent in the eigensolver. (general)
DEFF Research Database (Denmark)
Dahl, Jens Peder; Schleich, W. P.
2009-01-01
For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...... transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration....
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
Müller H.
2009-04-01
Full Text Available Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spectra. The introduced models are not based on any statements about the nature of the link or interaction between the elements of the oscillating system. Therefore the model statements are quite generally, what opens a wide field of possible applications.
International Nuclear Information System (INIS)
Wang Qing; Hou Yu-Long; Jing Jian; Long Zheng-Wen
2014-01-01
In this paper, we study symmetrical properties of two-dimensional (2D) screened Dirac Hydrogen atom and isotropic harmonic oscillator with scalar and vector potentials of equal magnitude (SVPEM). We find that it is possible for both cases to preserve so(3) and su(2) dynamical symmetries provided certain conditions are satisfied. Interestingly, the conditions for preserving these dynamical symmetries are exactly the same as non-relativistic screened Hydrogen atom and screened isotropic oscillator preserving their dynamical symmetries. Some intuitive explanations are proposed. (general)
Harmonic oscillators and resonance series generated by a periodic unstable classical orbit
Kazansky, A. K.; Ostrovsky, Valentin N.
1995-01-01
The presence of an unstable periodic classical orbit allows one to introduce the decay time as a purely classical magnitude: inverse of the Lyapunov index which characterizes the orbit instability. The Uncertainty Relation gives the corresponding resonance width which is proportional to the Planck constant. The more elaborate analysis is based on the parabolic equation method where the problem is effectively reduced to the multidimensional harmonic oscillator with the time-dependent frequency. The resonances form series in the complex energy plane which is equidistant in the direction perpendicular to the real axis. The applications of the general approach to various problems in atomic physics are briefly exposed.
Molecular Solid EOS based on Quasi-Harmonic Oscillator approximation for phonons
Energy Technology Data Exchange (ETDEWEB)
Menikoff, Ralph [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2014-09-02
A complete equation of state (EOS) for a molecular solid is derived utilizing a Helmholtz free energy. Assuming that the solid is nonconducting, phonon excitations dominate the specific heat. Phonons are approximated as independent quasi-harmonic oscillators with vibrational frequencies depending on the specific volume. The model is suitable for calibrating an EOS based on isothermal compression data and infrared/Raman spectroscopy data from high pressure measurements utilizing a diamond anvil cell. In contrast to a Mie-Gruneisen EOS developed for an atomic solid, the specific heat and Gruneisen coefficient depend on both density and temperature.
(1 + 1) Newton-Hooke group for the simple and damped harmonic oscillator
Brzykcy, Przemysław
2018-03-01
It is demonstrated that, in the framework of the orbit method, a simple and damped harmonic oscillator is indistinguishable at the level of an abstract Lie algebra. This opens a possibility for treating the dissipative systems within the orbit method. An in-depth analysis of the coadjoint orbits of the (1 + 1) dimensional Newton-Hooke group is presented. Furthermore, it is argued that the physical interpretation is carried by a specific realisation of the Lie algebra of smooth functions on a phase space rather than by an abstract Lie algebra.
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
International Nuclear Information System (INIS)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung
2009-01-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./
A hidden non-Abelian monopole in a 16-dimensional isotropic harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Le, Van-Hoang; Nguyen, Thanh-Son; Phan, Ngoc-Hung [Department of Physics, HCMC University of Pedagogy, 280 An Duong Vuong, Ward 10, Dist. 5, Ho Chi Minh City (Viet Nam)
2009-05-01
We suggest one variant of generalization of the Hurwitz transformation by adding seven extra variables that allow an inverse transformation to be obtained. Using this generalized transformation we establish the connection between the Schroedinger equation of a 16-dimensional isotropic harmonic oscillator and that of a nine-dimensional hydrogen-like atom in the field of a monopole described by a septet of potential vectors in a non-Abelian model of 28 operators. The explicit form of the potential vectors and all the commutation relations of the algebra are given./.
Attainable conditions and exact invariant for the time-dependent harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Guasti, Manuel Fernandez [Lab. de Optica Cuantica, Dep. de Fisica, Universidad A. Metropolitana, Unidad Iztapalapa, Mexico DF, Ap. Post. 55-534 (Mexico)
2006-09-22
The time-dependent oscillator equation is solved numerically for various trajectories in amplitude and phase variables. The solutions exhibit a finite time-dependent parameter whenever the squared amplitude times the derivative of the phase is invariant. If the invariant relationship does not hold, the time-dependent parameter has divergent singularities. These observations lead to the proposition that the harmonic oscillator equation with finite time-dependent parameter must have amplitude and phase solutions fulfilling the invariant relationship. Since the time-dependent parameter or the potential must be finite for any real oscillator implementation, the invariant must hold for any such physically realizable system.
Quantum entanglement in coupled harmonic oscillator systems: from micro to macro
Kao, Jhih-Yuan; Chou, Chung-Hsien
2016-07-01
We investigate the entanglement dynamics of several models of coupled harmonic oscillators, whereby a number of properties concerning entanglement have been scrutinized, such as how the environment affects entanglement of a system, and death and revival of entanglement. Among them, there are two models for which we are able to vary their particle numbers easily by assuming identicalness, thereby examining how the particle number affects entanglement. We have found that the upper bound of entanglement between identical oscillators is approximately inversely proportional to the particle number.
International Nuclear Information System (INIS)
Mota, R D; Granados, V D; Queijeiro, A; Garcia, J; Guzman, L
2003-01-01
We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method
Periodic Solutions of the Duffing Harmonic Oscillator by He's Energy Balance Method
Directory of Open Access Journals (Sweden)
A. M. El-Naggar
2015-11-01
Full Text Available Duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. This paper presents He´s Energy Balance Method (EBM for solving nonlinear differential equations. Two strong nonlinear cases have been studied analytically. Analytical results of the EBM are compared with the solutions obtained by using He´s Frequency Amplitude Formulation (FAF and numerical solutions using Runge-Kutta method. The results show the presented method is potentially to solve high nonlinear oscillator equations.
Verreault, René
2017-08-01
In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes' dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2-3 orders of magnitude is achieved.
Use of videos for students to see the effect of changing gravity on harmonic oscillators
Benge, Raymond; Young, Charlotte; Worley, Alan; Davis, Shirley; Smith, Linda; Gell, Amber
2010-03-01
In introductory physics classes, students are introduced to harmonic oscillators such as masses on springs and the simple pendulum. In derivation of the equations describing these systems, the term ``g'' for the acceleration due to gravity cancels in the equation for the period of a mass oscillating on a spring, but it remains in the equation for the period of a pendulum. Frequently there is a homework problem asking how the system described would behave on the Moon, Mars, etc. Students have to have faith in the equations. In January, 2009, a team of community college faculty flew an experiment aboard an aircraft in conjunction with NASA's Microgravity University program. The experiment flown was a study in harmonic oscillator and pendulum behavior under various gravity situations. The aircraft simulated zero gravity, Martian, Lunar, and hypergravity conditions. The experiments were video recorded for students to study the behavior of the systems in varying gravity conditions. These videos are now available on the internet for anyone to use in introductory physics classes.
Structural Vibration of A Flexible Complex System Under A Harmonic Oscillation Moving Force
Rusin, Jarosław
2017-10-01
This paper focuses on the free and forced transverse vibration of a double-string complex system with elastic interlayer under a harmonic oscillation moving force. The paper includes the study of a dynamic behaviour of a finite, simply supported double-string flexible complex system subject to harmonic force moving with a constant velocity on the top string. The strings are identical, parallel one upon the other. The elastic interlayer is described by the Winkler’s model consists of a Hookean resilient spring distributed in parallel. The classical solution of the response of complex systems subjected to harmonic oscillation force moving with a constant velocity has a form of an infinite series. But also, it is possible to show that in the considered case part of the solution can be presented in a closed, analytical form instead of an infinite series. The presented method to search for a solution in a closed-form is based on the observation that the solution of the system of partial differential equations in the form of an infinite series is also a solution of an appropriate system of ordinary differential equations. The double string connected in parallel by linear elastic elements can be studied as a theoretical model of composite structure in which impact of layer interaction, interlayer coupling effects and transverse wave effects is taken into account.
ABC of ladder operators for rationally extended quantum harmonic oscillator systems
Cariñena, José F.; Plyushchay, Mikhail S.
2017-07-01
The problem of construction of ladder operators for rationally extended quantum harmonic oscillator (REQHO) systems of a general form is investigated in the light of existence of different schemes of the Darboux-Crum-Krein-Adler transformations by which such systems can be generated from the quantum harmonic oscillator. Any REQHO system is characterized by the number of separated states in its spectrum, the number of ‘valence bands’ in which the separated states are organized, and by the total number of the missing energy levels and their position. All these peculiarities of a REQHO system are shown to be detected and reflected by a trinity (A^+/- , B^+/- , C^+/-) of the basic (primary) lowering and raising ladder operators related between themselves by certain algebraic identities with coefficients polynomially-dependent on the Hamiltonian. We show that all the secondary, higher-order ladder operators are obtainable by a composition of the basic ladder operators of the trinity which form the set of the spectrum-generating operators. Each trinity, in turn, can be constructed from the intertwining operators of the two complementary minimal schemes of the Darboux-Crum-Krein-Adler transformations.
On the measurement of a weak classical force coupled to a harmonic oscillator: experimental progress
International Nuclear Information System (INIS)
Bocko, M.F.; Onofrio, R.
1996-01-01
Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. copyright 1996 The American Physical Society
On harmonic oscillators on the two-dimensional sphere S2 and the hyperbolic plane H2
International Nuclear Information System (INIS)
Ranada, Manuel F.; Santander, Mariano
2002-01-01
Two Harmonic Oscillators (isotropic and nonisotropic 2:1) are studied on the two-dimensional sphere S 2 and the hyperbolic plane H 2 . Both systems are integrable and super-integrable with constants of motion quadratic in the momenta. These properties are shown to derive from a complex factorization for the constants of motion, which holds for arbitrary values of the curvature κ, and the dynamics of the Euclidean harmonic 1:1 and 2:1 oscillators is directly recovered for κ=0. The harmonic oscillators on either the standard unit sphere (radius R=1) or the unit Lobachewski plane ('radius' R=1) appear as the particular values of the κ-dependent potentials for the values κ=1 and κ=-1. Finally a particular potential is proposed for representing the general spherical (hyperbolic) n:1 anisotropic harmonic oscillator on a two-dimensional manifold of constant curvature
Defacio, B.; Vannevel, Alan; Brander, O.
1993-01-01
A formulation is given for a collection of phonons (sound) in a fluid at a non-zero temperature which uses the simple harmonic oscillator twice; one to give a stochastic thermal 'noise' process and the other which generates a coherent Glauber state of phonons. Simple thermodynamic observables are calculated and the acoustic two point function, 'contrast' is presented. The role of 'coherence' in an equilibrium system is clarified by these results and the simple harmonic oscillator is a key structure in both the formulation and the calculations.
International Nuclear Information System (INIS)
Santos, Marcelo Franca
2005-01-01
We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two by two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic, and state-independent manipulation of the harmonic oscillator quantum state
Viana-Gomes, J.; Peres, N. M. R.
2011-01-01
We derive the energy levels associated with the even-parity wavefunctions of the harmonic oscillator with an additional delta-function potential at the origin. Our results bring to the attention of students a non-trivial and analytical example of a modification of the usual harmonic oscillator potential, with emphasis on the modification of the…
Fundamental and Subharmonic Resonances of Harmonically Oscillation with Time Delay State Feedback
Directory of Open Access Journals (Sweden)
A.F. EL-Bassiouny
2006-01-01
Full Text Available Time delays occur in many physical systems. In particular, when automatic control is used with structural or mechanical systems, there exists a delay between measurement of the system state and corrective action. The concept of an equivalent damping related to the delay feedback is proposed and the appropriate choice of the feedback gains and the time delay is discussed from the viewpoint of vibration control. We investigate the fundamental resonance and subharmonic resonance of order one-half of a harmonically oscillation under state feedback control with a time delay. By using the multiple scale perturbation technique, the first order approximation of the resonances are derived and the effect of time delay on the resonances is investigated. The fixed points correspond to a periodic motion for the starting system and we show the external excitation-response and frequency-response curves. We analyze the effect of time delay and the other different parameters on these oscillations.
The Klauder-Daubechies construction of the phase-space path integral and the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Govaerts, Jan; Mattelaer, Olivier [Center for Particle Physics and Phenomenology (CP3), Institut de Physique Nucleaire, Universite catholique de Louvain (UCL), 2, Chemin du Cyclotron, B-1348 Louvain-la-Neuve (Belgium); Bwayi, Calvin Matondo [Department of Physics, University of Kinshasa (UNIKIN), Kinshasa (Congo, The Democratic Republic of the)], E-mail: Jan.Govaerts@uclouvain.be, E-mail: matymatondo@yahoo.fr, E-mail: Olivier.Mattelaer@uclouvain.be
2009-11-06
The canonical operator quantization formulation corresponding to the Klauder-Daubechies construction of the phase-space path integral is considered. This formulation is explicitly applied and solved in the case of the harmonic oscillator, thereby illustrating in a manner complementary to Klauder and Daubechies' original work some of the promising features offered by their construction of a quantum dynamics. The Klauder-Daubechies functional integral involves a regularization parameter eventually taken to vanish, which defines a new physical time scale. When extrapolated to the field theory context, besides providing a new regularization of short distance divergences, keeping a finite value for that time scale offers some tantalizing prospects when it comes to strong gravitational quantum systems.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
Lin Bi Hong; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here ...
Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry
International Nuclear Information System (INIS)
Alvarez, Pedro D.; Gomis, Joaquim; Kamimura, Kiyoshi; Plyushchay, Mikhail S.
2008-01-01
We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton-Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same (2+1)-dimensional exotic Newton-Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton-Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties
Crypto-harmonic oscillator in higher dimensions: classical and quantum aspects
International Nuclear Information System (INIS)
Ghosh, Subir; Majhi, Bibhas Ranjan
2008-01-01
We study complexified harmonic oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) who initiated the study of these Crypto-gauge invariant models that can be related to PT-symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints (in contrast to Smilga (2007 Preprint 0706.4064 (J. Phys. A: Math. Theor. at press)) where one deals with a single constraint) with a much richer constraint structure. Some common as well as distinct features in the study of the same Crypto-oscillator in different dimensions are revealed. We also quantize the two dimensional Crypto-oscillator
A time-discrete harmonic oscillator model of human car-following
Wagner, P.
2011-12-01
A time-discrete stochastic harmonic oscillator is presented as a model of human car-following behaviour. This describes especially the non-continuous control of a human driver - acceleration changes from time to time at so called action-points and is kept constant in between. Analytical results can be derived which allow to classify the different types of motion possible within this approach. These results show that with weaker control by the human, unstable behaviour of the oscillator becomes more likely. This is in line with common understanding about the causes of accidents. Finally, since even the stochastic behaviour of this model is in parts analytically tractable, the width of the speed-difference and distance fluctuations can be expressed as function of the model's parameter. This allows a fresh view on empirical car-following data and the identification of parameters from real data in the context of the theory presented here.
The optimal performance of a quantum refrigeration cycle working with harmonic oscillators
International Nuclear Information System (INIS)
Lin Bihong; Chen Jincan; Hua Ben
2003-01-01
The cycle model of a quantum refrigeration cycle working with many non-interacting harmonic oscillators and consisting of two isothermal and two constant-frequency processes is established. Based on the quantum master equation and semi-group approach, the general performance of the cycle is investigated. Expressions for some important performance parameters, such as the coefficient of performance, cooling rate, power input, and rate of the entropy production, are derived. Several interesting cases are discussed and, especially, the optimal performance of the cycle at high temperatures is discussed in detail. Some important characteristic curves of the cycle, such as the cooling rate versus coefficient of performance curves, the power input versus coefficient of performance curves, the cooling rate versus power input curves, and so on, are presented. The maximum cooling rate and the corresponding coefficient of performance are calculated. Other optimal performances are also analysed. The results obtained here are compared with those of an Ericsson or Stirling refrigeration cycle using an ideal gas as the working substance. Finally, the optimal performance of a harmonic quantum Carnot refrigeration cycle at high temperatures is derived easily
𝒩 = 2 supersymmetric harmonic oscillator: Basic brackets without canonical conjugate momenta
Srinivas, N.; Shukla, A.; Malik, R. P.
2015-09-01
We exploit the ideas of spin-statistics theorem, normal-ordering and the key concepts behind the symmetry principles to derive the canonical (anti)commutators for the case of a one (0 + 1)-dimensional (1D) 𝒩 = 2 supersymmetric (SUSY) harmonic oscillator (HO) without taking the help of the mathematical definition of canonical conjugate momenta with respect to the bosonic and fermionic variables of this toy model for the Hodge theory (where the continuous and discrete symmetries of the theory provide the physical realizations of the de Rham cohomological operators of differential geometry). In our present endeavor, it is the full set of continuous symmetries and their corresponding generators that lead to the derivation of basic (anti)commutators amongst the creation and annihilation operators that appear in the normal mode expansions of the dynamical fermionic and bosonic variables of our present 𝒩 = 2 SUSY theory of a HO. These basic brackets are in complete agreement with such kind of brackets that are derived from the standard canonical method of quantization scheme.
Fidler, Andrew F.; Engel, Gregory S.
2013-10-01
We present a theory for a bath model in which we approximate the adiabatic nuclear potential surfaces on the ground and excited electronic states by displaced harmonic oscillators that differ in curvature. Calculations of the linear and third-order optical response functions employ an effective short-time approximation coupled with the cumulant expansion. In general, all orders of correlation contribute to the optical response, indicating that the solvation process cannot be described as Gaussian within the model. Calculations of the linear absorption and fluorescence spectra resulting from the theory reveal a stronger temperature dependence of the Stokes shift along with a general asymmetry between absorption and fluorescence line shapes, resulting purely from the difference in the phonon side band. We discuss strategies for controlling spectral tuning and energy-transfer dynamics through the manipulation of the excited-state and ground-state curvature. Calculations of the nonlinear response also provide insights into the dynamics of the system-bath interactions and reveal that multidimensional spectroscopies are sensitive to a difference in curvature between the ground- and excited-state adiabatic surfaces. This extension allows for the elucidation of short-time dynamics of dephasing that are accessible in nonlinear spectroscopic methods.
Bogdan, V. M.; Bond, V. B.
1980-01-01
The deviation of the solution of the differential equation y' = f(t, y), y(O) = y sub O from the solution of the perturbed system z' = f(t, z) + g(t, z), z(O) = z sub O was investigated for the case where f and g are continuous functions on I x R sup n into R sup n, where I = (o, a) or I = (o, infinity). These functions are assumed to satisfy the Lipschitz condition in the variable z. The space Lip(I) of all such functions with suitable norms forms a Banach space. By introducing a suitable norm in the space of continuous functions C(I), introducing the problem can be reduced to an equivalent problem in terminology of operators in such spaces. A theorem on existence and uniqueness of the solution is presented by means of Banach space technique. Norm estimates on the rate of growth of such solutions are found. As a consequence, estimates of deviation of a solution due to perturbation are obtained. Continuity of the solution on the initial data and on the perturbation is established. A nonlinear perturbation of the harmonic oscillator is considered a perturbation of equations of the restricted three body problem linearized at libration point.
Stochastic and superharmonic stochastic resonances of a confined overdamped harmonic oscillator
Zhang, Lu; Lai, Li; Peng, Hao; Tu, Zhe; Zhong, Suchuan
2018-01-01
The dynamics of many soft condensed matter and biological systems is affected by space limitations, which produce some peculiar effects on the systems' stochastic resonance (SR) behavior. In this study, we propose a model where SR can be observed: a confined overdamped harmonic oscillator that is subjected to a sinusoidal driving force and is under the influence of a multiplicative white noise. The output response of the system is a periodic signal with harmonic frequencies that are odd multiples of the driving frequency. We verify the amplitude resonances at the driving frequencies and superharmonic frequencies that are equal to three, five, and seven times the driving frequency, using a numerical method based on the stochastic Taylor expansion. The synergistic effect of the multiplicative white noise, constant boundaries, and periodic driving force that can induce a SR in the output amplitude at the driving and superharmonic frequencies is found. The SR phenomenon found in this paper is sensitive to the driving amplitude and frequency, inherent potential parameter, and boundary width, thus leading to various resonance conditions. Therefore, the mechanism found could be beneficial for the characterization of these confined systems and could constitute an important tool for controlling their basic properties.
Improved time-dependent harmonic oscillator method for vibrationally inelastic collisions
International Nuclear Information System (INIS)
DePristo, A.E.
1985-01-01
A quantal solution to vibrationally inelastic collisions is presented based upon a linear expansion of the interaction potential around the time-dependent classical positions of all translational and vibrational degrees of freedom. The full time-dependent wave function is a product of a Gaussian translational wave packet and a multidimensional harmonic oscillator wave function, both centered around the appropriate classical position variables. The computational requirements are small since the initial vibrational coordinates are the equilibrium values in the classical trajectory (i.e., phase space sampling does not occur). Different choices of the initial width of the translational wave packet and the initial classical translational momenta are possible, and two combinations are investigated. The first involves setting the initial classical momenta equal to the quantal expectation value, and varying the width to satisfy normalization of the transition probability matrix. The second involves adjusting the initial classical momenta to ensure detailed balancing for each set of transitions, i→f and f→i, and varying the width to satisfy normalization. This choice illustrates the origin of the empirical correction of using the arithmetic average momenta as the initial classical momenta in the forced oscillator approximation. Both methods are tested for the collinear collision systems CO 2 --(He, Ne), and are found to be accurate except for near-resonant vibration--vibration exchange at low initial kinetic energies
Wu, Hao; Fan, Hong-Yi
2008-12-01
Eigenvalue-solution to those Hamiltonians involving non-commutative coordinates is not easily obtained. In this paper we apply the invariant eigen-operator (IEO) method to solving the energy spectrum of the three-mode harmonic oscillator in non-commutative space with the coordinate operators satisfying cyclic commutative relations, [X1,X2] = [X2,X3] = [X3,X1] = iθ, and this method seems effective and concise.
International Nuclear Information System (INIS)
Fueloep, L.
1987-10-01
The forceless mechanics of Hertz is a reformulation of the classical mechanics in a curved configuration space. The relationship between the forceless mechanics and the general relativity theory which uses curved Riemann spaces as well is investigated on the simple example of the harmonic oscillator. The mathematical similarities and differences and the different interpretations of similar formulas are discussed. Some formal constants of the Hertz mechanics have got concrete physical meanings in the general relativity. (D.Gy.)
Mota, R. D.; Xicoténcatl, M. A.; Granados, V. D.
2004-02-01
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
Energy Technology Data Exchange (ETDEWEB)
Mota, R D [Unidad Profesional Interdisciplinaria de IngenierIa y TecnologIas Avanzadas, IPN. Av. Instituto Politecnico Nacional 2580, Col. La Laguna Ticoman, 07340 Mexico DF (Mexico); Xicotencatl, M A [Departamento de Matematicas del Centro de Investigacion y Estudios Avanzados del IPN, Mexico DF, 07000 (Mexico); Granados, V D [Escuela Superior de FIsica y Matematicas, Instituto Politecnico Nacional, Ed. 9, Unidad Profesional Adolfo Lopez Mateos, 07738 Mexico DF (Mexico)
2004-02-20
In this work we introduce a generalization of the Jauch and Rohrlich quantum Stokes operators when the arrival direction from the source is unknown a priori. We define the generalized Stokes operators as the Jordan-Schwinger map of a triplet of harmonic oscillators with the Gell-Mann and Ne'eman matrices of the SU(3) symmetry group. We show that the elements of the Jordan-Schwinger map are the constants of motion of the three-dimensional isotropic harmonic oscillator. Also, we show that the generalized Stokes operators together with the Gell-Mann and Ne'eman matrices may be used to expand the polarization matrix. By taking the expectation value of the Stokes operators in a three-mode coherent state of the electromagnetic field, we obtain the corresponding generalized classical Stokes parameters. Finally, by means of the constants of motion of the classical 3D isotropic harmonic oscillator we describe the geometrical properties of the polarization ellipse.
CSIR Research Space (South Africa)
Grobler, TL
2012-06-01
Full Text Available It is proposed that the time series extracted from moderate resolution imaging spectroradiometer satellite data be modeled as a simple harmonic oscillator with additive colored noise. The colored noise ismodeled with an Ornstein–Uhlenbeck process...
A new look at the quantum mechanics of the harmonic oscillator
Energy Technology Data Exchange (ETDEWEB)
Kastrup, H.A.
2006-12-15
At first sight it is probably hard to believe that something new can be said about the harmonic oscillator (HO). But that is so indeed: Classically the Harmonic Oscillator (HO) is the generic example for the use of angle and action variables {phi} element of R mod 2{pi} and I>0. However, the transformation q= {radical}(2I)cos {phi}, p=-{radical}(2I)sin {phi} is only locally symplectic and singular for (q,p)=(0,0). Globally the phase space {l_brace}(q,p){r_brace} has the topological structure of the plane R{sup 2}, whereas the phase space {l_brace}({phi},I){r_brace} corresponds globally to the punctured plane R{sup 2}-(0,0) or to a simple cone S{sup 1} x R{sup +} with the tip deleted. This makes a qualitative difference as to the quantum theory of the two phase spaces: The quantizing canonical group for the plane R{sup 2} consists of the (centrally extended) translations generated by the Poisson Lie algebra basis {l_brace}q,p,1{r_brace}, whereas the corresponding canonical group of the phase space {l_brace}({phi},I){r_brace} is the group SO{up_arrow}(1,2)=Sp(2,R)/Z{sub 2}, where Sp(2,R) is the sympletic group of the plane, with the generating Poisson Lie algebra basis {l_brace}h{sub 0}=I,h{sub 1}=Icos{phi},h{sub 2}=-Isin{phi}{r_brace} which provides also the basic ''observables'' on {l_brace}({phi}, I){r_brace}. In the quantum mechanics of the ({phi},I)-model of the HO the three h{sub j} correspond to self-adjoint generators K{sub j}, j=0,1,2, of irreducible unitary representations from the positive discrete series of the group SO{up_arrow}(1,2) or one of its infinitely many covering groups, the representations parametrized by the Bargmann index k>0. This index k determines the ground state energy E{sub k,n=0}={Dirac_h}{omega}k of the ({phi},I)-Hamiltonian H(anti K)={Dirac_h}{omega}K{sub 0}. For an m-fold covering the lowest possible value for k is k=1/m, which can be made arbitrarily small by choosing m accordingly. This is not in contraction to
Van Assche, W.; Yáñez, R. J.; Dehesa, J. S.
1995-08-01
The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ``entropy of Hermite polynomials,'' i.e., the quantity Sn(H):= -∫-∞+∞H2n(x)log H2n(x) e-x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(-||x||m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423-4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ-1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129-132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Microwave Imaging Reflectometry for the study of Edge Harmonic Oscillations on DIII-D
Ren, X.; Chen, M.; Chen, X.; Domier, C. W.; Ferraro, N. M.; Kramer, G. J.; Luhmann, N. C., Jr.; Muscatello, C. M.; Nazikian, R.; Shi, L.; Tobias, B. J.; Valeo, E.
2015-10-01
Quiescent H-mode (QH-mode) is an ELM free mode of operation in which edge-localized harmonic oscillations (EHOs) are believed to enhance particle transport, thereby stabilizing ELMs and preventing damage to the divertor and plasma facing components. Microwave Imaging Reflectometer (MIR) enabling direct comparison between the measured and simulated 2D images of density fluctuations near the edge can determine the 2D structure of density oscillation, which can help to explain the physics behind EHO modes. MIR data sometimes indicate a counter-propagation between dominant (n=1) and higher harmonic modes of coherent EHOs in the steep gradient regions of the pedestal. To preclude diagnostic artifacts, we have performed forward modeling that includes possible optical mis-alignments to show that offsets between transmitting and receiving antennas do not account for this feature. We have also simulated the non-linear structure of the EHO modes, which induces multiple harmonics that are properly charaterized in the synthetic diagnostic. By excluding mis-alignments of optics as well as patially eliminating non-linearity of EHO mode structure as possible explanation for the data, counter-propagation observed in MIR data, which is not corroborated by external Mirnov coil array measurements, may be due to subtleties of the eigenmode structure, such as an inversion radius consistent with a magnetic island. Similar effects are observed in analysis of internal ECE-Imaging and BES data. The identification of a non-ideal structure motivates further exploration of nonlinear models of this instability. A shorter version of this contribution is due to be published in PoS at: 1st EPS conference on Plasma Diagnostics
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
Isar, Aurelian
1995-01-01
The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.
Demiralp, Metin
2010-09-01
This work focuses on the dynamics of a system of quantum multi harmonic oscillators whose Hamiltonian is conic in positions and momenta with time variant coefficients. While it is simple, this system is useful for modeling the dynamics of a number of systems in contemporary sciences where the equations governing spatial or temporal changes are described by sets of ODEs. The dynamical causal models used readily in neuroscience can be indirectly described by these systems. In this work, we want to show that it is possible to describe these systems using quantum wave function type entities and expectations if the dynamic of the system is related to a set of ODEs.
International Nuclear Information System (INIS)
Hernandez-Tenorio, C.; Belyaeva, T.L.; Serkin, V.N.
2007-01-01
The dynamics of nonlinear solitary waves is studied in the framework of the nonlinear Schroedinger equation model with time-dependent harmonic oscillator potential. The model allows one to analyse on general basis a variety of nonlinear phenomena appearing both in Bose-Einstein condensate, condensed matter physics, nonlinear optics, and biophysics. The soliton parametric resonance is investigated by using two complementary methods: the adiabatic perturbation theory and direct numerical experiments. Conditions for reversible and irreversible denaturation of soliton bound states are also considered
Leach, P. G. L.; Nucci, M. C.
2004-09-01
The classical MICZ-Kepler problem is shown to be reducible to an isotropic two-dimensional system of linear harmonic oscillators and a conservation law in terms of new variables related to the Ermanno-Bernoulli constants and the components of the Poincaré vector. An algorithmic route to linearization is shown based on Lie symmetry analysis and the reduction method [ Nucci, J. Math. Phys. 37, 1772 (1996) ]. First integrals are also obtained by symmetry analysis and the reduction method [ Marcelli and Nucci,J. Math. Phys. 44, 2111 (2002) ].
International Nuclear Information System (INIS)
Castro, A.S. de; Alberto, P.; Lisboa, R.; Malheiro, M.
2006-01-01
We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and γ 5 chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states
Time quantization and q-deformations
Energy Technology Data Exchange (ETDEWEB)
Albanese, Claudio; Lawi, Stephan [Department of Mathematics, University of Toronto, 100 St George Street, M5S 3G3, Toronto (Canada)
2004-02-25
We extend to quantum mechanics the technique of stochastic subordination, by means of which one can express any semi-martingale as a time-changed Brownian motion. As examples, we considered two versions of the q-deformed harmonic oscillator in both ordinary and imaginary time and show how these various cases can be understood as different patterns of time quantization rules.
International Nuclear Information System (INIS)
Cari, C; Suparmi, A
2013-01-01
The energy eigenvalues and eigenfunctions of Schrodinger equation for three dimensional harmonic oscillator potential plus Rosen-Morse non-central potential are investigated using NU method and Romanovski polynomial. The bound state energy eigenvalues are given in a closed form and corresponding radial wave functions are expressed in associated Laguerre polynomials while angular eigen functions are given in terms of Romanovski polynomials. The Rosen-Morse potential is considered to be a perturbation factor to the three dimensional harmonic oscillator potential that causes the increase of radial wave function amplitude and decrease of angular momentum length. Keywords: Schrodinger Equation, Three dimensional Harmonic Oscillator potential, Rosen-morse non-central potential, NU method, Romanovski Polynomials
Laas, Katrin; Mankin, Romi; Rekker, Astrid
2009-05-01
The influences of noise flatness and friction coefficient on the long-time behavior of the first two moments and the correlation function for the output signal of a harmonic oscillator with fluctuating frequency subjected to an external periodic force are considered. The colored fluctuations of the oscillator frequency are modeled as a trichotomous noise. The study is a follow up of the previous investigation of a stochastic oscillator [Phys. Rev. E 78, 031120 (2008)], where the connection between the occurrence of energetic instability and stochastic multiresonance is established. Here we report some unexpected results not considered in the previous work. Notably, we have found a nonmonotonic dependence of several stochastic resonance characteristics such as spectral amplification, variance of the output signal, and signal-to-noise ratio on the friction coefficient and on the noise flatness. In particular, in certain parameter regions spectral amplification exhibits a resonancelike enhancement at intermediate values of the friction coefficient.
ELM-free and inter-ELM divertor heat flux broadening induced by edge harmonics oscillation in NSTX
Gan, K. F.; Ahn, J.-W.; Gray, T. K.; Zweben, S. J.; Fredrickson, E. D.; Scotti, F.; Maingi, R.; Park, J.-K.; Canal, G. P.; Soukhanovskii, V. A.; Mclean, A. G.; Wirth, B. D.
2017-12-01
A new n = 1 dominated edge harmonic oscillation (EHO) has been found in NSTX. The new EHO, rotating toroidally in the counter-current direction and the opposite direction of the neutral beam, was observed during certain inter-ELM and ELM-free periods of H-mode operation. This EHO is associated with a significant broadening of the integral heat flux width ({λ\\operatorname{int}} ) by up to 150%, and a decrease in the divertor peak heat flux by >60%. An EHO induced filament was also observed by the gas puff imaging diagnostic. The toroidal rotating filaments could change the edge magnetic topology resulting in toroidal rotating strike point splitting and heat flux broadening. Experimental result of the counter current rotation of strike points splitting is consistent with the counter-current EHO.
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
Maths-type q-deformed coherent states for q>1
International Nuclear Information System (INIS)
Quesne, C.; Penson, K.A.; Tkachuk, V.M.
2003-01-01
Maths-type q-deformed coherent states with q>1 allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both position and momentum and are intelligent coherent states for the corresponding deformed Heisenberg algebra
An Application of the Harmonic Oscillator Model to Verify Dunning’s Theory of the Economic Growth
Directory of Open Access Journals (Sweden)
Marcin Salamaga
2013-09-01
Full Text Available Analogies with mechanisms ruling the natural world have oft en been sought in the course of economic phenomena.Th is paper is also an attempt to combine the physical phenomenon of a harmonious oscillator withthe theory of economic growth by J. H. Dunning (1981. In his theory, Dunning distinguished stages of economicgrowth of countries that imply the dependency between the investment position of countries and theirGDP per capita, while the graph presenting this dependency reminds a trajectory of oscillating motion of adamped harmonic oscillator. Th is analogy has given inspiration to reinterpret the theory of economy on thegrounds of the mechanism of a physical model. In this paper, the harmonious oscillator motion equation wasadapted to the description of dependencies shown in the theory of economic growth by J. H. Dunning. Th emathematical solution of this equation is properly parameterised and parameters are estimated with the useof the Gauss-Newton algorithm. Th e main objective of this paper is to allocate a specifi c stage in the economicgrowth to each country on the basis of the values of parameter estimations of the proposed cyclical models ofchanges in the net investment indicator.
Energy Technology Data Exchange (ETDEWEB)
Noguera, Norman, E-mail: norman.noguera@ucr.ac.cr [Departamento de Matemática, Universidad de Costa Rica. S.O (Costa Rica); Rózga, Krzysztof, E-mail: krzysztof.rozga@upr.edu [Department of Mathematical Sciences, University of Puerto Rico, Mayagüez, Puerto Rico 00681-5000 (United States)
2015-07-15
In this work, one provides a justification of the condition that is usually imposed on the parameters of the hypergeometric equation, related to the solutions of the stationary Schrödinger equation for the harmonic oscillator in two-dimensional constant curvature spaces, in order to determine the solutions which are square-integrable. One proves that in case of negative curvature, it is a necessary condition of square integrability and in case of positive curvature, a necessary condition of regularity. The proof is based on the analytic continuation formulas for the hypergeometric function. It is observed also that the same is true in case of a slightly more general potential than the one for harmonic oscillator.
Vasil'ev, M. G.
2017-02-01
A technique for measuring the crystal cross-sectional area with a weight sensor based on the difference between its readings at the extreme rod positions in the stepwise and continuous modes of modulation of the pulling rate is proposed for the low-thermal gradient Czochralski method. A change in the crystallization rate at harmonic oscillations of the pulling rate is estimated with the aim of conserving the quality of the growing crystal for this measurement method.
Stace, A. J.
1995-01-01
A simple Monte Carlo model is presented for simulating the motion of a quantum harmonic oscillator trapped in a rare gas cluster or matrix which is treated as a classical heat bath. Preliminary results are present for the system I 2·Ar 11 where it would appear that the bond length of the molecule is sensitive to the temperature of the cluster. It is anticipated that the model may be used to study how vibrating molecules are accommodated by rare gas clusters and solids.
Shattering a Cartesian Sceptical Dream
Directory of Open Access Journals (Sweden)
Stephen Hetherington
2004-06-01
Full Text Available Scepticism about external world knowledge is frequently claimed to emerge from Descartes’s dreaming argument. That argument supposedly challenges one to have some further knowledge — the knowledge that one is not dreaming that p — if one is to have even one given piece of external world knowledge that p. The possession of that further knowledge can seem espe-cially important when the dreaming possibility is genuinely Cartesian (with one’s dreaming that p being incompatible with the truth of one’s accompany-ing belief that p. But this paper shows why that Cartesian use of that possi-bility is not at all challenging. It is because that putative sceptical challenge reduces to a triviality which is incompatible with the sceptic’s having de-scribed some further piece of knowledge which is needed, if one is to have the knowledge that p.
Non-Cartesian parallel imaging reconstruction.
Wright, Katherine L; Hamilton, Jesse I; Griswold, Mark A; Gulani, Vikas; Seiberlich, Nicole
2014-11-01
Non-Cartesian parallel imaging has played an important role in reducing data acquisition time in MRI. The use of non-Cartesian trajectories can enable more efficient coverage of k-space, which can be leveraged to reduce scan times. These trajectories can be undersampled to achieve even faster scan times, but the resulting images may contain aliasing artifacts. Just as Cartesian parallel imaging can be used to reconstruct images from undersampled Cartesian data, non-Cartesian parallel imaging methods can mitigate aliasing artifacts by using additional spatial encoding information in the form of the nonhomogeneous sensitivities of multi-coil phased arrays. This review will begin with an overview of non-Cartesian k-space trajectories and their sampling properties, followed by an in-depth discussion of several selected non-Cartesian parallel imaging algorithms. Three representative non-Cartesian parallel imaging methods will be described, including Conjugate Gradient SENSE (CG SENSE), non-Cartesian generalized autocalibrating partially parallel acquisition (GRAPPA), and Iterative Self-Consistent Parallel Imaging Reconstruction (SPIRiT). After a discussion of these three techniques, several potential promising clinical applications of non-Cartesian parallel imaging will be covered. © 2014 Wiley Periodicals, Inc.
Energy Technology Data Exchange (ETDEWEB)
dos Santos Coelho, Leandro [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil); Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Santos Coelho, Leandro dos [Pontifical Catholic University of Parana, PUCPR Industrial and Systems Engineering Graduate Program, PPGEPS, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: leandro.coelho@pucpr.br; Mariani, Viviana Cocco [Pontifical Catholic University of Parana, PUCPR Mechanical Engineering Graduate Program, PPGEM, Imaculada Conceicao, 1155, Zip code 80215-901, Curitiba, PR (Brazil)], E-mail: viviana.mariani@pucpr.br
2008-11-15
Particle swarm optimization (PSO) algorithm is population-based heuristic global search algorithm inspired by social behavior patterns of organisms that live and interact within large groups. The PSO is based on researches on swarms such as fish schooling and bird flocking. Inspired by the classical PSO method and quantum mechanics theories, this work presents a quantum-inspired version of the PSO (QPSO) using the harmonic oscillator potential well (HQPSO) to solve economic dispatch problems. A 13-units test system with incremental fuel cost function that takes into account the valve-point loading effects is used to illustrate the effectiveness of the proposed HQPSO method compared with the simulation results based on the classical PSO, the QPSO, and other optimization algorithms reported in the literature.
Discourse Structure and Cartesian Scepticism. | Ryan | South ...
African Journals Online (AJOL)
I provide a new account of the nature of Cartesian scepticism, in which I show that if we draw on the notion of discourse structure we can show exactly how Cartesian scepticism is induced and that it is, in principle, impossible to dispel. The account proceeds by showing that, given the nature of discourse structure, there is no ...
Zernike Basis to Cartesian Transformations
Directory of Open Access Journals (Sweden)
Mathar, R. J.
2009-12-01
Full Text Available The radial polynomials of the 2D (circular and 3D (spherical Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.
Zernike basis to cartesian transformations
Directory of Open Access Journals (Sweden)
Mathar R.J.
2009-01-01
Full Text Available The radial polynomials of the 2D (circular and 3D (spherical Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.
Polarizability of deformed nuclei and energy shifts in muonic atoms
International Nuclear Information System (INIS)
Nali, P.F.; Quarati, P.
1980-01-01
The polarizability and nuclear-polarization energy shifts of nuclei composed of closed shells plus valence nucleons in muonic atoms have been calculated: the harmonic-oscillator results of the El polarizability and the energy shifts have been corrected by means of a perturbative approach, which takes into account the effects introduced by the deformation Nilsson potential. Furthermore, to take into account the core polarization effect, different harmonic-oscillator parameters for the core and the valence nucleons have been assumed. The energy shifts of a sequence of states occupied by the muon during its atomic electromagnetic cascade for the nuclei 17 O and 17 F, 41 Ca and 41 Sc have been calculated. (author)
Directory of Open Access Journals (Sweden)
Halimatus Sa’diyah
2017-12-01
Full Text Available The purpose of this research is to analyze of students' difficulties on the material elasticity and harmonic oscillation in the inquiry-based physics learning. It has eight stages. They are the orientation, the problem formulation, the formulation of hypotheses, the data obtaining, the testing hypotheses, conclusions, the implementation of the conclusions and generalizations, and the reflection stage. This research determines the student's learning difficulties on the each stage. The subject of this research is all of the students in X IPA 4 SMA N Sambungmacan Sragen. The amount of this research subject is thirty students. The method used in this research is descriptive qualitative. The data acquired with the learning process observation, the student's response questionnaire, and the student's cognitive tests. The results show that the student has difficulty in analyzing the elasticity and the force of deviation, speed, and acceleration concept, illustrates hooke law, and the matter's modulus elasticity. The difficult stages of the inquiry-based physics learning are the problem formulation, the formulation of hypotheses, the data obtaining, the testing hypotheses, conclusions, the implementation of the conclusions and generalizations, and the reflection stage.
Energy Technology Data Exchange (ETDEWEB)
Marquette, Ian, E-mail: i.marquette@uq.edu.au [School of Mathematics and Physics, The University of Queensland, Brisbane, QLD 4072 (Australia); Quesne, Christiane, E-mail: cquesne@ulb.ac.be [Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Campus de la Plaine CP229, Boulevard du Triomphe, B-1050 Brussels (Belgium)
2016-05-15
The purpose of this communication is to point out the connection between a 1D quantum Hamiltonian involving the fourth Painlevé transcendent P{sub IV}, obtained in the context of second-order supersymmetric quantum mechanics and third-order ladder operators, with a hierarchy of families of quantum systems called k-step rational extensions of the harmonic oscillator and related with multi-indexed X{sub m{sub 1,m{sub 2,…,m{sub k}}}} Hermite exceptional orthogonal polynomials of type III. The connection between these exactly solvable models is established at the level of the equivalence of the Hamiltonians using rational solutions of the fourth Painlevé equation in terms of generalized Hermite and Okamoto polynomials. We also relate the different ladder operators obtained by various combinations of supersymmetric constructions involving Darboux-Crum and Krein-Adler supercharges, their zero modes and the corresponding energies. These results will demonstrate and clarify the relation observed for a particular case in previous papers.
International Nuclear Information System (INIS)
Carow-Watamura, U.; Schlieker, M.; Watamura, S.
1991-01-01
We construct a differential calculus on the N-dimensional non-commutative Euclidean space, i.e., the space on which the quantum group SO q (N) is acting. The differential calculus is required to be manifestly covariant under SO q (N) transformations. Using this calculus, we consider the Schroedinger equation corresponding to the harmonic oscillator in the limit of q→1. The solution of it is given by q-deformed functions. (orig.)
Relation of deformed nonlinear algebras with linear ones
International Nuclear Information System (INIS)
Nowicki, A; Tkachuk, V M
2014-01-01
The relation between nonlinear algebras and linear ones is established. For a one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to a linear one with three operators. We also establish the relation between the Lie algebra of total angular momentum and corresponding nonlinear one. This relation gives a possibility to simplify and to solve the eigenvalue problem for the Hamiltonian in a nonlinear case using the reduction of this problem to the case of linear algebra. It is demonstrated in an example of a harmonic oscillator. (paper)
Q-deformed systems and constrained dynamics
International Nuclear Information System (INIS)
Shabanov, S.V.
1993-01-01
It is shown that quantum theories of the q-deformed harmonic oscillator and one-dimensional free q-particle (a free particle on the 'quantum' line) can be obtained by the canonical quantization of classical Hamiltonian systems with commutative phase-space variables and a non-trivial symplectic structure. In the framework of this approach, classical dynamics of a particle on the q-line coincides with the one of a free particle with friction. It is argued that q-deformed systems can be treated as ordinary mechanical systems with the second-class constraints. In particular, second-class constrained systems corresponding to the q-oscillator and q-particle are given. A possibility of formulating q-deformed systems via gauge theories (first-class constrained systems) is briefly discussed. (orig.)
The Cartesian Heritage of Bloom's Taxonomy
Bertucio, Brett
2017-01-01
This essay seeks to contribute to the critical reception of "Bloom's Taxonomy of Educational Objectives" by tracing the Taxonomy's underlying philosophical assumptions. Identifying Bloom's work as consistent with the legacy of Cartesian thought, I argue that its hierarchy of behavioral objectives provides a framework for certainty and…
Conversion of contours to cartesian grids
DEFF Research Database (Denmark)
Mann, Jakob; Broe, Brian Riget
A robust and efficient method of calculating a cartesian grid of heights or roughnesses from contour line maps is developed. The purpose of the grids is to serve as input for atmospheric flow solvers such as WAsP Engineering or EllipSys3D. The method builds on Delaunay triangulation constrained t...
Directory of Open Access Journals (Sweden)
Syed Masood
2016-12-01
Full Text Available In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
Energy Technology Data Exchange (ETDEWEB)
Masood, Syed [Department of Physics, International Islamic University, H-10 Sector, Islamabad (Pakistan); Faizal, Mir, E-mail: mirfaizalmir@gmail.com [Irving K. Barber School of Arts and Sciences, University of British Columbia – Okanagan, Kelowna, BC V1V 1V7 (Canada); Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB T1K 3M4 (Canada); Zaz, Zaid [Department of Electronics and Communication Engineering, University of Kashmir, Srinagar, Kashmir, 190006 (India); Ali, Ahmed Farag [Department of Physics, Faculty of Science, Benha University, Benha, 13518 (Egypt); Raza, Jamil [Department of Physics, International Islamic University, H-10 Sector, Islamabad (Pakistan); Shah, Mushtaq B. [Department of Physics, National Institute of Technology, Srinagar, Kashmir, 190006 (India)
2016-12-10
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
International Nuclear Information System (INIS)
Masood, Syed; Faizal, Mir; Zaz, Zaid; Ali, Ahmed Farag; Raza, Jamil; Shah, Mushtaq B.
2016-01-01
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The form of the generalized uncertainty principle used to motivate these results will be motivated by the space fractional quantum mechanics, and non-locality in quantum mechanical systems. We also analyse a specific limit of this generalized deformation for one dimensional system, and in that limit, a nonlocal deformation of the momentum operator generates a local deformation of all one dimensional quantum mechanical systems. We analyse the low energy effects of this deformation on a harmonic oscillator, Landau levels, Lamb shift, and potential barrier. We also demonstrate that this deformation leads to a discretization of space.
Static Aeroelastic Analysis with an Inviscid Cartesian Method
Rodriguez, David L.; Aftosmis, Michael J.; Nemec, Marian; Smith, Stephen C.
2014-01-01
An embedded-boundary, Cartesian-mesh flow solver is coupled with a three degree-of-freedom structural model to perform static, aeroelastic analysis of complex aircraft geometries. The approach solves a nonlinear, aerostructural system of equations using a loosely-coupled strategy. An open-source, 3-D discrete-geometry engine is utilized to deform a triangulated surface geometry according to the shape predicted by the structural model under the computed aerodynamic loads. The deformation scheme is capable of modeling large deflections and is applicable to the design of modern, very-flexible transport wings. The coupling interface is modular so that aerodynamic or structural analysis methods can be easily swapped or enhanced. After verifying the structural model with comparisons to Euler beam theory, two applications of the analysis method are presented as validation. The first is a relatively stiff, transport wing model which was a subject of a recent workshop on aeroelasticity. The second is a very flexible model recently tested in a low speed wind tunnel. Both cases show that the aeroelastic analysis method produces results in excellent agreement with experimental data.
Material translations in the Cartesian brain.
Bassiri, Nima
2012-03-01
This article reexamines the controversial doctrine of the pineal gland in Cartesian psychophysiology. It argues initially that Descartes' combined metaphysics and natural philosophy yield a distinctly human subject who is rational, willful, but also a living and embodied being in the world, formed in the union and through the dynamics of the interaction between the soul and the body. However, Descartes only identified one site at which this union was staged: the brain, and more precisely, the pineal gland, the small bulb of nervous tissue at the brain's center. The pineal gland was charged with the incredible task of ensuring the interactive mutuality between the soul and body, while also maintaining the necessary ontological incommensurability between them. This article reconsiders the theoretical obligations placed on the pineal gland as the site of the soul-body union, and looks at how the gland was consequently forced to adopt a very precarious ontological status. The article ultimately questions how successfully the Cartesian human could be localized in the pineal gland, while briefly considering the broader historical consequences of the ensuing equivalence of the self and brain. Copyright © 2011 Elsevier Ltd. All rights reserved.
GOD AND THE DEMON IN CARTESIAN AND AKAN PHILOSOPHIES
African Journals Online (AJOL)
HP
examine whether, and how, the human being who is deemed to know right and wrong is in some way portrayed in Cartesian and Akan philosophies as morally responsible for his or her actions, despite the potencies and influences of God and the demon. Knowledge and Activities of God and the Demon in Cartesian.
God and the demon in Cartesian and Akan philosophies: a ...
African Journals Online (AJOL)
I analyse presentations of God and the demon in Cartesian philosophy (as specifically found in his Meditations) and how they compare with the conceptions of God and the demon in indigenous Akan philosophy. Using the qualitative method, I also examine some implications of both the Cartesian and Akan notions of God ...
Revisiting the Cartesian model of pain.
Goldberg, Joel S
2008-01-01
In modern medicine, the Cartesian or nociceptive concept of chronic pain has been replaced with the biopsychosocial model in both theory and practice. This paper presents an argument along with observations in favor of chronic pain as a pure nociceptive experience separate from suffering and outlines theoretical and practical solutions to improve the diagnosis and treatment of patients who experience chronic pain. Theoretical solutions include increasing inhibitory descending neurotransmitters using monoamine oxidase inhibitors of subtype A in combination with dextroamphetamine, increasing beta endorphin through enzymology and/or ultrasound stimulation of the periaqueductal gray, developing long duration opioid analgesics using spin label probes of morphine and morphine analogs and destructive interference of nociceptive action potentials by eddy currents generated by a variable magnetic field. Practical solutions include prolonging local anesthetic blockade of small pain fibers with patient administered local anesthetic storage devices and abandonment of the multidisciplinary pain clinic.
An infinite family of superintegrable deformations of the Coulomb potential
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah [Centre de recherches mathematiques, CP 6128 succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada); Winternitz, Pavel, E-mail: post@CRM.UMontreal.C, E-mail: wintern@CRM.UMontreal.C [Centre de recherches mathematiques and Departement de mathematiques et de statistique, CP 6128 succ. Centre-Ville, Montreal, QC H3C 3J7 (Canada)
2010-06-04
We introduce a new family of Hamiltonians with a deformed Kepler-Coulomb potential dependent on an indexing parameter k. We show that this family is superintegrable for all rational k and compute the classical trajectories and quantum wavefunctions. We show that this system is related, via coupling constant metamorphosis, to a family of superintegrable deformations of the harmonic oscillator given by Tremblay, Turbiner and Winternitz. In doing so, we prove that all Hamiltonians with an oscillator term are related by coupling constant metamorphosis to systems with a Kepler-Coulomb term, both on Euclidean space. We also look at the effect of the transformation on the integrals of the motion, the classical trajectories and the wavefunctions, and give the transformed integrals explicitly for the classical system. (fast track communication)
Recurrence relations for the Cartesian derivatives of the Zernike polynomials.
Stephenson, Philip C L
2014-04-01
A recurrence relation for the first-order Cartesian derivatives of the Zernike polynomials is derived. This relation is used with the Clenshaw method to determine an efficient method for calculating the derivatives of any linear series of Zernike polynomials.
Spectral properties and stability of perturbed Cartesian product
Indian Academy of Sciences (India)
Prakash A Dabhi
This Banach algebra will be denoted by A ×T B. When T = 0, A ×T B is the Cartesian product space. Thus A ×T B can be regarded as a perturbation of the Cartesian product. When A is unital with identity e and θ : B → C is a multiplicative linear functional, then T : B → A defined by T(x) = θ(x)e (x ∈ B) is an algebra ...
Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.
Michael, J Robert; Volkov, Anatoliy
2015-03-01
The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.
Estimation of Cartesian Space Robot Trajectories Using Unit Quaternion Space
Directory of Open Access Journals (Sweden)
Alesš Ude
2014-08-01
Full Text Available The ability to estimate Cartesian space trajectories that include orientation is of great importance for many practical applications. While it is becoming easier to acquire trajectory data by computer vision methods, data measured by general-purpose vision or depth sensors are often rather noisy. Appropriate smoothing methods are thus needed in order to reconstruct smooth Cartesian space trajectories given noisy measurements. In this paper, we propose an optimality criterion for the problem of the smooth estimation of Cartesian space trajectories that include the end-effector orientation. Based on this criterion, we develop an optimization method for trajectory estimation which takes into account the special properties of the orientation space, which we represent by unit quaternions. The efficiency of the developed approach is discussed and experimental results are presented.
Constraints and spectra of a deformed quantum mechanics
Ching, Chee-Leong; Parwani, Rajesh R.; Singh, Kuldip
2012-10-01
We examine a deformed quantum mechanics in which the commutator between coordinates and momenta is a function of momenta. The Jacobi identity constraint on a two-parameter class of such modified commutation relations (MCR’s) shows that they encode an intrinsic maximum momentum; a subclass of which also implies a minimum position uncertainty. Maximum momentum causes the bound state spectrum of the one-dimensional harmonic oscillator to terminate at finite energy, whereby classical characteristics are observed for the studied cases. We then use a semiclassical analysis to discuss general concave potentials in one dimension and isotropic power-law potentials in higher dimensions. Among other conclusions, we find that in a subset of the studied MCR’s, the leading order energy shifts of bound states are of opposite sign compared to those obtained using string-theory motivated MCR’s, and thus these two cases are more easily distinguishable in potential experiments.
Dynamic visual cryptography on deformable finite element grids
Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.
2017-07-01
Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.
Hyperchaotic circuit with damped harmonic oscillators
DEFF Research Database (Denmark)
Lindberg, Erik; Murali, K.; Tamasevicius, A.
2001-01-01
capacitors and one nonlinear active conductor. The Lyapunov exponents are presented to confirm the hyperchaotic nature of the oscillations of the circuit. The nonlinear conductor is realized with a diode. A negative impedance converter and a linear resistor. The performance of the circuit is investigated...
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
Author Affiliations. B Bongioanni1 J L Torrea2. Departamento de Matemática, Facultad de Ingeniería Qímica, Universidad Nacional del Litoral, and Instituto de Matemática Aplicada del Litoral, Santa Fe (3000), Argentina; Departamento de Matemática, Facultad de Ciencias, Universidad Autónoma de Madrid, Spain ...
Information cloning of harmonic oscillator coherent states
Indian Academy of Sciences (India)
We show that it is possible to make arbitrary number of copies of coherent states with exactly the same information content as the original unknown state. Complete information about a coherent state is contained in the complex coherency parameter α. Thus by information cloning what we mean is the ability to make arbitrary ...
Sobolev spaces associated to the harmonic oscillator
Indian Academy of Sciences (India)
of Hermite functions is dense in any of them (Proposition 1). .... PROPOSITION 1. Let p be in the range 1
Perturbative Semiclassical Trace Formulae for Harmonic Oscillators
DEFF Research Database (Denmark)
Møller-Andersen, Jakob; Ögren, Magnus
2015-01-01
U(D) to O(D) symmetry breaking. We derive the gross structure of the semiclassical spectrum from periodic orbit theory, in the form of a perturbative (ħ → 0) trace formula. We then show how to apply the results to even-order polynomial potentials, possibly including mean-field terms. We have drawn...... the conclusion that the gross structure of the quantum spectrum is determined from only classical circular and diameter orbits for this class of systems....
QUANTUM THEORY OF DAMPED HARMONIC OSCILLATOR
African Journals Online (AJOL)
DJFLEX
However, the problem of quantum oscillator with time-varying frequency had been solved (Um et al,. 1987). The Hamiltonian of this model is usually quadratic in co-ordinates and momentum operators (Ikot et al, 2008). The quantum calculation is applied because it will give the information about the particle at intermediate ...
Virtual Prototyping through Co-simulation of a Cartesian Plotter
Groothuis, M.A.; Damstra, A.S.; Broenink, Johannes F.
This paper shows a model-based design trajectory for the development of real-time embedded control software using virtual prototyping. As a test case, a Cartesian plotter is designed. Functional correctness of the plotter software has been ensured by means of co-simulation using a virtual prototype
Power domination of the cartesian product of graphs
Directory of Open Access Journals (Sweden)
K.M. Koh
2016-04-01
Full Text Available In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs is a tree.
Geometry of good sets in n-fold Cartesian product
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Geometry of good sets in n-fold Cartesian product. A KŁOPOTOWSKI1, M G NADKARNI2,3 and. K P S BHASKARA RAO4. 1Université Paris XIII, Institut Galilée, 93430 Villetaneuse Cedex, France. 2Institute of Mathematical Sciences, C.I.T. Campus, Chennai 600 113, India. 3Chennai Mathematical Institute, Chennai 600 ...
Non-Cartesian MRI scan time reduction through sparse sampling
Wajer, F.T.A.W.
2001-01-01
Non-Cartesian MRI Scan-Time Reduction through Sparse Sampling Magnetic resonance imaging (MRI) signals are measured in the Fourier domain, also called k-space. Samples of the MRI signal can not be taken at will, but lie along k-space trajectories determined by the magnetic field gradients. MRI
The Thickness of Amalgamations and Cartesian Product of Graphs
Directory of Open Access Journals (Sweden)
Yang Yan
2017-08-01
Full Text Available The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.
The Louvain printers and the establishment of the Cartesian curriculum
Directory of Open Access Journals (Sweden)
Geert Vanpaemel
2012-03-01
Full Text Available With regard to the public circulation of knowledge, universities are often regarded as privileged institutions where information and ideas are formally transmitted through regulated didactic experiences. University life, however, provided a more complex environment in which various parallel and perhaps contradictory processes of transmission were at work. In this paper, we analyse a set of 55 engravings with scientific images, which started to appear around 1670 in student notebooks at the University of Louvain. These engravings, produced and sold by the Louvain printers Michael Hayé and Lambert Blendeff, were related to the philosophy curriculum of the Faculty of Arts but did not correspond entirely to the actual topics or doctrine taught. In fact, the obvious Cartesian orientation of the images was not in line with the more prudent position of the Faculty. This paper offers a preliminary analysis of the set of engravings and their role in the Cartesian reforms at Louvain.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Topics in graph theory graphs and their Cartesian product
Imrich, Wilfried; Rall, Douglas F
2008-01-01
From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.
SPECTRAL SETS AND TILES IN CARTESIAN PRODUCTS OVER ...
Indian Academy of Sciences (India)
41
Spectral set conjecture: A Borel set Ω ⊂ Rd of positive and finite. Lebesgue measure is a spectral set if and only if it ... Ω ⊂ G of positive and finite Haar measure is a spectral set if and only if it is a translational tile. ... Key words and phrases. p-adic number field, Cartesian product, tile, spectral set. This work was supported by ...
Naturalism and un-naturalism among the Cartesian physicians
Manning, Gideon
2008-01-01
Highlighting early modern medicine's program of explanation and intervention, I claim that there are two distinctive features of the physician's naturalism. These are, first, an explicit recognition that each patient had her own individual and highly particularized nature and, second, a self-conscious use of normative descriptions when characterizing a patient's nature as healthy (ordered) or unhealthy (disordered). I go on to maintain that in spite of the well documented Cartesian rejection ...
Kalman filter techniques for accelerated Cartesian dynamic cardiac imaging.
Feng, Xue; Salerno, Michael; Kramer, Christopher M; Meyer, Craig H
2013-05-01
In dynamic MRI, spatial and temporal parallel imaging can be exploited to reduce scan time. Real-time reconstruction enables immediate visualization during the scan. Commonly used view-sharing techniques suffer from limited temporal resolution, and many of the more advanced reconstruction methods are either retrospective, time-consuming, or both. A Kalman filter model capable of real-time reconstruction can be used to increase the spatial and temporal resolution in dynamic MRI reconstruction. The original study describing the use of the Kalman filter in dynamic MRI was limited to non-Cartesian trajectories because of a limitation intrinsic to the dynamic model used in that study. Here the limitation is overcome, and the model is applied to the more commonly used Cartesian trajectory with fast reconstruction. Furthermore, a combination of the Kalman filter model with Cartesian parallel imaging is presented to further increase the spatial and temporal resolution and signal-to-noise ratio. Simulations and experiments were conducted to demonstrate that the Kalman filter model can increase the temporal resolution of the image series compared with view-sharing techniques and decrease the spatial aliasing compared with TGRAPPA. The method requires relatively little computation, and thus is suitable for real-time reconstruction. Copyright © 2012 Wiley Periodicals, Inc.
A weakly-compressible Cartesian grid approach for hydrodynamic flows
Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D.
2017-11-01
The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (> 3) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article.
Forman, Christoph; Grimm, Robert; Hutter, Jana Maria; Maier, Andreas; Hornegger, Joachim; Zenge, Michael O
2013-01-01
Respiratory motion remains a major challenge for whole-heart coronary magnetic resonance angiography (CMRA). Recently, iterative reconstruction has been augmented with non-rigid motion compensation to correct for the effects of respiratory motion. The major challenge of this approach is the estimation of dense deformation fields. In this work, the application of such a motion-compensated reconstruction is proposed for accelerated 3D Cartesian whole-heart CMRA. Without the need for extra calibration data or user interaction, the nonrigid deformations due to respiratory motion are directly estimated on the acquired image data. In-vivo experiments on 14 healthy volunteers were performed to compare the proposed method with the result of a navigator-gated reference scan. While reducing the acquisition time by one third, the reconstructed images resulted in equivalent vessel sharpness of 0.44 +/- 0.06 mm(-1) and 0.45 +/- 0.05 mm(-1), respectively.
Cartesian moral philosophy and control over human beings
Solano Villareal, Diana
2016-01-01
This paper presents a deeper analysis of the Cartesian moral philosophy in the Discours de la méthode, Les passions de l’âme, and the Principia Philosophiae, also in search of arguments to make clear a relation of connection control of some human beings on other, and the mechanism by which this control hypothetical relationship between humans could manifest. Este artículo presenta un análisis más profundo de la filosofía moral cartesiana en el Discours de la méthode, Les passions de l’âme...
Squeezed states from a quantum deformed oscillator Hamiltonian
Energy Technology Data Exchange (ETDEWEB)
Ramírez, R. [IFLP, CONICET–Department of Mathematics, University of La Plata c.c. 67 1900, La Plata (Argentina); Reboiro, M., E-mail: marta.reboiro@gmail.com [IFLP, CONICET–Department of Physics, University of La Plata c.c. 67 1900, La Plata (Argentina)
2016-03-11
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Squeezed states from a quantum deformed oscillator Hamiltonian
International Nuclear Information System (INIS)
Ramírez, R.; Reboiro, M.
2016-01-01
The spectrum and the time evolution of a system, which is modeled by a non-hermitian quantum deformed oscillator Hamiltonian, is analyzed. The proposed Hamiltonian is constructed from a non-standard realization of the algebra of Heisenberg. We show that, for certain values of the coupling constants and for a range of values of the deformation parameter, the deformed Hamiltonian is a pseudo-hermitic Hamiltonian. We explore the conditions under which the Hamiltonian is similar to a Swanson Hamiltonian. Also, we show that the lowest eigenstate of the system is a squeezed state. We study the time evolution of the system, for different initial states, by computing the corresponding Wigner functions. - Highlights: • A generalization of the squeezed harmonic oscillator is constructed from a non-standard realization of the Heisenberg algebra. • It is proved that, for certain values of the parameters of the model, the Hamiltonian is a pseudo-hermitian Hamiltonian. • It is shown that the lowest eigenstate of the Hamiltonian is a squeezed state. • The squeezing behavior of the associated Gazeau–Klauder state, as a function of time, is discussed.
Chaotic motion in axially symmetric potentials with oblate quadrupole deformation
Energy Technology Data Exchange (ETDEWEB)
Letelier, Patricio S. [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Ramos-Caro, Javier, E-mail: javier@ime.unicamp.br [Departamento de Matematica Aplicada, IMECC, Universidade Estadual de Campinas, 13083-859, Campinas, SP (Brazil); Lopez-Suspes, Framsol, E-mail: framsol@gmail.com [Facultad de Telecomunicaciones, Universidad Santo Tomas and Escuela de Fisica, Universidad Industrial de Santander, Bucaramanga (Colombia)
2011-10-03
By computing the Poincare's surfaces of section and Lyapunov exponents, we study the effect of introducing an oblate quadrupole in the dynamics associated with two generic spherical potentials of physical interest: the central monopole and the isotropic harmonic oscillator. In the former case we find saddle points in the effective potential, in contrast to the statements presented by Gueron and Letelier in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. The results we show in the second case have application in nuclear or atomic physics. In particular, we find values of oblate deformation leading to a disappearance of shell structure in the single-particle spectrum. -- Highlights: → We find chaotic motion around a monopole with oblate quadrupole deformation. → This corrects the statements introduced in [E. Gueron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. → We present an alternative model for the potential due to an oblate deformed nuclei. → This leads to stochastic regions in the phase space of classical orbits. → It suggests that the shell structure of single-particle spectrum tends to disappear.
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
International Nuclear Information System (INIS)
Péron, Stéphanie; Benoit, Christophe
2013-01-01
This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.
Solus Secedo and Sapere Aude: Cartesian Meditation as Kantian Enlightenment
Directory of Open Access Journals (Sweden)
Suma Rajiva
2015-11-01
Full Text Available Recently Samuel Fleischacker has developed Kant’s model of enlightenment as a “minimalist enlightenment” in the tradition of a relatively thin proceduralism focused on the form of public debate and interaction. I want to discuss the possibility that such a minimalism, endorsed by Fleischacker, Habermas, Rawls, and others, benefits from a metaphysics of critical individual subjectivity as a prerequisite for the social proceduralism of the minimalist enlightenment. I argue that Kant’s enlightenment, metaphysically thicker than much contemporary proceduralism, constitutes a recovery and transformation of a subjective interiority deeply Cartesian in spirit and central to the reciprocity of the community of subjects in What is Enlightenment. This opens a space for a site of resistance to the social. Descartes’ solus secedo describes the analogical space of such a resistance for Kant’s sapere aude. The Meditations thus point forward implicitly to how a rational subject might achieve critical distance from tradition in its various forms, epistemic, ethical, moral, and political.
A System for Acoustic Field Measurement Employing Cartesian Robot
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Szczodrak Maciej
2016-09-01
Full Text Available A system setup for measurements of acoustic field, together with the results of 3D visualisations of acoustic energy flow are presented in the paper. Spatial sampling of the field is performed by a Cartesian robot. Automatization of the measurement process is achieved with the use of a specialized control system. The method is based on measuring the sound pressure (scalar and particle velocity(vector quantities. The aim of the system is to collect data with a high precision and repeatability. The system is employed for measurements of acoustic energy flow in the proximity of an artificial head in an anechoic chamber. In the measurement setup an algorithm for generation of the probe movement path is included. The algorithm finds the optimum path of the robot movement, taking into account a given 3D object shape present in the measurement space. The results are presented for two cases, first without any obstacle and the other - with an artificial head in the sound field.
On the research of flow around obstacle using the viscous Cartesian grid technique
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Liu Yan-Hua
2012-01-01
Full Text Available A new 2-D viscous Cartesian grid is proposed in current research. It is a combination of the existent body-fitted grid and Cartesian grid technology. On the interface of the two different type of grid, a fined triangular mesh is used to connect the two grids. Tests with flow around the cylinder and aerofoil NACA0012 show that the proposed scheme is easy for implement with high accuracy.
A Deformable Generic 3D Model of Haptoral Anchor of Monogenean
Teo, Bee Guan; Dhillon, Sarinder Kaur; Lim, Lee Hong Susan
2013-01-01
In this paper, a digital 3D model which allows for visualisation in three dimensions and interactive manipulation is explored as a tool to help us understand the structural morphology and elucidate the functions of morphological structures of fragile microorganisms which defy live studies. We developed a deformable generic 3D model of haptoral anchor of dactylogyridean monogeneans that can subsequently be deformed into different desired anchor shapes by using direct manipulation deformation technique. We used point primitives to construct the rectangular building blocks to develop our deformable 3D model. Point primitives are manually marked on a 2D illustration of an anchor on a Cartesian graph paper and a set of Cartesian coordinates for each point primitive is manually extracted from the graph paper. A Python script is then written in Blender to construct 3D rectangular building blocks based on the Cartesian coordinates. The rectangular building blocks are stacked on top or by the side of each other following their respective Cartesian coordinates of point primitive. More point primitives are added at the sites in the 3D model where more structural variations are likely to occur, in order to generate complex anchor structures. We used Catmull-Clark subdivision surface modifier to smoothen the surface and edge of the generic 3D model to obtain a smoother and more natural 3D shape and antialiasing option to reduce the jagged edges of the 3D model. This deformable generic 3D model can be deformed into different desired 3D anchor shapes through direct manipulation deformation technique by aligning the vertices (pilot points) of the newly developed deformable generic 3D model onto the 2D illustrations of the desired shapes and moving the vertices until the desire 3D shapes are formed. In this generic 3D model all the vertices present are deployed for displacement during deformation. PMID:24204903
A deformable generic 3D model of haptoral anchor of Monogenean.
Directory of Open Access Journals (Sweden)
Bee Guan Teo
Full Text Available In this paper, a digital 3D model which allows for visualisation in three dimensions and interactive manipulation is explored as a tool to help us understand the structural morphology and elucidate the functions of morphological structures of fragile microorganisms which defy live studies. We developed a deformable generic 3D model of haptoral anchor of dactylogyridean monogeneans that can subsequently be deformed into different desired anchor shapes by using direct manipulation deformation technique. We used point primitives to construct the rectangular building blocks to develop our deformable 3D model. Point primitives are manually marked on a 2D illustration of an anchor on a Cartesian graph paper and a set of Cartesian coordinates for each point primitive is manually extracted from the graph paper. A Python script is then written in Blender to construct 3D rectangular building blocks based on the Cartesian coordinates. The rectangular building blocks are stacked on top or by the side of each other following their respective Cartesian coordinates of point primitive. More point primitives are added at the sites in the 3D model where more structural variations are likely to occur, in order to generate complex anchor structures. We used Catmull-Clark subdivision surface modifier to smoothen the surface and edge of the generic 3D model to obtain a smoother and more natural 3D shape and antialiasing option to reduce the jagged edges of the 3D model. This deformable generic 3D model can be deformed into different desired 3D anchor shapes through direct manipulation deformation technique by aligning the vertices (pilot points of the newly developed deformable generic 3D model onto the 2D illustrations of the desired shapes and moving the vertices until the desire 3D shapes are formed. In this generic 3D model all the vertices present are deployed for displacement during deformation.
A deformable generic 3D model of haptoral anchor of Monogenean.
Teo, Bee Guan; Dhillon, Sarinder Kaur; Lim, Lee Hong Susan
2013-01-01
In this paper, a digital 3D model which allows for visualisation in three dimensions and interactive manipulation is explored as a tool to help us understand the structural morphology and elucidate the functions of morphological structures of fragile microorganisms which defy live studies. We developed a deformable generic 3D model of haptoral anchor of dactylogyridean monogeneans that can subsequently be deformed into different desired anchor shapes by using direct manipulation deformation technique. We used point primitives to construct the rectangular building blocks to develop our deformable 3D model. Point primitives are manually marked on a 2D illustration of an anchor on a Cartesian graph paper and a set of Cartesian coordinates for each point primitive is manually extracted from the graph paper. A Python script is then written in Blender to construct 3D rectangular building blocks based on the Cartesian coordinates. The rectangular building blocks are stacked on top or by the side of each other following their respective Cartesian coordinates of point primitive. More point primitives are added at the sites in the 3D model where more structural variations are likely to occur, in order to generate complex anchor structures. We used Catmull-Clark subdivision surface modifier to smoothen the surface and edge of the generic 3D model to obtain a smoother and more natural 3D shape and antialiasing option to reduce the jagged edges of the 3D model. This deformable generic 3D model can be deformed into different desired 3D anchor shapes through direct manipulation deformation technique by aligning the vertices (pilot points) of the newly developed deformable generic 3D model onto the 2D illustrations of the desired shapes and moving the vertices until the desire 3D shapes are formed. In this generic 3D model all the vertices present are deployed for displacement during deformation.
Multiscale geometric modeling of macromolecules I: Cartesian representation
Xia, Kelin; Feng, Xin; Chen, Zhan; Tong, Yiying; Wei, Guo-Wei
2014-01-01
This paper focuses on the geometric modeling and computational algorithm development of biomolecular structures from two data sources: Protein Data Bank (PDB) and Electron Microscopy Data Bank (EMDB) in the Eulerian (or Cartesian) representation. Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization. Variational multiscale surface definitions are proposed based on geometric flows and solvation analysis of biomolecular systems. Our approach leads to geometric and potential driven Laplace-Beltrami flows for biomolecular surface evolution and formation. The resulting surfaces are free of geometric singularities and minimize the total free energy of the biomolecular system. High order partial differential equation (PDE)-based nonlinear filters are employed for EMDB data processing. We show the efficacy of this approach in feature-preserving noise reduction. After the construction of protein multiresolution surfaces, we explore the analysis and characterization of surface morphology by using a variety of curvature definitions. Apart from the classical Gaussian curvature and mean curvature, maximum curvature, minimum curvature, shape index, and curvedness are also applied to macromolecular surface analysis for the first time. Our curvature analysis is uniquely coupled to the analysis of electrostatic surface potential, which is a by-product of our variational multiscale solvation models. As an expository investigation, we particularly emphasize the numerical algorithms and computational protocols for practical applications of the above multiscale geometric models. Such information may otherwise be scattered over the vast literature on this topic. Based on the curvature and electrostatic analysis from our multiresolution surfaces, we introduce a new concept, the
Large deformation frictional contact analysis with immersed boundary method
Navarro-Jiménez, José Manuel; Tur, Manuel; Albelda, José; Ródenas, Juan José
2018-01-01
This paper proposes a method of solving 3D large deformation frictional contact problems with the Cartesian Grid Finite Element Method. A stabilized augmented Lagrangian contact formulation is developed using a smooth stress field as stabilizing term, calculated by Zienckiewicz and Zhu Superconvergent Patch Recovery. The parametric definition of the CAD surfaces (usually NURBS) is considered in the definition of the contact kinematics in order to obtain an enhanced measure of the contact gap. The numerical examples show the performance of the method.
Advances in non-Cartesian parallel magnetic resonance imaging using the GRAPPA operator
Energy Technology Data Exchange (ETDEWEB)
Seiberlich, Nicole
2008-07-21
This thesis has presented several new non-Cartesian parallel imaging methods which simplify both gridding and the reconstruction of images from undersampled data. A novel approach which uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory called GRAPPA Operator Gridding (GROG) is described. GROG shifts any acquired k-space data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. The only requirements for GROG are a multi-channel acquisition and a calibration dataset for the determination of the GROG weights. Then an extension of GRAPPA Operator Gridding, namely Self-Calibrating GRAPPA Operator Gridding (SC-GROG) is discussed. SC-GROG is a method by which non-Cartesian data can be gridded using spatial information from a multi-channel coil array without the need for an additional calibration dataset, as required in standard GROG. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. Thereafter a simple, novel method for performing modified Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG to arrive at a non-aliased image is introduced. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. Finally a novel method of using GROG to mimic the bunched phase encoding acquisition (BPE) scheme is discussed. In MRI, it is generally assumed that an artifact-free image can be reconstructed only from sampled points which fulfill the Nyquist criterion. However, the BPE reconstruction is based on the Generalized Sampling Theorem of Papoulis, which states that a continuous signal can be reconstructed from sampled points as long as the points are on average sampled at the Nyquist frequency. A novel
Advances in non-Cartesian parallel magnetic resonance imaging using the GRAPPA operator
International Nuclear Information System (INIS)
Seiberlich, Nicole
2008-01-01
This thesis has presented several new non-Cartesian parallel imaging methods which simplify both gridding and the reconstruction of images from undersampled data. A novel approach which uses the concepts of parallel imaging to grid data sampled along a non-Cartesian trajectory called GRAPPA Operator Gridding (GROG) is described. GROG shifts any acquired k-space data point to its nearest Cartesian location, thereby converting non-Cartesian to Cartesian data. The only requirements for GROG are a multi-channel acquisition and a calibration dataset for the determination of the GROG weights. Then an extension of GRAPPA Operator Gridding, namely Self-Calibrating GRAPPA Operator Gridding (SC-GROG) is discussed. SC-GROG is a method by which non-Cartesian data can be gridded using spatial information from a multi-channel coil array without the need for an additional calibration dataset, as required in standard GROG. Although GROG can be used to grid undersampled datasets, it is important to note that this method uses parallel imaging only for gridding, and not to reconstruct artifact-free images from undersampled data. Thereafter a simple, novel method for performing modified Cartesian GRAPPA reconstructions on undersampled non-Cartesian k-space data gridded using GROG to arrive at a non-aliased image is introduced. Because the undersampled non-Cartesian data cannot be reconstructed using a single GRAPPA kernel, several Cartesian patterns are selected for the reconstruction. Finally a novel method of using GROG to mimic the bunched phase encoding acquisition (BPE) scheme is discussed. In MRI, it is generally assumed that an artifact-free image can be reconstructed only from sampled points which fulfill the Nyquist criterion. However, the BPE reconstruction is based on the Generalized Sampling Theorem of Papoulis, which states that a continuous signal can be reconstructed from sampled points as long as the points are on average sampled at the Nyquist frequency. A novel
LES of Internal Combustion Engine Flows Using Cartesian Overset Grids
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Falkenstein Tobias
2017-11-01
Full Text Available Accurate computations of turbulent flows using the Large-Eddy Simulation (LES technique with an appropriate SubFilter Scale (SFS model require low artificial dissipation such that the physical energy cascade process is not perturbed by numerical artifacts. To realize this in practical simulations, energy-conserving numerical schemes and high-quality computational grids are needed. If unstructured meshes are used, the latter requirement often makes grid generation for complex geometries very difficult. Structured Cartesian grids offer the advantage that uncertainties in mesh quality are reduced to choosing appropriate resolution. However, two intrinsic challenges of the structured approach are local mesh refinement and representation of complex geometries. In this work, the effectiveness of numerical methods which can be expected to reduce both drawbacks is assessed in engine flows, using a multi-physics inhouse code. The overset grid approach is utilized to arbitrarily combine grid patches of different spacing to a flow domain of complex shape during mesh generation. Walls are handled by an Immersed Boundary (IB method, which is combined with a wall function to treat underresolved boundary layers. A statistically stationary Spark Ignition (SI engine port flow is simulated at Reynolds numbers typical for engine operation. Good agreement of computed and measured integral flow quantities like overall pressure loss and tumble number is found. A comparison of simulated velocity fields to Particle Image Velocimetry (PIV measurement data concludes the validation of the enhanced numerical framework for both mean velocity and turbulent fluctuations. The performance of two SFS models, the dynamic Smagorinsky model with Lagrangian averaging along pathlines and the coherent structure model, is tested on different grids. Sensitivity of pressure loss and tumble ratio to the wall treatment and mesh refinement is presented. It is shown that increased wall
Problems of Cartesian Product Solved by Elementary School Students Sandra Maria Pinto MaginaI
Directory of Open Access Journals (Sweden)
Sandra Maria Pinto Magina
2018-03-01
Full Text Available The study investigated the solution of direct (which requires multiplication for its resolution and inverse (which requires division for its resolution Cartesian product problems by elementary education students, examining the level of problem complexity and the children procedures according to the type of problem. A total of 269 8 and 10 year-old students attending from 3rd to 5th grade, were asked 8 and 10 years to solve direct and inverse Cartesian product problems. As expected, the inverse problem was the most difficult one. The strategies showed that levels of combinatorial reasoning vary according to the type of problem. It was also found a progression in the solution of direct Cartesian product problems, but not in relation to the solution of inverse problems.
Directory of Open Access Journals (Sweden)
O. A. Domínguez-Ramírez
2006-01-01
Full Text Available Perception and interaction with virtual surfaces, through kinaesthetic sensation and visual stimuli, is the basic issue of a haptic interface. When the virtual or real object is in a remote location, and guidance is required to perceive kinaesthetic feedback, a haptic guidance scheme is required. In this document, with purpose of haptic-guided exploration, a new scheme for simultaneous control of force and cartesian position is proposed without using inverse kinematics, and without using the dynamic model of PHANToM, though a strict stability analysis includes the dynamic model of PHANToM. We rely on our previously proposed results to propose a new haptic cartesian controller to reduce the burden of computing cartesian forces in PHANToM. Furthermore, a time base generator for finite-time tracking is also proposed to achieve very fast tracking and high precision, which translated into high fidelity kinaesthetic feedback.
Free breathing whole-heart 3D CINE MRI with self-gated Cartesian trajectory.
Usman, M; Ruijsink, B; Nazir, M S; Cruz, G; Prieto, C
2017-05-01
To present a method that uses a novel free-running self-gated acquisition to achieve isotropic resolution in whole heart 3D Cartesian cardiac CINE MRI. 3D cardiac CINE MRI using navigator gating results in long acquisition times. Recently, several frameworks based on self-gated non-Cartesian trajectories have been proposed to accelerate this acquisition. However, non-Cartesian reconstructions are computationally expensive due to gridding, particularly in 3D. In this work, we propose a novel highly efficient self-gated Cartesian approach for 3D cardiac CINE MRI. Acquisition is performed using CArtesian trajectory with Spiral PRofile ordering and Tiny golden angle step for eddy current reduction (so called here CASPR-Tiger). Data is acquired continuously under free breathing (retrospective ECG gating, no preparation pulses interruption) for 4-5min and 4D whole-heart volumes (3D+cardiac phases) with isotropic spatial resolution are reconstructed from all available data using a soft gating technique combined with temporal total variation (TV) constrained iterative SENSE reconstruction. For data acquired on eight healthy subjects and three patients, the reconstructed images using the proposed method had good contrast and spatio-temporal variations, correctly recovering diastolic and systolic cardiac phases. Non-significant differences (P>0.05) were observed in cardiac functional measurements obtained with proposed 3D approach and gold standard 2D multi-slice breath-hold acquisition. The proposed approach enables isotropic 3D whole heart Cartesian cardiac CINE MRI in 4 to 5min free breathing acquisition. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.
Werner, F.; Gdaniec, N.; Knopp, T.
2017-05-01
Magnetic particle imaging (MPI) is a quantitative imaging modality that allows us to determine the distribution of superparamagnetic nanoparticles. Sampling is achieved by moving a field-free point (FFP) along a specific trajectory through the volume of interest. The magnetic material that lies along the path or in the close vicinity of the FFP changes its magnetization and induces a voltage in the surrounding receiver coils. Various trajectories for the FFP are conceivable, but most experimental MPI scanners either use a Cartesian or a Lissajous sampling trajectory. For the first time, this study compares both sampling methods experimentally using an MPI scanner that allows us to implement both sampling patterns. By default, the scanner is capable of scanning 2D and 3D field of views using a Lissajous trajectory. But since it also has a 1D mode, it is possible to perform Cartesian measurements by shifting the 1D scan line in a perpendicular direction to the FFP movement using the focus field. These line scans are jointly reconstructed to obtain a 2D image. In a further step, the unidirectional Cartesian trajectory is improved by interchanging the excitation and the focus-field direction leading to a bidirectional Cartesian trajectory. Our findings reveal similar results for the bidirectional Cartesian and Lissajous trajectory concerning the overall image quality and sensitivity. In a more detailed view, the bidirectional Cartesian trajectory achieves a slightly higher spatial center resolution, whereas the Lissajous trajectory is more efficient regarding the temporal resolution since less acquisition time is needed to reach an adequate image quality.
Random subspaces for encryption based on a private shared Cartesian frame
International Nuclear Information System (INIS)
Bartlett, Stephen D.; Hayden, Patrick; Spekkens, Robert W.
2005-01-01
A private shared Cartesian frame is a novel form of private shared correlation that allows for both private classical and quantum communication. Cryptography using a private shared Cartesian frame has the remarkable property that asymptotically, if perfect privacy is demanded, the private classical capacity is three times the private quantum capacity. We demonstrate that if the requirement for perfect privacy is relaxed, then it is possible to use the properties of random subspaces to nearly triple the private quantum capacity, almost closing the gap between the private classical and quantum capacities
Developing seamless method to calculate heat convection and conduction on cartesian grid
International Nuclear Information System (INIS)
Tanno, I.; Morinishi, K.; Matsuno, K.; Nishida, H.
2005-01-01
In these days, studying and developing algorithms which calculate fluid flows which have interfaces or bodies on cartesian grid become trend of computational fluid dynamics area. In this paper, we propose Virtual Flux Method (VFM) which calculates heat and fluid flow around interfaces or bodies on cartesian grid. This method enables to seamlessly calculate heat convection on the surface of the bodies and fluid and heat conduction inside bodies. In three dimensional calculations of shell and tube type heat exchangers, there is a possibility that fluid inside and outside tubes and heat flow between these fluid and tube bodies are calculated without any kind of extra algorithms but VFM. (author)
The First Orchestrated Attack on Spinoza: Johannes Melchioris and the Cartesian Network in Utrecht.
Gootjes, Albert
2018-01-01
This article examines the immediate Dutch reception of the Tractatus theologico-politicus. Using newfound archival sources it demonstrates that the anti-Spinoza activity of the Cartesians in Utrecht extends far beyond the well-known writings of Lambertus van Velthuysen and Regnerus van Mansveld. Their Cartesian network not only produced the very first public refutation to appear, but also formed a center for coordinating much of the Dutch response to Spinoza. This engagement, it is argued in closing, must be accounted for in Spinoza reception history, and forms the background to the mysterious visit Spinoza paid to Utrecht in the summer of 1673.
DEFF Research Database (Denmark)
Hansen, N.; Huang, X.; Hughes, D.A.
2004-01-01
Microstructural characterization and modeling has shown that a variety of metals deformed by different thermomechanical processes follows a general path of grain subdivision, by dislocation boundaries and high angle boundaries. This subdivision has been observed to very small structural scales...
Expanding from discrete Cartesian to permutation Gene-pool Optimal Mixing Evolutionary Algorithms
P.A.N. Bosman (Peter); N.H. Luong (Ngoc Hoang); D. Thierens (Dirk)
2016-01-01
textabstractThe recently introduced Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) family, which includes the Linkage Tree Genetic Algorithm (LTGA), has been shown to scale excellently on a variety of discrete, Cartesian-space, optimization problems. This paper shows that GOMEA can quite
Directory of Open Access Journals (Sweden)
Fanxi LYU
2017-06-01
Full Text Available To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design, a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper. Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algorithms. The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual (GMRES algorithm. During computation, solution-based mesh adaptation is also applied so as to capture flow features more accurately. An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead. According to the characteristics of the Cartesian grids, the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces, which can significantly improve the solution converging speed. The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing, a DLR-F4 wing-body, and an unconventional figuration of a blended wing body (BWB. The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation, and the results suggest its capacity in application for aircraft conceptual design.
Embodying Learning: Post-Cartesian Pedagogy and the Academic Study of Religion
Lelwica, Michelle Mary
2009-01-01
This paper explores the concept and practice of "embodied pedagogy" as an alternative to the Cartesian approach to knowledge that is tacitly embedded in traditional modes of teaching and learning about religion. My analysis highlights a class I co-teach that combines the study of Aikido (a Japanese martial art) with seminar-style discussions of…
Rapid Non-Cartesian Parallel Imaging Reconstruction on Commodity Graphics Hardware
DEFF Research Database (Denmark)
Sørensen, Thomas Sangild; Atkinson, David; Boubertakh, Redha
2008-01-01
This presentation describes an implementation of non-Cartesian SENSE and kt-SENSE accelerated on commodity graphics hardware. This inexpensive hardware platform is now fully programmable and very suited for solving reconstruction problems. We show that for both SENSE and kt-SENSE the reconstruction...
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
then a continuous symmetry transformation (point, contact or higher-order) that leaves the action functional invariant yields a conservation law. Thus studies in symmetries and conservation laws of a physical system using this theorem require the associated equation of motion to follow from the action principle [2]. The object ...
Diatomic Molecules Effective Potential for an Harmonic Oscillator ...
African Journals Online (AJOL)
A model anharmonic potential was considered and was used in the Schrödinger time independent wave equation to describe a carbon monoxide molecule. Central difference scheme was used in approximating the derivative term in the Schrödinger equation leading to a tri-diagonal band system of equation. The method of ...
Laser cooling of a harmonic oscillator's bath with optomechanics
Xu, Xunnong; Taylor, Jacob
Thermal noise reduction in mechanical systems is a topic both of fundamental interest for studying quantum physics at the macroscopic level and for application of interest, such as building high sensitivity mechanics based sensors. Similar to laser cooling of neutral atoms and trapped ions, the cooling of mechanical motion by radiation pressure can take single mechanical modes to their ground state. Conventional optomechanical cooling is able to introduce additional damping channel to mechanical motion, while keeping its thermal noise at the same level, and as a consequence, the effective temperature of the mechanical mode is lowered. However, the ratio of temperature to quality factor remains roughly constant, preventing dramatic advances in quantum sensing using this approach. Here we propose an efficient scheme for reducing the thermal load on a mechanical resonator while improving its quality factor. The mechanical mode of interest is assumed to be weakly coupled to its heat bath but strongly coupled to a second mechanical mode, which is cooled by radiation pressure coupling to a red detuned cavity field. We also identify a realistic optomechanical design that has the potential to realize this novel cooling scheme. Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, MD 20742, USA.
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
2016-12-03
Dec 3, 2016 ... Model of cosmology, on a mass–energy equivalence basis, observed that the Universe consists of about. 26.8% dark matter, 68.3% dark energy (DE) and 4.9% ordinary matter. So, about 95% of the Universe remains elusive to us. Most quantum field theories predict the magnitude of the vacuum energy ...
Investigation of Coupled Harmonic Oscillations with a V-Scope.
Trumper, Ricardo; Wiener, Achiam
1994-01-01
In this paper, experiments with equal-length and different-length coupled pendulums were carried out measuring the frequency of energy exchange between them using microcomputer-based technology. The experiment described in this paper would be most appropriate for an introductory mechanics laboratory course. (15 references) (LZ)
On quantum harmonic oscillator being subjected to absolute ...
Indian Academy of Sciences (India)
In this paper, assuming a boundary condition that the product of momentum and position, or the product of energy density and position remains constant in the QHO, it is established that a particle subjected to increasing frequencies becomes gradually subtler to transform into a very high dormant potential energy. This very ...
Rigorous quantum limits on monitoring free masses and harmonic oscillators
Roy, S. M.
2018-03-01
There are heuristic arguments proposing that the accuracy of monitoring position of a free mass m is limited by the standard quantum limit (SQL): σ2( X (t ) ) ≥σ2( X (0 ) ) +(t2/m2) σ2( P (0 ) ) ≥ℏ t /m , where σ2( X (t ) ) and σ2( P (t ) ) denote variances of the Heisenberg representation position and momentum operators. Yuen [Phys. Rev. Lett. 51, 719 (1983), 10.1103/PhysRevLett.51.719] discovered that there are contractive states for which this result is incorrect. Here I prove universally valid rigorous quantum limits (RQL), viz. rigorous upper and lower bounds on σ2( X (t ) ) in terms of σ2( X (0 ) ) and σ2( P (0 ) ) , given by Eq. (12) for a free mass and by Eq. (36) for an oscillator. I also obtain the maximally contractive and maximally expanding states which saturate the RQL, and use the contractive states to set up an Ozawa-type measurement theory with accuracies respecting the RQL but beating the standard quantum limit. The contractive states for oscillators improve on the Schrödinger coherent states of constant variance and may be useful for gravitational wave detection and optical communication.
Harmonic oscillator in Snyder space: The classical case and the ...
Indian Academy of Sciences (India)
ω = 8.5 · 10−4 (continuous line), and for normal q(t) (dashed line). Figure 2. Plot for the two branches of Snyder p(t) with l = 10−5 and ω = 8.5 · 10−4 (continuous line), and for normal p(t) (dashed line). where d is a suitable constant in order to achieve the initial condition q(t = 0) = 1, and p can be expressed in terms of q:.
Phase-space treatment of the driven quantum harmonic oscillator
Indian Academy of Sciences (India)
2017-02-22
Feb 22, 2017 ... force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum .... Magnus expansion. In §3, the wave functions ±(q, p, t) of the simultaneous values of position q and momen- tum p are constructed in terms of pq and qp ...
Nonlinear Analysis of a Cross-Coupled Quadrature Harmonic Oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2004-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator leading to an expression for the trade-off between signal quadrature and close-in phase noise. The theory shows that nonlinearity in the coupling transconductance results in AM-PM noise close to the carrier, which...... increases with the coupling strength. The results are compared with SPECTRE RF simulations....
Instabilities of the harmonic oscillator with fluctuating damping
Méndez, Vicenç; Horsthemke, Werner; Mestres, Pau; Campos, Daniel
2011-10-01
We investigate the instabilities of a linear damped oscillator due to fluctuations of the damping parameter. The fluctuations are driven either by Gaussian white noise or Poisson white noise (white shot noise). We consider three notions of stability. The first two are the well-known notions of stability in the mean and stability in the mean square. We introduce the concept of thermodynamic stability, corresponding to a nonpositive rate of energy dissipation at all times. We derive analytical results for the various instability thresholds, confirm the validity of our approach for white shot noise by numerical simulations, and obtain the unexpected result that mean-square and thermodynamic stability coincide for the two types of white noise.
Symmetries and conservation laws of the damped harmonic oscillator
Indian Academy of Sciences (India)
We work with a formulation of Noether-symmetry analysis which uses the properties of infinitesimal point transformations in the space-time variables to establish the association between symmetries and conservation laws of a dynamical system. Here symmetries are expressed in the form of generators. We have studied the ...
International Nuclear Information System (INIS)
Zhang Wen; Haas, Stephan
2009-01-01
An implementation of the fast multiple method (FMM) is performed for magnetic systems with long-ranged dipolar interactions. Expansion in spherical harmonics of the original FMM is replaced by expansion of polynomials in Cartesian coordinates, which is considerably simpler. Under open boundary conditions, an expression for multipole moments of point dipoles in a cell is derived. These make the program appropriate for nanomagnetic simulations, including magnetic nanoparticles and ferrofluids. The performance is optimized in terms of cell size and parameter set (expansion order and opening angle) and the trade off between computing time and accuracy is quantitatively studied. A rule of thumb is proposed to decide the appropriate average number of dipoles in the smallest cells, and an optimal choice of parameter set is suggested. Finally, the superiority of Cartesian coordinate FMM is demonstrated by comparison to spherical harmonics FMM and FFT.
A Cartesian Adaptive Level Set Method for Two-Phase Flows
Ham, F.; Young, Y.-N.
2003-01-01
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
Smith, C U
2001-08-01
J. C. Eccles (1903-1997) had a highly distinguished career in neurophysiology, being awarded the Nobel Prize for Medicine or Physiology in 1963. This paper sets him within the Cartesian tradition of British neurophysiology initiated by Thomas Henry Huxley in the mid-19th century. It shows how the mind-brain problematique of the Cartesian tradition troubled him throughout his career, leading him finally to a solution in terms of quantum microphysics and microphysiology. This position, which has subsequently become fashionable, is discussed and shown (at least in the form Eccles espoused) to provide no solution to the problem posed by Descartes in the early 17th century. Copyright 2001 Academic Press.
Robust Adaptive Control of a Free-Floating Space Robot System in Cartesian Space
Directory of Open Access Journals (Sweden)
Fuhai Zhang
2015-11-01
Full Text Available This paper presents a novel, robust, adaptive trajectory-tracking control scheme for the free-floating space robot system in Cartesian space. The dynamic equation of the free-floating space robot system in Cartesian space is derived from the augmented variable method. The proposed basic robust adaptive controller is able to deal with parametric and non-parametric uncertainties simultaneously. Another advantage of the control scheme is that the known and unknown external disturbance bounds can be considered using a modification of the parameter-estimation law. In addition, three cases are certified to achieve robustness for both parametric uncertainties and external disturbances. The simulation results show that the control scheme can ensure stable tracking of the desired trajectory of the end-effector.
Kim, Seungil
2010-01-01
In this paper, we study the spectrum of the operator which results when the Perfectly Matched Layer (PML) is applied in Cartesian geometry to the Laplacian on an unbounded domain. This is often thought of as a complex change of variables or "complex stretching." The reason that such an operator is of interest is that it can be used to provide a very effective domain truncation approach for approximating acoustic scattering problems posed on unbounded domains. Stretching associated with polar or spherical geometry lead to constant coefficient operators outside of a bounded transition layer and so even though they are on unbounded domains, they (and their numerical approximations) can be analyzed by more standard compact perturbation arguments. In contrast, operators associated with Cartesian stretching are non-constant in unbounded regions and hence cannot be analyzed via a compact perturbation approach. Alternatively, to show that the scattering problem PML operator associated with Cartesian geometry is stable for real nonzero wave numbers, we show that the essential spectrum of the higher order part only intersects the real axis at the origin. This enables us to conclude stability of the PML scattering problem from a uniqueness result given in a subsequent publication. © 2009 Elsevier Inc. All rights reserved.
Many-particle hydrodynamic interactions in parallel-wall geometry: Cartesian-representation method
International Nuclear Information System (INIS)
Blawzdziewicz, J.; Wajnryb, E.; Bhattacharya, S.
2005-01-01
This talk will describe the results of our theoretical and numerical studies of hydrodynamic interactions in a suspension of spherical particles confined between two parallel planar walls, under creeping-flow conditions. We propose an efficient algorithm for evaluating many-particle friction matrix in this system-no Stokesian-dynamics algorithm of this kind has been available so far. Our approach involves expanding the fluid velocity field in the wall-bounded suspension into spherical and Cartesian fundamental sets of Stokes flows. The spherical set is used to describe the interaction of the fluid with the particles and the Cartesian set to describe the interaction with the walls. At the core of our method are transformation relations between the spherical and Cartesian fundamental sets. Using the transformation formulas, we derive a system of linear equations for the force multipoles induced on the particle surfaces; the coefficients in these equations are given in terms of lateral Fourier integrals corresponding to the directions parallel to the walls. The force-multipole equations have been implemented in a numerical algorithm for the evaluation of the multiparticle friction matrix in the wall-bounded system. The algorithm involves subtraction of the particle-wall and particle-particle lubrication contributions to accelerate the convergence of the results with the spherical-harmonics order, and a subtraction of the single-wall contributions to accelerate the convergence of the Fourier integrals. (author)
Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators
Directory of Open Access Journals (Sweden)
Za'er S. Abo-Hammour
2011-12-01
Full Text Available A novel continuous genetic algorithm (CGA along with distance algorithm for solving collisions‐free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D‐H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non‐ redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.
Continuous Genetic Algorithms for Collision-Free Cartesian Path Planning of Robot Manipulators
Directory of Open Access Journals (Sweden)
Za'er S. Abo-Hammour
2011-12-01
Full Text Available A novel continuous genetic algorithm (CGA along with distance algorithm for solving collisions-free path planning problem for robot manipulators is presented in this paper. Given the desired Cartesian path to be followed by the manipulator, the robot configuration as described by the D-H parameters, and the available stationary obstacles in the workspace of the manipulator, the proposed approach will autonomously select a collision free path for the manipulator that minimizes the deviation between the generated and the desired Cartesian path, satisfy the joints limits of the manipulator, and maximize the minimum distance between the manipulator links and the obstacles. One of the main features of the algorithm is that it avoids the manipulator kinematic singularities due to the inclusion of forward kinematics model in the calculations instead of the inverse kinematics. The new robot path planning approach has been applied to two different robot configurations; 2R and PUMA 560, as non-redundant manipulators. Simulation results show that the proposed CGA will always select the safest path avoiding obstacles within the manipulator workspace regardless of whether there is a unique feasible solution, in terms of joint limits, or there are multiple feasible solutions. In addition to that, the generated path in Cartesian space will be of very minimal deviation from the desired one.
Cyclones and Vortices: Alejo Carpentier's Reasons of State as Cartesian Discourse
Directory of Open Access Journals (Sweden)
Joseph F. O'Neill
1978-01-01
Full Text Available Alejo Carpentier's Reasons of State is a reconstruction of Cartesian discourse that is paradoxically both fantastic and baroque in its implications. Building upon the assumption that Cartesianism is typically baroque and therefore a dynamism, rather than a dichotomy of subject and object, the novel proceeds in the form of a retrospective deathbed narrative to suggest the radically anti-Cartesian polarization of subject and object in fin de siècle Latin America by portraying its dictator/narrator as a man whose world-view, like his culture's, is schizophrenically divided between magical realism and positivist progressivism. This ambiguous narrative perception is comparable to that of the literary genre known as the fantastic, whose several subjective themes are found to be operative in Reasons of State . Their working-out in the novel, however, is not exclusively psychological or socio-psychological. Ultimately they assume in the narrator's retrospective reflections a metaphorical character that effects a paradoxical synthesis of the prevailing opposed epistemologies: a self-aware folk consciousness that, in its dependence upon contradiction, is indisputably baroque.
International Nuclear Information System (INIS)
Wu Hongchun; Xie Zhongsheng; Zhu Xuehua
1994-01-01
The nodal discrete-ordinate transport calculating model of anisotropy scattering problem in three-dimensional cartesian geometry is given. The computing code NOTRAN/3D has been encoded and the satisfied conclusion is gained
Santucci, Domiziana; Lee, Sheila S.; Hartman, Heidi; Walgampaya, Shyama; AlObaidy, Mamdoh; Ramalho, Miguel; Dale, Brian M.; Semelka, Richard C.
2017-01-01
Abstract Objective: The purpose of this study was to compare two short-tau inversion recovery (STIR) sequences, Cartesian and radial (BLADE) acquisitions, for breast magnetic resonance imaging (MRI) examinations. Materials and Methods: Ninety-six women underwent 1.5 T breast MRI exam (48 Cartesian and 48 BLADE). Qualitative analysis including image artifacts, image quality, fat-suppression, chest-wall depiction, lesion detection, lymph node depiction and overall impression were evaluated by...
Muralidharan, Balaji; Menon, Suresh
2018-03-01
A high-order adaptive Cartesian cut-cell method, developed in the past by the authors [1] for simulation of compressible viscous flow over static embedded boundaries, is now extended for reacting flow simulations over moving interfaces. The main difficulty related to simulation of moving boundary problems using immersed boundary techniques is the loss of conservation of mass, momentum and energy during the transition of numerical grid cells from solid to fluid and vice versa. Gas phase reactions near solid boundaries can produce huge source terms to the governing equations, which if not properly treated for moving boundaries, can result in inaccuracies in numerical predictions. The small cell clustering algorithm proposed in our previous work is now extended to handle moving boundaries enforcing strict conservation. In addition, the cell clustering algorithm also preserves the smoothness of solution near moving surfaces. A second order Runge-Kutta scheme where the boundaries are allowed to change during the sub-time steps is employed. This scheme improves the time accuracy of the calculations when the body motion is driven by hydrodynamic forces. Simple one dimensional reacting and non-reacting studies of moving piston are first performed in order to demonstrate the accuracy of the proposed method. Results are then reported for flow past moving cylinders at subsonic and supersonic velocities in a viscous compressible flow and are compared with theoretical and previously available experimental data. The ability of the scheme to handle deforming boundaries and interaction of hydrodynamic forces with rigid body motion is demonstrated using different test cases. Finally, the method is applied to investigate the detonation initiation and stabilization mechanisms on a cylinder and a sphere, when they are launched into a detonable mixture. The effect of the filling pressure on the detonation stabilization mechanisms over a hyper-velocity sphere launched into a hydrogen
Dong, Liang; Niu, Qian
2015-03-01
It is well known that elastic deformation in crystal can be described in the language of a metric. However, how the metric couples to the one-electron Hamiltonian in a deformed crystal is not very clear. By coordinate transformation from a Cartesian frame to lattice frame where all coordinates of ions are fixed, the metric emerges naturally both in the kinetic energy and potential energy of an electron. Besides, the velocity field of ions is also manifested in the Hamiltonian, which resembles the role of a vector potential. When the deformation slowly varies both in space and time, the wave-packet method can be used to study the Berry phase effect of deformation. This method applies to finite-strain cases and is accurate up to the first order of strain gradient. Different deformation effects are discussed, such as piezoelectricity, flexoelectricity and curving effect of a two-dimensional material
Fara, Patricia
2008-12-01
Few original portraits exist of René Descartes, yet his theories of vision were central to Enlightenment thought. French philosophers combined his emphasis on sight with the English approach of insisting that ideas are not innate, but must be built up from experience. In particular, Denis Diderot criticised Descartes's views by describing how Nicholas Saunderson--a blind physics professor at Cambridge--relied on touch. Diderot also made Saunderson the mouthpiece for some heretical arguments against the existence of God.
Motion correction for functional MRI with three-dimensional hybrid radial-Cartesian EPI.
Graedel, Nadine N; McNab, Jennifer A; Chiew, Mark; Miller, Karla L
2017-08-01
Subject motion is a major source of image degradation for functional MRI (fMRI), especially when using multishot sequences like three-dimensional (3D EPI). We present a hybrid radial-Cartesian 3D EPI trajectory enabling motion correction in k-space for functional MRI. The EPI "blades" of the 3D hybrid radial-Cartesian EPI sequence, called TURBINE, are rotated about the phase-encoding axis to fill out a cylinder in 3D k-space. Angular blades are acquired over time using a golden-angle rotation increment, allowing reconstruction at flexible temporal resolution. The self-navigating properties of the sequence are used to determine motion parameters from a high temporal-resolution navigator time series. The motion is corrected in k-space as part of the image reconstruction, and evaluated for experiments with both cued and natural motion. We demonstrate that the motion correction works robustly and that we can achieve substantial artifact reduction as well as improvement in temporal signal-to-noise ratio and fMRI activation in the presence of both severe and subtle motion. We show the potential for hybrid radial-Cartesian 3D EPI to substantially reduce artifacts for application in fMRI, especially for subject groups with significant head motion. The motion correction approach does not prolong the scan, and no extra hardware is required. Magn Reson Med 78:527-540, 2017. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2016 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine.
International Nuclear Information System (INIS)
Biondo, Elliott D.; Davis, Andrew; Wilson, Paul P.H.
2016-01-01
Highlights: • A CAD-based shutdown dose rate analysis workflow has been implemented. • Cartesian and superimposed tetrahedral mesh are fully supported. • Biased and unbiased photon source sampling options are available. • Hybrid Monte Carlo/deterministic techniques accelerate photon transport. • The workflow has been validated with the FNG-ITER benchmark problem. - Abstract: In fusion energy systems (FES) high-energy neutrons born from burning plasma activate system components to form radionuclides. The biological dose rate that results from photons emitted by these radionuclides after shutdown—the shutdown dose rate (SDR)—must be quantified for maintenance planning. This can be done using the Rigorous Two-Step (R2S) method, which involves separate neutron and photon transport calculations, coupled by a nuclear inventory analysis code. The geometric complexity and highly attenuating configuration of FES motivates the use of CAD geometry and advanced variance reduction for this analysis. An R2S workflow has been created with the new capability of performing SDR analysis directly from CAD geometry with Cartesian or tetrahedral meshes and with biased photon source sampling, enabling the use of the Consistent Adjoint Driven Importance Sampling (CADIS) variance reduction technique. This workflow has been validated with the Frascati Neutron Generator (FNG)-ITER SDR benchmark using both Cartesian and tetrahedral meshes and both unbiased and biased photon source sampling. All results are within 20.4% of experimental values, which constitutes satisfactory agreement. Photon transport using CADIS is demonstrated to yield speedups as high as 8.5·10 5 for problems using the FNG geometry.
Energy Technology Data Exchange (ETDEWEB)
Biondo, Elliott D., E-mail: biondo@wisc.edu; Davis, Andrew, E-mail: davisa@engr.wisc.edu; Wilson, Paul P.H., E-mail: wilsonp@engr.wisc.edu
2016-05-15
Highlights: • A CAD-based shutdown dose rate analysis workflow has been implemented. • Cartesian and superimposed tetrahedral mesh are fully supported. • Biased and unbiased photon source sampling options are available. • Hybrid Monte Carlo/deterministic techniques accelerate photon transport. • The workflow has been validated with the FNG-ITER benchmark problem. - Abstract: In fusion energy systems (FES) high-energy neutrons born from burning plasma activate system components to form radionuclides. The biological dose rate that results from photons emitted by these radionuclides after shutdown—the shutdown dose rate (SDR)—must be quantified for maintenance planning. This can be done using the Rigorous Two-Step (R2S) method, which involves separate neutron and photon transport calculations, coupled by a nuclear inventory analysis code. The geometric complexity and highly attenuating configuration of FES motivates the use of CAD geometry and advanced variance reduction for this analysis. An R2S workflow has been created with the new capability of performing SDR analysis directly from CAD geometry with Cartesian or tetrahedral meshes and with biased photon source sampling, enabling the use of the Consistent Adjoint Driven Importance Sampling (CADIS) variance reduction technique. This workflow has been validated with the Frascati Neutron Generator (FNG)-ITER SDR benchmark using both Cartesian and tetrahedral meshes and both unbiased and biased photon source sampling. All results are within 20.4% of experimental values, which constitutes satisfactory agreement. Photon transport using CADIS is demonstrated to yield speedups as high as 8.5·10{sup 5} for problems using the FNG geometry.
Rapid compressed sensing reconstruction of 3D non-Cartesian MRI.
Baron, Corey A; Dwork, Nicholas; Pauly, John M; Nishimura, Dwight G
2018-05-01
Conventional non-Cartesian compressed sensing requires multiple nonuniform Fourier transforms every iteration, which is computationally expensive. Accordingly, time-consuming reconstructions have slowed the adoption of undersampled 3D non-Cartesian acquisitions into clinical protocols. In this work we investigate several approaches to minimize reconstruction times without sacrificing accuracy. The reconstruction problem can be reformatted to exploit the Toeplitz structure of matrices that are evaluated every iteration, but it requires larger oversampling than what is strictly required by nonuniform Fourier transforms. Accordingly, we investigate relative speeds of the two approaches for various nonuniform Fourier transform kernel sizes and oversampling for both GPU and CPU implementations. Second, we introduce a method to minimize matrix sizes by estimating the image support. Finally, density compensation weights have been used as a preconditioning matrix to improve convergence, but this increases noise. We propose a more general approach to preconditioning that allows a trade-off between accuracy and convergence speed. When using a GPU, the Toeplitz approach was faster for all practical parameters. Second, it was found that properly accounting for image support can prevent aliasing errors with minimal impact on reconstruction time. Third, the proposed preconditioning scheme improved convergence rates by an order of magnitude with negligible impact on noise. With the proposed methods, 3D non-Cartesian compressed sensing with clinically relevant reconstruction times (<2 min) is feasible using practical computer resources. Magn Reson Med 79:2685-2692, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Analysis of a Cartesian PML approximation to acoustic scattering problems in and
Bramble, James H.
2013-08-01
We consider the application of a perfectly matched layer (PML) technique applied in Cartesian geometry to approximate solutions of the acoustic scattering problem in the frequency domain. The PML is viewed as a complex coordinate shift ("stretching") and leads to a variable complex coefficient equation for the acoustic wave posed on an infinite domain, the complement of the bounded scatterer. The use of Cartesian geometry leads to a PML operator with simple coefficients, although, still complex symmetric (non-Hermitian). The PML reformulation results in a problem whose solution coincides with the original solution inside the PML layer while decaying exponentially outside. The rapid decay of the PML solution suggests truncation to a bounded domain with a convenient outer boundary condition and subsequent finite element approximation (for the truncated problem). This paper provides new stability estimates for the Cartesian PML approximations both on the infinite and the truncated domain. We first investigate the stability of the infinite PML approximation as a function of the PML strength σ0. This is done for PML methods which involve continuous piecewise smooth stretching as well as piecewise constant stretching functions. We next introduce a truncation parameter M which determines the size of the PML layer. Our analysis shows that the truncated PML problem is stable provided that the product of Mσ0 is sufficiently large, in which case the solution of the problem on the truncated domain converges exponentially to that of the original problem in the domain of interest near the scatterer. This justifies the simple computational strategy of selecting a fixed PML layer and increasing σ0 to obtain the desired accuracy. The results of numerical experiments varying M and σ0 are given which illustrate the theoretically predicted behavior. © 2013 Elsevier B.V. All rights reserved.
DEFF Research Database (Denmark)
Häyrynen, Teppo; Østerkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz
2017-01-01
Recently, an open geometry Fourier modal method based on a new combination ofan open boundary condition and a non-uniform $k$-space discretization wasintroduced for rotationally symmetric structures providing a more efficientapproach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am....... A33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D)Cartesian coordinates allowing for the modeling of rectangular geometries inopen space. The open boundary condition is a consequence of having an infinitecomputational domain described using basis functions that expand...... moreaccurate and efficient modeling of open 3D nanophotonic structures....
ON FINITE DIFFERENCE SCHEMES FOR THE 3-D WAVE EQUATION USING NON-CARTESIAN GRIDS
B. Hamilton; S. Bilbao
2013-01-01
In this paper, we investigate ﬁnite difference schemes forthe 3-D wave equation using 27-point stencils on the cubiclattice, a 13-point stencil on the face-centered cubic (FCC)lattice, and a 9-point stencil on the body-centered cubic(BCC) lattice. The tiling of the wavenumber space for nonCartesian grids is considered in order to analyse numericaldispersion. Schemes are compared for computational efﬁ-ciency in terms of minimising numerical wave speed error.It is shown that the 13-point scheme...
International Nuclear Information System (INIS)
Schlegel, H.B.; Binkley, J.S.; Pople, J.A.
1984-01-01
Formulas are developed for the first and second derivatives of two electron integrals over Cartesian Gaussians. Integrals and integral derivatives are evaluated by the Rys polynomial method. Higher angular momentum functions are not used to calculate the integral derivatives; instead the integral formulas are differentiated directly to produce compact and efficient expressions for the integral derivatives. The use of this algorithm in the ab initio molecular orbital programs gaussIan 80 and gaussIan 82 is discussed. Representative timings for some small molecules with several basis sets are presented. This method is compared with previously published algorithms and its computational merits are discussed
Rosenzweig, Sebastian; Holme, Hans Christian Martin; Wilke, Robin N; Voit, Dirk; Frahm, Jens; Uecker, Martin
2018-04-01
The development of a calibrationless parallel imaging method for accelerated simultaneous multi-slice (SMS) MRI based on Regularized Nonlinear Inversion (NLINV), evaluated using Cartesian and radial fast low-angle shot (FLASH). NLINV is a parallel imaging method that jointly estimates image content and coil sensitivities using a Newton-type method with regularization. Here, NLINV is extended to SMS-NLINV for reconstruction and separation of all simultaneously acquired slices. The performance of the extended method is evaluated for different sampling schemes using phantom and in vivo experiments based on Cartesian and radial SMS-FLASH sequences. The basic algorithm was validated in Cartesian experiments by comparison with ESPIRiT. For Cartesian and radial sampling, improved results are demonstrated compared to single-slice experiments, and it is further shown that sampling schemes using complementary samples outperform schemes with the same samples in each partition. The extension of the NLINV algorithm for SMS data was implemented and successfully demonstrated in combination with a Cartesian and radial SMS-FLASH sequence. Magn Reson Med 79:2057-2066, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.
Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft
Directory of Open Access Journals (Sweden)
Yuma Fukushima
2015-01-01
Full Text Available The linearized Euler equations (LEEs solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.
Aligning Spinoza with Descartes: An informed Cartesian account of the truth bias.
Street, Chris N H; Kingstone, Alan
2017-08-01
There is a bias towards believing information is true rather than false. The Spinozan account claims there is an early, automatic bias towards believing. Only afterwards can people engage in an effortful re-evaluation and disbelieve the information. Supporting this account, there is a greater bias towards believing information is true when under cognitive load. However, developing on the Adaptive Lie Detector (ALIED) theory, the informed Cartesian can equally explain this data. The account claims the bias under load is not evidence of automatic belief; rather, people are undecided, but if forced to guess they can rely on context information to make an informed judgement. The account predicts, and we found, that if people can explicitly indicate their uncertainty, there should be no bias towards believing because they are no longer required to guess. Thus, we conclude that belief formation can be better explained by an informed Cartesian account - an attempt to make an informed judgment under uncertainty. © 2016 The British Psychological Society.
Single-breath-hold 3-D CINE imaging of the left ventricle using Cartesian sampling.
Wetzl, Jens; Schmidt, Michaela; Pontana, François; Longère, Benjamin; Lugauer, Felix; Maier, Andreas; Hornegger, Joachim; Forman, Christoph
2018-02-01
Our objectives were to evaluate a single-breath-hold approach for Cartesian 3-D CINE imaging of the left ventricle with a nearly isotropic resolution of [Formula: see text] and a breath-hold duration of [Formula: see text]19 s against a standard stack of 2-D CINE slices acquired in multiple breath-holds. Validation is performed with data sets from ten healthy volunteers. A Cartesian sampling pattern based on the spiral phyllotaxis and a compressed sensing reconstruction method are proposed to allow 3-D CINE imaging with high acceleration factors. The fully integrated reconstruction uses multiple graphics processing units to speed up the reconstruction. The 2-D CINE and 3-D CINE are compared based on ventricular function parameters, contrast-to-noise ratio and edge sharpness measurements. Visual comparisons of corresponding short-axis slices of 2-D and 3-D CINE show an excellent match, while 3-D CINE also allows reformatting to other orientations. Ventricular function parameters do not significantly differ from values based on 2-D CINE imaging. Reconstruction times are below 4 min. We demonstrate single-breath-hold 3-D CINE imaging in volunteers and three example patient cases, which features fast reconstruction and allows reformatting to arbitrary orientations.
High resource of azimuthal entanglement in terms of Cartesian variables of noncollinear biphotons
Fedorov, M. V.
2018-01-01
Single-particle and coincidence distributions of photons are analyzed for the noncollinear frequency-degenerate type-I regime of spontaneous parametric down-conversion. Noncollinearity itself is shown to provide a new mechanism of strong broadening of the single-particle distributions in Cartesian components of the photon's transverse wave vectors. Related to this, the degree of entanglement appears to be very high in agreement with the earlier performed analysis in the formalism of spherical angles characterizing photon's wave vectors [Phys. Rev. A 93, 033830 (2016), 10.1103/PhysRevA.93.033830]. In Cartesian variables, very broad curves of single-particle distributions are found to have a rather unusual and peculiar shape. In theory, the key reason for these effects is the reduction of the total wave function of two photons over one of two orthogonal degrees of freedom. In the suggested and discussed experimental schemes this means that all photons of the emission cone have to be taken into account rather than only photons propagating in one given plane which is a common practice in many experiments.
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Domiziana Santucci
Full Text Available Abstract Objective: The purpose of this study was to compare two short-tau inversion recovery (STIR sequences, Cartesian and radial (BLADE acquisitions, for breast magnetic resonance imaging (MRI examinations. Materials and Methods: Ninety-six women underwent 1.5 T breast MRI exam (48 Cartesian and 48 BLADE. Qualitative analysis including image artifacts, image quality, fat-suppression, chest-wall depiction, lesion detection, lymph node depiction and overall impression were evaluated by three blinded readers. Signal to noise ratios (SNRs were calculated. Cronbach's alpha test was used to assess inter-observer agreement. Subanalyses of image quality, chest-wall depiction and overall impression in 15 patients with implants and image quality in 31 patients with clips were correlated using Pearson test. Wilcoxon rank sum test and t-test were performed. Results: Motion artifacts were present in 100% and in 0% of the Cartesian and the BLADE exams, respectively. Chemical-shift artifacts were present in 8% of the Cartesian exams. Flow artifacts were more frequent on BLADE. BLADE sequence was statistically superior to Cartesian for all qualitative features (p < 0.05 except for fat-suppression (p = 0.054. In the subanalysis, BLADE was superior for implants and clips (p < 0.05. SNR was statistically greater for BLADE (48.35 vs. 16.17. Cronbach ranged from 0.502 to 0.813. Conclusion: BLADE appears to be superior to Cartesian acquisition of STIR imaging as measured by improved image quality, fewer artifacts, and improved chest wall and lymph node depiction.
Parametric Deformation of Discrete Geometry for Aerodynamic Shape Design
Anderson, George R.; Aftosmis, Michael J.; Nemec, Marian
2012-01-01
We present a versatile discrete geometry manipulation platform for aerospace vehicle shape optimization. The platform is based on the geometry kernel of an open-source modeling tool called Blender and offers access to four parametric deformation techniques: lattice, cage-based, skeletal, and direct manipulation. Custom deformation methods are implemented as plugins, and the kernel is controlled through a scripting interface. Surface sensitivities are provided to support gradient-based optimization. The platform architecture allows the use of geometry pipelines, where multiple modelers are used in sequence, enabling manipulation difficult or impossible to achieve with a constructive modeler or deformer alone. We implement an intuitive custom deformation method in which a set of surface points serve as the design variables and user-specified constraints are intrinsically satisfied. We test our geometry platform on several design examples using an aerodynamic design framework based on Cartesian grids. We examine inverse airfoil design and shape matching and perform lift-constrained drag minimization on an airfoil with thickness constraints. A transport wing-fuselage integration problem demonstrates the approach in 3D. In a final example, our platform is pipelined with a constructive modeler to parabolically sweep a wingtip while applying a 1-G loading deformation across the wingspan. This work is an important first step towards the larger goal of leveraging the investment of the graphics industry to improve the state-of-the-art in aerospace geometry tools.
Wu, Bofeng; Huang, Chao-Guang
2018-04-01
The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.
A simplified presentation of the multigroup analytic nodal method in 2-D Cartesian geometry
International Nuclear Information System (INIS)
Hebert, Alain
2008-01-01
The nodal diffusion algorithms used in many production reactor simulation codes are originating from a common ancestry developed in the 1970s, the analytic nodal method (ANM) of the QUANDRY code. However, this original presentation of the ANM is complex and makes difficult the calculation of the nodal coupling matrices. Moreover, QUANDRY is limited to two-energy groups and its generalization to more groups appears laborious. We are presenting a simplified implementation of the ANM requiring only limited programming work. This formulation is consistent with the initial QUANDRY implementation and is easily generalizable to arbitrary G-group problems. A Matlab script is provided to highlight the simplicity of our presentation. For the sake of clarity, our implementation is limited to G-group, 2-D Cartesian geometry
Energy Technology Data Exchange (ETDEWEB)
Zanette, Rodrigo; Petersen, Caudio Zen [Univ. Federal de Pelotas, Capao do Leao (Brazil). Programa de Pos Graduacao em Modelagem Matematica; Schramm, Marcello [Univ. Federal de Pelotas (Brazil). Centro de Engenharias; Zabadal, Jorge Rodolfo [Univ. Federal do Rio Grande do Sul, Tramandai (Brazil)
2017-05-15
In this paper a solution for the one-dimensional steady state Multilayer Multigroup Neutron Diffusion Equation in cartesian geometry by Fictitious Borders Power Method and a perturbative analysis of this solution is presented. For each new iteration of the power method, the neutron flux is reconstructed by polynomial interpolation, so that it always remains in a standard form. However when the domain is long, an almost singular matrix arises in the interpolation process. To eliminate this singularity the domain segmented in R regions, called fictitious regions. The last step is to solve the neutron diffusion equation for each fictitious region in analytical form locally. The results are compared with results present in the literature. In order to analyze the sensitivity of the solution, a perturbation in the nuclear parameters is inserted to determine how a perturbation interferes in numerical results of the solution.
Cartesian coupled coherent states simulations: Ne(n)Br2 dissociation as a test case.
Reed, Stewart K; González-Martínez, Maykel L; Rubayo-Soneira, Jesús; Shalashilin, Dmitrii V
2011-02-07
In this article, we describe coupled coherent states (CCS) simulations of vibrational predissociation of weakly bounded complexes. The CCS method is implemented in the Cartesian frame in a manner that is similar to classical molecular dynamics. The calculated lifetimes of the vibrationally excited Ne-Br(2)(ν) complexes agree with experiment and previous calculations. Although the CCS method is, in principle, a fully quantum approach, in practice it typically becomes a semiclassical technique at long times. This is especially true following dissociation events. Consequently, it is very difficult to converge the quantum calculations of the final Br(2) vibrational distributions after predissociation and of the autocorrelation functions. However, the main advantage of the method is that it can be applied with relative ease to determine the lifetimes of larger complexes and, in order to demonstrate this, preliminary results for tetra- and penta-atomic clusters are reported.
International Nuclear Information System (INIS)
Ceolin, Celina; Vilhena, Marco T.; Petersen, Claudio Z.
2009-01-01
In this work we report an analytical solution for the monoenergetic neutron diffusion kinetic equation in cartesian geometry. Bearing in mind that the equation for the delayed neutron precursor concentration is a first order linear differential equation in the time variable, to make possible the application of the GITT approach to the kinetic equation, we introduce a fictitious diffusion term multiplied by a positive small value ε. By this procedure, we are able to solve this set of equations. Indeed, applying the GITT technique to the modified diffusion kinetic equation, we come out with a matrix differential equation which has a well known analytical solution when ε goes to zero. We report numerical simulations as well study of numerical convergence of the results attained. (author)
Li, Shuo; Zhu, Yanchun; Xie, Yaoqin; Gao, Song
2018-01-01
Dynamic magnetic resonance imaging (DMRI) is used to noninvasively trace the movements of organs and the process of drug delivery. The results can provide quantitative or semiquantitative pathology-related parameters, thus giving DMRI great potential for clinical applications. However, conventional DMRI techniques suffer from low temporal resolution and long scan time owing to the limitations of the k-space sampling scheme and image reconstruction algorithm. In this paper, we propose a novel DMRI sampling scheme based on a golden-ratio Cartesian trajectory in combination with a compressed sensing reconstruction algorithm. The results of two simulation experiments, designed according to the two major DMRI techniques, showed that the proposed method can improve the temporal resolution and shorten the scan time and provide high-quality reconstructed images.
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Shuo Li
Full Text Available Dynamic magnetic resonance imaging (DMRI is used to noninvasively trace the movements of organs and the process of drug delivery. The results can provide quantitative or semiquantitative pathology-related parameters, thus giving DMRI great potential for clinical applications. However, conventional DMRI techniques suffer from low temporal resolution and long scan time owing to the limitations of the k-space sampling scheme and image reconstruction algorithm. In this paper, we propose a novel DMRI sampling scheme based on a golden-ratio Cartesian trajectory in combination with a compressed sensing reconstruction algorithm. The results of two simulation experiments, designed according to the two major DMRI techniques, showed that the proposed method can improve the temporal resolution and shorten the scan time and provide high-quality reconstructed images.
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Eduardo Izaguirre
2011-09-01
Full Text Available This paper presents a kinematic cartesian control scheme of 3 degree of freedom parallel robot driven by electro-pneumatic actuators based on exteroceptive pose measurement system. The inverse kinematics model is used to obtain the desired joint position coordinates from the time-varying trajectory given in task space. The proposal cascade control scheme in task space is based in two loops, the inner loop consisting in a decoupled joint position control and the outer loop which is designed to obtain an appropriate task space trajectory tracking. In order to avoid the on-line computation of direct kinematics an arrangement of inertial sensor and optical encoders are employed to provide the accurate pose measurement of end-effector. The experiment's results demonstrate the great performance of the proposed control scheme in industrial motion tracking application.
Dakin, Gautier; Després, Bruno; Jaouen, Stéphane
2018-01-01
We propose a new high-order accurate numerical boundary treatment for solving hyperbolic systems of conservation laws and Euler equations using a Lagrange-remap approach on Cartesian grids in cases of physical boundaries not aligned with the mesh. The method is an adaptation of the Inverse Lax-Wendroff procedure [34-38] to the Lagrange-remap approach, which considerably alleviates the algebra. High-order accurate ghost values of conservative variables are imposed using Taylor expansions whose coefficients are found by inverting a (linear or non-linear) system which is well posed in all our examples. For 2D problems, a least-square procedure is added to prevent extrapolation instabilities. The Lagrange-remap formalism also provides a simpler fluid-structure coupling which is also described. Numerical examples are given for the linear case and Euler equations in 1D and 2D.
A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains
Johansen, Hans; Colella, Phillip
1998-11-01
We present a numerical method for solving Poisson's equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. We treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservative differencing of second-order accurate fluxes on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows us to use multigrid iterations with a simple point relaxation strategy. We have combined this with an adaptive mesh refinement (AMR) procedure. We provide evidence that the algorithm is second-order accurate on various exact solutions and compare the adaptive and nonadaptive calculations.
Wade, Derick
2006-03-01
Adjectives are supposed to describe the associated noun more fully or definitively, and the adjective physical is sometimes added to words such as medicine, rehabilitation and disability. What increase in description does its use allow? The adjective was probably added when rehabilitation started to develop for several reasons: it contrasted the mode of treatment with pharmacology and surgery; it contrasted the nature of the supposed aetiology with emotionally generated disorders, especially shell-shock; and it justified the presence of rehabilitation within the profession of medicine. Its continued use, however, perpetuates a Cartesian, dualist philosophy. This editorial uses the World Health Organization International Classification of Functioning (WHO ICF) model of illness to analyse its continued use, and concludes that its continued use may disadvantage both patients and the practice of rehabilitation.
A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2001-01-01
This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.
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Zimmerman Peter A
2010-06-01
Full Text Available Abstract Background Diagnosis of infectious diseases now benefits from advancing technology to perform multiplex analysis of a growing number of variables. These advances enable simultaneous surveillance of markers characterizing species and strain complexity, mutations associated with drug susceptibility, and antigen-based polymorphisms in relation to evaluation of vaccine effectiveness. We have recently developed assays detecting single nucleotide polymorphisms (SNPs in the P. falciparum genome that take advantage of post-PCR ligation detection reaction and fluorescent microsphere labeling strategies. Data from these assays produce a spectrum of outcomes showing that infections result from single to multiple strains. Traditional methods for distinguishing true positive signal from background can cause false positive diagnoses leading to incorrect interpretation of outcomes associated with disease treatment. Results Following analysis of Plasmodium falciparum dihydrofolate reductase SNPs associated with resistance to a commonly used antimalarial drug, Fansidar (Sulfadoxine/pyrimethamine, and presumably neutral SNPs for parasite strain differentiation, we first evaluated our data after setting a background signal based on the mean plus three standard deviations for known negative control samples. Our analysis of single allelic controls suggested that background for the absent allele increased as the concentration of the target allele increased. To address this problem, we introduced a simple change of variables from customary (X,Y (Cartesian coordinates to planar polar coordinates (X = rcos(θ, Y = rsin(θ. Classification of multidimensional fluorescence signals based on histograms of angular and radial data distributions proved more effective than classification based on Cartesian thresholds. Comparison with known diallelic dilution controls suggests that histogram-based classification is effective for major:minor allele concentration ratios as
Path Planning of Free-Floating Robot in Cartesian Space Using Direct Kinematics
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Wenfu Xu
2008-11-01
Full Text Available Dynamic singularities make it difficult to plan the Cartesian path of freefloating robot. In order to avoid its effect, the direct kinematic equations are used for path planning in the paper. Here, the joint position, rate and acceleration are bounded. Firstly, the joint trajectories are parameterized by polynomial or sinusoidal functions. And the two parametric functions are compared in details. It is the first contribution of the paper that polynomial functions can be used when the joint angles are limited(In the similar work of other researchers, only sinusoidla functions could be used. Secondly, the joint functions are normalized and the system of equations about the parameters is established by integrating the differential kinematics equations. Normalization is another contribution of the paper. After normalization, the boundary of the parameters is determined beforehand, and the general criterion to assign the initial guess of the unknown parameters is supplied. The criterion is independent on the planning conditions such as the total time tf. Finally, the parametes are solved by the iterative Newtonian method. Modification of tf may not result in the recalculation of the parameters. Simulation results verify the path planning method.
Häyrynen, Teppo; Osterkryger, Andreas Dyhl; de Lasson, Jakob Rosenkrantz; Gregersen, Niels
2017-09-01
Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform k-space discretization was introduced for rotationally symmetric structures, providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A33, 1298 (2016)JOAOD61084-752910.1364/JOSAA.33.001298]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates, allowing for the modeling of rectangular geometries in open space. The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier k space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence, enabling more accurate and efficient modeling of open 3D nanophotonic structures.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
International Nuclear Information System (INIS)
Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-01-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
ASAM v2.7: a compressible atmospheric model with a Cartesian cut cell approach
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M. Jähn
2015-02-01
Full Text Available In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat–long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.
The Dirac equation in external fields: Variable separation in Cartesian coordinates
International Nuclear Information System (INIS)
Shishkin, G.V.; Cabos, W.D.
1991-01-01
The method of separation of variables in the Dirac equation proposed in an earlier work by one of the present authors [J. Math. Phys. 30, 2132 (1989)] is developed for the complete set of interactions of the Dirac particle. The essence of the method consists of the separation of the first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with or between the operator of the equation is not assumed. This approach, which is perfectly justified in the presence of gravitational [Theor. Math. Phys. 70, 204 (1987)] or vector fields [J. Math. Phys. 30, 2132 (1989)], permits one to find all the possibilities of separation of variables in the Dirac equation in the case of the most general set of external fields. The complete set of interactions of the Dirac particle is determined by the symmetry group of equations, namely, viz. the SU(4) group. The interactions are scalar, vector, tensor, pseudovector and pseudoscalar. The analysis in this article is limited to Cartesian coordinates. The corresponding results for the general curvilinear coordinates will be presented in a future paper
López-Muñoz, Francisco; Rubio, Gabriel; Molina, Juan D; Alamo, Cecilio
2011-04-25
The relationship between the "passions" (emotions or feelings) and psychopathology has been a constant throughout the history of medicine. In this context, melancholy was considered a perversion of the soul (corruption of the passions). One of the most influential authors on this subject was René Descartes, who discussed it in his work The Treatise on the Passions of the Soul (1649). Descartes believed that "passions" were sensitive movements that the soul experienced due to its union with the body (res extensa). According to this theory, the soul was located in the pineal gland, where it was actively involved in overseeing the functions of the "human machine" and kept its dysfunctions under control, by circulating animal spirits. Descartes described sadness as one of "the six primitive passions of the soul", which leads to melancholy if not remedied. Cartesian theories had a great deal of influence on the way that mental pathologies were considered throughout the entire 17th century (Spinoza, Willis, Pitcairn) and during much of the 18th century (Le Cat, Tissot). From the 19th century onwards, emotional symptomatology finally began to be used in diagnostic criteria for mood disorders. Copyright © 2011 Elsevier Inc. All rights reserved.
Viability of Bioprinted Cellular Constructs Using a Three Dispenser Cartesian Printer.
Dennis, Sarah Grace; Trusk, Thomas; Richards, Dylan; Jia, Jia; Tan, Yu; Mei, Ying; Fann, Stephen; Markwald, Roger; Yost, Michael
2015-09-22
Tissue engineering has centralized its focus on the construction of replacements for non-functional or damaged tissue. The utilization of three-dimensional bioprinting in tissue engineering has generated new methods for the printing of cells and matrix to fabricate biomimetic tissue constructs. The solid freeform fabrication (SFF) method developed for three-dimensional bioprinting uses an additive manufacturing approach by depositing droplets of cells and hydrogels in a layer-by-layer fashion. Bioprinting fabrication is dependent on the specific placement of biological materials into three-dimensional architectures, and the printed constructs should closely mimic the complex organization of cells and extracellular matrices in native tissue. This paper highlights the use of the Palmetto Printer, a Cartesian bioprinter, as well as the process of producing spatially organized, viable constructs while simultaneously allowing control of environmental factors. This methodology utilizes computer-aided design and computer-aided manufacturing to produce these specific and complex geometries. Finally, this approach allows for the reproducible production of fabricated constructs optimized by controllable printing parameters.
International Nuclear Information System (INIS)
Abreu, Marcos P. de; Alves Filho, Hermes; Barros, Ricardo C.
2001-01-01
We describe hybrid spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: the use of the standard discretized spatial balance SN equations; the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (author)
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Mochamad Diki Muliyawan
2017-12-01
Full Text Available Abstrak -- Dengan munculnya teknologi manufaktur aditif pada pertengahan 1980-an, teknologi pencetakan tiga dimensi (3D yang mencetak benda dengan mengandalkan ekstrusi termoplastik untuk pembuatan prototipe/pemodelan. Bahan termoplastik yang digunakan adalah Asam Polylatic (PLA dan Acrylonitrile Butadiene Styrene (ABS yang dicetak dengan cara dicairkan mengunakan nozzel yang dialirkan secara berlapis lapis sehingga membentuk sebuah benda. Rancang bangun konstruksi rangka mesin 3D printer tipe cartesian berbasis FDM dengan penggerak menggunakan 3 sumbu utama yaitu sumbu X dengan panjang area cetak 380 mm ,sumbu Y dengan panjang area cetak 400 mm,dan sumbu Z dengan panjang area cetak 380 mm, dan material yang digunakan yaitu baja JIS G3103 1995 SS400, dan Alumunium Al1100. Penelitian ini bertujuan untuk memperoleh kekuatan rangka batang sumbu Z, dan sumbu X dengan, menganalisa kekuatan pada leadscrew sumbu Y dan sumbu Z, menganalisa kekuatan sabuk timing, memperoleh nilai kekuatan pada kampuh las pada rangka Y,Z. Hasil analisa pada rangka sumbu X nilai tegangan tegangan ijin 18 MPa maka dianggap aman, analisa gaya buckling pada rangka sumbu Z adalah sebesar pembebanan 15,147 Kg maka dianggap aman, tegangan geser= 0,38 MPa tegangan geser maksimum = 0,42 MPa maka dianggap aman untuk lead screw sumbu Y, tegangan geser
Path Planning of Free-Floating Robot in Cartesian Space Using Direct Kinematics
Directory of Open Access Journals (Sweden)
Wenfu Xu
2007-03-01
Full Text Available Dynamic singularities make it difficult to plan the Cartesian path of free-floating robot. In order to avoid its effect, the direct kinematic equations are used for path planning in the paper. Here, the joint position, rate and acceleration are bounded. Firstly, the joint trajectories are parameterized by polynomial or sinusoidal functions. And the two parametric functions are compared in details. It is the first contribution of the paper that polynomial functions can be used when the joint angles are limited(In the similar work of other researchers, only sinusoidla functions could be used. Secondly, the joint functions are normalized and the system of equations about the parameters is established by integrating the differential kinematics equations. Normalization is another contribution of the paper. After normalization, the boundary of the parameters is determined beforehand, and the general criterion to assign the initial guess of the unknown parameters is supplied. The criterion is independent on the planning conditions such as the total time tf. Finally, the parametes are solved by the iterative Newtonian method. Modification of tf may not result in the recalculation of the parameters. Simulation results verify the path planning method.
A Trajectory Generation Method Based on Edge Detection for Auto-Sealant Cartesian Robot
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Eka Samsul Maarif
2014-07-01
Full Text Available This paper presents algorithm ingenerating trajectory for sealant process using captured image. Cartesian robot as auto-sealant in manufacturing process has increased productivity, reduces human error and saves time. But, different sealant path in many engine models means not only different trajectory but also different program. Therefore robot with detection ability to generate its own trajectory is needed. This paper describes best lighting technique in capturing image and applies edge detection in trajectory generation as the solution. The algorithm comprises image capturing, Canny edge detection, integral projection in localizing outer most edge, scanning coordinates, and generating vector direction codes. The experiment results show that the best technique is diffuse lighting at 10 Cd. The developed method gives connected point to point trajectory which forms sealant path with a point to next point distance is equal to 90° motor rotation. Directional movement for point to point trajectory is controlled by generated codes which are ready to be sent by serial communication to robot controller as instruction for motors which actuate axes X and Y directions.
The Cartesian doctor, François Bayle (1622-1709), on psychosomatic explanation.
Easton, Patricia
2011-06-01
There are two standing, incompatible accounts of Descartes' contributions to the study of psychosomatic phenomena that pervade histories of medicine, psychology, and psychiatry. The first views Descartes as the father of "rational psychology" a tradition that defines the soul as a thinking, unextended substance. The second account views Descartes as the father of materialism and the machine metaphor. The consensus is that Descartes' studies of optics and motor reflexes and his conception of the body-machine metaphor made early and important contributions to physiology and neuroscience but otherwise his impact was minimal. These predominately negative assessments of Descartes' contributions give a false impression of the role his philosophy played in the development of medicine and psychiatry in seventeenth-century France and beyond. I explore Descartes' influence in the little-known writings of a doctor from Toulouse, François Bayle (1622-1709). A study of Bayle gives us occasion to rethink the nature and role of psychosomatic explanation in Descartes' philosophy. The portrait I present is of a Cartesian science that had an actual and lasting effect on medical science and practice, and may offer something of value to practitioners today. Copyright © 2010 Elsevier Ltd. All rights reserved.
Peano—A Traversal and Storage Scheme for Octree-Like Adaptive Cartesian Multiscale Grids
Weinzierl, Tobias
2011-01-01
Almost all approaches to solving partial differential equations (PDEs) are based upon a spatial discretization of the computational domain-a grid. This paper presents an algorithm to generate, store, and traverse a hierarchy of d-dimensional Cartesian grids represented by a (k = 3)- spacetree, a generalization of the well-known octree concept, and it also shows the correctness of the approach. These grids may change their adaptive structure throughout the traversal. The algorithm uses 2d + 4 stacks as data structures for both cells and vertices, and the storage requirements for the pure grid reduce to one bit per vertex for both the complete grid connectivity structure and the multilevel grid relations. Since the traversal algorithm uses only stacks, the algorithm\\'s cache hit rate is continually higher than 99.9 percent, and the runtime per vertex remains almost constant; i.e., it does not depend on the overall number of vertices or the adaptivity pattern. We use the algorithmic approach as the fundamental concept for a mesh management for d-dimensional PDEs and for a matrix-free PDE solver represented by a compact discrete 3 d-point operator. In the latter case, one can implement a Jacobi smoother, a Krylov solver, or a geometric multigrid scheme within the presented traversal scheme which inherits the low memory requirements and the good memory access characteristics directly. © 2011 Society for Industrial and Applied Mathematics.
Vogman, Genia
Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space
Başar, Erol; Güntekin, Bahar
2007-04-01
The Cartesian System is a fundamental conceptual and analytical framework related and interwoven with the concept and applications of Newtonian Dynamics. In order to analyze quantum processes physicist moved to a Probabilistic Cartesian System in which the causality principle became a probabilistic one. This means the trajectories of particles (obeying quantum rules) can be described only with the concept of cloudy wave packets. The approach to the brain-body-mind problem requires more than the prerequisite of modern physics and quantum dynamics. In the analysis of the brain-body-mind construct we have to include uncertain causalities and consequently multiple uncertain causalities. These multiple causalities originate from (1) nonlinear properties of the vegetative system (e.g. irregularities in biochemical transmitters, cardiac output, turbulences in the vascular system, respiratory apnea, nonlinear oscillatory interactions in peristalsis); (2) nonlinear behavior of the neuronal electricity (e.g. chaotic behavior measured by EEG), (3) genetic modulations, and (4) additional to these physiological entities nonlinear properties of physical processes in the body. The brain shows deterministic chaos with a correlation dimension of approx. D(2)=6, the smooth muscles approx. D(2)=3. According to these facts we propose a hyper-probabilistic approach or a hyper-probabilistic Cartesian System to describe and analyze the processes in the brain-body-mind system. If we add aspects as our sentiments, emotions and creativity to this construct, better said to this already hyper-probabilistic construct, this "New Cartesian System" is more than hyper-probabilistic, it is a nebulous system, we can predict the future only in a nebulous way; however, despite this chain of reasoning we can still provide predictions on brain-body-mind incorporations. We tentatively assume that the processes or mechanisms of the brain-body-mind system can be analyzed and predicted similar to the
Directory of Open Access Journals (Sweden)
Panou G.
2017-02-01
Full Text Available The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney’s method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.
Panou, G.; Korakitis, R.
2017-02-01
The direct geodesic problem on an oblate spheroid is described as an initial value problem and is solved numerically using both geodetic and Cartesian coordinates. The geodesic equations are formulated by means of the theory of differential geometry. The initial value problem under consideration is reduced to a system of first-order ordinary differential equations, which is solved using a numerical method. The solution provides the coordinates and the azimuths at any point along the geodesic. The Clairaut constant is not used for the solution but it is computed, allowing to check the precision of the method. An extensive data set of geodesics is used, in order to evaluate the performance of the method in each coordinate system. The results for the direct geodesic problem are validated by comparison to Karney's method. We conclude that a complete, stable, precise, accurate and fast solution of the problem in Cartesian coordinates is accomplished.
An interior-point method for the Cartesian P*(k-linear complementarity problem over symmetric cones
Directory of Open Access Journals (Sweden)
B Kheirfam
2014-06-01
Full Text Available A novel primal-dual path-following interior-point algorithm for the Cartesian P*(k-linear complementarity problem over symmetric cones is presented. The algorithm is based on a reformulation of the central path for finding the search directions. For a full Nesterov-Todd step feasible interior-point algorithm based on the new search directions, the complexity bound of the algorithm with small-update approach is the best-available bound.
Folio, Les R; Fischer, Tatjana; Shogan, Paul; Frew, Michael; Dwyer, Andrew; Provenzale, James M
2011-08-01
The purpose of this study is to determine the agreement with which radiologists identify wound paths in vivo on MDCT and calculate missile trajectories on the basis of Cartesian coordinates using a Cartesian positioning system (CPS). Three radiologists retrospectively identified 25 trajectories on MDCT in 19 casualties who sustained penetrating trauma in Iraq. Trajectories were described qualitatively in terms of directional path descriptors and quantitatively as trajectory vectors. Directional descriptors, trajectory angles, and angles between trajectories were calculated based on Cartesian coordinates of entrance and terminus or exit recorded in x, y image and table space (z) using a Trajectory Calculator created using spreadsheet software. The consistency of qualitative descriptor determinations was assessed in terms of frequency of observer agreement and multirater kappa statistics. Consistency of trajectory vectors was evaluated in terms of distribution of magnitude of the angles between vectors and the differences between their paraaxial and parasagittal angles. In 68% of trajectories, the observers' visual assessment of qualitative descriptors was congruent. Calculated descriptors agreed across observers in 60% of the trajectories. Estimated kappa also showed good agreement (0.65-0.79, p trajectory vectors were within 20° across observers. Results show agreement of visually assessed and calculated qualitative descriptors and trajectory angles among observers. The Trajectory Calculator describes trajectories qualitatively similar to radiologists' visual assessment, showing the potential feasibility of automated trajectory analysis.
Peng, Bo; Blackman, Eric
2018-01-01
Closely interacting binary stars can incur Common Envelope Evolution (CEE) when at least one of the stars enters a giant phase. The extent to which CEE leads to envelope ejection and how tight the binaries become after CEE as a function of the mass and type of the companion stars has a broad range of phenomenological implications for both low mass and high mass binary stellar systems. Global simulations of CEE are emerging, but to understand the underlying physics of CEE and make connections with analytic formalisms, it helpful to employ reduced numerical models. Here we present results and analyses from simulations of gravitational drag using a Cartesian approach. Using AstroBEAR, a parallelized hydrodynamic/MHD simulation code, we simulate a system in which a 0.1 MSun main sequence secondary star is embedded in gas characteristic of the Envelope of a 3 MSun AGB star. The relative motion of the secondary star against the stationary envelope is represented by a supersonic wind that immerses a point particle, which is initially at rest, yet gradually dragged by the wind. Our approach differs from previous related wind-tunnel work by MacLeod et al. (2015,2017) in that we allow the particle to be displaced, offering a direct measurement of the drag force from its motion. We verify the validity of our method, extract the accretion rate of material in the wake via numerical integration, and compare the results between our method and previous work. We also use the results to help constrain the efficiency parameter in widely used analytic parameterizations of CEE.
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald
2013-12-01
We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.
International Nuclear Information System (INIS)
Barros, R.C.; Filho, H.A.; Oliveira, F.B.S.; Silva, F.C. da
2004-01-01
Presented here are the advances in spectral nodal methods for discrete ordinates (SN) eigenvalue problems in Cartesian geometry. These coarse-mesh methods are based on three ingredients: (i) the use of the standard discretized spatial balance SN equations; (ii) the use of the non-standard spectral diamond (SD) auxiliary equations in the multiplying regions of the domain, e.g. fuel assemblies; and (iii) the use of the non-standard spectral Green's function (SGF) auxiliary equations in the non-multiplying regions of the domain, e.g., the reflector. In slab-geometry the hybrid SD-SGF method generates numerical results that are completely free of spatial truncation errors. In X,Y-geometry, we obtain a system of two 'slab-geometry' SN equations for the node-edge average angular fluxes by transverse-integrating the X,Y-geometry SN equations separately in the y- and then in the x-directions within an arbitrary node of the spatial grid set up on the domain. In this paper, we approximate the transverse leakage terms by constants. These are the only approximations considered in the SD-SGF-constant nodal method, as the source terms, that include scattering and eventually fission events, are treated exactly. Moreover, we describe in this paper the progress of the approximate SN albedo boundary conditions for substituting the non-multiplying regions around the nuclear reactor core. We show numerical results to typical model problems to illustrate the accuracy of spectral nodal methods for coarse-mesh SN criticality calculations. (Author)
The effect of object-centered instructions in Cartesian and polar coordinates on saccade vector
Edelman, Jay A.; Mieses, Alexa M.; Konnova, Kira; Shiu, David
2017-01-01
Express saccades (ES) are the most reflexive saccadic eye movements, with very short reaction times of 70–110 ms. It is likely that ES have the shortest saccade reaction times (SRTs) possible given the known physiological and anatomical delays present in sensory and motor systems. Nevertheless, it has been demonstrated that a vector displacement of ES to spatially extended stimuli can be influenced by spatial cognition. Edelman, Kristjansson, and Nakayama (2007) found that when two horizontally separated visual stimuli appear at a random location, the spatial vector, but not the reaction time, of human ES is strongly influenced by an instruction to make a saccade to one side (either left or right) of a visual stimulus array. Presently, we attempt to extend these findings of cognitive effects on saccades in three ways: (a) determining whether ES could be affected by other types of spatial instructions: vertical, polar amplitude, and polar direction; (b) determining whether these spatial effects increased with practice; and (c) determining how these effects depended on SRTs. The results demonstrate that both types of Cartesian as well as polar amplitude instructions strongly affect ES vector, but only modestly affect SRTs. Polar direction instructions had sizable effects only on nonreflexive saccades where the visual stimuli could be viewed for several hundred milliseconds prior to saccade execution. Short- (trial order within a block) and long-term (experience across several sessions) practice had little effect, though the effect of instruction increased with SRT. Such findings suggest a generalized, innate ability of cognition to affect the most reflexive saccadic eye movements. PMID:28265650
Deformations of superconformal theories
International Nuclear Information System (INIS)
Córdova, Clay; Dumitrescu, Thomas T.; Intriligator, Kenneth
2016-01-01
We classify possible supersymmetry-preserving relevant, marginal, and irrelevant deformations of unitary superconformal theories in d≥3 dimensions. Our method only relies on symmetries and unitarity. Hence, the results are model independent and do not require a Lagrangian description. Two unifying themes emerge: first, many theories admit deformations that reside in multiplets together with conserved currents. Such deformations can lead to modifications of the supersymmetry algebra by central and non-central charges. Second, many theories with a sufficient amount of supersymmetry do not admit relevant or marginal deformations, and some admit neither. The classification is complicated by the fact that short superconformal multiplets display a rich variety of sporadic phenomena, including supersymmetric deformations that reside in the middle of a multiplet. We illustrate our results with examples in diverse dimensions. In particular, we explain how the classification of irrelevant supersymmetric deformations can be used to derive known and new constraints on moduli-space effective actions.
Mechanics of deformable bodies
Sommerfeld, Arnold Johannes Wilhelm
1950-01-01
Mechanics of Deformable Bodies: Lectures on Theoretical Physics, Volume II covers topics on the mechanics of deformable bodies. The book discusses the kinematics, statics, and dynamics of deformable bodies; the vortex theory; as well as the theory of waves. The text also describes the flow with given boundaries. Supplementary notes on selected hydrodynamic problems and supplements to the theory of elasticity are provided. Physicists, mathematicians, and students taking related courses will find the book useful.
Diffeomorphic Statistical Deformation Models
DEFF Research Database (Denmark)
Hansen, Michael Sass; Hansen, Mads/Fogtman; Larsen, Rasmus
2007-01-01
In this paper we present a new method for constructing diffeomorphic statistical deformation models in arbitrary dimensional images with a nonlinear generative model and a linear parameter space. Our deformation model is a modified version of the diffeomorphic model introduced by Cootes et al....... The modifications ensure that no boundary restriction has to be enforced on the parameter space to prevent folds or tears in the deformation field. For straightforward statistical analysis, principal component analysis and sparse methods, we assume that the parameters for a class of deformations lie on a linear...
Intracrystalline deformation of calcite
Bresser, J.H.P. de
1991-01-01
It is well established from observations on natural calcite tectonites that intracrystalline plastic mechanisms are important during the deformation of calcite rocks in nature. In this thesis, new data are presented on fundamental aspects of deformation behaviour of calcite under conditions where
Branduardi, Davide; Faraldo-Gómez, José D.
2014-01-01
The string method is a molecular-simulation technique that aims to calculate the minimum free-energy path of a chemical reaction or conformational transition, in the space of a pre-defined set of reaction coordinates that is typically highly dimensional. Any descriptor may be used as a reaction coordinate, but arguably the Cartesian coordinates of the atoms involved are the most unprejudiced and intuitive choice. Cartesian coordinates, however, present a non-trivial problem, in that they are not invariant to rigid-body molecular rotations and translations, which ideally ought to be unrestricted in the simulations. To overcome this difficulty, we reformulate the framework of the string method to integrate an on-the-fly structural-alignment algorithm. This approach, referred to as SOMA (String method with Optimal Molecular Alignment), enables the use of Cartesian reaction coordinates in freely tumbling molecular systems. In addition, this scheme permits the dissection of the free-energy change along the most probable path into individual atomic contributions, thus revealing the dominant mechanism of the simulated process. This detailed analysis also provides a physically-meaningful criterion to coarse-grain the representation of the path. To demonstrate the accuracy of the method we analyze the isomerization of the alanine dipeptide in vacuum and the chair-to-inverted-chair transition of β-D mannose in explicit water. Notwithstanding the simplicity of these systems, the SOMA approach reveals novel insights into the atomic mechanism of these isomerizations. In both cases, we find that the dynamics and the energetics of these processes are controlled by interactions involving only a handful of atoms in each molecule. Consistent with this result, we show that a coarse-grained SOMA calculation defined in terms of these subsets of atoms yields nearidentical minimum free-energy paths and committor distributions to those obtained via a highly-dimensional string. PMID
Deformation mechanisms in experimentally deformed Boom Clay
Desbois, Guillaume; Schuck, Bernhard; Urai, Janos
2016-04-01
Bulk mechanical and transport properties of reference claystones for deep disposal of radioactive waste have been investigated since many years but little is known about microscale deformation mechanisms because accessing the relevant microstructure in these soft, very fine-grained, low permeable and low porous materials remains difficult. Recent development of ion beam polishing methods to prepare high quality damage free surfaces for scanning electron microscope (SEM) is opening new fields of microstructural investigation in claystones towards a better understanding of the deformation behavior transitional between rocks and soils. We present results of Boom Clay deformed in a triaxial cell in a consolidated - undrained test at a confining pressure of 0.375 MPa (i.e. close to natural value), with σ1 perpendicular to the bedding. Experiments stopped at 20 % strain. As a first approximation, the plasticity of the sample can be described by a Mohr-Coulomb type failure envelope with a coefficient of cohesion C = 0.117 MPa and an internal friction angle ϕ = 18.7°. After deformation test, the bulk sample shows a shear zone at an angle of about 35° from the vertical with an offset of about 5 mm. We used the "Lamipeel" method that allows producing a permanent absolutely plane and large size etched micro relief-replica in order to localize and to document the shear zone at the scale of the deformed core. High-resolution imaging of microstructures was mostly done by using the BIB-SEM method on key-regions identified after the "Lamipeel" method. Detailed BIB-SEM investigations of shear zones show the following: the boundaries between the shear zone and the host rock are sharp, clay aggregates and clastic grains are strongly reoriented parallel to the shear direction, and the porosity is significantly reduced in the shear zone and the grain size is smaller in the shear zone than in the host rock but there is no evidence for broken grains. Comparison of microstructures
International Nuclear Information System (INIS)
Anderson, D.V.; Breazeal, J.; Finan, C.H.; Johnston, B.M.
1976-01-01
ABCXYZ is a computer code for obtaining the Cartesian components of the vector potential and the magnetic field on an observed grid from an arrangement of current-carrying wires. Arbitrary combinations of straight line segments, arcs, and loops are allowed in the specification of the currents. Arbitrary positions and orientations of the current-carrying elements are also allowed. Specification of the wire diameter permits the computation of well-defined fields, even in the interiors of the conductors. An optical feature generates magnetic field lines. Extensive graphical and printed output is available to the user including contour, grid-line, and field-line plots. 12 figures, 1 table
Evans, D
1975-08-01
A discussion of the essential deformity in calcaneo-valgus feet develops a theme originally put forward in 1961 on the relapsed club foot (Evans 1961). Whereas in the normal foot the medial and lateral columns are about equal in length, in talipes equino-varus the lateral column is longer and in calcaneo-valgus shorter than the medial column. The suggestion is that in the treatment of both deformities the length of the columns be made equal. A method is described of treating calcaneo-valgus deformity by inserting cortical bone grafts taken from the tibia to elongate the anterior end of the calcaneus.
A short note on the use of the red-black tree in Cartesian adaptive mesh refinement algorithms
Hasbestan, Jaber J.; Senocak, Inanc
2017-12-01
Mesh adaptivity is an indispensable capability to tackle multiphysics problems with large disparity in time and length scales. With the availability of powerful supercomputers, there is a pressing need to extend time-proven computational techniques to extreme-scale problems. Cartesian adaptive mesh refinement (AMR) is one such method that enables simulation of multiscale, multiphysics problems. AMR is based on construction of octrees. Originally, an explicit tree data structure was used to generate and manipulate an adaptive Cartesian mesh. At least eight pointers are required in an explicit approach to construct an octree. Parent-child relationships are then used to traverse the tree. An explicit octree, however, is expensive in terms of memory usage and the time it takes to traverse the tree to access a specific node. For these reasons, implicit pointerless methods have been pioneered within the computer graphics community, motivated by applications requiring interactivity and realistic three dimensional visualization. Lewiner et al. [1] provides a concise review of pointerless approaches to generate an octree. Use of a hash table and Z-order curve are two key concepts in pointerless methods that we briefly discuss next.
Extremely deformable structures
2015-01-01
Recently, a new research stimulus has derived from the observation that soft structures, such as biological systems, but also rubber and gel, may work in a post critical regime, where elastic elements are subject to extreme deformations, though still exhibiting excellent mechanical performances. This is the realm of ‘extreme mechanics’, to which this book is addressed. The possibility of exploiting highly deformable structures opens new and unexpected technological possibilities. In particular, the challenge is the design of deformable and bi-stable mechanisms which can reach superior mechanical performances and can have a strong impact on several high-tech applications, including stretchable electronics, nanotube serpentines, deployable structures for aerospace engineering, cable deployment in the ocean, but also sensors and flexible actuators and vibration absorbers. Readers are introduced to a variety of interrelated topics involving the mechanics of extremely deformable structures, with emphasis on ...
International Nuclear Information System (INIS)
Aprahamian, A.
1992-01-01
Quadrupole oscillations around a deformed shape give rise to vibrations in deformed nuclei. Single phonon vibrations of K = 0 (β) and K = 2 (γ) are a systematic feature in deformed nuclei, but the existence of multi-phonon vibrations had remained an open question until the recently reported results in 168 Er. In this nucleus, a two-phonon K = 4(γγ) band was observed at approximately 2.5 times the energy of the single γ vibration. The authors have studied several deformed rare-earth nuclei using the ( 4 He,2n) reaction in order to map out the systematic behavior of these multi-phonon vibrations. Recently, they have identified a similar K = 4 band in 154 Gd
Modelling Protein-induced Membrane Deformation using Monte Carlo and Langevin Dynamics Simulations
Radhakrishnan, R.; Agrawal, N.; Ramakrishnan, N.; Kumar, P. B. Sunil; Liu, J.
2010-11-01
In eukaryotic cells, internalization of extracellular cargo via the cellular process of endocytosis is orchestrated by a variety of proteins, many of which are implicated in membrane deformation/bending. We model the energetics of deformations membranes by using the Helfrich Hamiltonian using two different formalisms: (i) Cartesian or Monge Gauge using Langevin dynamics; (ii) Curvilinear coordinate system using Monte Carlo (MC). Monge gauge approach which has been extensively studied is limited to small deformations of the membrane and cannot describe extreme deformations. Curvilinear coordinate approach can handle large deformation limits as well as finite-temperature membrane fluctuations; here we employ an unstructured triangular mesh to compute the local curvature tensor, and we evolve the membrane surface using a MC method. In our application, we compare the two approaches (i and ii above) to study how the spatial assembly of curvature inducing proteins leads to vesicle budding from a planar membrane. We also quantify how the curvature field of the membrane impacts the spatial segregation of proteins.
The Spherical Deformation Model
DEFF Research Database (Denmark)
Hobolth, Asgar
2003-01-01
Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...... a single central section of the object. We use maximum-likelihood-based inference for this purpose and demonstrate the suggested methods on real data....
Shell structure of octupole deformation
International Nuclear Information System (INIS)
Zhang Xizhen; Dong Baoguo
1992-01-01
A convenient definition of intrinsic frame of an octupole deformed shape was proposed recently. The octupole deformation potential was expanded on the bases of irreducible representations of group O h . Based on the parameterization given in previous paper, the shell structures of octupole deformation which cover all possible octupole deformed shapes were studied
Gillies, Val; Harden, Angela; Johnson, Katherine; Reavey, Paula; Strange, Vicki; Willig, Carla
2004-03-01
The research presented in this paper uses memory work as a method to explore six women's collective constructions of two embodied practices, sweating and pain. The paper identifies limitations in the ways in which social constructionist research has theorized the relationship between discourse and materiality, and it proposes an approach to the study of embodiment which enjoins, rather than bridges, the discursive and the non-discursive. The paper presents an analysis of 25 memories of sweating and pain which suggests that Cartesian dualism is central to the women's accounts of their experiences. However, such dualism does not operate as a stable organizing principle. Rather, it offers two strategies for the performance of a split between mind and body. The paper traces the ways in which dualism can be both functional and restrictive, and explores the tensions between these two forms. The paper concludes by identifiying opportunities and limitations associated with memory work as a method for studying embodiment.
Autogenous Deformation of Concrete
DEFF Research Database (Denmark)
Autogenous deformation of concrete can be defined as the free deformation of sealed concrete at a constant temperature. A number of observed problems with early age cracking of high-performance concretes can be attributed to this phenomenon. During the last 10 years , this has led to an increased...... focus on autogenous deformation both within concrete practice and concrete research. Since 1996 the interest has been significant enough to hold international, yearly conferences entirely devoted to this subject. The papers in this publication were presented at two consecutive half-day sessions...... at the American Concrete Institute’s Fall Convention in Phoenix, Arizona, October 29, 2002. All papers have been reviewed according to ACI rules. This publication, as well as the sessions, was sponsored by ACI committee 236, Material Science of Concrete. The 12 presentations from 8 different countries indicate...
Packings of deformable spheres
Mukhopadhyay, Shomeek; Peixinho, Jorge
2011-07-01
We present an experimental study of disordered packings of deformable spheres. Fluorescent hydrogel spheres immersed in water together with a tomography technique enabled the imaging of the three-dimensional arrangement. The mechanical behavior of single spheres subjected to compression is first examined. Then the properties of packings of a randomized collection of deformable spheres in a box with a moving lid are tested. The transition to a state where the packing withstands finite stresses before yielding is observed. Starting from random packed states, the power law dependence of the normal force versus packing fraction or strain at different velocities is quantified. Furthermore, a compression-decompression sequence at low velocities resulted in rearrangements of the spheres. At larger packing fractions, a saturation of the mean coordination number took place, indicating the deformation and faceting of the spheres.
Hamilton, Scott; Hamilton, Trevor J.
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes’s “radical” or “mind-body” dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes’s famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student’s understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student’s understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur. PMID:26321981
Hamilton, Scott; Hamilton, Trevor J
2015-01-01
A fundamental discussion in lower-level undergraduate neuroscience and psychology courses is Descartes's "radical" or "mind-body" dualism. According to Descartes, our thinking mind, the res cogitans, is separate from the body as physical matter or substance, the res extensa. Since the transmission of sensory stimuli from the body to the mind is a physical capacity shared with animals, it can be confused, misled, or uncertain (e.g., bodily senses imply that ice and water are different substances). True certainty thus arises from within the mind and its capacity to doubt physical stimuli. Since this doubting mind is a thinking thing that is distinct from bodily stimuli, truth and certainty are reached through the doubting mind as cogito ergo sum, or the certainty of itself as it thinks: hence Descartes's famous maxim, I think, therefore I am. However, in the last century of Western philosophy, with nervous system investigation, and with recent advances in neuroscience, the potential avenues to explore student's understanding of the epistemology and effects of Cartesian mind-body dualism has expanded. This article further explores this expansion, highlighting pedagogical practices and tools instructors can use to enhance a psychology student's understanding of Cartesian dualistic epistemology, in order to think more critically about its implicit assumptions and effects on learning. It does so in two ways: first, by offering instructors an alternative philosophical perspective to dualistic thinking: a mind-body holism that is antithetical to the assumed binaries of dualistic epistemology. Second, it supplements this philosophical argument with a practical component: simple mind-body illusions that instructors may use to demonstrate contrary epistemologies to students. Combining these short philosophical and neuroscience arguments thereby acts as a pedagogical tool to open new conceptual spaces within which learning may occur.
Directory of Open Access Journals (Sweden)
Isabel G. Gamero Cabrera
2017-07-01
Full Text Available In this paper, I analyse Judith Butler’s recent critics against the Cartesian scepticism and the posTmodern constructivism (indentified by Preciado and Haraway’s works, in order to explain Butler’s distance from constructivism and, at the same time, to assert the ethical and potentially universal dimension of her defence of the precarious lives.
Nanolaminate deformable mirrors
Papavasiliou, Alexandros P.; Olivier, Scot S.
2009-04-14
A deformable mirror formed out of two layers of a nanolaminate foil attached to a stiff substrate is introduced. Deformation is provided by an electrostatic force between two of the layers. The internal stiffness of the structure allows for high-spatial-frequency shapes. The nanolaminate foil of the present invention allows for a high-quality mirror surface. The device achieves high precision in the vertical direction by using foils with accurately controlled thicknesses, but does not require high precision in the lateral dimensions, allowing such mirrors to be fabricated using crude lithography techniques. Such techniques allow structures up to about the meter scale to be fabricated.
Marginally Deformed Starobinsky Gravity
DEFF Research Database (Denmark)
Codello, A.; Joergensen, J.; Sannino, Francesco
2015-01-01
We show that quantum-induced marginal deformations of the Starobinsky gravitational action of the form $R^{2(1 -\\alpha)}$, with $R$ the Ricci scalar and $\\alpha$ a positive parameter, smaller than one half, can account for the recent experimental observations by BICEP2 of primordial tensor modes....
Formation and subdivision of deformation structures during plastic deformation
DEFF Research Database (Denmark)
Jakobsen, B.; Poulsen, H.F.; Lienert, U.
2006-01-01
of individual, deeply embedded dislocation structures. During tensile deformation of pure copper, dislocation-free regions were identified. They showed an unexpected intermittent dynamics, for example, appearing and disappearing with proceeding deformation and even displaying transient splitting behavior....... Insight into these processes is relevant for an understanding of the strength and work-hardening of deformed materials....
International Nuclear Information System (INIS)
Mshelia, E.D.
1994-07-01
The method of normal coordinates of the theory of vibrations is used in decoupling the motion of n oscillators (1 ≤ n ≤4) representing intrinsic degrees of freedom coupled to collective motion in a quantum mechanical model that allows the determination of the probability for energy transfer from collective to intrinsic excitations in a dissipative system. (author). 21 refs
International Nuclear Information System (INIS)
Guseinov, I.I.; Mamedov, B.A.; Ekenoglu, A.S.
2006-01-01
A unified treatment of Franck-Condon (FC) overlap integrals with arbitrary values of parameters is described. These integrals are represented in terms of binomial coefficients. For quick calculations, the binomial coefficients are stored in the memory of the computer. Therefore, the CPU time has been greatly reduced. Numerical results presented agree excellently with those obtained in the literature. (orig.)
Lin, Lifeng; Wang, Huiqi; Huang, Xipei; Wen, Yongxian
2018-03-01
For a fractional linear oscillator subjected to both parametric excitation of trichotomous noise and external excitation of bias-signal-modulated trichotomous noise, the generalized stochastic resonance (GSR) phenomena are investigated in this paper in case the noises are cross-correlative. First, the generalized Shapiro-Loginov formula and generalized fractional Shapiro-Loginov formula are derived. Then, by using the generalized (fractional) Shapiro-Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is obtained. The numerical results show that the evolution of the output amplitude amplification is nonmonotonic with the frequency of periodic signal, the noise parameters, and the fractional order. The GSR phenomena, including single-peak GSR, double-peak GSR and triple-peak GSR, are observed in this system. In addition, the interplay of the multiplicative trichotomous noise, bias-signal-modulated trichotomous noise and memory can induce and diversify the stochastic multi-resonance (SMR) phenomena, and the two kinds of trichotomous noises play opposite roles on the GSR.
AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator
DEFF Research Database (Denmark)
Djurhuus, Torsten; Krozer, Viktor; Vidkjær, Jens
2006-01-01
We derive the dynamic equations governing the cross-coupled quadrature oscillator, perturbed by noise, leading to an expression for the close-in phase noise. The theory shows that a nonlinear coupling transconductance results in AM-PM noise conversion close to the carrier, which increases...... with the coupling strength. A simple linear time-domain model is employed to illustrate the results...
Application of He’s Energy Balance Method to Duffing-Harmonic Oscillators
DEFF Research Database (Denmark)
Momeni, M.; Jamshidi, j.; Barari, Amin
2011-01-01
In this article, He's energy balance method is applied for calculating angular frequencies of nonlinear Duffing oscillators. This method offers a promising approach by constructing a Hamiltonian for the nonlinear oscillator. We illustrate that the energy balance is very effective and convenient...... and does not require linearization or small perturbation. Contrary to the conventional methods, in energy balance, only one iteration leads to high accuracy of the solutions. It is predicted that the energy balance method finds wide applications in engineering problems....
Direct Simulation Monte Carlo Application of the Three Dimensional Forced Harmonic Oscillator Model
2017-12-07
challenges of implementing the full array of VV transitions mentioned earlier. Note here that an account of VV processes is not expected to influence the...method. It takes into account the microscopic reversibility between the excitation and deexcitation processes, and it satisfies the detailed balance...probabilities and is suitable for the direct simulation Monte Carlo method. It takes into account the microscopic reversibility between the excitation
Directory of Open Access Journals (Sweden)
Suchuan Zhong
2016-01-01
Full Text Available The stochastic resonance (SR characteristics of a generalized Langevin linear system driven by a multiplicative noise and a periodically modulated noise are studied (the two noises are correlated. In this paper, we consider a generalized Langevin equation (GLE driven by an internal noise with long-memory and long-range dependence, such as fractional Gaussian noise (fGn and Mittag-Leffler noise (M-Ln. Such a model is appropriate to characterize the chemical and biological solutions as well as to some nanotechnological devices. An exact analytic expression of the output amplitude is obtained. Based on it, some characteristic features of stochastic resonance phenomenon are revealed. On the other hand, by the use of the exact expression, we obtain the phase diagram for the resonant behaviors of the output amplitude versus noise intensity under different values of system parameters. These useful results presented in this paper can give the theoretical basis for practical use and control of the SR phenomenon of this mathematical model in future works.
Postural deformities in Parkinson's disease
Doherty, K.M.; Warrenburg, B.P.C. van de; Peralta, M.C.; Silveira-Moriyama, L.; Azulay, J.P.; Gershanik, O.S.; Bloem, B.R.
2011-01-01
Postural deformities are frequent and disabling complications of Parkinson's disease (PD) and atypical parkinsonism. These deformities include camptocormia, antecollis, Pisa syndrome, and scoliosis. Recognition of specific postural syndromes might have differential diagnostic value in patients
Cosmetic and Functional Nasal Deformities
... nasal complaints. Nasal deformity can be categorized as “cosmetic” or “functional.” Cosmetic deformity of the nose results in a less ... taste , nose bleeds and/or recurrent sinusitis . A cosmetic or functional nasal deformity may occur secondary to ...
International Nuclear Information System (INIS)
Lima, A.F. de
2003-01-01
The q-deformed kink of the λφ 4 -model is obtained via the normalisable ground state eigenfunction of a fluctuation operator associated with the q-deformed hyperbolic functions. The kink mass, the bosonic zero-mode and the q-deformed potential in 1+1 dimensions are found. (author)
[Babies with cranial deformity].
Feijen, Michelle M W; Claessens, Edith A W M Habets; Dovens, Anke J Leenders; Vles, Johannes S; van der Hulst, Rene R W J
2009-01-01
Plagiocephaly was diagnosed in a baby aged 4 months and brachycephaly in a baby aged 5 months. Positional or deformational plagio- or brachycephaly is characterized by changes in shape and symmetry of the cranial vault. Treatment options are conservative and may include physiotherapy and helmet therapy. During the last two decades the incidence of positional plagiocephaly has increased in the Netherlands. This increase is due to the recommendation that babies be laid on their backs in order to reduce the risk of sudden infant death syndrome. We suggest the following: in cases of positional preference of the infant, referral to a physiotherapist is indicated. In cases of unacceptable deformity of the cranium at the age 5 months, moulding helmet therapy is a possible treatment option.
Deformation Theory ( Lecture Notes )
Czech Academy of Sciences Publication Activity Database
Doubek, M.; Markl, Martin; Zima, P.
2007-01-01
Roč. 43, č. 5 (2007), s. 333-371 ISSN 0044-8753. [Winter School Geometry and Physics/27./. Srní, 13.01.2007-20.01.2007] R&D Projects: GA ČR GA201/05/2117 Institutional research plan: CEZ:AV0Z10190503 Keywords : deformation * Mauerer-Cartan equation * strongly homotopy Lie algebra Subject RIV: BA - General Mathematics
Deformations of fractured rock
International Nuclear Information System (INIS)
Stephansson, O.
1977-09-01
Results of the DBM and FEM analysis in this study indicate that a suitable rock mass for repository of radioactive waste should be moderately jointed (about 1 joint/m 2 ) and surrounded by shear zones of the first order. This allowes for a gentle and flexible deformation under tectonic stresses and prevent the development of large cross-cutting failures in the repository area. (author)
Strauss, Karl F.; Sheldon, Douglas J.
2011-01-01
Several missions and instruments in the conceptual design phase rely on the technique of interferometry to create detectable fringe patterns. The intimate emplacement of reflective material upon electron device cells based upon chalcogenide material technology permits high-speed, predictable deformation of the reflective surface to a subnanometer or finer resolution with a very high degree of accuracy. In this innovation, a layer of reflective material is deposited upon a wafer containing (perhaps in the millions) chalcogenic memory cells with the reflective material becoming the front surface of a mirror and the chalcogenic material becoming a means of selectively deforming the mirror by the application of heat to the chalcogenic material. By doing so, the mirror surface can deform anywhere from nil to nanometers in spots the size of a modern day memory cell, thereby permitting realtime tuning of mirror focus and reflectivity to mitigate aberrations caused elsewhere in the optical system. Modern foundry methods permit the design and manufacture of individual memory cells having an area of or equal to the Feature (F) size of the design (assume 65 nm). Fabrication rules and restraints generally require the instantiation of one memory cell to another no closer than 1.5 F, or, for this innovation, 90 nm from its neighbor in any direction. Chalcogenide is a semiconducting glass compound consisting of a combination of chalcogen ions, the ratios of which vary according to properties desired. It has been shown that the application of heat to cells of chalcogenic material cause a large alteration in resistance to the range of 4 orders of magnitude. It is this effect upon which chalcogenidebased commercial memories rely. Upon removal of the heat source, the chalcogenide rapidly cools and remains frozen in the excited state. It has also been shown that the chalcogenide expands in volume because of the applied heat, meaning that the coefficient of expansion of chalcogenic
Directory of Open Access Journals (Sweden)
J. Ju
2017-07-01
Full Text Available The flexible Cartesian robotic manipulator (FCRM is coming into widespread application in industry. Because of the feeble rigidity and heavy deflection, the dynamic characteristics of the FCRM are easily influenced by external disturbances which mainly concentrate in the driving end and the load end. Thus, with the influence of driving base disturbance and terminal load considered, the motion differential equations of the FCRM under the plane motion of the base are constructed, which contain the forced and non-linear parametric excitations originated from the disturbances of base lateral and axial motion respectively. Considering the relationship between the coefficients of the motion differential equations and the mode shapes of the flexible manipulator, the analytic expressions of the mode shapes with terminal load are deduced. Then, based on multiple scales method and rectangular coordinate transformation, the average equations of the FCRM are derived to analyze the influence mechanism of base disturbance and terminal load on the system parametric vibration stability. The results show that terminal load mainly affects the node locations of mode shapes and mode frequencies of the FCRM, and the axial motion disturbance of the driving base introduces parametric excitation while the lateral motion disturbance generates forced excitation for the transverse vibration model of the FCRM. Furthermore, with the increase of the base excitation acceleration and terminal load, the parametric vibration instability region of the FCRM increases significantly. This study will be helpful for the dynamic characteristics analysis and vibration control of the FCRM.
Liégeois, Vincent; Champagne, Benoît; Lazzeretti, Paolo
2008-06-28
Two molecular properties, the nuclear electromagnetic hypershielding (psi(gamma,alphabeta) ('I)) and the gradient of the electric dipole-magnetic dipole polarizability (nabla(Igamma)G(alphabeta) (')), have been calculated using the time-dependent Hartree-Fock method. Provided the Hellmann-Feynman theorem is satisfied, these quantities are equivalent and are related through the nabla(Igamma)G(alphabeta) (')=eZ(I)psi(gamma,alphabeta) ('I) relation, where Z(I) is the atomic number of atom I and e the magnitude of the electron charge. In such a case, the determination of the nuclear electromagnetic hypershielding presents the computational advantage over the evaluation of the gradient of G(alphabeta) (') of requiring only the knowledge of nine mixed second-order derivatives of the density matrix with respect to both electric and magnetic fields (D(alpha,beta)(-omega,omega)) instead of the 3N (N is the number of atoms) derivatives of the density matrix with respect to the Cartesian coordinates (D(Igamma)). It is shown here for the H(2)O(2) molecule that very large basis sets such as the aug-cc-pVQZ or the R12 basis are required to satisfy the Hellmann-Feynman theorem. These basis set requirements have been substantiated by considering the corresponding rototranslational sum rules. The origin dependence of the rototranslational sum rules for the gradient of G(alphabeta) (') has then been theoretically described and verified for the H(2)O(2) molecule.
Emílio Borges; João Pedro Braga; Jadson Cláudio Belchior
2007-01-01
A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational ...
International Nuclear Information System (INIS)
McGavin, Dennis G; Tennant, W Craighead
2009-01-01
In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS 3 and BS 5 . Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, 1-bar Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
Lugauer, Felix; Wetzl, Jens; Forman, Christoph; Schneider, Manuel; Kiefer, Berthold; Hornegger, Joachim; Nickel, Dominik; Maier, Andreas
2018-01-25
Our aim was to develop and validate a 3D Cartesian Look-Locker [Formula: see text] mapping technique that achieves high accuracy and whole-liver coverage within a single breath-hold. The proposed method combines sparse Cartesian sampling based on a spatiotemporally incoherent Poisson pattern and k-space segmentation, dedicated for high-temporal-resolution imaging. This combination allows capturing tissue with short relaxation times with volumetric coverage. A joint reconstruction of the 3D + inversion time (TI) data via compressed sensing exploits the spatiotemporal sparsity and ensures consistent quality for the subsequent multistep [Formula: see text] mapping. Data from the National Institute of Standards and Technology (NIST) phantom and 11 volunteers, along with reference 2D Look-Locker acquisitions, are used for validation. 2D and 3D methods are compared based on [Formula: see text] values in different abdominal tissues at 1.5 and 3 T. [Formula: see text] maps obtained from the proposed 3D method compare favorably with those from the 2D reference and additionally allow for reformatting or volumetric analysis. Excellent agreement is shown in phantom [bias[Formula: see text] see text] see text] mapping with high accuracy and precision is feasible in one breath-hold using spatiotemporally incoherent, sparse 3D Cartesian sampling.
Inoue, Yuuji; Yoneyama, Masami; Nakamura, Masanobu; Takemura, Atsushi
2018-03-07
The two-dimensional Cartesian turbo spin-echo (TSE) sequence is widely used in routine clinical studies, but it is sensitive to respiratory motion. We investigated the k-space orders in Cartesian TSE that can effectively reduce motion artifacts. The purpose of this study was to demonstrate the relationship between k-space order and degree of motion artifacts using a moving phantom. We compared the degree of motion artifacts between linear and asymmetric k-space orders. The actual spacing of ghost artifacts in the asymmetric order was doubled compared with that in the linear order in the free-breathing situation. The asymmetric order clearly showed less sensitivity to incomplete breath-hold at the latter half of the imaging period. Because of the actual number of partitions of the k-space and the temporal filling order, the asymmetric k-space order of Cartesian TSE was superior to the linear k-space order for reduction of ghosting motion artifacts.
Deformable Simplicial Complexes
DEFF Research Database (Denmark)
Misztal, Marek Krzysztof
triangles/tetrahedra marked as outside from those marked as inside. Such an approach allows for robust topological adaptivity. Among other advantages of the deformable simplicial complexes there are: space adaptivity, ability to handle and preserve sharp features, possibility for topology control. We....... One particular advantage of DSC is the fact that as an alternative to topology adaptivity, topology control is also possible. This is exploited in the construction of cut loci on tori where a front expands from a single point on a torus and stops when it self-intersects....
Nuclear fuel deformation phenomena
International Nuclear Information System (INIS)
Van Brutzel, L.; Dingreville, R.; Bartel, T.J.
2015-01-01
Nuclear fuel encounters severe thermomechanical environments. Its mechanical response is profoundly influenced by an underlying heterogeneous microstructure but also inherently dependent on the temperature and stress level histories. The ability to adequately simulate the response of such microstructures, to elucidate the associated macroscopic response in such extreme environments is crucial for predicting both performance and transient fuel mechanical responses. This chapter discusses key physical phenomena and the status of current modelling techniques to evaluate and predict fuel deformations: creep, swelling, cracking and pellet-clad interaction. This chapter only deals with nuclear fuel; deformations of cladding materials are discussed elsewhere. An obvious need for a multi-physics and multi-scale approach to develop a fundamental understanding of properties of complex nuclear fuel materials is presented. The development of such advanced multi-scale mechanistic frameworks should include either an explicit (domain decomposition, homogenisation, etc.) or implicit (scaling laws, hand-shaking,...) linkage between the different time and length scales involved, in order to accurately predict the fuel thermomechanical response for a wide range of operating conditions and fuel types (including Gen-IV and TRU). (authors)
Rotary deformity in degenerative spondylolisthesis
International Nuclear Information System (INIS)
Kang, Sung Gwon; Kim, Jeong; Kho, Hyen Sim; Yun, Sung Su; Oh, Jae Hee; Byen, Ju Nam; Kim, Young Chul
1994-01-01
We studied to determine whether the degenerative spondylolisthesis has rotary deformity in addition to forward displacement. We have made analysis of difference of rotary deformity between the 31 study groups of symptomatic degenerative spondylolisthesis and 31 control groups without any symptom, statistically. We also reviewed CT findings in 15 study groups. The mean rotary deformity in study groups was 6.1 degree(the standard deviation is 5.20), and the mean rotary deformity in control groups was 2.52 degree(the standard deviation is 2.16)(p < 0.01). The rotary deformity can be accompanied with degenerative spondylolisthesis. We may consider the rotary deformity as a cause of symptomatic degenerative spondylolisthesis in case that any other cause is not detected
Rotary deformity in degenerative spondylolisthesis
Energy Technology Data Exchange (ETDEWEB)
Kang, Sung Gwon; Kim, Jeong; Kho, Hyen Sim; Yun, Sung Su; Oh, Jae Hee; Byen, Ju Nam; Kim, Young Chul [Chosun University College of Medicine, Gwangju (Korea, Republic of)
1994-05-15
We studied to determine whether the degenerative spondylolisthesis has rotary deformity in addition to forward displacement. We have made analysis of difference of rotary deformity between the 31 study groups of symptomatic degenerative spondylolisthesis and 31 control groups without any symptom, statistically. We also reviewed CT findings in 15 study groups. The mean rotary deformity in study groups was 6.1 degree(the standard deviation is 5.20), and the mean rotary deformity in control groups was 2.52 degree(the standard deviation is 2.16)(p < 0.01). The rotary deformity can be accompanied with degenerative spondylolisthesis. We may consider the rotary deformity as a cause of symptomatic degenerative spondylolisthesis in case that any other cause is not detected.
Neutron halo in deformed nuclei
International Nuclear Information System (INIS)
Zhou Shangui; Meng Jie; Ring, P.; Zhao Enguang
2010-01-01
Halo phenomena in deformed nuclei are investigated within a deformed relativistic Hartree Bogoliubov (DRHB) theory. These weakly bound quantum systems present interesting examples for the study of the interdependence between the deformation of the core and the particles in the halo. Contributions of the halo, deformation effects, and large spatial extensions of these systems are described in a fully self-consistent way by the DRHB equations in a spherical Woods-Saxon basis with the proper asymptotic behavior at a large distance from the nuclear center. Magnesium and neon isotopes are studied and detailed results are presented for the deformed neutron-rich and weakly bound nucleus 44 Mg. The core of this nucleus is prolate, but the halo has a slightly oblate shape. This indicates a decoupling of the halo orbitals from the deformation of the core. The generic conditions for the occurrence of this decoupling effects are discussed.
Radiologic evaluation of foot deformities
International Nuclear Information System (INIS)
Erlemann, R.; Fischedick, A.R.; Peters, P.E.
1986-01-01
In order to analyze foot deformities, the foot is divided into three compartments. Their normal and pathological positions are defined by the alignment of the bones' axes. The various foot deformities can be put down to a malalignment of the particular compartments. X-ray analysis of the malalignment allows a diagnosis to be made. The most important congenital and acquired foot deformities are discussed. (orig.) [de
Man'ko, V I
1993-01-01
Brownian motion may be embedded in the Fock space of bosonic free field in one dimension.Extending this correspondence to a family of creation and annihilation operators satisfying a q-deformed algebra, the notion of q-deformation is carried from the algebra to the domain of stochastic processes.The properties of q-deformed Brownian motion, in particular its non-Gaussian nature and cumulant structure,are established.
Plate Like Convection with Viscous Strain Weakening and Corresponding Surface Deformation Pattern
Fuchs, L.; Becker, T. W.
2017-12-01
How plate tectonic surface motions are generated by mantle convection on Earth and possibly other terrestrial type planets has recently become more readily accessible with fully dynamic convection computations. However, it remains debated how plate-like the behavior in such models truly is, and in particular how the well plate boundary dynamics are captured in models which typically exclude the effects of deformation history and memory. Here, we analyze some of the effects of viscous strain weakening on plate behavior and the interactions between interior convection dynamics and surface deformation patterns. We use the finite element code CitcomCU to model convection in a 3D Cartesian model setup. The models are internally heated, with an Arrhenius-type temperature dependent viscosity including plastic yielding and viscous strain weakening (VSW) and healing (VSWH). VSW can mimic first order features of more complex damage mechanisms such as grain-size dependent rheology. Besides plate diagnostic parameters (Plateness, Mobility, and Toroidal: Poloidal ratio) to analyze the tectonic behavior our models, we also explore how "plate boundaries" link to convective patterns. In a first model series, we analyze general surface deformation patterns without VSW. In the early stages, deformation patterns are clearly co-located with up- and downwelling limbs of convection. Along downwellings strain-rates are high and localized, whereas upwellings tend to lead to broad zones of high deformation. At a more advanced stage, however, the plates' interior is highly deformed due to continuous strain accumulation and resurfaced inherited strain. Including only VSW leads to more localized deformation along downwellings. However, at a more advanced stage plate-like convection fails due an overall weakening of the material. This is prevented including strain healing. Deformation pattern at the surface more closely coincide with the internal convection patterns. The average surface
Deformable paper origami optoelectronic devices
He, Jr-Hau
2017-01-19
Deformable optoelectronic devices are provided, including photodetectors, photodiodes, and photovoltaic cells. The devices can be made on a variety of paper substrates, and can include a plurality of fold segments in the paper substrate creating a deformable pattern. Thin electrode layers and semiconductor nanowire layers can be attached to the substrate, creating the optoelectronic device. The devices can be highly deformable, e.g. capable of undergoing strains of 500% or more, bending angles of 25° or more, and/or twist angles of 270° or more. Methods of making the deformable optoelectronic devices and methods of using, e.g. as a photodetector, are also provided.
International Nuclear Information System (INIS)
Ogievetsky, O.; Pillin, M.; Schmidke, W.B.; Wess, J.; Zumino, B.
1993-01-01
In this lecture I discuss the algebraic structure of a q-deformed four-vector space. It serves as a good example of quantizing Minkowski space. To give a physical interpretation of such a quantized Minkowski space we construct the Hilbert space representation and find that the relevant time and space operators have a discrete spectrum. Thus the q-deformed Minkowski space has a lattice structure. Nevertheless this lattice structure is compatible with the operation of q-deformed Lorentz transformations. The generators of the q-deformed Lorentz group can be represented as linear operators in the same Hilbert space. (orig.)
Deformation behaviour of turbine foundations
International Nuclear Information System (INIS)
Koch, W.; Klitzing, R.; Pietzonka, R.; Wehr, J.
1979-01-01
The effects of foundation deformation on alignment in turbine generator sets have gained significance with the transition to modern units at the limit of design possibilities. It is therefore necessary to obtain clarification about the remaining operational variations of turbine foundations. Static measurement programmes, which cover both deformation processes as well as individual conditions of deformation are described in the paper. In order to explain the deformations measured structural engineering model calculations are being undertaken which indicate the effect of limiting factors. (orig.) [de
International Nuclear Information System (INIS)
Honarvar, M; Rohling, R; Lobo, J; Mohareri, O; Salcudean, S E
2015-01-01
To produce images of tissue elasticity, the vibro-elastography technique involves applying a steady-state multi-frequency vibration to tissue, estimating displacements from ultrasound echo data, and using the estimated displacements in an inverse elasticity problem with the shear modulus spatial distribution as the unknown. In order to fully solve the inverse problem, all three displacement components are required. However, using ultrasound, the axial component of the displacement is measured much more accurately than the other directions. Therefore, simplifying assumptions must be used in this case. Usually, the equations of motion are transformed into a Helmholtz equation by assuming tissue incompressibility and local homogeneity. The local homogeneity assumption causes significant imaging artifacts in areas of varying elasticity. In this paper, we remove the local homogeneity assumption. In particular we introduce a new finite element based direct inversion technique in which only the coupling terms in the equation of motion are ignored, so it can be used with only one component of the displacement. Both Cartesian and cylindrical coordinate systems are considered. The use of multi-frequency excitation also allows us to obtain multiple measurements and reduce artifacts in areas where the displacement of one frequency is close to zero. The proposed method was tested in simulations and experiments against a conventional approach in which the local homogeneity is used. The results show significant improvements in elasticity imaging with the new method compared to previous methods that assumes local homogeneity. For example in simulations, the contrast to noise ratio (CNR) for the region with spherical inclusion increases from an average value of 1.5–17 after using the proposed method instead of the local inversion with homogeneity assumption, and similarly in the prostate phantom experiment, the CNR improved from an average value of 1.6 to about 20. (paper)
Sunvisson, Helena; Habermann, Barbara; Weiss, Sara; Benner, Patricia
2009-10-01
Using three paradigm cases of persons living with Parkinson's Disease (PD) the authors make a case for augmenting and enriching a Cartesian medical account of the pathophysiology of PD with an enriched understanding of the lived body experience of PD, the lived implications of PD for a particular person's concerns and coping with the illness. Linking and adding a thick description of the lived experience of PD can enrich caregiving imagination and attunement to the patient's possibilities, concerns and constraints. The work of Merleau-Ponty is used to articulate the middle terms of the lived experience of dwelling in a lifeworld. Examining lived experience of embodied intentionality, skilled bodily capacities as highlighted in Merleau-Ponty's non-mechanistic physiology opens new therapeutic, coping and caregiving possibilities. Matching temporal rhythms can decrease the stress of being assisted with activities of daily living. For example, caregivers and patients alike can be taught strategies for extending their lived bodily capacities by altering rhythms, by shifting hyperactivity to different parts of the body and other strategies that change the perceptual experience associated with walking in different environment. A medical account of the pathophysiology of PD is nessessary and useful, but not sufficient for designing caregiving in ways that enrich and extend the existential skills of dwelling of persons with PD. The dominance of mechanistic physiology makes caregivers assume that it is the 'real discourse' about the disease, causing researchers and caregivers alike to overlook the equally real lived experience of the patient which requires different descriptive discourses and different sources of understanding. Lack of dialogue between the two discourses is tragic for patients because caregivers need both in order to provide attuned, effective caregiving.
Levine, Evan; Daniel, Bruce; Vasanawala, Shreyas; Hargreaves, Brian; Saranathan, Manojkumar
2017-05-01
To enable robust, high spatio-temporal-resolution three-dimensional Cartesian MRI using a scheme incorporating a novel variable density random k-space sampling trajectory allowing flexible and retrospective selection of the temporal footprint with compressed sensing (CS). A complementary Poisson-disc k-space sampling trajectory was designed to allow view sharing and varying combinations of reduced view sharing with CS from the same prospective acquisition. These schemes were used for two-point Dixon-based dynamic contrast-enhanced MRI (DCE-MRI) of the breast and abdomen. Results were validated in vivo with a novel approach using variable-flip-angle data, which was retrospectively accelerated using the same methods but offered a ground truth. In breast DCE-MRI, the temporal footprint could be reduced 2.3-fold retrospectively without introducing noticeable artifacts, improving depiction of rapidly enhancing lesions. Further, experiments with variable-flip-angle data showed that reducing view sharing improved accuracy in reconstruction and T 1 mapping. In abdominal MRI, 2.3-fold and 3.6-fold reductions in temporal footprint allowed reduced motion artifacts. The complementary-Poisson-disc k-space sampling trajectory allowed a retrospective spatiotemporal resolution tradeoff using CS and view sharing, imparting robustness to motion and contrast enhancement. The technique was also validated using a novel approach of fully acquired variable-flip-angle acquisition. Magn Reson Med 77:1774-1785, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Deformations of surface singularities
Szilárd, ágnes
2013-01-01
The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems, important examples and connections to other areas of mathematics. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. This also is supported by review articles providing some global picture and an abundance of examples. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several op...
Fraktalnist deformational relief polycrystalline aluminum
Directory of Open Access Journals (Sweden)
М.В. Карускевич
2006-02-01
Full Text Available The possibility of the fractal geometry method application for the analisys of surface deformation structures under cyclic loading is presented.It is shown, that deformation relief of the alclad aluminium alloyes meets the criteria of the fractality. For the fractal demention estimation the method of “box-counting”can be applied.
Plastic Deformation of Metal Surfaces
DEFF Research Database (Denmark)
Hansen, Niels; Zhang, Xiaodan; Huang, Xiaoxu
2013-01-01
Plastic deformation of metal surfaces by sliding and abrasion between moving parts can be detrimental. However, when the plastic deformation is controlled for example by applying different peening techniques hard surfaces can be produced which can increase the fracture resistance and fatigue life...
Nuclear deformation at finite temperature.
Alhassid, Y; Gilbreth, C N; Bertsch, G F
2014-12-31
Deformation, a key concept in our understanding of heavy nuclei, is based on a mean-field description that breaks the rotational invariance of the nuclear many-body Hamiltonian. We present a method to analyze nuclear deformations at finite temperature in a framework that preserves rotational invariance. The auxiliary-field Monte Carlo method is used to generate a statistical ensemble and calculate the probability distribution associated with the quadrupole operator. Applying the technique to nuclei in the rare-earth region, we identify model-independent signatures of deformation and find that deformation effects persist to temperatures higher than the spherical-to-deformed shape phase-transition temperature of mean-field theory.
Nuclear Deformation at Finite Temperature
Alhassid, Y.; Gilbreth, C. N.; Bertsch, G. F.
2014-12-01
Deformation, a key concept in our understanding of heavy nuclei, is based on a mean-field description that breaks the rotational invariance of the nuclear many-body Hamiltonian. We present a method to analyze nuclear deformations at finite temperature in a framework that preserves rotational invariance. The auxiliary-field Monte Carlo method is used to generate a statistical ensemble and calculate the probability distribution associated with the quadrupole operator. Applying the technique to nuclei in the rare-earth region, we identify model-independent signatures of deformation and find that deformation effects persist to temperatures higher than the spherical-to-deformed shape phase-transition temperature of mean-field theory.
Deformation of Man Made Objects
Ibrahim, Mohamed
2012-07-01
We introduce a framework for 3D object deformation with primary focus on man-made objects. Our framework enables a user to deform a model while preserving its defining characteristics. Moreover, our framework enables a user to set constraints on a model to keep its most significant features intact after the deformation process. Our framework supports a semi-automatic constraint setting environment, where some constraints could be automatically set by the framework while others are left for the user to specify. Our framework has several advantages over some state of the art deformation techniques in that it enables a user to add new features to the deformed model while keeping its general look similar to the input model. In addition, our framework enables the rotation and extrusion of different parts of a model.
Czech Academy of Sciences Publication Activity Database
Glombíček, Petr
2010-01-01
Roč. 24, č. 24 (2010), s. 133-141 ISSN 0231-5955 R&D Projects: GA AV ČR(CZ) KJB900090704 Institutional research plan: CEZ:AV0Z90090514 Keywords : le bon sens * Seneca * sensus communis Subject RIV: AA - Philosophy ; Religion
Energy Technology Data Exchange (ETDEWEB)
Inakura, T. [University of Tsukuba, Institute for Physics, Tsukuba (Japan); Nakatsukasa, T. [RIKEN Nishina Center, Theoretical Nuclear Physics Laboratory, Wako (Japan); Yabana, K. [University of Tsukuba, Institute for Physics, Tsukuba (Japan); University of Tsukuba, Center for Computational Sciences, Tsukuba (Japan)
2009-12-15
We undertake a systematic calculation on electric-dipole responses of even-even nuclei for a wide mass region employing a fully self-consistent Hartree-Fock plus RPA approach. For an easy implementation of the fully self-consistent calculation, the finite-amplitude method which we have proposed recently is employed. We calculated dipole responses in Cartesian mesh representation, which can deal with deformed nuclei but do not include pairing correlation. The systematic calculation has reached Nickel isotopes. The calculated results show reasonable agreement for heavy nuclei while the average excitation energies are underestimated for light nuclei. We show a systematic comparison of the splitting of the peak energy with the ground-state deformation. (orig.)
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
On infinitesimal conformai deformations of surfaces
Directory of Open Access Journals (Sweden)
Юлия Степановна Федченко
2014-11-01
Full Text Available A new form of basic equations for conformai deformations is found. The equations involve tensor fields of displacement vector only. Conditions for trivial deformations as well as infinitesimal conformai deformations are studied.
Energy Technology Data Exchange (ETDEWEB)
Sfetsos, Konstadinos [Department of Nuclear and Particle Physics, Faculty of Physics, University of Athens,Athens 15784 (Greece); Thompson, Daniel C. [Theoretische Natuurkunde, Vrije Universiteit Brussel andThe International Solvay Institutes,Pleinlaan 2, B-1050, Brussels (Belgium)
2014-12-29
We examine a recently proposed class of integrable deformations to two-dimensional conformal field theories. These λ-deformations interpolate between a WZW model and the non-Abelian T-dual of a Principal Chiral Model on a group G or, between a G/H gauged WZW model and the non-Abelian T-dual of the geometric coset G/H. λ-deformations have been conjectured to represent quantum group q-deformations for the case where the deformation parameter is a root of unity. In this work we show how such deformations can be given an embedding as full string backgrounds whose target spaces satisfy the equations of type-II supergravity. One illustrative example is a deformation of the Sl(2,ℝ)/U(1) black-hole CFT. A further example interpolates between the ((SU(2)×SU(2))/(SU(2)))×((SL(2,ℝ)×SL(2,ℝ))/(SL(2,ℝ)))×U(1){sup 4} gauged WZW model and the non-Abelian T-dual of AdS{sub 3}×S{sup 3}×T{sup 4} supported with Ramond flux.
Directory of Open Access Journals (Sweden)
Emílio Borges
2007-04-01
Full Text Available A simple method to obtain molecular Cartesian coordinates as a function of vibrational normal modes is presented in this work. The method does not require the definition of special matrices, like the F and G of Wilson, neither of group theory. The Eckart's conditions together with the diagonalization of kinetic and potential energy are the only required expressions. This makes the present approach appropriate to be used as a preliminary study for more advanced concepts concerning vibrational analysis. Examples are given for diatomic and triatomic molecules.
Energy Technology Data Exchange (ETDEWEB)
Anderson, D.V.; Breazeal, J.; Finan, C.H.; Johnston, B.M.
1976-09-14
ABCXYZ is a computer code for obtaining the Cartesian components of the vector potential and the magnetic field on an observed grid from an arrangement of current-carrying wires. Arbitrary combinations of straight line segments, arcs, and loops are allowed in the specification of the currents. Arbitrary positions and orientations of the current-carrying elements are also allowed. Specification of the wire diameter permits the computation of well-defined fields, even in the interiors of the conductors. An optical feature generates magnetic field lines. Extensive graphical and printed output is available to the user including contour, grid-line, and field-line plots. 12 figures, 1 table.
Deforming tachyon kinks and tachyon potentials
International Nuclear Information System (INIS)
Afonso, Victor I.; Bazeia, Dionisio; Brito, Francisco A.
2006-01-01
In this paper we investigate deformation of tachyon potentials and tachyon kink solutions. We consider the deformation of a DBI type action with gauge and tachyon fields living on D1-brane and D3-brane world-volume. We deform tachyon potentials to get other consistent tachyon potentials by using properly a deformation function depending on the gauge field components. Resolutions of singular tachyon kinks via deformation and applications of deformed tachyon potentials to scalar cosmology scenario are discussed
Yao, Lingxing; Mori, Yoichiro
2017-12-01
Osmotic forces and solute diffusion are increasingly seen as playing a fundamental role in cell movement. Here, we present a numerical method that allows for studying the interplay between diffusive, osmotic and mechanical effects. An osmotically active solute obeys a advection-diffusion equation in a region demarcated by a deformable membrane. The interfacial membrane allows transmembrane water flow which is determined by osmotic and mechanical pressure differences across the membrane. The numerical method is based on an immersed boundary method for fluid-structure interaction and a Cartesian grid embedded boundary method for the solute. We demonstrate our numerical algorithm with the test case of an osmotic engine, a recently proposed mechanism for cell propulsion.
Non-linear elastic deformations
Ogden, R W
1997-01-01
Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Anisotropic Ripple Deformation in Phosphorene.
Kou, Liangzhi; Ma, Yandong; Smith, Sean C; Chen, Changfeng
2015-05-07
Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here, we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression-induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.
Axisymmetric finite deformation membrane problems
Energy Technology Data Exchange (ETDEWEB)
Feng, W.W.
1980-12-12
Many biomechanic problems involve the analysis of finite deformation axisymmetric membranes. This paper presents the general formulation for solving a class of axisymmetric membrane problems. The material nonlinearity, as well as the geometric nonlinearity, is considered. Two methods are presented to solve these problems. The first method is solving a set of differential equilibrium equations. The governing equations are reduced to three first-order ordinary-differential equations with explicit derivatives. The second method is the Ritz method where a general potential energy functional valid for all axisymmetric deformed positions is presented. The geometric admissible functions that govern the deformed configuration are written in terms of a series with unknown coefficients. These unknown coefficients are determined by the minimum potential energy principle that of all geometric admissible deformed configurations, the equilibrium configuration minimizes the potential energy. Some examples are presented. A comparison between these two methods is mentioned.
Deterritorializing Drawing - transformation/deformation
DEFF Research Database (Denmark)
Brabrand, Helle
2012-01-01
and deformation as two very different categories. Moves of transformation produce new places or singularities in a series, making a Figure emerge that switches between force and form and between transformation and deformation. Deformation is acted out by sensation, passing from one ‘order’ to another. Bacon...... deformation, about painting the sensation, which is essentially rhythm, making Figure-rhythm relations appear as vibrations that flow through the body - making resonance. Deleuze, with Bergson, argues that art extracts ’a little time in a pure state’ from the everyday repetitions, and thereby opens...... the capacity of the body to be affected by change. The everyday and the ceremonial body, the ordinary and the aberrant movement – these poles generate a passage rather than a difference from the one to the other: from attitude or position to gesture or kinaesthetic twist. Known from without through perception...
Shape Deformations in Atomic Nuclei
Hamamoto, Ikuko; Mottelson, Ben R.
2011-01-01
The ground states of some nuclei are described by densities and mean fields that are spherical, while others are deformed. The existence of non-spherical shape in nuclei represents a spontaneous symmetry breaking.
Nonlinear Deformable-body Dynamics
Luo, Albert C J
2010-01-01
"Nonlinear Deformable-body Dynamics" mainly consists in a mathematical treatise of approximate theories for thin deformable bodies, including cables, beams, rods, webs, membranes, plates, and shells. The intent of the book is to stimulate more research in the area of nonlinear deformable-body dynamics not only because of the unsolved theoretical puzzles it presents but also because of its wide spectrum of applications. For instance, the theories for soft webs and rod-reinforced soft structures can be applied to biomechanics for DNA and living tissues, and the nonlinear theory of deformable bodies, based on the Kirchhoff assumptions, is a special case discussed. This book can serve as a reference work for researchers and a textbook for senior and postgraduate students in physics, mathematics, engineering and biophysics. Dr. Albert C.J. Luo is a Professor of Mechanical Engineering at Southern Illinois University, Edwardsville, IL, USA. Professor Luo is an internationally recognized scientist in the field of non...
M theory on deformed superspace
Faizal, Mir
2011-11-01
In this paper we will analyze a noncommutative deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) theory in N=1 superspace formalism. We will then analyze the Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetries for this deformed ABJM theory, and its linear as well as nonlinear gauges. We will show that the sum of the gauge fixing term and the ghost term for this deformed ABJM theory can be expressed as a combination of the total BRST and the total anti-BRST variation, in Landau and nonlinear gauges. We will show that in Landau and Curci-Ferrari gauges deformed ABJM theory is invariant under an additional set of symmetry transformations. We will also discuss the effect that the addition of a bare mass term has on this theory.
Polygonal deformation bands in sandstone
Antonellini, Marco; Nella Mollema, Pauline
2017-04-01
We report for the first time the occurrence of polygonal faults in sandstone, which is compelling given that layer-bound polygonal fault systems have been observed so far only in fine-grained sediments such as clay and chalk. The polygonal faults are dm-wide zones of shear deformation bands that developed under shallow burial conditions in the lower portion of the Jurassic Entrada Fm (Utah, USA). The edges of the polygons are 1 to 5 meters long. The shear deformation bands are organized as conjugate faults along each edge of the polygon and form characteristic horst-like structures. The individual deformation bands have slip magnitudes ranging from a few mm to 1.5 cm; the cumulative average slip magnitude in a zone is up to 10 cm. The deformation bands heaves, in aggregate form, accommodate a small isotropic horizontal extension (strain Crosscutting relationships are rare. The interactions of the deformation bands are similar to those of mode I opening fractures. Density inversion, that takes place where under-compacted and over-pressurized layers (Carmel Fm) lay below normally compacted sediments (Entrada Sandstone), may be an important process for polygonal deformation bands formation. The gravitational sliding and soft sediment structures typically observed within the Carmel Fm support this hypothesis. Soft sediment deformation may induce polygonal faulting in the section of the Entrada Sandstone just above the Carmel Fm. The permeability of the polygonal deformation bands is approximately 10-14 to 10-13 m2, which is less than the permeability of the host, Entrada Sandstone (range 10-12 to 10-11 m2). The documented fault networks have important implications for evaluating the geometry of km-scale polygonal fault systems in the subsurface, top seal integrity, as well as constraining paleo-tectonic stress regimes.
Unitary deformations of counterdiabatic driving
Takahashi, Kazutaka
2015-04-01
We study a deformation of the counterdiabatic-driving Hamiltonian as a systematic strategy for an adiabatic control of quantum states. Using a unitary transformation, we design a convenient form of the driver Hamiltonian. We apply the method to a particle in a confining potential and discrete systems to find explicit forms of the Hamiltonian and discuss the general properties. The method is derived by using the quantum brachistochrone equation, which shows the existence of a nontrivial dynamical invariant in the deformed system.
Directory of Open Access Journals (Sweden)
Fábio V. Magalhães
2005-01-01
Full Text Available A non-informative cue (C elicits an inhibition of manual reaction time (MRT to a visual target (T. We report an experiment to examine if the spatial distribution of this inhibitory effect follows Polar or Cartesian coordinate systems. C appeared at one out of 8 isoeccentric (7o positions, the C-T angular distances (in polar coordinates were 0º or multiples of 45º and ISI were 100 or 800ms. Our main findings were: (a MRT was maximal when C- T distance was 0o and minimal when C-T distance was 180o and (b besides an angular distance effect, there is a meridian effect. When C and T occurred in the same quadrant, MRT was longer than when T and C occurred at the same distance (45o but on different sides of vertical or horizontal meridians. The latter finding indicates that the spatial distribution of the cue inhibitory effects is based on a Cartesian coordinate system.
International Nuclear Information System (INIS)
Kirkpatrick, M.P.; Armfield, S.W.; Kent, J.H.
2003-01-01
A method is presented for representing curved boundaries for the solution of the Navier-Stokes equations on a non-uniform, staggered, three-dimensional Cartesian grid. The approach involves truncating the Cartesian cells at the boundary surface to create new cells which conform to the shape of the surface. We discuss in some detail the problems unique to the development of a cut cell method on a staggered grid. Methods for calculating the fluxes through the boundary cell faces, for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second-order accuracy in space. In addition, a novel 'cell-linking' method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell-merging approaches. Techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces. The new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at Re=40 and is shown to give significant improvement over a staircase boundary formulation. Finally, it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a Reynolds number of 800. Good agreement is obtained with experimental results for this flow
Directory of Open Access Journals (Sweden)
Kuczyński Paweł
2014-06-01
Full Text Available The paper deals with a solution of radiation heat transfer problems in enclosures filled with nonparticipating medium using ray tracing on hierarchical ortho-Cartesian meshes. The idea behind the approach is that radiative heat transfer problems can be solved on much coarser grids than their counterparts from computational fluid dynamics (CFD. The resulting code is designed as an add-on to OpenFOAM, an open-source CFD program. Ortho-Cartesian mesh involving boundary elements is created based upon CFD mesh. Parametric non-uniform rational basis spline (NURBS surfaces are used to define boundaries of the enclosure, allowing for dealing with domains of complex shapes. Algorithm for determining random, uniformly distributed locations of rays leaving NURBS surfaces is described. The paper presents results of test cases assuming gray diffusive walls. In the current version of the model the radiation is not absorbed within gases. However, the ultimate aim of the work is to upgrade the functionality of the model, to problems in absorbing, emitting and scattering medium projecting iteratively the results of radiative analysis on CFD mesh and CFD solution on radiative mesh.
Deformed configurations, band structures and spectroscopic ...
Indian Academy of Sciences (India)
2014-03-20
Mar 20, 2014 ... The deformed configurations and rotational band structures in =50 Ge and Se nuclei are studied by deformed Hartree–Fock with quadrupole constraint and angular momentum projection. Apart from the `almost' spherical HF solution, a well-deformed configuration occurs at low excitation. A deformed ...
Associative and Lie deformations of Poisson algebras
Remm, Elisabeth
2011-01-01
Considering a Poisson algebra as a non associative algebra satisfying the Markl-Remm identity, we study deformations of Poisson algebras as deformations of this non associative algebra. This gives a natural interpretation of deformations which preserves the underlying associative structure and we study deformations which preserve the underlying Lie algebra.
Bilateral cleft lip nasal deformity
Directory of Open Access Journals (Sweden)
Singh Arun
2009-01-01
Full Text Available Bilateral cleft lip nose deformity is a multi-factorial and complex deformity which tends to aggravate with growth of the child, if not attended surgically. The goals of primary bilateral cleft lip nose surgery are, closure of the nasal floor and sill, lengthening of the columella, repositioning of the alar base, achieving nasal tip projection, repositioning of the lower lateral cartilages, and reorienting the nares from horizontal to oblique position. The multiplicity of procedures in the literature for correction of this deformity alludes to the fact that no single procedure is entirely effective. The timing for surgical intervention and its extent varies considerably. Early surgery on cartilage may adversely affect growth and development; at the same time, allowing the cartilage to grow in an abnormal position and contributing to aggravation of deformity. Some surgeons advocate correction of deformity at an early age. However, others like the cartilages to grow and mature before going in for surgery. With peer pressure also becoming an important consideration during the teens, the current trend is towards early intervention. There is no unanimity in the extent of nasal dissection to be done at the time of primary lip repair. While many perform limited nasal dissection for the fear of growth retardation, others opt for full cartilage correction at the time of primary surgery itself. The value of naso-alveolar moulding (NAM too is not universally accepted and has now more opponents than proponents. Also most centres in the developing world have neither the personnel nor the facilities for the same. The secondary cleft nasal deformity is variable and is affected by the extent of the original abnormality, any prior surgeries performed and alteration due to nasal growth. This article reviews the currently popular methods for correction of nasal deformity associated with bilateral cleft lip, it′s management both at the time of cleft lip repair
Plastic deformation of indium nanostructures
International Nuclear Information System (INIS)
Lee, Gyuhyon; Kim, Ju-Young; Burek, Michael J.; Greer, Julia R.; Tsui, Ting Y.
2011-01-01
Highlights: → Indium nanopillars display two different deformation mechanisms. → ∼80% exhibited low flow stresses near that of bulk indium. → Low strength nanopillars have strain rate sensitivity similar to bulk indium. → ∼20% of compressed indium nanopillars deformed at nearly theoretical strengths. → Low-strength samples do not exhibit strength size effects. - Abstract: Mechanical properties and morphology of cylindrical indium nanopillars, fabricated by electron beam lithography and electroplating, are characterized in uniaxial compression. Time-dependent deformation and influence of size on nanoscale indium mechanical properties were investigated. The results show two fundamentally different deformation mechanisms which govern plasticity in these indium nanostructures. We observed that the majority of indium nanopillars deform at engineering stresses near the bulk values (Type I), with a small fraction sustaining flow stresses approaching the theoretical limit for indium (Type II). The results also show the strain rate sensitivity and flow stresses in Type I indium nanopillars are similar to bulk indium with no apparent size effects.
Static response of deformable microchannels
Christov, Ivan C.; Sidhore, Tanmay C.
2017-11-01
Microfluidic channels manufactured from PDMS are a key component of lab-on-a-chip devices. Experimentally, rectangular microchannels are found to deform into a non-rectangular cross-section due to fluid-structure interactions. Deformation affects the flow profile, which results in a nonlinear relationship between the volumetric flow rate and the pressure drop. We develop a framework, within the lubrication approximation (l >> w >> h), to self-consistently derive flow rate-pressure drop relations. Emphasis is placed on handling different types of elastic response: from pure plate-bending, to half-space deformation, to membrane stretching. The ``simplest'' model (Stokes flow in a 3D rectangular channel capped with a linearly elastic Kirchhoff-Love plate) agrees well with recent experiments. We also simulate the static response of such microfluidic channels under laminar flow conditions using ANSYSWorkbench. Simulations are calibrated using experimental flow rate-pressure drop data from the literature. The simulations provide highly resolved deformation profiles, which are difficult to measure experimentally. By comparing simulations, experiments and our theoretical models, we show good agreement in many flow/deformation regimes, without any fitting parameters.
Coirier, William John
1994-01-01
A Cartesian, cell-based scheme for solving the Euler and Navier-Stokes equations in two dimensions is developed and tested. Grids about geometrically complicated bodies are generated automatically, by recursive subdivision of a single Cartesian cell encompassing the entire flow domain. Where the resulting cells intersect bodies, polygonal 'cut' cells are created. The geometry of the cut cells is computed using polygon-clipping algorithms. The grid is stored in a binary-tree data structure which provides a natural means of obtaining cell-to-cell connectivity and of carrying out solution-adaptive refinement. The Euler and Navier-Stokes equations are solved on the resulting grids using a finite-volume formulation. The convective terms are upwinded, with a limited linear reconstruction of the primitive variables used to provide input states to an approximate Riemann solver for computing the fluxes between neighboring cells. A multi-stage time-stepping scheme is used to reach a steady-state solution. Validation of the Euler solver with benchmark numerical and exact solutions is presented. An assessment of the accuracy of the approach is made by uniform and adaptive grid refinements for a steady, transonic, exact solution to the Euler equations. The error of the approach is directly compared to a structured solver formulation. A non smooth flow is also assessed for grid convergence, comparing uniform and adaptively refined results. Several formulations of the viscous terms are assessed analytically, both for accuracy and positivity. The two best formulations are used to compute adaptively refined solutions of the Navier-Stokes equations. These solutions are compared to each other, to experimental results and/or theory for a series of low and moderate Reynolds numbers flow fields. The most suitable viscous discretization is demonstrated for geometrically-complicated internal flows. For flows at high Reynolds numbers, both an altered grid-generation procedure and a
Making Deformable Template Models Operational
DEFF Research Database (Denmark)
Fisker, Rune
2000-01-01
for estimation of the model parameters, which applies a combination of a maximum likelihood and minimum distance criterion. Another contribution is a very fast search based initialization algorithm using a filter interpretation of the likelihood model. These two methods can be applied to most deformable template......Deformable template models are a very popular and powerful tool within the field of image processing and computer vision. This thesis treats this type of models extensively with special focus on handling their common difficulties, i.e. model parameter selection, initialization and optimization....... A proper handling of the common difficulties is essential for making the models operational by a non-expert user, which is a requirement for intensifying and commercializing the use of deformable template models. The thesis is organized as a collection of the most important articles, which has been...
Foam rheology at large deformation
Géminard, J.-C.; Pastenes, J. C.; Melo, F.
2018-04-01
Large deformations are prone to cause irreversible changes in materials structure, generally leading to either material hardening or softening. Aqueous foam is a metastable disordered structure of densely packed gas bubbles. We report on the mechanical response of a foam layer subjected to quasistatic periodic shear at large amplitude. We observe that, upon increasing shear, the shear stress follows a universal curve that is nearly exponential and tends to an asymptotic stress value interpreted as the critical yield stress at which the foam structure is completely remodeled. Relevant trends of the foam mechanical response to cycling are mathematically reproduced through a simple law accounting for the amount of plastic deformation upon increasing stress. This view provides a natural interpretation to stress hardening in foams, demonstrating that plastic effects are present in this material even for minute deformation.
Computing layouts with deformable templates
Peng, Chi-Han
2014-07-22
In this paper, we tackle the problem of tiling a domain with a set of deformable templates. A valid solution to this problem completely covers the domain with templates such that the templates do not overlap. We generalize existing specialized solutions and formulate a general layout problem by modeling important constraints and admissible template deformations. Our main idea is to break the layout algorithm into two steps: a discrete step to lay out the approximate template positions and a continuous step to refine the template shapes. Our approach is suitable for a large class of applications, including floorplans, urban layouts, and arts and design. Copyright © ACM.
DEFF Research Database (Denmark)
Huang, X.; Borrego, A.; Pantleon, W.
2001-01-01
The relation between the polycrystal deformation and single crystal deformation has been studied for pure polycrystalline copper deformed in tension. The dislocation microstructure has been analyzed for grains of different orientation by transmission electron microscopy (TEM) and three types...
Deformations of the Almheiri-Polchinski model
Energy Technology Data Exchange (ETDEWEB)
Kyono, Hideki; Okumura, Suguru; Yoshida, Kentaroh [Department of Physics, Kyoto University, Kitashirakawa Oiwake-cho, Kyoto 606-8502 (Japan)
2017-03-31
We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS{sub 2} metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter-term on the regularized screen close to the singularity.
Van Gorder, Robert A
2013-04-01
We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrödinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and we also relate this solution back to the solution obtained in the arclength reference frame (the intrinsic coordinate system). Finally, we discuss nonmonotone coordinate scalings and their application for finding self-intersections of vortex filaments. These self-intersecting vortex filaments are likely unstable and collapse into other structures or dissipate completely.
International Nuclear Information System (INIS)
Borges, Volnei; Vilhena, Marco Tullio; Fernandes, Julio Cesar Lombaldo
2011-01-01
In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two dimensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTS N method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTS N nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature. (author)
Energy Technology Data Exchange (ETDEWEB)
Borges, Volnei; Vilhena, Marco Tullio, E-mail: borges@ufrgs.b, E-mail: vilhena@pq.cnpq.b [Universidade Federal do Rio Grande do Sul (PROMEC/UFRGS), Porto Alegre, RS (Brazil). Programa de Pos-Graduacao em Engenharia Mecanica; Fernandes, Julio Cesar Lombaldo, E-mail: julio.lombaldo@ufrgs.b [Universidade Federal do Rio Grande do Sul (DMPA/UFRGS), Porto Alegre, RS (Brazil). Dept. de Matematica Pura e Aplicada. Programa de Pos Graduacao em Matematica Aplicada
2011-07-01
In this work, we report on a closed-form formulation for the build-up factor and absorbed energy, in one and two dimensional Cartesian geometry for photons and electrons, in the Compton energy range. For the one-dimensional case we use the LTS{sub N} method, assuming the Klein-Nishina scattering kernel for the determination of the angular radiation intensity for photons. We apply the two-dimensional LTS{sub N} nodal solution for the averaged angular radiation evaluation for the two-dimensional case, using the Klein-Nishina kernel for photons and the Compton kernel for electrons. From the angular radiation intensity we construct a closed-form solution for the build-up factor and evaluate the absorbed energy. We present numerical simulations and comparisons against results from the literature. (author)
Directory of Open Access Journals (Sweden)
Jiran L.
2016-06-01
Full Text Available Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA. Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.
Spatiotemporal deformations of reflectionless potentials
Horsley, S. A. R.; Longhi, S.
2017-08-01
Reflectionless potentials for classical or matter waves represent an important class of scatteringless systems encountered in different areas of physics. Here we mathematically demonstrate that there is a family of non-Hermitian potentials that, in contrast to their Hermitian counterparts, remain reflectionless even when deformed in space or time. These are the profiles that satisfy the spatial Kramers-Kronig relations. We start by considering scattering of matter waves for the Schrödinger equation with an external field, where a moving potential is observed in the Kramers-Henneberger reference frame. We then generalize this result to the case of electromagnetic waves, by considering a slab of reflectionless material that both is scaled and has its center displaced as an arbitrary function of position. We analytically and numerically demonstrate that the backscattering from these profiles remains zero, even for extreme deformations. Our results indicate the supremacy of non-Hermitian Kramers-Kronig potentials over reflectionless Hermitian potentials in keeping their reflectionless property under deformation and could find applications to, e.g., reflectionless optical coatings of highly deformed surfaces based on perfect absorption.
Deformable Models for Eye Tracking
DEFF Research Database (Denmark)
Vester-Christensen, Martin; Leimberg, Denis; Ersbøll, Bjarne Kjær
2005-01-01
A deformable template method for eye tracking on full face images is presented. The strengths of the method are that it is fast and retains accuracy independently of the resolution. We compare the me\\$\\backslash\\$-thod with a state of the art active contour approach, showing that the heuristic...
Simulation of rock deformation behavior
Directory of Open Access Journals (Sweden)
Я. И. Рудаев
2016-12-01
Full Text Available A task of simulating the deformation behavior of geomaterials under compression with account of over-extreme branch has been addressed. The physical nature of rock properties variability as initially inhomogeneous material is explained by superposition of deformation and structural transformations of evolutionary type within open nonequilibrium systems. Due to this the description of deformation and failure of rock is related to hierarchy of instabilities within the system being far from thermodynamic equilibrium. It is generally recognized, that the energy function of the current stress-strain state is a superposition of potential component and disturbance, which includes the imperfection parameter accounting for defects not only existing in the initial state, but also appearing under load. The equation of state has been obtained by minimizing the energy function by the order parameter. The imperfection parameter is expressed through the strength deterioration, which is viewed as the internal parameter of state. The evolution of strength deterioration has been studied with the help of Fokker – Planck equation, which steady form corresponds to rock statical stressing. Here the diffusion coefficient is assumed to be constant, while the function reflecting internal sliding and loosening of the geomaterials is assumed as an antigradient of elementary integration catastrophe. Thus the equation of state is supplemented with a correlation establishing relationship between parameters of imperfection and strength deterioration. While deformation process is identified with the change of dissipative media, coupled with irreversible structural fluctuations. Theoretical studies are proven with experimental data obtained by subjecting certain rock specimens to compression.
Cleft deformities (lip and palate)
African Journals Online (AJOL)
dell
Background: Cleft deformities (lip and palate) have been reported to be the most common congenital craniofacial anomaly in several settings. In Uganda, though two previous studies were conducted to determine the incidence of cleft lip and palate, the estimates obtained from those studies may not be precise given the ...
Deformations of topological open strings
Hofman, C.; Ma, Whee Ky
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra - the complex of multilinear maps on the boundary Hilbert space.
Deformation mechanisms of nanotwinned Al
Energy Technology Data Exchange (ETDEWEB)
Zhang, Xinghang [Texas A & M Univ., College Station, TX (United States)
2016-11-10
The objective of this project is to investigate the role of different types of layer interfaces on the formation of high density stacking fault (SF) in Al in Al/fcc multilayers, and understand the corresponding deformation mechanisms of the films. Stacking faults or twins can be intentionally introduced (via growth) into certain fcc metals with low stacking fault energy (such as Cu, Ag and 330 stainless steels) to achieve high strength, high ductility, superior thermal stability and good electrical conductivity. However it is still a major challenge to synthesize these types of defects into metals with high stacking fault energy, such as Al. Although deformation twins have been observed in some nanocrystalline Al powders by low temperature, high strain rate cryomilling or in Al at the edge of crack tip or indentation (with the assistance of high stress intensity factor), these deformation techniques typically introduce twins sporadically and the control of deformation twin density in Al is still not feasible. This project is designed to test the following hypotheses: (1) Certain type of layer interfaces may assist the formation of SF in Al, (2) Al with high density SF may have deformation mechanisms drastically different from those of coarse-grained Al and nanotwinned Cu. To test these hypotheses, we have performed the following tasks: (i) Investigate the influence of layer interfaces, stresses and deposition parameters on the formation and density of SF in Al. (ii) Understand the role of SF on the deformation behavior of Al. In situ nanoindentation experiments will be performed to probe deformation mechanisms in Al. The major findings related to the formation mechanism of twins and mechanical behavior of nanotwinned metals include the followings: 1) Our studies show that nanotwins can be introduced into metals with high stacking fault energy, in drastic contrast to the general anticipation. 2) We show two strategies that can effectively introduce growth twins in
Treatment of hallux valgus deformity.
Fraissler, Lukas; Konrads, Christian; Hoberg, Maik; Rudert, Maximilian; Walcher, Matthias
2016-08-01
Hallux valgus deformity is a very common pathological condition which commonly produces painful disability. It is characterised as a combined deformity with a malpositioning of the first metatarsophalangeal joint caused by a lateral deviation of the great toe and a medial deviation of the first metatarsal bone.Taking the patient's history and a thorough physical examination are important steps. Anteroposterior and lateral weight-bearing radiographs of the entire foot are crucial for adequate assessment in the treatment of hallux valgus.Non-operative treatment of the hallux valgus cannot correct the deformity. However, insoles and physiotherapy in combination with good footwear can help to control the symptoms.There are many operative techniques for hallux valgus correction. The decision on which surgical technique is used depends on the degree of deformity, the extent of degenerative changes of the first metatarsophalangeal joint and the shape and size of the metatarsal bone and phalangeal deviation. The role of stability of the first tarsometatarsal joint is controversial.Surgical techniques include the modified McBride procedure, distal metatarsal osteotomies, metatarsal shaft osteotomies, the Akin osteotomy, proximal metatarsal osteotomies, the modified Lapidus fusion and the hallux joint fusion. Recently, minimally invasive percutaneous techniques have gained importance and are currently being evaluated more scientifically.Hallux valgus correction is followed by corrective dressings of the great toe post-operatively. Depending on the procedure, partial or full weight-bearing in a post-operative shoe or cast immobilisation is advised. Post-operative radiographs are taken in regular intervals until osseous healing is achieved. Cite this article: Fraissler L, Konrads C, Hoberg M, Rudert M, Walcher M. Treatment of hallux valgus deformity. EFORT Open Rev 2016;1:295-302. DOI: 10.1302/2058-5241.1.000005.
Thorax deformity, joint hypermobility and anxiety disorder
International Nuclear Information System (INIS)
Gulsun, M.; Dumlu, K.; Erbas, M.; Yilmaz, Mehmet B.; Pinar, M.; Tonbul, M.; Celik, C.; Ozdemir, B.
2007-01-01
Objective was to evaluate the association between thorax deformities, panic disorder and joint hypermobility. The study includes 52 males diagnosed with thorax deformity, and 40 healthy male controls without thorax deformity, in Tatvan Bitlis and Isparta, Turkey. The study was carried out from 2004 to 2006. The teleradiographic and thoracic lateral images of the subjects were evaluated to obtain the Beighton scores; subjects psychiatric conditions were evaluated using the Structured Clinical Interview for DSM-IV Axis I Disorders (SCID-1), and the Hamilton Anxiety Scale (HAM-A) was applied in order to determine the anxiety levels. Both the subjects and controls were compared in sociodemographic, anxiety levels and joint mobility levels. In addition, males with joint hypermobility and thorax deformity were compared to the group with thorax deformity without joint hypermobility. A significant difference in HAM-A scores was found between the groups with thorax deformity and without. In addition, 21 subjects with thorax deformity met the joint hypermobility criteria in the group with thorax deformity and 7 subjects without thorax deformity met the joint hypermobility criteria in the group without thorax deformity, according to Beighton scoring. The Beighton score of subjects with thorax deformity were significantly different from those of the group without deformity. Additionally, anxiety scores of the males with thorax deformity and joint hypermobility were found higher than males with thorax deformity without joint hypermobility. Anxiety disorders, particularly panic disorder, have a significantly higher distribution in males subjects with thorax deformity compared to the healthy control group. In addition, the anxiety level of males with thorax deformity and joint hypermobility is higher than males with thorax deformity without joint hypermobility. (author)
Highly deformable bones: unusual deformation mechanisms of seahorse armor.
Porter, Michael M; Novitskaya, Ekaterina; Castro-Ceseña, Ana Bertha; Meyers, Marc A; McKittrick, Joanna
2013-06-01
Multifunctional materials and devices found in nature serve as inspiration for advanced synthetic materials, structures and robotics. Here, we elucidate the architecture and unusual deformation mechanisms of seahorse tails that provide prehension as well as protection against predators. The seahorse tail is composed of subdermal bony plates arranged in articulating ring-like segments that overlap for controlled ventral bending and twisting. The bony plates are highly deformable materials designed to slide past one another and buckle when compressed. This complex plate and segment motion, along with the unique hardness distribution and structural hierarchy of each plate, provide seahorses with joint flexibility while shielding them against impact and crushing. Mimicking seahorse armor may lead to novel bio-inspired technologies, such as flexible armor, fracture-resistant structures or prehensile robotics. Copyright © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
CubeSat Deformable Mirror Demonstration
National Aeronautics and Space Administration — The goal of the CubeSat Deformable Mirror Demonstration is to characterize the performance of a small deformable mirror over a year in low-Earth orbit. Small form...
Prediction of deformity in spinal tuberculosis
Jutte, Paul; Wuite, Sander; The, Bertram; van Altena, Richard; Veldhuizen, Albert
Tuberculosis of the spine may cause kyphosis, which may in turn cause late paraplegia, respiratory compromise, and unsightly deformity. Surgical correction therefore may be considered for large or progressive deformities. We retrospectively analyzed clinical and radiographic parameters to predict
Shell effects in the nuclear deformation energy
International Nuclear Information System (INIS)
Ross, C.K.
1973-01-01
A new approach to shell effects in the Strutinsky method for calculating nuclear deformation energy is evaluated and the suggestion of non-conservation of angular momentum in the same method is resolved. Shell effects on the deformation energy in rotational bands of deformed nuclei are discussed. (B.F.G.)
Deformed configurations, band structures and spectroscopic ...
Indian Academy of Sciences (India)
2014-03-20
Mar 20, 2014 ... Here, we study theoretically the low-lying as well as the excited deformed bands and their electromagnetic properties to search for various structures, spherical and deformed, of the exotic nuclei 82Ge and 84Se by employing the deformed Hartree–Fock (HF) and angular momentum (J) projection method ...
Conformal deformation of Riemann space and torsion
International Nuclear Information System (INIS)
Pyzh, V.M.
1981-01-01
Method for investigating conformal deformations of Riemann spaces using torsion tensor, which permits to reduce the second ' order equations for Killing vectors to the system of the first order equations, is presented. The method is illustrated using conformal deformations of dimer sphere as an example. A possibility of its use when studying more complex deformations is discussed [ru
Phase space deformations in phantom cosmology
López, J. L.; Sabido, M.; Yee-Romero, C.
2018-03-01
We discuss the physical consequences of general phase space deformations on the minisuperspace of phantom cosmology. Based on the principle of physically equivalent descriptions in the deformed theory, we investigate for what values of the deformation parameters the arising descriptions are physically equivalent. We also construct and solve the quantum model and derive the semiclassical dynamics.
Relativistic description of deformed nuclei
International Nuclear Information System (INIS)
Price, C.E.
1988-01-01
The author has shown that relativistic Hartree calculations using parameters that have been fit to the properties of nuclear matter can provide a good description of both spherical and axially deformed nuclei. The quantitative agreement with experiment is equivalent to that which was obtained in non-relativistic calculations using Skyrme interactions. The equilibrium deformation is strongly correlated with the size of the spin-orbit splitting, and that parameter sets which give roughly the correct value for this splitting provide the best agreement with the quadrupole moments in the s-d shell. Finally, for closed shell +/- 1 nuclei, it was shown that the self-consistent calculations are able to reproduce the experimental magnetic moments. This was not possible in relativistic calculations which include only the effects of the valence orbital
Nucleon deformation. A status report
International Nuclear Information System (INIS)
Papanicolas, C.N.
2003-01-01
The conjectured deformation of hadrons and its experimental verification offer a particularly fertile ground for understanding the intricate dynamics of their constituents and QCD at the confinement scale. The detailed study of the N→Δ transition is viewed as the preferred method of experimental investigation of this central issue in hadronic physics. A brief overview of the field is presented, followed by a presentation of the most recent results from Bates N→Δ program. The new Bates/OOPS data at Q 2 =0.127 GeV/c 2 yield R SM =(-6.27±0.32 stat+sys ±0.10 model )% and R EM =(-2.00±0.40 stat+sys ±0.27 model )% and they exclude a spherical nucleon and/or Δ. The magnitude and the origin of the deformation is the focus of the ongoing and planned investigations. (orig.)
Hindfoot Arthrodesis for Neuropathic Deformity
Directory of Open Access Journals (Sweden)
Peng-Ju Huang
2007-03-01
Full Text Available Acquired neurologic disorders of the foot lead to arthrosis, deformities, instabilities, and functional disabilities. Hindfoot arthrodesis is the current option available for irreducible or nonbraceable deformities of neuropathic feet. However, the role of ankle arthrodesis in these patients has been questioned because of high nonunion and complication rates. From 1990 to 2001, 17 cases of acquired neuropathic foot deformities were treated by four tibiotalocalcaneal (TTC arthrodeses and 13 ankle arthrodeses. TTC arthrodesis was performed on cases with combined ankle and subtalar arthritis or cases whose deformities or instabilities could not be corrected by ankle fusion alone. There was no nonunion of TTC arthrodesis and seven ununited ankle arthrodeses were salvaged by two TTC-attempted arthrodeses and five revision ankle-attempted arthrodeses. Eventually in these cases, there was one nonunion in TTC arthrodesis and one nonunion in revision ankle arthrodesis. The final fusion rate was 88% (15 of 17 cases with average union time of 6.9 months (range, 2.5–18 months. The American Orthopaedic Foot and Ankle Society ankle hind-foot functional scores were evaluated: one was excellent (5.8%, seven were good (41%, eight were fair (53.3%, and one was poor (5.8% in terms of total functional outcome. We conclude that TTC arthrodesis is indicated for cases with ankle and subtalar involvement and ankle arthrodesis is an alternative for cases with intact subtalar joint. We recommend revision ankle arthrodesis if the ankle fails to fuse and the bone stock of the talus is adequate. TTC arthrodesis is reserved for ankles with poor bone stock of the talus with fragmentation.
Deterritorializing Drawing - transformation/deformation
DEFF Research Database (Denmark)
Brabrand, Helle
2012-01-01
but also from within by sensations, body ‘images’ are different to all other images. Twisting these body images make a mode of operation of art. The paper will address the above issues discussing modes of operation and appearance of my actual project. Acting in the reality of drawing, the project confront...... the body, situated in real time and depth, with drawing transforming and deforming time and depth....
Shapeable sheet without plastic deformation
Oppenheimer, Naomi; Witten, Thomas A.
2015-11-01
Randomly crumpled sheets have shape memory. In order to understand the basis of this form of memory, we simulate triangular lattices of springs whose lengths are altered to create a topography with multiple potential energy minima. We then deform these lattices into different shapes and investigate their ability to retain the imposed shape when the energy is relaxed. The lattices are able to retain a range of curvatures. Under moderate forcing from a state of local equilibrium, the lattices deform by several percent but return to their retained shape when the forces are removed. By increasing the forcing until an irreversible motion occurs, we find that the transitions between remembered shapes show cooperativity among several springs. For fixed lattice structures, the shape memory tends to decrease as the lattice is enlarged; we propose ways to counter this decrease by modifying the lattice geometry. We survey the energy landscape by displacing individual nodes. An extensive fraction of these nodes proves to be bistable; they retain their displaced position when the energy is relaxed. Bending the lattice to a stable curved state alters the pattern of bistable nodes. We discuss this shapeability in the context of other forms of material memory and contrast it with the shapeability of plastic deformation. We outline the prospects for making real materials based on these principles.
Faraday instability in deformable domains
International Nuclear Information System (INIS)
Pucci, G.
2013-01-01
Hydrodynamical instabilities are usually studied either in bounded regions or free to grow in space. In this article we review the experimental results of an intermediate situation, in which an instability develops in deformable domains. The Faraday instability, which consists in the formation of surface waves on a liquid experiencing a vertical forcing, is triggered in floating liquid lenses playing the role of deformable domains. Faraday waves deform the lenses from the initial circular shape and the mutual adaptation of instability patterns with the lens boundary is observed. Two archetypes of behaviour have been found. In the first archetype a stable elongated shape is reached, the wave vector being parallel to the direction of elongation. In the second archetype the waves exceed the response of the lens border and no equilibrium shape is reached. The lens stretches and eventually breaks into fragments that have a complex dynamics. The difference between the two archetypes is explained by the competition between the radiation pressure the waves exert on the lens border and its response due to surface tension.
Micromechanisms of deformation in shales
Bonnelye, A.; Gharbi, H.; Hallais, S.; Dimanov, A.; Bornert, M.; Picard, D.; Mezni, M.; Conil, N.
2017-12-01
One of the envisaged solutions for nuclear wastes disposal is underground repository in shales. For this purpose, the Callovo Oxfordian (Cox) argillaceous formation is extensively studied. The hydro-mechanical behavior of the argillaceous rock is complex, like the multiphase and multi-scale structured material itself. The argilaceous matrix is composed of interstratified illite-smectite particles, it contains detritic quartz and calcite, accessory pyrite, and the rock porosity ranges from micrometre to nanometre scales. Besides the bedding anisotropy, structural variabilities exist at all scales, from the decametric-metric scales of the geological formation to the respectively millimetric and micrometric scales of the aggregates of particles and clay particles Our study aims at understanding the complex mechanisms which are activated at the micro-scale and are involved in the macroscopic inelastic deformation of such a complex material. Two sets of experiments were performed, at two scales on three bedding orientations (90°, 45° and 0°). The first set was dedicated to uniaxial deformation followed with an optical set-up with a pixel resolution of 0.55µm. These experiments allowed us to see the fracture propagation with different patterns depending on the bedding orientation. For the second set of experiments, an experimental protocol was developed in order to perform uniaxial deformation experiment at controlled displacement rate, inside an environmental scanning electron microscope (ESEM), under controlled relative humidity, in order to preserve as much as possible the natural state of saturation of shales. We aimed at characterizing the mechanical anisotropy and the mechanisms involved in the deformation, with an image resolution below the micormeter. The observed sample surfaces were polished by broad ion beam in order to reveal the fine microstructures of the argillaceous matrix. In both cases, digital images were acquired at different loading stages during
Energy Technology Data Exchange (ETDEWEB)
Marmolino, Ciro [Dipartimento di Scienze e Tecnologie dell' Ambiente e del Territorio-DiSTAT, Universita del Molise, Contrada Fonte Lappone, I-86090 Pesche (Italy)
2011-10-15
The paper describes the occurrence of stochastic heating of dust particles in dusty plasmas as an energy instability due to the correlations between dust grain charge and electric field fluctuations. The possibility that the mean energy (''temperature'') of dust particles can grow in time has been found both from the self-consistent kinetic description of dusty plasmas taking into account charge fluctuations [U. de Angelis, A. V. Ivlev, V. N. Tsytovich, and G. E. Morfill, Phys. Plasmas 12(5), 052301 (2005)] and from a Fokker-Planck approach to systems with variable charge [A. V. Ivlev, S. K. Zhdanov, B. A. Klumov, and G. E. Morfill, Phys. Plasmas 12(9), 092104 (2005)]. Here, a different derivation is given by using the mathematical techniques of the so called multiplicative stochastic differential equations. Both cases of ''fast'' and ''slow'' fluctuations are discussed.
International Nuclear Information System (INIS)
Cole, D.C.
1985-01-01
The theory of stochastic electrodynamics involves the behavior of classical charged particles in the presence of classical electromagnetic zero-point radiation. Past researchers have shown that this theory has close connections with quantum phenomena. Here, this theory is further explored with regard to its predictions of the physical behavior of classical harmonic dipole oscillators relativistically uniformly accelerated through classical electromagnetic zero-point radiation. Part One treats a uniformly accelerated oscillator, unrestricted in its direction of oscillation. In Part Two, for the first time in either the classical or quantum literature, the thermal effects of acceleration are shown to hold for a particular spatially extended system. A set of relationships are derived in Part Three between the electromagnetic fields of an unaccelerated, fluctuating electric dipole oscillator and the correlation functions of homogeneous, isotopic random classical electromagnetic radiation
Averaging theorems in finite deformation plasticity
Nemat-Nasser, S C
1999-01-01
The transition from micro- to macro-variables of a representative volume element (RVE) of a finitely deformed aggregate (e.g., a composite or a polycrystal) is explored. A number of exact fundamental results on averaging techniques, $9 valid at finite deformations and rotations of any arbitrary heterogeneous continuum, are obtained. These results depend on the choice of suitable kinematic and dynamic variables. For finite deformations, the deformation gradient and $9 its rate, and the nominal stress and its rate, are optimally suited for the averaging purposes. A set of exact identities is presented in terms of these variables. An exact method for homogenization of an ellipsoidal inclusion in an $9 unbounded finitely deformed homogeneous solid is presented, generalizing Eshelby's method for application to finite deformation problems. In terms of the nominal stress rate and the rate of change of the deformation gradient, $9 measured relative to any arbitrary state, a general phase-transformation problem is con...
Directory of Open Access Journals (Sweden)
Monica Fernandes Abreu
2010-09-01
Full Text Available Esta reflexão pretende mostrar o discurso racional cartesiano na segunda prova da existência de Deus. Para tanto, Descartes se depara com uma pergunta central: qual a causa da existência da res cogitans que é finita e possui a ideia de infinito? A resposta é encontrada na desproporcionalidade ontológica entre o finito e o infinito. Essa desproporcionalidade é elucidada mediante dois conceitos: o princípio de causalidade que determina que a causa deve ser igual ou superior a coisa causada e o princípio de criação contínua em que a causa que criou o ser não é menor do que aquela que o conserva em sua existência. As objeções destacadas no texto contra os argumentos cartesianos foram escolhas deliberadas que servem para elucidar a importância da racionalidade como fundamento para a prova da existência de Deus. A relação entre o entendimento e a liberdade, apresentada no texto sucintamente, justifica a impossibilidade da res cogitans ser causa de si mesma.Palavras-chave: Infinito; finito; causalidade; criação contínua AbstractThis essay aims to show the rational Cartesian discourse on the second proof of God’s existence. In order to do so, Descartes faces a core question: which is the cause for the existence of the res cogitans that is finite in front of the idea of the infinite? The answer is found in the ontological disproportionality between the finite and the infinite. This disproportionality is elucidated through a couple crucial concepts: the principle of causality, which determines that the cause must be equal or superior to the caused thing and the principle of continuous creation, in which the cause that created the being is not inferior than the one that preserves its existence. The objections highlighted in the text against the Cartesian arguments were deliberated choices, to elucidate the relevance of rationality as the foundation for the proof of God’s existence. The relation between the understanding
Hamilton, Nicholas; Cal, Raúl Bayoán
2015-01-01
A 4 × 3 wind turbine array in a Cartesian arrangement was constructed in a wind tunnel setting with four configurations based on the rotational sense of the rotor blades. The fourth row of devices is considered to be in the fully developed turbine canopy for a Cartesian arrangement. Measurements of the flow field were made with stereo particle-image velocimetry immediately upstream and downstream of the selected model turbines. Rotational sense of the turbine blades is evident in the mean spanwise velocity W and the Reynolds shear stress - v w ¯ . The flux of kinetic energy is shown to be of greater magnitude following turbines in arrays where direction of rotation of the blades varies. Invariants of the normalized Reynolds stress anisotropy tensor (η and ξ) are plotted in the Lumley triangle and indicate that distinct characters of turbulence exist in regions of the wake following the nacelle and the rotor blade tips. Eigendecomposition of the tensor yields principle components and corresponding coordinate system transformations. Characteristic spheroids representing the balance of components in the normalized anisotropy tensor are composed with the eigenvalues yielding shapes predicted by the Lumley triangle. Rotation of the coordinate system defined by the eigenvectors demonstrates trends in the streamwise coordinate following the rotors, especially trailing the top-tip of the rotor and below the hub. Direction of rotation of rotor blades is shown by the orientation of characteristic spheroids according to principle axes. In the inflows of exit row turbines, the normalized Reynolds stress anisotropy tensor shows cumulative effects of the upstream turbines, tending toward prolate shapes for uniform rotational sense, oblate spheroids for streamwise organization of rotational senses, and a mixture of characteristic shapes when the rotation varies by row. Comparison between the invariants of the Reynolds stress anisotropy tensor and terms from the mean
SU-F-J-158: Respiratory Motion Resolved, Self-Gated 4D-MRI Using Rotating Cartesian K-Space Sampling
Energy Technology Data Exchange (ETDEWEB)
Han, F; Zhou, Z; Yang, Y; Sheng, K; Hu, P [UCLA School of Medicine, Los Angeles, CA (United States)
2016-06-15
Purpose: Dynamic MRI has been used to quantify respiratory motion of abdominal organs in radiation treatment planning. Many existing 4D-MRI methods based on 2D acquisitions suffer from limited slice resolution and additional stitching artifacts when evaluated in 3D{sup 1}. To address these issues, we developed a 4D-MRI (3D dynamic) technique with true 3D k-space encoding and respiratory motion self-gating. Methods: The 3D k-space was acquired using a Rotating Cartesian K-space (ROCK) pattern, where the Cartesian grid was reordered in a quasi-spiral fashion with each spiral arm rotated using golden angle{sup 2}. Each quasi-spiral arm started with the k-space center-line, which were used as self-gating{sup 3} signal for respiratory motion estimation. The acquired k-space data was then binned into 8 respiratory phases and the golden angle ensures a near-uniform k-space sampling in each phase. Finally, dynamic 3D images were reconstructed using the ESPIRiT technique{sup 4}. 4D-MRI was performed on 6 healthy volunteers, using the following parameters (bSSFP, Fat-Sat, TE/TR=2ms/4ms, matrix size=500×350×120, resolution=1×1×1.2mm, TA=5min, 8 respiratory phases). Supplemental 2D real-time images were acquired in 9 different planes. Dynamic locations of the diaphragm dome and left kidney were measured from both 4D and 2D images. The same protocol was also performed on a MRI-compatible motion phantom where the motion was programmed with different amplitude (10–30mm) and frequency (3–10/min). Results: High resolution 4D-MRI were obtained successfully in 5 minutes. Quantitative motion measurements from 4D-MRI agree with the ones from 2D CINE (<5% error). The 4D images are free of the stitching artifacts and their near-isotropic resolution facilitates 3D visualization and segmentation of abdominal organs such as the liver, kidney and pancreas. Conclusion: Our preliminary studies demonstrated a novel ROCK 4D-MRI technique with true 3D k-space encoding and respiratory
Myllyla, R.; Ahola, R.; Kopola, H.; Kostamovaara, J.; Voho, P.
1986-07-01
The determination of position and orientation errors made by large-scale cartesian coordinate robots using latest 3D-measurement methods has proved to be difficult in practise. A method has been developed to determine the mechanical inaccuracies of linear motions, perpendiculars, deflections, rotations and bends of a robot, relative to the common reference coordinates of the robot and the work area. The measurement method is based on the use of a laser diode and a position sensitive detector (PSD). A PSD is an optoelectronic sensor capable of providing position data about a light spot incident on its surface. The dual-axis, non-discrete PSD provides continuous analog X- and Y-axis information as the light spot transverses its active area. It senses the centroid of the light spot so that the position daa is indpendent of the focus of the spot. The PSD typically has an active area of - 1 cm - 20 cm , a resolution of 1/5000, nonlinearity of + 1% - + 15% and a fast response enabling accurate detection even of a rapidly moving light spot. The system developed consists of a laser diode transmitter, two beam splitters, a retro-reflective mirror, a PSD based receiver and a microcomputer unit for controlling the system and analysing the measured information. The divergence of the laser diode transmitter is - 0.1 mrad, it is small in size and lightweight (about 100 g), the direction of the laser beam of a fastened transmitter can easily be adjusted and it can be modulated electronically. The direction of the laser beam is not so sensitive to temperature variations as is for example an He-Ne-laser. The effective size of the PSD is enlarged with the aid of optics to have a diameter of 10 cm. Using a modulated laser beam the background light can be compensated. The position data from the PSD receiver to the memory of the microcomputer is gathered continuously and information is produced by a graphic printer in the form of graphs or numbers. This enables the measurement of the
Three-dimensional motion and deformation estimation of deformable mesh
Deknuydt, Albert A.; Desmet, Stefaan; Cox, Kris; Van Eycken, Luc
2000-04-01
Recently real-time capture of dynamic 3D-objects has become feasible. The dynamic models obtained by various techniques, come in the form of separate highly detailed 3D-meshes with texture at video-rates. These represent such an amount of data, as to hamper manipulation, editing and rendering. Data- compression techniques can alleviate this problem. Independent decimation of the separate meshes, is an inferior solution for what is really time varying mesh. Firstly, it causes unnatural flickering, and secondly, it leaves the inter-mesh correlation unexploited. Therefore, a hybrid technique might be a better solution. It consists of an 'intra' compression scheme working on still mesh, a 3D motion estimator/predictor, and a coder for the prediction errors and side information (motion vectors and mesh segmentation). We describe a technique to segment a deforming mesh into regions with locally-uniform motion. We start by interpreting the motion as samples of a 3D vector field. In each point, we estimate the translation, rotation and divergence of the vector field. As human faces are rather incompressible, we ignore the divergence component. Then, we cluster the population with the criterion of similar translation and rotation. Results show that it allows to segment a deforming human face into approximately 200 regions of locally-uniform rigid motion, while keeping the motion prediction error under 5 percent. This is good enough for efficient compression.
Deformation retracts of Stein spaces
International Nuclear Information System (INIS)
Hamm, H.; Mihalache, N.
1995-01-01
If X is an n-dimensional Stein space, it was proved that X has the homotopy type of a CW-complex of dimension≤n and in the algebraic case this was proved with the additional conclusion that the CW-complex is finite. In this paper the authors give an answer to the question if there exists a subset Q of X with the same topological properties as X, for instance Q is a strong deformation retract of X, and Q is a CW-complex of dimension≤n. 15 refs
Inflationary Perturbations from Deformed CFT
Van der Schaar, J P
2004-01-01
We present a new method to calculate the spectrum of (slow-roll) inflationary perturbations, inspired by the conjectured dS/CFT correspondence. We show how the standard result for the spectrum of inflationary perturbations can be obtained from deformed CFT correlators, whose behavior is determined by the Callan-Symanzik equation. We discuss the possible advantages of this approach and end with some comments on the role of holography in dS/CFT and its relation to the universal nature of the spectrum of inflationary perturbations.
Formation Flying and Deformable Instruments
International Nuclear Information System (INIS)
Rio, Yvon
2009-01-01
Astronomers have always attempted to build very stable instruments. They fight all that can cause mechanical deformation or image motion. This has led to well established technologies (autoguide, active optics, thermal control, tip/tilt correction), as well as observing methods based on the use of controlled motion (scanning, micro scanning, shift and add, chopping and nodding). Formation flying disturbs this practice. It is neither possible to reduce the relative motion to very small amplitudes, nor to control it at will. Some impacts on Simbol-X instrument design, and operation are presented.
Deformable Mirrors Correct Optical Distortions
2010-01-01
By combining the high sensitivity of space telescopes with revolutionary imaging technologies consisting primarily of adaptive optics, the Terrestrial Planet Finder is slated to have imaging power 100 times greater than the Hubble Space Telescope. To this end, Boston Micromachines Corporation, of Cambridge, Massachusetts, received Small Business Innovation Research (SBIR) contracts from the Jet Propulsion Laboratory for space-based adaptive optical technology. The work resulted in a microelectromechanical systems (MEMS) deformable mirror (DM) called the Kilo-DM. The company now offers a full line of MEMS DMs, which are being used in observatories across the world, in laser communication, and microscopy.
Wilde-Piorko, M.; Polkowski, M.
2016-12-01
Seismic wave travel time calculation is the most common numerical operation in seismology. The most efficient is travel time calculation in 1D velocity model - for given source, receiver depths and angular distance time is calculated within fraction of a second. Unfortunately, in most cases 1D is not enough to encounter differentiating local and regional structures. Whenever possible travel time through 3D velocity model has to be calculated. It can be achieved using ray calculation or time propagation in space. While single ray path calculation is quick it is complicated to find the ray path that connects source with the receiver. Time propagation in space using Fast Marching Method seems more efficient in most cases, especially when there are multiple receivers. In this presentation final release of a Python module pySeismicFMM is presented - simple and very efficient tool for calculating travel time from sources to receivers. Calculation requires regular 2D or 3D velocity grid either in Cartesian or geographic coordinates. On desktop class computer calculation speed is 200k grid cells per second. Calculation has to be performed once for every source location and provides travel time to all receivers. pySeismicFMM is free and open source. Development of this tool is a part of authors PhD thesis. Source code of pySeismicFMM will be published before Fall Meeting. National Science Centre Poland provided financial support for this work via NCN grant DEC-2011/02/A/ST10/00284.
Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.
2018-01-01
We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.
Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team
2017-11-01
We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).
Kedia, Kushal S.
2014-09-01
In this paper, we present a second-order numerical method for simulations of reacting flow around heat-conducting immersed solid objects. The method is coupled with a block-structured adaptive mesh refinement (SAMR) framework and a low-Mach number operator-split projection algorithm. A "buffer zone" methodology is introduced to impose the solid-fluid boundary conditions such that the solver uses symmetric derivatives and interpolation stencils throughout the interior of the numerical domain; irrespective of whether it describes fluid or solid cells. Solid cells are tracked using a binary marker function. The no-slip velocity boundary condition at the immersed wall is imposed using the staggered mesh. Near the immersed solid boundary, single-sided buffer zones (inside the solid) are created to resolve the species discontinuities, and dual buffer zones (inside and outside the solid) are created to capture the temperature gradient discontinuities. The development discussed in this paper is limited to a two-dimensional Cartesian grid-conforming solid. We validate the code using benchmark simulations documented in the literature. We also demonstrate the overall second-order convergence of our numerical method. To demonstrate its capability, a reacting flow simulation of a methane/air premixed flame stabilized on a channel-confined bluff-body using a detailed chemical kinetics model is discussed. © 2014 Elsevier Inc.
Directory of Open Access Journals (Sweden)
Tristan J Webb
2014-04-01
Full Text Available When we see a human sitting down, standing up, or walking, we can recognise one of these poses independently of the individual, or we can recognise the individual person, independently of the pose. The same issues arise for deforming objects. For example, if we see a flag deformed by the wind, either blowing out or hanging languidly, we can usually recognise the flag, independently of its deformation; or we can recognise the deformation independently of the identity of the flag. We hypothesize that these types of recognition can be implemented by the primate visual system using temporo-spatial continuity as objects transform as a learning principle. In particular, we hypothesize that pose or deformation can be learned under conditions in which large numbers of different people are successively seen in the same pose, or objects in the same deformation. We also hypothesize that person-specific representations that are independent of pose, and object-specific representations that are independent of deformation and view, could be built, when individual people or objects are observed successively transforming from one pose or deformation and view to another. These hypotheses were tested in a simulation of the ventral visual system, VisNet, that uses temporal continuity, implemented in a synaptic learning rule with a short-term memory trace of previous neuronal activity, to learn invariant representations. It was found that depending on the statistics of the visual input, either pose-specific or deformation-specific representations could be built that were invariant with respect to individual and view; or that identity-specific representations could be built that were invariant with respect to pose or deformation and view. We propose that this is how pose-specific and pose-invariant, and deformation-specific and deformation-invariant, perceptual representations are built in the brain.
Deformation Characteristics of Composite Structures
Directory of Open Access Journals (Sweden)
Theddeus T. AKANO
2016-08-01
Full Text Available The composites provide design flexibility because many of them can be moulded into complex shapes. The carbon fibre-reinforced epoxy composites exhibit excellent fatigue tolerance and high specific strength and stiffness which have led to numerous advanced applications ranging from the military and civil aircraft structures to the consumer products. However, the modelling of the beams undergoing the arbitrarily large displacements and rotations, but small strains, is a common problem in the application of these engineering composite systems. This paper presents a nonlinear finite element model which is able to estimate the deformations of the fibre-reinforced epoxy composite beams. The governing equations are based on the Euler-Bernoulli beam theory (EBBT with a von Kármán type of kinematic nonlinearity. The anisotropic elasticity is employed for the material model of the composite material. Moreover, the characterization of the mechanical properties of the composite material is achieved through a tensile test, while a simple laboratory experiment is used to validate the model. The results reveal that the composite fibre orientation, the type of applied load and boundary condition, affect the deformation characteristics of the composite structures. The nonlinearity is an important factor that should be taken into consideration in the analysis of the fibre-reinforced epoxy composites.
Deformable human body model development
Energy Technology Data Exchange (ETDEWEB)
Wray, W.O.; Aida, T.
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). A Deformable Human Body Model (DHBM) capable of simulating a wide variety of deformation interactions between man and his environment has been developed. The model was intended to have applications in automobile safety analysis, soldier survivability studies and assistive technology development for the disabled. To date, we have demonstrated the utility of the DHBM in automobile safety analysis and are currently engaged in discussions with the U.S. military involving two additional applications. More specifically, the DHBM has been incorporated into a Virtual Safety Lab (VSL) for automobile design under contract to General Motors Corporation. Furthermore, we have won $1.8M in funding from the U.S. Army Medical Research and Material Command for development of a noninvasive intracranial pressure measurement system. The proposed research makes use of the detailed head model that is a component of the DHBM; the project duration is three years. In addition, we have been contacted by the Air Force Armstrong Aerospace Medical Research Laboratory concerning possible use of the DHBM in analyzing the loads and injury potential to pilots upon ejection from military aircraft. Current discussions with Armstrong involve possible LANL participation in a comparison between DHBM and the Air Force Articulated Total Body (ATB) model that is the current military standard.
Deformation Based Curved Shape Representation.
Demisse, Girum G; Aouada, Djamila; Ottersten, Bjorn
2017-06-02
In this paper, we introduce a deformation based representation space for curved shapes in Rn. Given an ordered set of points sampled from a curved shape, the proposed method represents the set as an element of a finite dimensional matrix Lie group. Variation due to scale and location are filtered in a preprocessing stage, while shapes that vary only in rotation are identified by an equivalence relationship. The use of a finite dimensional matrix Lie group leads to a similarity metric with an explicit geodesic solution. Subsequently, we discuss some of the properties of the metric and its relationship with a deformation by least action. Furthermore, invariance to reparametrization or estimation of point correspondence between shapes is formulated as an estimation of sampling function. Thereafter, two possible approaches are presented to solve the point correspondence estimation problem. Finally, we propose an adaptation of k-means clustering for shape analysis in the proposed representation space. Experimental results show that the proposed representation is robust to uninformative cues, e.g. local shape perturbation and displacement. In comparison to state of the art methods, it achieves a high precision on the Swedish and the Flavia leaf datasets and a comparable result on MPEG-7, Kimia99 and Kimia216 datasets.
Deformation Models Tracking, Animation and Applications
Torres, Arnau; Gómez, Javier
2013-01-01
The computational modelling of deformations has been actively studied for the last thirty years. This is mainly due to its large range of applications that include computer animation, medical imaging, shape estimation, face deformation as well as other parts of the human body, and object tracking. In addition, these advances have been supported by the evolution of computer processing capabilities, enabling realism in a more sophisticated way. This book encompasses relevant works of expert researchers in the field of deformation models and their applications. The book is divided into two main parts. The first part presents recent object deformation techniques from the point of view of computer graphics and computer animation. The second part of this book presents six works that study deformations from a computer vision point of view with a common characteristic: deformations are applied in real world applications. The primary audience for this work are researchers from different multidisciplinary fields, s...
Microstructural evolution during tensile deformation of polypropylenes
International Nuclear Information System (INIS)
Dasari, A.; Rohrmann, J.; Misra, R.D.K.
2003-01-01
Tensile deformation processes occurring at varying strain rates in high and low crystallinity polypropylenes and ethylene-propylene di-block copolymers have been investigated by scanning electron microscopy. This is examined for both long and short chain polymeric materials. The deformation processes in different polymeric materials show striking dissimilarities in spite of the common propylene matrix. Additionally, the deformation behavior of long and their respective short chain polymers was different. Deformation mechanisms include crazing/tearing, wedging, ductile ploughing, fibrillation, and brittle fracture. The different modes of deformation are depicted in the form of strain rate-strain diagrams. At a constant strain rate, the strain to fracture follows the sequence: high crystallinity polypropylenes< low crystallinity polypropylenes< ethylene-propylene di-block copolymers, indicative of the trend in resistance to plastic deformation
Nonlinear continuum mechanics and large inelastic deformations
Dimitrienko, Yuriy I
2010-01-01
This book provides a rigorous axiomatic approach to continuum mechanics under large deformation. In addition to the classical nonlinear continuum mechanics - kinematics, fundamental laws, the theory of functions having jump discontinuities across singular surfaces, etc. - the book presents the theory of co-rotational derivatives, dynamic deformation compatibility equations, and the principles of material indifference and symmetry, all in systematized form. The focus of the book is a new approach to the formulation of the constitutive equations for elastic and inelastic continua under large deformation. This new approach is based on using energetic and quasi-energetic couples of stress and deformation tensors. This approach leads to a unified treatment of large, anisotropic elastic, viscoelastic, and plastic deformations. The author analyses classical problems, including some involving nonlinear wave propagation, using different models for continua under large deformation, and shows how different models lead t...
Deformable mirrors development program at ESO
Stroebele, Stefan; Vernet, Elise; Brinkmann, Martin; Jakob, Gerd; Lilley, Paul; Casali, Mark; Madec, Pierre-Yves; Kasper, Markus
2016-07-01
Over the last decade, adaptive optics has become essential in different fields of research including medicine and industrial applications. With this new need, the market of deformable mirrors has expanded a lot allowing new technologies and actuation principles to be developed. Several E-ELT instruments have identified the need for post focal deformable mirrors but with the increasing size of the telescopes the requirements on the deformable mirrors become more demanding. A simple scaling up of existing technologies from few hundred actuators to thousands of actuators will not be sufficient to satisfy the future needs of ESO. To bridge the gap between available deformable mirrors and the future needs for the E-ELT, ESO started a development program for deformable mirror technologies. The requirements and the path to get the deformable mirrors for post focal adaptive optics systems for the E-ELT is presented.
Structural refinement and coarsening in deformed metals
DEFF Research Database (Denmark)
Hansen, N.; Huang, X.; Xing, Q.
2005-01-01
The microstructural refinement by plastic deformation is analysed in terms of key parameters, the spacing between and the misorientation angle across the boundaries subdividing the structure. Coarsening of such structures by annealing is also characterised. For both deformed and annealed structur......, good agreement has been found between experimental measurements of the flow stress and calculated values. Commercial purity aluminium is used as an example and deformed by cold rolling and by accumulative roll bonding....
3D geodetic monitoring slope deformations
Directory of Open Access Journals (Sweden)
Weiss Gabriel
1996-06-01
Full Text Available For plenty of slope failures that can be found in Slovakia is necessary and very important their geodetic monitoring (because of their activity, reactivisations, checks. The paper gives new methodologies for these works, using 3D terrestrial survey technologies for measurements in convenient deformation networks. The design of an optimal type of deformation model for various kinds of landslides and their exact processing with an efficient testing procedure to determine the kinematics of the slope deformations are presented too.
Thermodynamic analysis of elastic-plastic deformation
International Nuclear Information System (INIS)
Lubarda, V.
1981-01-01
The complete set of constitutive equations which fully describes the behaviour of material in elastic-plastic deformation is derived on the basis of thermodynamic analysis of the deformation process. The analysis is done after the matrix decomposition of the deformation gradient is introduced into the structure of thermodynamics with internal state variables. The free energy function, is decomposed. Derive the expressions for the stress response, entropy and heat flux, and establish the evolution equation. Finally, we establish the thermodynamic restrictions of the deformation process. (Author) [pt
Deformation effect on spectral statistics of nuclei
Sabri, H.; Jalili Majarshin, A.
2018-02-01
In this study, we tried to get significant relations between the spectral statistics of atomic nuclei and their different degrees of deformations. To this aim, the empirical energy levels of 109 even-even nuclei in the 22 ≤ A ≤ 196 mass region are classified as their experimental and calculated quadrupole, octupole, hexadecapole and hexacontatetrapole deformations values and analyzed by random matrix theory. Our results show an obvious relation between the regularity of nuclei and strong quadrupole, hexadecapole and hexacontatetrapole deformations and but for nuclei that their octupole deformations are nonzero, we have observed a GOE-like statistics.
Deformation and fracture mechanics of engineering materials
National Research Council Canada - National Science Library
Hertzberg, Richard W; Vinci, Richard Paul; Hertzberg, Jason L
2012-01-01
"Hertzberg's 5th edition of Deformation & Fracture Mechanics of Engineering Materials offers several new features including a greater number and variety of homework problems using more computational software...
Origami-enabled deformable silicon solar cells
Energy Technology Data Exchange (ETDEWEB)
Tang, Rui; Huang, Hai; Liang, Hanshuang; Liang, Mengbing [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287 (United States); Tu, Hongen; Xu, Yong [Electrical and Computer Engineering, Wayne State University, 5050 Anthony Wayne Dr., Detroit, Michigan 48202 (United States); Song, Zeming; Jiang, Hanqing, E-mail: hanqing.jiang@asu.edu [School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, Arizona 85287 (United States); Yu, Hongyu, E-mail: hongyu.yu@asu.edu [School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287 (United States); School of Earth and Space Exploration, Arizona State University, Tempe, Arizona 85287 (United States)
2014-02-24
Deformable electronics have found various applications and elastomeric materials have been widely used to reach flexibility and stretchability. In this Letter, we report an alternative approach to enable deformability through origami. In this approach, the deformability is achieved through folding and unfolding at the creases while the functional devices do not experience strain. We have demonstrated an example of origami-enabled silicon solar cells and showed that this solar cell can reach up to 644% areal compactness while maintaining reasonable good performance upon cyclic folding/unfolding. This approach opens an alternative direction of producing flexible, stretchable, and deformable electronics.
Origami-enabled deformable silicon solar cells
International Nuclear Information System (INIS)
Tang, Rui; Huang, Hai; Liang, Hanshuang; Liang, Mengbing; Tu, Hongen; Xu, Yong; Song, Zeming; Jiang, Hanqing; Yu, Hongyu
2014-01-01
Deformable electronics have found various applications and elastomeric materials have been widely used to reach flexibility and stretchability. In this Letter, we report an alternative approach to enable deformability through origami. In this approach, the deformability is achieved through folding and unfolding at the creases while the functional devices do not experience strain. We have demonstrated an example of origami-enabled silicon solar cells and showed that this solar cell can reach up to 644% areal compactness while maintaining reasonable good performance upon cyclic folding/unfolding. This approach opens an alternative direction of producing flexible, stretchable, and deformable electronics
International Nuclear Information System (INIS)
Ghaffari, Seyed Amin; Viazzo, Stéphane; Schneider, Kai; Bontoux, Patrick
2015-01-01
Highlights: • An algorithm for numerical simulation of fish-like swimming is proposed. • A new 4th order direct solver for the solution of the Poisson equation is presented. • The penalization method proved to be efficient in dealing with fluid–structure interactions. • Double exponential denoising of the hydrodynamic coefficients is crucial in the algorithm. • An efficient law for rotation control of an anguilliform swimmer is proposed. - Abstract: We present an efficient algorithm for simulation of deformable bodies interacting with two-dimensional incompressible fluid flows. The temporal and spatial discretizations of the Navier-Stokes equations in vorticity stream-function formulation are based on classical fourth-order Runge-Kutta scheme and compact finite differences, respectively. Using a uniform Cartesian grid we benefit from the advantage of a new fourth-order direct solver for the Poisson equation to ensure the incompressibility constraint down to machine zero over an optimal grid. For introducing a deformable body in fluid flow, the volume penalization method is used. A Lagrangian structured grid with prescribed motion covers the deformable body which is interacting with the surrounding fluid due to the hydrodynamic forces and the torque calculated on the Eulerian reference grid. An efficient law for controlling the curvature of an anguilliform fish, swimming toward a prescribed goal, is proposed which is based on the geometrically exact theory of nonlinear beams and quaternions. Validation of the developed method shows the efficiency and expected accuracy of the algorithm for fish-like swimming and also for a variety of fluid/solid interaction problems
Typhoon-Induced Ground Deformation
Mouyen, M.; Canitano, A.; Chao, B. F.; Hsu, Y.-J.; Steer, P.; Longuevergne, L.; Boy, J.-P.
2017-11-01
Geodetic instruments now offer compelling sensitivity, allowing to investigate how solid Earth and surface processes interact. By combining surface air pressure data, nontidal sea level variations model, and rainfall data, we systematically analyze the volumetric deformation of the shallow crust at seven borehole strainmeters in Taiwan induced by 31 tropical cyclones (typhoons) that made landfall to the island from 2004 to 2013. The typhoon's signature consists in a ground dilatation due to air pressure drop, generally followed by a larger ground compression. We show that this compression phase can be mostly explained by the mass loading of rainwater that falls on the ground and concentrates in the valleys towards the strainmeter sensitivity zone. Further, our analysis shows that borehole strainmeters can help quantifying the amount of rainwater accumulating and flowing over a watershed during heavy rainfalls, which is a useful constraint for building hydrological models.
Precise object tracking under deformation
International Nuclear Information System (INIS)
Saad, M.H
2010-01-01
The precise object tracking is an essential issue in several serious applications such as; robot vision, automated surveillance (civil and military), inspection, biomedical image analysis, video coding, motion segmentation, human-machine interface, visualization, medical imaging, traffic systems, satellite imaging etc. This frame-work focuses on the precise object tracking under deformation such as scaling , rotation, noise, blurring and change of illumination. This research is a trail to solve these serious problems in visual object tracking by which the quality of the overall system will be improved. Developing a three dimensional (3D) geometrical model to determine the current pose of an object and predict its future location based on FIR model learned by the OLS. This framework presents a robust ranging technique to track a visual target instead of the traditional expensive ranging sensors. The presented research work is applied to real video stream and achieved high precession results.
DEA deformed stretchable patch antenna
International Nuclear Information System (INIS)
Jiang, X-J; Jalali Mazlouman, S; Menon, C; Mahanfar, A; Vaughan, R G
2012-01-01
A stretchable patch antenna (SPA) whose frequency is tuned by a planar dielectric elastomer actuator (DEA) is presented in this paper. This mechanically reconfigurable antenna system has a configuration resembling a pre-stretched silicone belt. Part of the belt is embedded with a layer of conductive liquid metal to form the patch antenna. Part of the belt is sandwiched between conductive electrodes to form the DEA. Electrical activation of the DEA results in a contraction of the patch antenna, and as a result, in a variation of its resonance frequency. Design and fabrication steps of this system are presented. Measurement results for deformation, resonance frequency variation and efficiency of the patch antenna are also presented. (paper)
Deterritorializing Drawing - transformation/deformation
DEFF Research Database (Denmark)
Brabrand, Helle
2012-01-01
the capacity of the body to be affected by change. The everyday and the ceremonial body, the ordinary and the aberrant movement – these poles generate a passage rather than a difference from the one to the other: from attitude or position to gesture or kinaesthetic twist. Known from without through perception...... but also from within by sensations, body ‘images’ are different to all other images. Twisting these body images make a mode of operation of art. The paper will address the above issues discussing modes of operation and appearance of my actual project. Acting in the reality of drawing, the project confront...... criticises figurative as well as abstract painting as passing through the brain and not acting directly upon the senses. Figurative and abstract painting both fail to liberate the Figure, implementing transformation of form, but not attaining deformations of bodies. Bacon, then, is concerned about...
Deformation quantization: Twenty years after
International Nuclear Information System (INIS)
Sternheimer, Daniel
1998-01-01
We first review the historical developments, both in physics and in mathematics, that preceded (and in some sense provided the background of) deformation quantization. Then we describe the birth of the latter theory and its evolution in the past twenty years, insisting on the main conceptual developments and keeping here as much as possible on the physical side. For the physical part the accent is put on its relations to, and relevance for, 'conventional' physics. For the mathematical part we concentrate on the questions of existence and equivalence, including most recent developments for general Poisson manifolds; we touch also noncommutative geometry and index theorems, and relations with group theory, including quantum groups. An extensive (though very incomplete) bibliography is appended and includes background mathematical literature
Developing a Virtual Rock Deformation Laboratory
Zhu, W.; Ougier-simonin, A.; Lisabeth, H. P.; Banker, J. S.
2012-12-01
Experimental rock physics plays an important role in advancing earthquake research. Despite its importance in geophysics, reservoir engineering, waste deposits and energy resources, most geology departments in U.S. universities don't have rock deformation facilities. A virtual deformation laboratory can serve as an efficient tool to help geology students naturally and internationally learn about rock deformation. Working with computer science engineers, we built a virtual deformation laboratory that aims at fostering user interaction to facilitate classroom and outreach teaching and learning. The virtual lab is built to center around a triaxial deformation apparatus in which laboratory measurements of mechanical and transport properties such as stress, axial and radial strains, acoustic emission activities, wave velocities, and permeability are demonstrated. A student user can create her avatar to enter the virtual lab. In the virtual lab, the avatar can browse and choose among various rock samples, determine the testing conditions (pressure, temperature, strain rate, loading paths), then operate the virtual deformation machine to observe how deformation changes physical properties of rocks. Actual experimental results on the mechanical, frictional, sonic, acoustic and transport properties of different rocks at different conditions are compiled. The data acquisition system in the virtual lab is linked to the complied experimental data. Structural and microstructural images of deformed rocks are up-loaded and linked to different deformation tests. The integration of the microstructural image and the deformation data allows the student to visualize how forces reshape the structure of the rock and change the physical properties. The virtual lab is built using the Game Engine. The geological background, outstanding questions related to the geological environment, and physical and mechanical concepts associated with the problem will be illustrated on the web portal. In
Precise Object Tracking under Deformation
International Nuclear Information System (INIS)
Saad, M.H.
2010-01-01
The precise object tracking is an essential issue in several serious applications such as; robot vision, automated surveillance (civil and military), inspection, biomedical image analysis, video coding, motion segmentation, human-machine interface, visualization, medical imaging, traffic systems, satellite imaging etc. This framework focuses on the precise object tracking under deformation such as scaling, rotation, noise, blurring and change of illumination. This research is a trail to solve these serious problems in visual object tracking by which the quality of the overall system will be improved. Developing a three dimensional (3D) geometrical model to determine the current pose of an object and predict its future location based on FIR model learned by the OLS. This framework presents a robust ranging technique to track a visual target instead of the traditional expensive ranging sensors. The presented research work is applied to real video stream and achieved high precession results. xiiiThe precise object tracking is an essential issue in several serious applications such as; robot vision, automated surveillance (civil and military), inspection, biomedical image analysis, video coding, motion segmentation, human-machine interface, visualization, medical imaging, traffic systems, satellite imaging etc. This framework focuses on the precise object tracking under deformation such as scaling, rotation, noise, blurring and change of illumination. This research is a trail to solve these serious problems in visual object tracking by which the quality of the overall system will be improved. Developing a three dimensional (3D) geometrical model to determine the current pose of an object and predict its future location based on FIR model learned by the OLS. This framework presents a robust ranging technique to track a visual target instead of the traditional expensive ranging sensors. The presented research work is applied to real video stream and achieved high
DEFF Research Database (Denmark)
Hong, C.S.; Tao, N.R.; Lu, K.
2009-01-01
A clear grain orientation dependence of deformation twinning has been identified in coarse-grained copper subjected to dynamic plastic deformation. Deformation twins tend to occur in grains with orientations near the [0 0 1] corner but not in grains near the [1 0 1] corner, which can be explained...
Han, Fei; Zhou, Ziwu; Han, Eric; Gao, Yu; Nguyen, Kim-Lien; Finn, J Paul; Hu, Peng
2017-08-01
To develop and validate a cardiac-respiratory self-gating strategy for the recently proposed multiphase steady-state imaging with contrast enhancement (MUSIC) technique. The proposed SG strategy uses the ROtating Cartesian K-space (ROCK) sampling, which allows for retrospective k-space binning based on motion surrogates derived from k-space center line. The k-space bins are reconstructed using a compressed sensing algorithm. Ten pediatric patients underwent cardiac MRI for clinical reasons. The original MUSIC and 2D-CINE images were acquired as a part of the clinical protocol, followed by the ROCK-MUSIC acquisition, all under steady-state intravascular distribution of ferumoxytol. Subjective scores and image sharpness were used to compare the images of ROCK-MUSIC and original MUSIC. All scans were completed successfully without complications. The ROCK-MUSIC acquisition took 5 ± 1 min, compared to 8 ± 2 min for the original MUSIC. Image scores of ROCK-MUSIC were significantly better than original MUSIC at the ventricular outflow tracts (3.9 ± 0.3 vs. 3.3 ± 0.6, P ROCK-MUSIC in the other anatomic locations. ROCK-MUSIC provided images of equal or superior image quality compared to original MUSIC, and this was achievable with 40% savings in scan time and without the need for physiologic signal. Magn Reson Med 78:472-483, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Saranathan, Manojkumar; Rettmann, Dan W; Hargreaves, Brian A; Clarke, Sharon E; Vasanawala, Shreyas S
2012-06-01
To develop and evaluate a multiphasic contrast-enhanced MRI method called DIfferential Sub-sampling with Cartesian Ordering (DISCO) for abdominal imaging. A three-dimensional, variable density pseudo-random k-space segmentation scheme was developed and combined with a Dixon-based fat-water separation algorithm to generate high temporal resolution images with robust fat suppression and without compromise in spatial resolution or coverage. With institutional review board approval and informed consent, 11 consecutive patients referred for abdominal MRI at 3 Tesla (T) were imaged with both DISCO and a routine clinical three-dimensional SPGR-Dixon (LAVA FLEX) sequence. All images were graded by two radiologists using quality of fat suppression, severity of artifacts, and overall image quality as scoring criteria. For assessment of arterial phase capture efficiency, the number of temporal phases with angiographic phase and hepatic arterial phase was recorded. There were no significant differences in quality of fat suppression, artifact severity or overall image quality between DISCO and LAVA FLEX images (P > 0.05, Wilcoxon signed rank test). The angiographic and arterial phases were captured in all 11 patients scanned using the DISCO acquisition (mean number of phases were two and three, respectively). DISCO effectively captures the fast dynamics of abdominal pathology such as hyperenhancing hepatic lesions with a high spatio-temporal resolution. Typically, 1.1 × 1.5 × 3 mm spatial resolution over 60 slices was achieved with a temporal resolution of 4-5 s. Copyright © 2012 Wiley Periodicals, Inc.
Küstner, Thomas; Würslin, Christian; Schwartz, Martin; Martirosian, Petros; Gatidis, Sergios; Brendle, Cornelia; Seith, Ferdinand; Schick, Fritz; Schwenzer, Nina F; Yang, Bin; Schmidt, Holger
2017-08-01
To enable fast and flexible high-resolution four-dimensional (4D) MRI of periodic thoracic/abdominal motion for motion visualization or motion-corrected imaging. We proposed a Cartesian three-dimensional k-space sampling scheme that acquires a random combination of k-space lines in the ky/kz plane. A partial Fourier-like constraint compacts the sampling space to one half of k-space. The central k-space line is periodically acquired to allow an extraction of a self-navigated respiration signal used to populate a k-space of multiple breathing positions. The randomness of the acquisition (induced by periodic breathing pattern) yields a subsampled k-space that is reconstructed using compressed sensing. Local image evaluations (coefficient of variation and slope steepness through organs) reveal information about motion resolvability. Image quality is inspected by a blinded reading. Sequence and reconstruction method are made publicly available. The method is able to capture and reconstruct 4D images with high image quality and motion resolution within a short scan time of less than 2 min. These findings are supported by restricted-isometry-property analysis, local image evaluation, and blinded reading. The proposed method provides a clinical feasible setup to capture periodic respiratory motion with a fast acquisition protocol and can be extended by further surrogate signals to capture additional periodic motions. Retrospective parametrization allows for flexible tuning toward the targeted applications. Magn Reson Med 78:632-644, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Nuclear deformation: a proton-neutron effect
International Nuclear Information System (INIS)
Dobaczewski, J.
1988-01-01
The Hartree-Fock plus BCS method with the Skyrme interaction is used to analyse the equilibrium deformations of nuclei in the A≅100 region. It is shown that the theoretical results are consistent with the N n N p classification scheme. Relations between the nuclear deformation effects and the neutron-proton interaction are discussed
Exactly marginal deformations from exceptional generalised geometry
Energy Technology Data Exchange (ETDEWEB)
Ashmore, Anthony [Merton College, University of Oxford,Merton Street, Oxford, OX1 4JD (United Kingdom); Mathematical Institute, University of Oxford,Andrew Wiles Building, Woodstock Road, Oxford, OX2 6GG (United Kingdom); Gabella, Maxime [Institute for Advanced Study,Einstein Drive, Princeton, NJ 08540 (United States); Graña, Mariana [Institut de Physique Théorique, CEA/Saclay,91191 Gif-sur-Yvette (France); Petrini, Michela [Sorbonne Université, UPMC Paris 05, UMR 7589, LPTHE,75005 Paris (France); Waldram, Daniel [Department of Physics, Imperial College London,Prince Consort Road, London, SW7 2AZ (United Kingdom)
2017-01-27
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS{sub 5} flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS{sub 5} flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Cyclic Plastic Deformation and Welding Simulation
Ten Horn, C.H.L.J.
2003-01-01
One of the concerns of a fitness for purpose analysis is the quantification of the relevant material properties. It is known from experiments that the mechanical properties of a material can change due to a monotonic plastic deformation or a cyclic plastic deformation. For a fitness for purpose
Deformed metals - structure, recrystallisation and strength
DEFF Research Database (Denmark)
Hansen, Niels; Juul Jensen, Dorte
2011-01-01
It is shown how new discoveries and advanced experimental techniques in the last 25 years have led to paradigm shifts in the analysis of deformation and annealing structures of metals and in the way the strength of deformed samples is related to structural parameters. This is described in three...... sections: structural evolution by grain subdivision, recovery and recrystallisation and strength-structure relationships....
Thermally assisted deformation of structural superplastics and ...
Indian Academy of Sciences (India)
Optimal structural superplasticity and the deformation of nanostructured materials in the thermally activated region are regarded as being caused by the same physical process. In this analysis, grain/interphase boundary sliding controls the rate of deformation at the level of atomistics. Boundary sliding develops to a ...
Seismic subsidence deformation of moisturised loess
RASULOV RUSTAM KHAYATOVICH
2016-01-01
The results of experimental studies the influence of seismic subsidence on deformation of loess at different accelerations are being described by the author. The methods of laboratory and field studies on soil’s seismic subsidence are provided. The factors affecting the seismic subsidence of the soil deformation are identified.
Einstein-Riemann Gravity on Deformed Spaces
Directory of Open Access Journals (Sweden)
Julius Wess
2006-12-01
Full Text Available A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms. Considering the corresponding Hopf algebra we find that the deformed gravity is based on a deformation of the Hopf algebra.
Structural refinement and coarsening in deformed metals
DEFF Research Database (Denmark)
Hansen, N.; Huang, X.; Xing, Q.
2005-01-01
The microstructural refinement by plastic deformation is analysed in terms of key parameters, the spacing between and the misorientation angle across the boundaries subdividing the structure. Coarsening of such structures by annealing is also characterised. For both deformed and annealed structures...
Exactly marginal deformations from exceptional generalised geometry
International Nuclear Information System (INIS)
Ashmore, Anthony; Gabella, Maxime; Graña, Mariana; Petrini, Michela; Waldram, Daniel
2017-01-01
We apply exceptional generalised geometry to the study of exactly marginal deformations of N=1 SCFTs that are dual to generic AdS 5 flux backgrounds in type IIB or eleven-dimensional supergravity. In the gauge theory, marginal deformations are parametrised by the space of chiral primary operators of conformal dimension three, while exactly marginal deformations correspond to quotienting this space by the complexified global symmetry group. We show how the supergravity analysis gives a geometric interpretation of the gauge theory results. The marginal deformations arise from deformations of generalised structures that solve moment maps for the generalised diffeomorphism group and have the correct charge under the generalised Reeb vector, generating the R-symmetry. If this is the only symmetry of the background, all marginal deformations are exactly marginal. If the background possesses extra isometries, there are obstructions that come from fixed points of the moment maps. The exactly marginal deformations are then given by a further quotient by these extra isometries. Our analysis holds for any N=2 AdS 5 flux background. Focussing on the particular case of type IIB Sasaki-Einstein backgrounds we recover the result that marginal deformations correspond to perturbing the solution by three-form flux at first order. In various explicit examples, we show that our expression for the three-form flux matches those in the literature and the obstruction conditions match the one-loop beta functions of the dual SCFT.
Deliberate deformation of concrete after casting
Grunewald, S.; Janssen, B.; Schipper, H.R.; Vollers, K.J.; Walraven, J.C.
2012-01-01
This paper discusses the effect of intentional deformation of a flexible formwork after casting of the concrete and the influence of the characteristics of concrete in the fresh state on the quality of a concrete element. This deformation is intended to bring the concrete element in its desired