Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
NASA Technical Reports Server (NTRS)
Freund, Roland
1989-01-01
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Small diameter symmetric networks from linear groups
NASA Technical Reports Server (NTRS)
Campbell, Lowell; Carlsson, Gunnar E.; Dinneen, Michael J.; Faber, Vance; Fellows, Michael R.; Langston, Michael A.; Moore, James W.; Multihaupt, Andrew P.; Sexton, Harlan B.
1992-01-01
In this note is reported a collection of constructions of symmetric networks that provide the largest known values for the number of nodes that can be placed in a network of a given degree and diameter. Some of the constructions are in the range of current potential engineering significance. The constructions are Cayley graphs of linear groups obtained by experimental computation.
2d PDE Linear Symmetric Matrix Solver
Energy Science and Technology Software Center (ESTSC)
1983-10-01
ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
Soliton dynamics in symmetric and non-symmetric complex potentials
NASA Astrophysics Data System (ADS)
Kominis, Yannis
2015-01-01
Soliton propagation dynamics under the presence of a complex potential are investigated. A large variety of qualitatively different potentials, including periodic, semi-infinite periodic and localized potentials, is considered. Cases of both symmetric and non-symmetric potentials are studied in terms of their effect on soliton dynamics. The rich set of dynamical features of soliton propagation includes dynamical trapping, periodic and non-periodic soliton mass variation and non-reciprocal scattering dynamics. These features are systematically investigated with the utilization of an effective particle phase space approach which is shown in remarkable agreement with direct numerical simulations. The generality of the results enables the consideration of potential applications where the inhomogeneity of the gain and loss is appropriately engineered in order to provide desirable soliton dynamics.
Complex symmetric matrices with strongly stable iterates
NASA Technical Reports Server (NTRS)
Tadmor, E.
1985-01-01
Complex-valued symmetric matrices are studied. A simple expression for the spectral norm of such matrices is obtained, by utilizing a unitarily congruent invariant form. A sharp criterion is provided for identifying those symmetric matrices whose spectral norm is not exceeding one: such strongly stable matrices are usually sought in connection with convergent difference approximations to partial differential equations. As an example, the derived criterion is applied to conclude the strong stability of a Lax-Wendroff scheme.
Experimental scheme for unambiguous discrimination of linearly independent symmetric states
Jimenez, O.; Burgos-Inostroza, E.; Delgado, A.; Saavedra, C.; Sanchez-Lozano, X.
2007-12-15
We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among N linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.
Symmetric nested complexes of fullerenes.
Mar, Naveicy; Sansores, Luis Enrique; Muhl, Stephen; Ramos, Estrella; Salcedo, Roberto
2015-04-01
Large fullerenes such as C180 and C116 can be used as hosts for other molecules of the same family. Based on this idea, two complexes were designed, one in which C180 accepts a C60 molecule as a guest and the other in which C20 was placed inside C116. The behavior of these new assemblies was closer to that of a large endohedral complex rather than onion-like. There were marked differences between the systems. In the first system, there was minor interaction between the two cages but the association resulted in a more stable thermodynamic state. In the second system, there was strong electronic interchange between the cages, and the thermodynamic results suggest that such a combination might be useful for forming stable C20. PMID:25823391
Optical solitons in the parity-time-symmetric Bessel complex potential
NASA Astrophysics Data System (ADS)
Hu, Sumei; Hu, Wei
2012-11-01
Optical solitons in the parity-time (PT)-symmetric Bessel complex potential are studied, including the linear case, and self-focusing and self-defocusing nonlinear cases. For the linear case, the PT-symmetric breaking points, eigenvalues and the eigenfunction for different modulated depths of the PT-symmetric Bessel complex potential are obtained numerically. The PT-symmetric breaking points increase linearly with increasing the real part of the modulated depths of the PT potential. Below the PT-symmetric breaking points, the eigenfunctions of linear modes are symmetrical; however, the symmetries of the eigenfunction break above the PT-symmetric breaking points. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. The eigenvalue for the linear case is equal to the critical propagation constant bc of the existing soliton. Fundamental solitons are stable in the whole region and multipole solitons are stable with the propagation constants being close to bc both for self-focusing and self-defocusing nonlinearities. The range of solitons’ stability decreases with an increase of the number of the intensity peaks of the solitons.
Evolution of linear perturbations in spherically symmetric dust spacetimes
NASA Astrophysics Data System (ADS)
February, S.; Larena, J.; Clarkson, C.; Pollney, D.
2014-09-01
We present results from a numerical code implementing a new method to solve the master equations describing the evolution of linear perturbations in a spherically symmetric but inhomogeneous background. This method can be used to simulate several configurations of physical interest, such as relativistic corrections to structure formation, the lensing of gravitational waves (GWs) and the evolution of perturbations in a cosmological void model. This paper focuses on the latter problem, i.e. structure formation in a Hubble scale void in the linear regime. This is considerably more complicated than linear perturbations of a homogeneous and isotropic background because the inhomogeneous background leads to coupling between density perturbations and rotational modes of the spacetime geometry, as well as GWs. Previous analyses of this problem ignored this coupling in the hope that the approximation does not affect the overall dynamics of structure formation in such models. We show that for a giga-parsec void, the evolution of the density contrast is well approximated by the previously studied decoupled evolution only for very large-scale modes. However, the evolution of the gravitational potentials within the void is inaccurate at more than the 10% level, and is even worse on small scales.
Passive PT -symmetric couplers without complex optical potentials
NASA Astrophysics Data System (ADS)
Lee, Yi-Chan; Liu, Jibing; Chuang, You-Lin; Hsieh, Min-Hsiu; Lee, Ray-Kuang
2015-11-01
In addition to the implementation of parity-time-(PT -) symmetric optical systems by carefully and actively controlling the gain and loss, we show that a 2 ×2 PT -symmetric Hamiltonian has a unitarily equivalent representation without complex optical potentials in the resulting optical coupler. Through the Naimark dilation in operator algebra, passive PT -symmetric couplers can thus be implemented with a refractive index of real values and asymmetric coupling coefficients. This opens up the possibility to implement general PT -symmetric systems with state-of-the-art asymmetric slab waveguides, dissimilar optical fibers, or cavities with chiral mirrors.
Linear perturbations of self-gravitating spherically symmetric configurations
NASA Astrophysics Data System (ADS)
Chaverra, Eliana; Ortiz, Néstor; Sarbach, Olivier
2013-02-01
We present a new covariant, gauge-invariant formalism describing linear metric perturbation fields on any spherically symmetric background in general relativity. The advantage of this formalism relies in the fact that it does not require a decomposition of the perturbations into spherical tensor harmonics. Furthermore, it does not assume the background to be vacuum, nor does it require its staticity. In the particular case of vacuum perturbations, we derive two master equations describing the propagation of arbitrary linear gravitational waves on a Schwarzschild black hole. When decomposed into spherical harmonics, they reduce to covariant generalizations of the well-known Regge-Wheeler and Zerilli equations. Next, we discuss the general case where the metric perturbations are coupled to matter fields and derive a new constrained wave system describing the propagation of three gauge-invariant scalars from which the complete metric perturbations can be reconstructed. We apply our formalism to the Einstein-Euler system, dividing the fluid perturbations into two parts. The first part, which decouples from the metric perturbations, obeys simple advection equations along the background flow and describes the propagation of the entropy and the vorticity. The second part describes a perturbed potential flow, and together with the metric perturbations, it forms a closed wave system.
The solitons in parity-time symmetric mixed Bessel linear potential and modulated nonlinear lattices
NASA Astrophysics Data System (ADS)
Chen, Haibo; Hu, Sumei
2014-12-01
The optical solitons in parity-time (PT) symmetric mixed Bessel linear potential and modulated nonlinear lattices are studied, including linear case, and self-focusing modulated nonlinear lattices' cases. For linear case, the PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of PT symmetry Bessel complex potential, are obtained numerically. The eigenvalue for linear case is equal to the critical propagation constant bc of soliton existence. With increasing of the depth of the nonlinear lattices, the power of fundamental solitons decreases and the beam width changes little, but the power of multipole solitons increases and the beam width decreases. Fundamental solitons are stable in the whole region and multipole solitons are stable with the propagation constants close to bc. The range of multipole solitons stability decreases with increasing of the depth of the nonlinear lattices.
Experimental beta limits of symmetric linear heliac configurations
NASA Astrophysics Data System (ADS)
Spanjers, G. G.; Nelson, B. A.; Ribe, F. L.; Jarboe, T. R.
1994-08-01
Helically symmetric heliac equilibria [H. P. Furth, Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1966), Vol. 1, p. 103] are formed on the High Beta Q Machine (HBQM) [C. M. Greenfield, Phys. Fluids B 2, 133 (1990)] by using a fast-rising central conductor (hardcore) current in conjunction with a shock-heated l=1 stellarator configuration. The equilibria are found to possess a high global beta and the plasma pressure is approximately a flux-surface quantity. Under the effects of plasma, the magnetic well is found to deepen and the rotational transform is greatly increased and becomes highly sheared, owing to plasma currents induced by the fast-rising hardcore current. In the second phase of the experiment, the equilibrium fields of the symmetric heliac are lowered while maintaining the same shock heating in an attempt to raise the global beta. No substantial change in global beta is seen, indicating that the configuration forms at the beta limit in the shock-heated HBQM, and that the plasma beta seen in the first phase of the experiment is the symmetric heliac beta limit.
Experimental beta limits of symmetric linear heliac configurations
Spanjers, G.G.; Nelson, B.A.; Ribe, F.L.; Jarboe, T.R. )
1994-08-01
Helically symmetric heliac equilibria [H. P. Furth, [ital Plasma] [ital Physics] [ital and] [ital Controlled] [ital Fusion] [ital Research] (International Atomic Energy Agency, Vienna, 1966), Vol. 1, p. 103] are formed on the High Beta Q Machine (HBQM) [C. M. Greenfield, Phys. Fluids B [bold 2], 133 (1990)] by using a fast-rising central conductor (hardcore) current in conjunction with a shock-heated [ital l]=1 stellarator configuration. The equilibria are found to possess a high global beta and the plasma pressure is approximately a flux-surface quantity. Under the effects of plasma, the magnetic well is found to deepen and the rotational transform is greatly increased and becomes highly sheared, owing to plasma currents induced by the fast-rising hardcore current. In the second phase of the experiment, the equilibrium fields of the symmetric heliac are lowered while maintaining the same shock heating in an attempt to raise the global beta. No substantial change in global beta is seen, indicating that the configuration forms at the beta limit in the shock-heated HBQM, and that the plasma beta seen in the first phase of the experiment is the symmetric heliac beta limit.
Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems.
Choi, Sou-Cheng T; Saunders, Michael A
2014-02-01
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. PMID:25328255
Model-size reduction for the non-linear dynamic analysis of quasi-symmetric structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
A numerical technique is developed to reduce the size of models describing the nonlinear dynamic response of quasi-symmetric structures (i.e., structures with unsymmetric geometry). The response vectors of the structure are approximated by a linear combination of the symmetric and antisymmetric vectors at each time step. The mathematical formulation and numerical implementation of the method are described in detail, and results for a shallow laminated anisotropic panel of quadrilateral planform are presented in graphs and normalized contour plots.
Symmetric linear systems - An application of algebraic systems theory
NASA Technical Reports Server (NTRS)
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Solitons supported by complex PT-symmetric Gaussian potentials
NASA Astrophysics Data System (ADS)
Hu, Sumei; Ma, Xuekai; Lu, Daquan; Yang, Zhenjun; Zheng, Yizhou; Hu, Wei
2011-10-01
The existence and stability of fundamental, dipole, and tripole solitons in Kerr nonlinear media with parity-time-symmetric Gaussian complex potentials are reported. Fundamental solitons are stable not only in deep potentials but also in shallow potentials. Dipole and tripole solitons are stable only in deep potentials, and tripole solitons are stable in deeper potentials than for dipole solitons. The stable regions of solitons increase with increasing potential depth. The power of solitons increases with increasing propagation constant or decreasing modulation depth of the potentials.
A new Krylov-subspace method for symmetric indefinite linear systems
Freund, R.W.; Nachtigal, N.M.
1994-10-01
Many important applications involve the solution of large linear systems with symmetric, but indefinite coefficient matrices. For example, such systems arise in incompressible flow computations and as subproblems in optimization algorithms for linear and nonlinear programs. Existing Krylov-subspace iterations for symmetric indefinite systems, such as SYMMLQ and MINRES, require the use of symmetric positive definite preconditioners, which is a rather unnatural restriction when the matrix itself is highly indefinite with both many positive and many negative eigenvalues. In this note, the authors describe a new Krylov-subspace iteration for solving symmetric indefinite linear systems that can be combined with arbitrary symmetric preconditioners. The algorithm can be interpreted as a special case of the quasi-minimal residual method for general non-Hermitian linear systems, and like the latter, it produces iterates defined by a quasi-minimal residual property. The proposed method has the same work and storage requirements per iteration as SYMMLQ or MINRES, however, it usually converges in considerably fewer iterations. Results of numerical experiments are reported.
Closed form evaluation of symmetric two-sided complex integrals
NASA Technical Reports Server (NTRS)
Winkelstein, R.
1981-01-01
Evaluation of two-sided complex integrals is often required when analyzing linear systems to determine signal variances resulting from stochastic inputs and system noise bandwidths. Algebraic solutions of integrals in a closed matrix equation form, using coefficients of the numerator and denominator polynomials, are presented. The closed forms provide the possibility of obtaining some insight into parameter sensitivity in addition to greatly reducing the computational complexity required by the normal method of evaluation by residues.
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin E-mail: izumi@phys.ntu.edu.tw
2012-12-01
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
Thiel, C.; Zanthier, J. von; Bastin, T.; Solano, E.; Agarwal, G. S.
2007-11-09
We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.
Complex bodies with memory: Linearized setting
NASA Astrophysics Data System (ADS)
Mariano, Paolo Maria; Paoletti, Paolo
2009-06-01
The mechanics of complex bodies with memory effects is discussed in linearized setting. The attention is focused on the characterization of free energies in terms of minimum work and maximum recoverable work in the bulk and along a discontinuity surface endowed with its own surface energy, a surface internal to the body. To this aim, use is made of techniques proposed by Del Piero. Consequences of the Clausius-Duhem inequality are investigated for complex bodies with instantaneous linear elastic response.
Lie algebraic approach to potential energy surface for symmetrical linear tetratomic molecule
NASA Astrophysics Data System (ADS)
Wang, Xiaoyan; Ding, Shiliang
2004-02-01
Using Lie algebraic method, we obtain the fitting coefficients of an effective Hamiltonian operator, which conveniently describes vibration spectra of symmetrical linear tetratomic molecules, including both stretching and bending modes. With the classical limit of the Hamiltonian and the kinetic energy equal to zero, we get the potential energy surface of the linear symmetry tetratomic molecule. For an example, we use the method to calculate the potential energy surface of C 2D 2. We fit 41 data with 7 coefficients; the data are from Iachello et al. [J. Mol. Spectrosc. 149 (1991) 132]. The fitting rms is 6.68 cm -1. At last, we use the potential energy surface to get the force constants and the dissociation energy. The method can be applied to a number of linear symmetry tetratomic molecules.
Bugenhagen, B E C; Prosenc, M H
2016-04-25
The synthesis of symmetric and non-symmetric 5,5'-linked disalophen Ni(ii) complexes by the Suzuki-Miyaura-reaction is reported. Also, the synthesis and structural characterization of four Ni(ii)-precursor complexes are presented. The 5-Br-substituted mononuclear complexes and are coupled to the pinacolborane substituted complexes and yielding the four dinuclear dinickel complexes in good yields. The crystal structure of dinuclear complex was obtained revealing a coplanar arrangement between the two salophen fragments. Electronic spectra as well as DFT-calculations on the ground states and excitation energies are reported and they reveal a small coupling between the electronically saturated Ni-salophen complexes. PMID:27040080
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
2015-01-01
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations. PMID:26639941
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
NASA Astrophysics Data System (ADS)
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
2015-12-01
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices.
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
2015-01-01
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations. PMID:26639941
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
1997-01-01
A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates that are subjected to linearly varying edge loads, uniform shear loads, or combinations of these loads is presented. The study focuses on the effects of the shape of linearly varying edge load distribution, plate orthotropy, and plate flexural anisotropy on plate buckling behavior. In addition, the study exmines the interaction of linearly varying edge loads and uniform shear loads with plate flexural anisotropy and orthotropy. Results obtained by using a special purpose nondimensional analysis that is well suited for parametric studies of clamped and simply supported plates are presented for [+/- theta](sub s), thin graphite-epoxy laminates that are representative of spacecraft structural components. Also, numerous generic buckling-design charts are presented for a wide range of nondimensional parameters that are applicable to a broad class of laminate constructions. These charts show explicitly the effects of flexural orthotropy and flexural anisotropy on plate buckling behavior for linearly varying edge loads, uniform shear loads, or combinations of these loads. The most important finding of the present study is that specially orthotropic and flexurally anisotropic plates that are subjected to an axial edge load distribution that is tension dominated can support shear loads that are larger in magnitude than the shear buckling load.
Trellis Decoding Complexity of Linear Block Codes
NASA Technical Reports Server (NTRS)
Kiely, A. B.; McEliece, R. J.; Lin, W.; Ekroot, L.; Dolinar, S.
1995-01-01
We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code, or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: if a trellis is optimum with respect to this partial ordering, it has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.
Crystal structure of the human mitochondrial chaperonin symmetrical football complex
Nisemblat, Shahar; Yaniv, Oren; Parnas, Avital; Frolow, Felix; Azem, Abdussalam
2015-01-01
Human mitochondria harbor a single type I chaperonin system that is generally thought to function via a unique single-ring intermediate. To date, no crystal structure has been published for any mammalian type I chaperonin complex. In this study, we describe the crystal structure of a football-shaped, double-ring human mitochondrial chaperonin complex at 3.15 Å, which is a novel intermediate, likely representing the complex in an early stage of dissociation. Interestingly, the mitochondrial chaperonin was captured in a state that exhibits subunit asymmetry within the rings and nucleotide symmetry between the rings. Moreover, the chaperonin tetradecamers show a different interring subunit arrangement when compared to GroEL. Our findings suggest that the mitochondrial chaperonins use a mechanism that is distinct from the mechanism of the well-studied Escherichia coli system. PMID:25918392
NASA Astrophysics Data System (ADS)
Marcotte, D.
2016-04-01
The turning bands method (TBM) is a commonly used method of simulation for large Gaussian fields, its O(N) complexity being unsurpassed (N denotes the number of points to simulate). TBM can be implemented either in the spatial or the spectral domains. In the multivariate anisotropic case, spatial versions of TBM are currently available only for the linear model of coregionalization (LMC). For anisotropic non-LMC with symmetrical covariances only the spectral version is currently available. The spectral domain approach can be slow in the case of non-differentiable covariances due to the numerous frequencies to sample. Here a derivation of the equations is provided for simulating the anisotropic non-LMC directly in the spatial domain and the method is illustrated with two synthetic examples. The approach allows the specification of many different direct and cross-covariance components, each with possibly different geometric anisotropies and different model types. The complexity of the new multivariate approach remains O(N). Hence, a case of two variables defining an anisotropic non-LMC is simulated over one billion points in less than one hour on a desktop computer. These results help enlarge the scope of application of the TBM. The method can be easily implemented in any existing TBM program.
Dzhunushaliev, Vladimir; Folomeev, Vladimir; Singleton, Douglas; Myrzakulov, Ratbay
2010-08-15
In this paper we investigate wormhole and spherically symmetric solutions in four-dimensional gravity plus a matter source consisting of a ghost scalar field with a sine-Gordon potential. For the wormhole solutions we also include the possibility of electric and/or magnetic charges. For both types of solutions we perform a linear stability analysis and show that the wormhole solutions are stable and that when one turns on the electric and/or magnetic field the solution remains stable. The linear stability analysis of the spherically symmetric solutions indicates that they can be stable or unstable depending on one of the parameters of the system. This result for the spherically symmetric solution is nontrivial since a previous investigation of four-dimensional gravity plus a ghost scalar field with a {lambda}{phi}{sup 4} interaction found only unstable spherically symmetric solutions. Both the wormhole and spherically symmetric solutions presented here asymptotically go to anti-de Sitter space-time.
NASA Astrophysics Data System (ADS)
Zhang, Li
2005-04-01
By using the displacement harmonic variant method and the compact density matrix approach, the linear and nonlinear intersubband refractive index changes (RICs) in a semiparabolic quantum well (QW) with applied electric field have been investigated in detail. The simple analytical formulae for the linear and nonlinear RICs in the system were also deduced. The symmetrical parabolic QWs with applied electric fields were taken into account for comparison. Numerical calculations on typical GaAs QWs were performed. The dependence of the linear and nonlinear RICs on the incident optical intensity, the frequencies of the confined potential of the QWs and the strength of the applied electric field were discussed. Results reveal that the RICs in the semiparabolic quantum well system sensitively depend on these factors. The calculation also shows that the semiparabolic QW is a more ideal nonlinear optical system relative to the symmetric parabolic QW systems.
Preconditioning the bidomain model with almost linear complexity
NASA Astrophysics Data System (ADS)
Pierre, Charles
2012-01-01
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its discretisation displays an ill-conditioned system matrix to be inverted at each time step: simulations based on the bidomain model therefore are associated with high computational costs. In this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues (the torso). The preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi-definite. A block LU decomposition of the system together with a heuristic approximation (referred to as the monodomain approximation) are the key ingredients for the preconditioning definition. Numerical results are provided for two test cases: a 2D test case on a realistic slice of the thorax based on a segmented heart medical image geometry, a 3D test case involving a small cubic slab of tissue with orthotropic anisotropy. The analysis of the resulting computational cost (both in terms of CPU time and of iteration number) shows an almost linear complexity with the problem size, i.e. of type nlog α( n) (for some constant α) which is optimal complexity for such problems.
Horner, D.A.; Colgan, J.; Martin, F.; McCurdy, C.W.; Pindzola, M.S.; Rescigno, T.N.
2004-06-01
Symmetrized complex amplitudes for the double photoionization of helium are computed by the time-dependent close-coupling and exterior complex scaling methods, and it is demonstrated that both methods are capable of the direct calculation of these amplitudes. The results are found to be in excellent agreement with each other and in very good agreement with results of other ab initio methods and experiment.
Krylov subspace methods for complex non-Hermitian linear systems. Thesis
NASA Technical Reports Server (NTRS)
Freund, Roland W.
1991-01-01
We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Transparency of the complex PT-symmetric potentials for coherent injection
NASA Astrophysics Data System (ADS)
Ahmed, Zafar; Nathan, Joseph Amal; Ghosh, Dona
2016-02-01
Two port s-matrix for a complex PT-symmetric potential may have uni-modular eigenvalues. If this happens for all energies, there occurs a perfect emission of waves at both ends. We call this phenomenon transparency which is distinctly different from coherent perfect absorption with or without lasing. Using the versatile PT-symmetric complex Scarf II (scattering) potential, we demonstrate analytically that the transparency can occur regardless of whether PT-symmetry is unbroken or broken or if there are only scattering states. In these three cases, for a given value of the strength of the real part, the strength of the imaginary part |V2 | of the potential lies in (0 ,Vα) , (Vα ,Vβ) and (0 ,Vβ) respectively. Several other numerically solved potentials also support our findings.
Single-molecule Observation of Protein Folding in Symmetric GroEL-(GroES)2 Complexes*
Takei, Yodai; Iizuka, Ryo; Ueno, Taro; Funatsu, Takashi
2012-01-01
The chaperonin, GroEL, is an essential molecular chaperone that mediates protein folding together with its cofactor, GroES, in Escherichia coli. It is widely believed that the two rings of GroEL alternate between the folding active state coupled to GroES binding during the reaction cycle. In other words, an asymmetric GroEL-GroES complex (the bullet-shaped complex) is formed throughout the cycle, whereas a symmetric GroEL-(GroES)2 complex (the football-shaped complex) is not formed. We have recently shown that the football-shaped complex coexists with the bullet-shaped complex during the reaction cycle. However, how protein folding proceeds in the football-shaped complex remains poorly understood. Here, we used GFP as a substrate to visualize protein folding in the football-shaped complex by single-molecule fluorescence techniques. We directly showed that GFP folding occurs in both rings of the football-shaped complex. Remarkably, the folding was a sequential two-step reaction, and the kinetics were in excellent agreement with those in the bullet-shaped complex. These results demonstrate that the same reactions take place independently in both rings of the football-shaped complex to facilitate protein folding. PMID:23048033
A Symmetrical Tetramer for S. aureus Pyruvate Carboxylase in Complex with Coenzyme A
Yu, L.; Xiang, S; Lasso, G; Gil, D; Valle, M; Tong, L
2009-01-01
Pyruvate carboxylase (PC) is a conserved metabolic enzyme with important cellular functions. We report crystallographic and cryo-electron microscopy (EM) studies of Staphylococcus aureus PC (SaPC) in complex with acetyl-CoA, an allosteric activator, and mutagenesis, biochemical, and structural studies of the biotin binding site of its carboxyltransferase (CT) domain. The disease-causing A610T mutation abolishes catalytic activity by blocking biotin binding to the CT active site, and Thr908 might play a catalytic role in the CT reaction. The crystal structure of SaPC in complex with CoA reveals a symmetrical tetramer, with one CoA molecule bound to each monomer, and cryo-EM studies confirm the symmetrical nature of the tetramer. These observations are in sharp contrast to the highly asymmetrical tetramer of Rhizobium etli PC in complex with ethyl-CoA. Our structural information suggests that acetyl-CoA promotes a conformation for the dimer of the biotin carboxylase domain of PC that might be catalytically more competent.
Non-linear resonances in the forced responses of plates. I - Symmetric responses of circular plates
NASA Technical Reports Server (NTRS)
Sridhar, S.; Mook, D. T.; Nayfeh, A. H.
1975-01-01
The dynamic analogue of the von Karman equations is used to study the symmetric response of a circular plate to a harmonic excitation when the frequency of the excitation is near one of the natural frequencies. It is shown that, in general, when there is no internal resonance (i.e., the natural frequencies are not commensurable), only the mode having a frequency near that of the excitation is strongly excited (i.e., is needed to represent the response in the first approximation). A clamped, circular plate is used as a numerical example to show that, when there is an internal resonance, more than one of the modes involved in this resonance can be strongly excited; moreover, when more than one mode is strongly excited, the lower modes can dominate the response, even when the frequency of the excitation is near that of the highest mode. This possibility was not revealed by any of the earlier studies which were based on the same governing equations.
Gao, Ying; Cartledge, John C; Karar, Abdullah S; Yam, Scott S-H; O'Sullivan, Maurice; Laperle, Charles; Borowiec, Andrzej; Roberts, Kim
2014-01-27
Perturbation based nonlinearity pre-compensation has been performed for a 128 Gbit/s single-carrier dual-polarization 16-ary quadrature-amplitude-modulation (DP 16-QAM) signal. Without any performance degradation, a complexity reduction factor of 6.8 has been demonstrated for a transmission distance of 3600 km by combining symmetric electronic dispersion compensation and root-raised-cosine pulse shaping with a roll-off factor of 0.1. Transmission over 4200 km of standard single-mode fiber with EDFA amplification was achieved for the 128 Gbit/s DP 16-QAM signals with a forward error correction (FEC) threshold of 2 × 10(-2). PMID:24515126
NASA Astrophysics Data System (ADS)
Shalaby, Abouzeid M.
2014-04-01
In this work, we stress the existence of isomorphisms which map complex contours from the upper half to contours in the lower half of the complex plane. The metric operator is found to depend on the chosen contour but the maps connecting different contours are norm-preserving. To elucidate these features, we parametrized the contour z = -2i√ {1+ix} considered in Phys. Rev. D 73, 085002 (2006) for the study of wrong sign x4 theory. For the parametrized contour of the form z = a√ {b+icx}, we found that there exists an equivalent Hermitian Hamiltonian provided that a2c is taken to be real. The equivalent Hamiltonian is b-independent but the metric operator is found to depend on all the parameters a, b and c. Different values of these parameters generate different metric operators which define different Hilbert spaces. All these Hilbert spaces are isomorphic to each other even for the parameter values that define contours with ends in two adjacent wedges. As an example, we showed that the transition amplitudes associated with the contour z = -2i√ {1+ix} are exactly the same as those calculated using the contour z = √ {1+ix}, which is not {PT}-symmetric and has ends in two adjacent wedges in the complex plane.
Internal pilots for a class of linear mixed models with Gaussian and compound symmetric data
Gurka, Matthew J.; Coffey, Christopher S.; Muller, Keith E.
2015-01-01
SUMMARY An internal pilot design uses interim sample size analysis, without interim data analysis, to adjust the final number of observations. The approach helps to choose a sample size sufficiently large (to achieve the statistical power desired), but not too large (which would waste money and time). We report on recent research in cerebral vascular tortuosity (curvature in three dimensions) which would benefit greatly from internal pilots due to uncertainty in the parameters of the covariance matrix used for study planning. Unfortunately, observations correlated across the four regions of the brain and small sample sizes preclude using existing methods. However, as in a wide range of medical imaging studies, tortuosity data have no missing or mistimed data, a factorial within-subject design, the same between-subject design for all responses, and a Gaussian distribution with compound symmetry. For such restricted models, we extend exact, small sample univariate methods for internal pilots to linear mixed models with any between-subject design (not just two groups). Planning a new tortuosity study illustrates how the new methods help to avoid sample sizes that are too small or too large while still controlling the type I error rate. PMID:17318914
Haldar, Shubhasis; Gupta, Amit J; Yan, Xiao; Miličić, Goran; Hartl, F Ulrich; Hayer-Hartl, Manajit
2015-06-19
The chaperonin GroEL, a cylindrical complex consisting of two stacked heptameric rings, and its lid-like cofactor GroES form a nano-cage in which a single polypeptide chain is transiently enclosed and allowed to fold unimpaired by aggregation. GroEL and GroES undergo an ATP-regulated interaction cycle that serves to close and open the folding cage. Recent reports suggest that the presence of non-native substrate protein alters the GroEL/ES reaction by shifting it from asymmetric to symmetric complexes. In the asymmetric reaction mode, only one ring of GroEL is GroES bound and the two rings function sequentially, coupled by negative allostery. In the symmetric mode, both GroEL rings are GroES bound and are folding active simultaneously. Here, we find that the results of assays based on fluorescence resonance energy transfer recently used to quantify symmetric complexes depend strongly on the fluorophore pair used. We therefore developed a novel assay based on fluorescence cross-correlation spectroscopy to accurately measure GroEL:GroES stoichiometry. This assay avoids fluorophore labeling of GroEL and the use of GroEL cysteine mutants. Our results show that symmetric GroEL:GroES2 complexes are substantially populated only in the presence of non-foldable model proteins, such as α-lactalbumin and α-casein, which "over-stimulate" the GroEL ATPase and uncouple the negative GroEL inter-ring allostery. In contrast, asymmetric complexes are dominant both in the absence of substrate and in the presence of foldable substrate proteins. Moreover, uncoupling of the GroEL rings and formation of symmetric GroEL:GroES2 complexes is suppressed at physiological ATP:ADP concentration. We conclude that the asymmetric GroEL:GroES complex represents the main folding active form of the chaperonin. PMID:25912285
Hickey, Robert J.; Gillard, Timothy M.; Lodge, Timothy P.; Bates, Frank S.
2015-08-28
Rheological evidence of composition fluctuations in disordered diblock copolymers near the order disorder transition (ODT) has been documented in the literature over the past three decades, characterized by a failure of time–temperature superposition (tTS) to reduce linear dynamic mechanical spectroscopy (DMS) data in the terminal viscoelastic regime to a temperature-independent form. However, for some materials, most notably poly(styrene-b-isoprene) (PS–PI), no signature of these rheological features has been found. We present small-angle X-ray scattering (SAXS) results on symmetric poly(cyclohexylethylene-b-ethylene) (PCHE–PE) diblock copolymers that confirm the presence of fluctuations in the disordered state and DMS measurements that also show no sign of the features ascribed to composition fluctuations. Assessment of DMS results published on five different diblock copolymer systems leads us to conclude that the effects of composition fluctuations can be masked by highly asymmetric block dynamics, thereby resolving a long-standing disagreement in the literature and reinforcing the importance of mechanical contrast in understanding the dynamics of ordered and disordered block polymers.
Solving complex-valued linear systems via equivalent real formulations
DAY,DAVID M.; HEROUX,MICHAEL A.
2000-05-22
Most algorithms used in preconditioned iterative methods are generally applicable to complex valued linear systems, with real valued linear systems simply being a special case. However, most iterative solver packages available today focus exclusively on real valued systems, or deal with complex valued systems as an afterthought. One obvious approach to addressing this problem is to recast the complex problem into one of a several equivalent real forms and then use a real valued solver to solve the related system. However, well-known theoretical results showing unfavorable spectral properties for the equivalent real forms have diminished enthusiasm for this approach. At the same time, experience has shown that there are situations where using an equivalent real form can be very effective. In this paper, the authors explore this approach, giving both theoretical and experimental evidence that an equivalent real form can be useful for a number of practical situations. Furthermore, they show that by making good use of some of the advance features of modem solver packages, they can easily generate equivalent real form preconditioners that are computationally efficient and mathematically identical to their complex counterparts. Using their techniques, they are able to solve very ill-conditioned complex valued linear systems for a variety of large scale applications. However, more importantly, they shed more light on the effectiveness of equivalent real forms and more clearly delineate how and when they should be used.
The asymmetric solitons in two-dimensional parity-time-symmetric potentials
NASA Astrophysics Data System (ADS)
Chen, Haibo; Hu, Sumei
2016-01-01
We investigate the properties in two-dimensional (2D) special parity-time (PT) symmetric complex potentials. The linear case of this special 2D PT-symmetric complex potential and self-focusing nonlinear cases are discussed. For linear case, the eigenvalues and eigenfunction for different loss or gain level of the PT-symmetric complex potentials are obtained numerically. For nonlinear cases, the existence of asymmetric solitons and PT-symmetric solitons is studied in this PT symmetric system. The eigenvalue for linear case is equal to the critical propagation constant bc of existing PT-symmetric solitons. When the PT-symmetric soliton's propagation constant reaches a certain threshold bc1, a branch of asymmetric solitons can bifurcate out from the branch of PT-symmetric solitons.
Lamerichs, R.M.J.N.; Boelens, R.; van der Marel, G.A.; van Boom, J.H.; Kaptein, R.; Buck, F.; Fera, B.; Rueterjans, H. )
1989-04-04
A complex between the lac repressor headpiece and a fully symmetric tight-binding 22 bp lac operator was studied by 2D NMR. Several 2D NOE spectra were recorded for the complex in both H{sub 2}O and {sup 2}H{sub 2}O. Many NOE cross-peaks between the headpiece and DNA could be identified, and changes in the chemical shift of the DNA protons upon complex formation were analyzed. Comparison of these data with those obtained for a complex between the headpiece and a 14 bp half-operator, studied previously, shows that two headpieces form a specific complex with the 22 bp lac operator in which each headpiece binds in the same way as found for the 14 bp complex. The orientation of the recognition helix in the major groove of DNA in these complexes is opposite with respect to the dyad axis to that found for other repressors.
Near consensus complex linear and nonlinear social networks
NASA Astrophysics Data System (ADS)
Ling, Bingo Wing-Kuen; Ho, Charlotte Yuk-Fan; Wang, Lidong; Teo, Kok-Lay; Tse, Chi K.; Dai, Qingyun
2014-05-01
Some of the nodes of complex social networks may support for a given proposal, while the rest of the nodes may be against the given proposal. Even though all the nodes support for or are against the given proposal, the decision certitudes of individual nodes may be different. In this case, the steady state values of the decision certitudes of the majority of the nodes are either higher than or lower than a threshold value. Deriving the near consensus property is a key to the analysis of the behaviors of complex social networks. So far, no result on the behaviors of the complex social networks satisfying the near consensus property has been reported. Hence, it is useful to extend the definition of the exact consensus property to that of a near consensus property and investigate the behaviors of the complex social networks satisfying the near consensus property. This paper extends the definition of exact consensus complex social networks to that of near consensus complex social networks. For complex linear social networks, this paper investigates the relationships among the vectors representing the steady state values of the decision certitudes of the nodes, the influence weight matrix and the set of vectors representing the initial state values of the decision certitudes of the nodes under a given near consensus specification. The above analysis is based on the Eigen theory. For complex nonlinear social networks with certain types of nonlinearities, the relationship between the influence weight matrix and the vectors representing the steady state values of the decision certitudes of the nodes is studied. When a complex nonlinear social network does not achieve the exact consensus property, the optimal near consensus condition that the complex social network can achieve is derived. This problem is formulated as an optimization problem. The total number of nodes that the decision certitudes of the nodes are either higher than or lower than a threshold value is maximized subject to the corresponding near consensus specification. The optimization problem is a nonsmooth optimization problem. The nonsmooth constraints are first approximated by smooth constraints. Then, the approximated optimization problem is solved via a conventional smooth optimization approach. Computer numerical simulation results as well as the comparisons of the behaviors of complex nonlinear social networks to those of the complex linear social networks are presented. The obtained results demonstrate that some complex social networks can satisfy the near consensus property but not the exact consensus property. Also, the conditions for the near consensus property are dependent on the types of nonlinearities, the influence weight matrix and the vectors representing the initial state values of the decision certitudes of the nodes.
Trellis complexity bounds for decoding linear block codes
NASA Technical Reports Server (NTRS)
Kiely, A. B.; Dolinar, S.; Ekroot, L.; Mceliece, R. J.; Lin, W.
1995-01-01
We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: If a trellis is optimum with respect to this partial ordering, if has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.
NASA Astrophysics Data System (ADS)
Shang, Jing; Yuan, Ting; Zhu, Hua
2016-03-01
A high quality four-dimensional intermolecular PES for Ar-CS2 involving the Q1 and Q3 normal modes for the ν1 symmetric stretching vibration and ν3 antisymmetric stretching vibration of CS2 is presented. Two vibrationally averaged potentials with CS2 at the vibrational ground and ν1 + ν3 excited states are generated from the four-dimensional potential. Each potential has a T-shaped global minimum and two equivalent linear minima. The radial DVR/angular FBR method and the Lanczos algorithm are applied to calculate the rovibrational energy levels and bound states. The predicted band origin shift of the complex is -0.0495 cm-1. The spectroscopic parameters are also predicted.
Devassy, Lini; Jisha, Chandroth P; Alberucci, Alessandro; Kuriakose, V C
2015-08-01
Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a PT-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the PT breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations. PMID:26382483
A 2.5 mW 370 mV/pF high linearity stray-immune symmetrical readout circuit for capacitive sensors
NASA Astrophysics Data System (ADS)
Kaimin, Zhou; Ziqiang, Wang; Chun, Zhang; Zhihua, Wang
2012-06-01
A stray-insensitive symmetrical capacitance-to-voltage converter for capacitive sensors is presented. By introducing a reference branch, a symmetrical readout circuit is realized. The linear input range is increased, and the systematic offsets of two input op-amps are cancelled. The common-mode noise and even-order distortion are also rejected. A chopper stabilization technique is adopted to further reduce the offset and flicker noise of the op-amps, and a Verilog-A-based varactor is used to model the real variable sensing capacitor. Simulation results show that the output voltage of this proposed readout circuit responds correctly, while the under-test capacitance changes with a frequency of 1 kHz. A metal-insulator-metal capacitor array is designed on chip for measurement, and the measurement results show that this circuit achieves sensitivity of 370 mV/pF, linearity error below 1% and power consumption as low as 2.5 mW. This symmetrical readout circuit can respond to an FPGA controlled sensing capacitor array changed every 1 ms.
Simple Linear Inverse for Complex Sources in Early Warning
NASA Astrophysics Data System (ADS)
Karakus, G.; Heaton, T. H.
2012-12-01
In this project we aim to determine a foreshock/mainshock pair in real time. That is, we are trying to determine the timing and amplitudes of events in a complex sequence (e.g. foreshock/mainshock pair) in an ongoing earthquake. We are assuming random phase in seismograms so that energy envelopes add linearly which provides the opportunity to pose the problem as a linear least squares inverse problem. We are working on a methodology to solve the least squares problem in real time. The advantage is that the inverse problem can be regularized (unlike traditional deconvolution). We parameterize earthquakes as moments in time windows. Then the problem becomes linear as the determination of the amplitude of the moment in each time window. We first construct the Green's functions for the energy envelopes derived from the predicted envelopes of channels of ground motion of the Virtual Seismologist (VS) (Cua, G. and Heaton, T. 2007). Then, these Green's functions are deconvolved (in a generalized way) from the energy envelopes of seismic records using a damped least-squares inversion in order to determine the amplitude of the moment in each time window. There is a positivity constraint that the amplitude of the moments be positive everywhere. Because the VS predicted envelopes are defined for earthquakes of magnitude 6.5 and below, this technique is not used for very large events.
NASA Technical Reports Server (NTRS)
Dunham, R. S.
1976-01-01
FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.
On complexity of trellis structure of linear block codes
NASA Technical Reports Server (NTRS)
Lin, Shu
1990-01-01
The trellis structure of linear block codes (LBCs) is discussed. The state and branch complexities of a trellis diagram (TD) for a LBC is investigated. The TD with the minimum number of states is said to be minimal. The branch complexity of a minimal TD for a LBC is expressed in terms of the dimensions of specific subcodes of the given code. Then upper and lower bounds are derived on the number of states of a minimal TD for a LBC, and it is shown that a cyclic (or shortened cyclic) code is the worst in terms of the state complexity among the LBCs of the same length and dimension. Furthermore, it is shown that the structural complexity of a minimal TD for a LBC depends on the order of its bit positions. This fact suggests that an appropriate permutation of the bit positions of a code may result in an equivalent code with a much simpler minimal TD. Boolean polynomial representation of codewords of a LBC is also considered. This representation helps in study of the trellis structure of the code. Boolean polynomial representation of a code is applied to construct its minimal TD. Particularly, the construction of minimal trellises for Reed-Muller codes and the extended and permuted binary primitive BCH codes which contain Reed-Muller as subcodes is emphasized. Finally, the structural complexity of minimal trellises for the extended and permuted, and double-error-correcting BCH codes is analyzed and presented. It is shown that these codes have relatively simple trellis structure and hence can be decoded with the Viterbi decoding algorithm.
NASA Astrophysics Data System (ADS)
Brazhnyi, Valeriy A.; Malomed, Boris A.
2012-07-01
We construct families of symmetric, antisymmetric, and asymmetric solitary modes in one-dimensional bichromatic lattices with the second-harmonic-generating (χ(2)) nonlinearity concentrated at a pair of sites placed at distance l. The lattice can be built as an array of optical waveguides. Solutions are obtained in an implicit analytical form, which is made explicit in the case of adjacent nonlinear sites, l=1. The stability is analyzed through the computation of eigenvalues for small perturbations and verified by direct simulations. In the cascading limit, which corresponds to a large mismatch q, the system becomes tantamount to the recently studied single-component lattice with two embedded sites carrying the cubic nonlinearity. The modes undergo qualitative changes with the variation of q. In particular, at l⩾2, the symmetry-breaking bifurcation, which creates asymmetric states from symmetric ones, is supercritical and subcritical for small and large values of q, respectively, while the bifurcation is always supercritical at l=1. In the experiment, the corresponding change of the phase transition between the second and first kinds may be implemented by varying the mismatch, via the wavelength of the input beam. The existence threshold (minimum total power) for the symmetric modes vanishes exactly at q=0, which suggests a possibility to create the solitary mode using low-power beams. The stability of solution families also changes with q.
Li, Yang; Wilson, Justin J; Do, Loi H; Apfel, Ulf-Peter; Lippard, Stephen J
2012-08-21
A triptycene-based bis(benzoxazole) diacid ligand H(2)L2(Ph4) bearing sterically encumbering groups was synthesized. Treatment of H(2)L2(Ph4) with Fe(OTf)(3) afforded a C(2)-symmetric trinuclear iron(III) complex, [NaFe(3)(L2(Ph4))(2)(μ(3)-O)(μ-O(2)CCPh(3))(2)(H(2)O)(3)](OTf)(2) (8). The triiron core of this complex adopts the well known "basic iron acetate" structure where the heteroleptic carboxylates, comprising two Ph(3)CCO(2)(-) and two (L2(Ph4))(2-) ligands, donate the six carboxylate bridges. The (L2(Ph4))(2-) ligand undergoes only minor conformational changes upon formation of the complex. PMID:22751622
Overlapping community detection in complex networks using symmetric binary matrix factorization.
Zhang, Zhong-Yuan; Wang, Yong; Ahn, Yong-Yeol
2013-06-01
Discovering overlapping community structures is a crucial step to understanding the structure and dynamics of many networks. In this paper we develop a symmetric binary matrix factorization model to identify overlapping communities. Our model allows us not only to assign community memberships explicitly to nodes, but also to distinguish outliers from overlapping nodes. In addition, we propose a modified partition density to evaluate the quality of community structures. We use this to determine the most appropriate number of communities. We evaluate our methods using both synthetic benchmarks and real-world networks, demonstrating the effectiveness of our approach. PMID:23848725
Linear Viscoelasticity and Swelling of Polyelectrolyte Complex Coacervates
NASA Astrophysics Data System (ADS)
Hamad, Fawzi; Colby, Ralph
2012-02-01
The addition of near equimolar amounts of poly(diallyldimethylammonium chloride) to poly(isobutylene-alt-maleate sodium), results in formation of a polyelectrolyte complex coacervate. Zeta-potential titrations conclude that these PE-complexes are nearly charge-neutral. Swelling and rheological properties are studied at different salt concentrations in the surrounding solution. The enhanced swelling observed at high salt concentration suggests the system behaves like a polyampholyte gel, and weaker swelling at very low salt concentrations implies polyelectrolyte gel behavior. Linear viscoelastic oscillatory shear measurements indicate that the coacervates are viscoelastic liquids and that increasing ionic strength of the medium weakens the electrostatic interactions between charged units, lowering the relaxation time and viscosity. We use the time-salt superposition idea recently proposed by Spruijt, et al., allowing us to construct master curves for these soft materials. Similar swelling properties observed when varying molecular weights. Rheological measurements reveal that PE-complexes with increasing molecular weight polyelectrolytes form a network with higher crosslink density, suggesting time-molecular weight superposition idea.
Data bank homology search algorithm with linear computation complexity.
Strelets, V B; Ptitsyn, A A; Milanesi, L; Lim, H A
1994-06-01
A new algorithm for data bank homology search is proposed. The principal advantages of the new algorithm are: (i) linear computation complexity; (ii) low memory requirements; and (iii) high sensitivity to the presence of local region homology. The algorithm first calculates indicative matrices of k-tuple 'realization' in the query sequence and then searches for an appropriate number of matching k-tuples within a narrow range in database sequences. It does not require k-tuple coordinates tabulation and in-memory placement for database sequences. The algorithm is implemented in a program for execution on PC-compatible computers and tested on PIR and GenBank databases with good results. A few modifications designed to improve the selectivity are also discussed. As an application example, the search for homology of the mouse homeotic protein HOX 3.1 is given. PMID:7922689
Complex dynamics in the Oregonator model with linear delayed feedback
NASA Astrophysics Data System (ADS)
Sriram, K.; Bernard, S.
2008-06-01
The Belousov-Zhabotinsky (BZ) reaction can display a rich dynamics when a delayed feedback is applied. We used the Oregonator model of the oscillating BZ reaction to explore the dynamics brought about by a linear delayed feedback. The time-delayed feedback can generate a succession of complex dynamics: period-doubling bifurcation route to chaos; amplitude death; fat, wrinkled, fractal, and broken tori; and mixed-mode oscillations. We observed that this dynamics arises due to a delay-driven transition, or toggling of the system between large and small amplitude oscillations, through a canard bifurcation. We used a combination of numerical bifurcation continuation techniques and other numerical methods to explore the dynamics in the strength of feedback-delay space. We observed that the period-doubling and quasiperiodic route to chaos span a low-dimensional subspace, perhaps due to the trapping of the trajectories in the small amplitude regime near the canard; and the trapped chaotic trajectories get ejected from the small amplitude regime due to a crowding effect to generate chaotic-excitable spikes. We also qualitatively explained the observed dynamics by projecting a three-dimensional phase portrait of the delayed dynamics on the two-dimensional nullclines. This is the first instance in which it is shown that the interaction of delay and canard can bring about complex dynamics.
NASA Astrophysics Data System (ADS)
Erickson, John; Neidhart, David J.; Vandrie, John; Kempf, Dale J.; Wang, Xiu Chun; Norbeck, Daniel W.; Plattner, Jacob J.; Rittenhouse, Judith W.; Turon, Mary; Wideburg, Norman; Kohlbrenner, William E.; Simmer, Robert; Helfrich, Rosalind; Paul, Deborah A.; Knigge, Mark
1990-08-01
A two-fold (C_2) symmetric inhibitor of the protease of human immunodeficiency virus type-1 (HIV-1) has been designed on the basis of the three-dimensional symmetry of the enzyme active site. The symmetric molecule inhibited both protease activity and acute HIV-1 infection in vitro, was at least 10,000-fold more potent against HIV-1 protease than against related enzymes, and appeared to be stable to degradative enzymes. The 2.8 angstrom crystal structure of the inhibitor-enzyme complex demonstrated that the inhibitor binds to the enzyme in a highly symmetric fashion.
Hasan, Mohammad; Ghatak, Ananya; Mandal, Bhabani Prasad
2014-05-15
We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. -- Highlights: •Energy ranges for CC and CPA are obtained explicitly for complex WS potential. •Analytical conditions for CC and CPA for PT symmetric WS potential are obtained. •Conditions for left and right CC are shown to be different. •Conditions for CC and CPA are shown to be that of SS for the time reversed system. •Our model shows the great flexibility of frequencies for CC and CPA.
Isomeric interconversion in the linear Cl--HD anion complex
NASA Astrophysics Data System (ADS)
Wilson, R. L.; Loh, Z. M.; Wild, D. A.; Bieske, E. J.; Buchachenko, A. A.
2004-08-01
The rotationally resolved infrared photodissociation spectrum of Cl--HD is measured in the HD stretch region. Two Σ-Σ bands are observed, corresponding to transitions from the ground state [the (vHD=0, n=0) level] and first excited intermolecular bend state [the (vHD=0, n=1) level]. The (vHD=0, n=0) and (vHD=0, n=1) states are predominantly associated with the linear Cl-⋯DH and Cl-⋯HD geometries, respectively. The spectrum is complicated by perturbative interactions between levels of the (vHD=0, n=0) and (vHD=0, n=1) rotational manifolds and between levels of the (vHD=1, n=0) and (vHD=1, n=1) rotational manifolds. A global fit to the transition frequencies, taking the lower and upper state perturbations into account, yields zero-order rotational and centrifugal distortion constants and allows us to establish that the (vHD=0, n=1, J″=0) level lies 13.7 cm-1 above the (vHD=0, n=0, J″=0) level. Rovibrational energy level calculations performed using a recent ab initio potential energy surface confirm the picture emerging from the experimental data and provide good agreement with measured molecular parameters. The results emphasize the importance of quantum mechanical interconversion between two isomeric structures of a simple anion complex.
Lolli, Graziano; Ranchio, Alessandro; Battistutta, Roberto
2014-02-21
CK2 is a protein kinase essential for cell viability whose activity is altered in several cancers. Its mechanisms of regulation differ from those common to other eukaryotic protein kinases and are not entirely established yet. Here we present crystal structures of the monomeric form of the α2β2 holoenzyme that allow refining a formerly proposed structural model for activity regulation by oligomerization. Previous crystal structures of the CK2 holoenzyme show an asymmetric arrangement of the two α catalytic subunits around the obligate β2 regulatory subunits. Asymmetric α2β2 tetramers are organized in trimeric rings that correspond to inactive forms of the enzyme. The new crystal structures presented here reveal the symmetric architecture of the isolated active tetramers. The dimension and the nature of the α/β interfaces configure the holoenzyme as a strong complex that does not spontaneously dissociate in solution, in accordance with the low dissociation constant (∼4 nM). PMID:24175891
Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Phan, Huy P.
2016-01-01
The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…
Çay, Sevim; Köse, Muhammet; Tümer, Ferhan; Gölcü, Ayşegül; Tümer, Mehmet
2015-12-01
4-Methoxy-2,6-bis(hydroxymethyl)phenol (1) was prepared from the reaction of 4-methoxyphenol and formaldehyde. The compound (1) was then oxidized to the 4-methoxy-2,6-diformylphenol (2) compound. Molecular structure of compound (2) was determined by X-ray diffraction method. A new symmetric porphyrin Schiff base ligand 4-methoxy-2,6-bis[5-(4-iminophenyl)-10,15,20-triphenylporphyrin]phenol (L) was prepared from the reaction of the 5-(4-aminophenyl)-10,15,20-triphenylporphyrin (TTP-NH2) and the compound (2) in the toluene solution. The metal complexes (Cu(II), Fe(III), Mn(III), Pt(II) and Zn(II)) of the ligand (L) were synthesized and characterized by the spectroscopic and analytical methods. The DNA (fish sperm FSdsDNA) binding studies of the ligand and its complexes were performed using UV-vis spectroscopy. Additionally, superoxide dismutase activities of the porphyrin Schiff base metal complexes were investigated. Additionally, electrochemical, photoluminescence and thermal properties of the compounds were investigated. PMID:26172470
Gerdes, Allison; Bond, Marcus R
2009-10-01
The title compound, (C2H8N)8[Ni3Cl12]Cl2, crystallizes as linear [Ni3Cl12]6- complex anions with inversion symmetry, separated from one another by dimethylammonium cations and noncoordinated chloride ions. The gross structural arrangement of the trinickel complex is as a segment of face-sharing NiCl6 octahedra similar to the (NiCl3)n chains of CsNiCl3-type compounds. On closer inspection, the regular coordination geometry of the complex consists of octahedral NiCl6 in the center linked by two symmetrically bridging chloride ions to square-pyramidal NiCl5 on each end. A long semicoordinate bond is formed by each of the terminal Ni(II) cations, to give a 5+1 coordination geometry and form an asymmetric bridge to the central Ni(II) cation. The dimethylammonium cations surround the complex with an extensive hydrogen-bonding network, linking the complex to the noncoordinated chloride ions. Asymmetric bridging in the complex arises from short hydrogen bonds from the same dimethylammonium cation to the apical and asymmetric bridging chloride ions, causing the complex to scissor outward. PMID:19805875
Zhang, Xuepeng; Xu, Xianyan; Xu, Huiying; Zhang, Xiting; Phillips, David Lee; Zhao, Cunyuan
2014-06-23
Density functional calculations are utilized to explore the hydrolysis mechanisms of the phosphomonoester 4-nitrophenyl phosphate catalyzed by a symmetrical zinc(II) complex. The formation process and properties of the active catalyst are verified. Eight plausible mechanisms are proposed and categorized into three groups. All of the proposed mechanisms, except for Mechanism 7 (see text), are S(N)2-type addition-substitution reaction pathways. Nucleophilic attack at the ortho position occurs in Mechanism 7 with a relatively high reaction barrier. Mechanisms 1 and 2 in the monocatalyst model, Mechanisms 5 to 7 in the sandwich-dual-catalyst model, as well as the nucleophilic addition-substitution step in Mechanism 8 are concerted reaction pathways, whereas the rest appear to occur in a stepwise manner. Meanwhile, the explicit solvent model is utilized to consider direct hydrogen bonds and solvation interactions and these results indicate that the added water molecule is involved in the hydrolysis process, but does not change the mechanisms significantly. Mechanism 8, with the lowest reaction barrier, is the most favored reaction pathway of the eight proposed mechanisms, although Mechanisms 1, 4, and 6 are in competition with Mechanism 8. In consideration of the zinc(II) complex concentration, Mechanism 1 is only the predominant reaction pathway at a low zinc(II) complex concentration; Mechanisms 4 and 6 tend to be more competitive with increasing concentration of the zinc(II) complexes, and Mechanism 8 is favored at high zinc(II) complex concentrations. Our calculated results are consistent with, and can be used to systematically interpret, experimental observations. More importantly, insightful suggestions are made regarding the catalyst design and selection of the reaction environment. PMID:24692392
Complex modes and solvability of nonclassical linear systems
NASA Astrophysics Data System (ADS)
Caughey, T. K.; Ma, F.
1993-03-01
Some basic properties of nonclassical linear systems are examined to determine necessary and sufficient conditions under which nonclassical linear systems can be decoupled or become solvable in n-space. It was found that a necessary and sufficient condition under which a nonclassical system can be decoupled is for the coefficient matrices M, C, and K (where M is the mass matrix, C is the damping matrix, and K is the stiffness matrix) to be diagonalizable and pairwise commutative.
On the solutions of some linear complex quaternionic equations.
Bolat, Cennet; İpek, Ahmet
2014-01-01
Some complex quaternionic equations in the type AX - XB = C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained. PMID:25101318
NASA Astrophysics Data System (ADS)
Albin, Michael; de, William; Horrocks, W., Jr.; Liotta, Frank J.
1982-01-01
The Eu(III) complex of the octadentate macrocyclic ligand, 1,4,7,10-tetraazacyclododecane-N,N',N'',N''' -tetraacetate, DOTA, has been examined by luminescence excitation, emission, and lifetime spectroscopy using pulsed dye laser techniques. The results confirm the expected axially symmetric nature of the major component in solution and reveal that 1.2 ± 0.4 water molecules arc coordinatcd to the Eu(III) ion in the complex.
Gross, Joshua B.; Krutzler, Amanda J.; Carlson, Brian M.
2014-01-01
The genetic regulators of regressive craniofacial morphologies are poorly understood. To shed light on this problem, we examined the freshwater fish Astyanax mexicanus, a species with surface-dwelling and multiple independent eyeless cave-dwelling forms. Changes affecting the skull in cavefish include morphological alterations to the intramembranous circumorbital bones encircling the eye. Many of these modifications, however, have evolved separately from eye loss, such as fragmentation of the third suborbital bone. To understand the genetic architecture of these eye-independent craniofacial alterations, we developed and scored 33 phenotypes in the context of an F2 hybrid mapping pedigree bred from Pachón cavefish and surface fish. We discovered several individuals exhibiting dramatic left–right differences in bone formation, such as extensive fragmentation on the right side only. This observation, along with well-known eye size asymmetry in natural cave-dwelling animals, led us to further evaluate left–right genetic differences for the craniofacial complex. We discovered three phenotypes, inclusive of bone fragmentation and fusion, which demonstrated a directional heritable basis only on one side. Interestingly, the overall areas of affected bones were genetically symmetric. Phenotypic effect plots of these novel craniofacial QTL revealed that cave alleles are associated with abnormal conditions such as bony fusion and fragmentation. Moreover, many linked loci overlapped with other cave-associated traits, suggesting regressive craniofacial changes may evolve through linkage or as antagonistic pleiotropic consequences of cave-associated adaptations. These novel findings illuminate significant craniofacial changes accompanying evolution in complete darkness and reveal complex changes to the skull differentially influenced by genetic changes affecting the left and right sides. PMID:24496009
Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo
2015-01-01
Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. PMID:26345131
Stability and complexity of small random linear systems
NASA Astrophysics Data System (ADS)
Hastings, Harold
2010-03-01
We explore the stability of the small random linear systems, typically involving 10-20 variables, motivated by dynamics of the world trade network and the US and Canadian power grid. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof.
Quantifying Stability in Complex Networks: From Linear to Basin Stability
NASA Astrophysics Data System (ADS)
Kurths, Jürgen
The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. Specifically, we employ a component-wise version of basin stability, a nonlinear inspection scheme, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. Various statistics from our ensemble simulations all support one main finding: The widespread and cheapest of all connection schemes, namely dead ends and dead trees, strongly diminish stability. For the Northern European power system we demonstrate that the inverse is also true: `Healing' dead ends by addition of transmission lines substantially enhances stability. This indicates a crucial smart-design principle for tomorrow's sustainable power grids: add just a few more lines to avoid dead ends. Further, we analyse the particular function of certain network motifs to promote the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design. Moreover, it will be shown that basin stability enables uncovering the mechanism for explosive synchronization and understanding of evolving networks. Reference: P. Menck, J. Heitzig, N. Marwan, and J. Kurths, Nature Physics 9, 89 (2013) P. Menck, J. Heitzig, J. Kurths, and H. Schellnhuber, Nature Communication 5, 3969 (2014) P. Schultz, J. Heitzig, and J. Kurths, New Journal Physics 16, 125001 (2014) V. Kohar, P. Ji, A. Choudhary, S. Sinha, and J. Kurths, Phys. Rev. E 90, 022812 (2014) Y. Zou, T. Pereira, M. Small, Z. Liu, and J. Kurths, Phys. Rev. Lett. 112, 114102 (2014)
Chemical bonding in a linear chromium metal string complex.
Wu, Lai-Chin; Thomsen, Maja K; Madsen, Solveig R; Schmoekel, Mette; Jørgensen, Mads R V; Cheng, Ming-Chuan; Peng, Shie-Ming; Chen, Yu-Sheng; Overgaard, Jacob; Iversen, Bo B
2014-12-01
A combined experimental and theoretical electron density study of the shortest trichromium metal wire, Cr3(dpa)4Cl2·(C2H5OC2H5)(x)(CH2Cl2)(1-x) (1, dpa = bis(2-pyridyl)amido), is reported. High resolution X-ray diffraction data has been collected both at 100 K using a conventional X-ray source (DS1) and at 15 K using a synchrotron X-ray source (DS2). The linear chromium string is terminated by Cl(-) ions at both ends, and each Cr atom is also coordinated by four N atoms from bridging dpa ligands. The two Cr-Cr bond distances are unequal at 100 K (with d(Cr1-Cr2) being 0.029 Å shorter than d(Cr2-Cr3)) but at 15 K they are almost equal (0.002 Å difference). Analysis of the slightly elongated thermal ellipsoids of the Cr2 atom suggests that it is not due to disorder, but the presence of a shallow potential energy surface. Laplacian maps clearly show local valence shell charge concentration (VSCC) in the electron density along the bisector of the equatorial Cr-N bonds. Integration over the atomic basins indicates that Cr2 has smaller atomic charge and volume than Cr1 and Cr3. The topological characterization of the Cr-Cr bonds indicates partly covalent characters with electron density at the bond critical point of ∼0.3 e Å(-3) and negative total energy density. The delocalization index of Cr-Cr is 0.8 for Cr1-Cr2 and 0.08 for Cr1-Cr3. Second-order perturbation analysis shows high stabilization energy of the Cr-Cr bonds (E(2) ∼ 190 kcal mol(-1)). Delocalization indices and source function and natural bond orbital analyses are all indicative of localized Cr-Cr bonding interactions. PMID:25383889
Humphries, T D; Sheppard, D A; Buckley, C E
2015-06-30
For homoleptic 18-electron complex hydrides, an inverse linear correlation has been established between the T-deuterium bond length (T = Fe, Co, Ni) and the average electronegativity of the metal countercations. This relationship can be further employed towards aiding structural solutions and predicting physical properties of novel complex transition metal hydrides. PMID:26077621
K?os, J S; Sommer, J-U
2011-05-28
We study complexes composed of one dendrimer of generation G = 4 (G4 dendrimer) with N(t) = 32 charged terminal groups and an oppositely charged linear polyelectrolyte accompanied by neutralizing counterions in an athermal solvent using Monte Carlo simulations based on the bond fluctuation model. In our study both the full Coulomb potential and the excluded volume interactions are taken into account explicitly with the reduced temperature ? and the chain length N(ch) as the main simulation parameters. Our calculations indicate that there exist three temperature ranges that determine the behavior of such complexes. At ?(complex) stable charged dendrimer-linear polyelectrolyte complexes are formed first, which are subsequently accompanied by selective counterion localization within the complex interior at ?(loc) ? ?(complex), and counterion condensation as temperature is further decreased below ?(cond) < ?(loc). In particular, we observe that condensation takes place exclusively on the excess charges in the complex and thus no condensation is observed at the compensation point (N(ch) = N(t)), irrespective of ?. For N(ch) ? N(t) the complex is overally charged. Furthermore, we discuss the size and structure of the dendrimer and the linear polyelectrolyte within the complex, as well as spatial distributions of monomers and counterions. Conformations of the chain in the bound state are analysed in terms of loops, trains, and tails. PMID:21639472
Kotani, Shunsuke; Kai, Kosuke; Shimoda, Yasushi; Hu, Hao; Gao, Shen; Sugiura, Masaharu; Ogasawara, Masamichi; Nakajima, Makoto
2016-02-01
By using a phosphine oxide-catalyzed enantioselective double aldol reaction, we achieved the concise construction of C2 -symmetric 1,9-diarylnonanoids, enabling the synthesis of (-)-ericanone from p-hydroxybenzaldehyde in 6 steps with 65 % overall yield. The enantioselective double aldol reaction is useful for establishing C2 -symmetric 1,9-diaryl-3,7-dihydroxy-5-nonanones with a single operation. Furthermore, the use of o-nosyl-protected p-hydroxybenzaldehyde and a 4,4'-disubstituted BINAP dioxide catalyst dramatically improved the reactivity and selectivity in the double aldol reaction, enabling the total synthesis of (-)-ericanone with high yield and with excellent enantiopurity. PMID:26610889
Some comparisons of complexity in dictionary-based and linear computational models.
Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello
2011-03-01
Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator. PMID:21094023
NASA Astrophysics Data System (ADS)
Bahaffi, Saleh O.; Abdel Aziz, Ayman A.; El-Naggar, Maher M.
2012-08-01
A novel series of four copper(II) complexes were synthesized by thermal reaction of copper acetate salt with symmetrical tetradentate Schiff bases, N,N'bis(o-vanillin)4,5-dimethyl-l,2-phenylenediamine (H2L1), N,N'bis(salicylaldehyde)4,5-dimethyl-1,2-phenylenediamine (H2L2), N,N'bis(o-vanillin)4,5-dichloro-1,2-phenylenediamine (H2L3) and N,N'bis(salicylaldehyde)4,5-dichloro-1,2-phenylenediamine (H2L4), respectively. All the new synthesized complexes were characterized by using of microanalysis, FT-IR, UV-Vis, magnetic measurements, ESR, and conductance measurements, respectively. The data revealed that all the Schiff bases (H2L1-4) coordinate in their deprotonated forms and behave as tetradentate NOON coordinated ligands. Moreover, their copper(II) complexes have square planar geometry with general formula [CuL1-4]. The binding of the complexes with calf thymus DNA (CT-DNA) was investigated by UV-Vis spectrophotometry, fluorescence quenching and viscosity measurements. The results indicated that the complexes bind to CT-DNA through an intercalative mode. From the biological activity view, the copper(II) complexes and their parent ligands were screened for their in vitro antibacterial activity against the bacterial species Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli and Pseudomonas aeruginosai by well diffusion method. The complexes showed an increased activity in comparison to some standard drugs.
Hodgkinson, Roy; Del Grosso, Alessandro; Clarkson, Guy; Wills, Martin
2016-02-18
A series of complexes containing the iron-cyclopentadienone structure were prepared by cyclising bis-propargylic alcohols and their derivatives with iron pentacarbonyl. The resulting complexes were characterised and tested in the catalysis of ketone reduction and alcohol oxidation. The complexes are competent catalysts for ketone reduction and alcohol oxidations. PMID:26837422
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier; Gutierrez, German
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Nonlinear {PT}-symmetric plaquettes
NASA Astrophysics Data System (ADS)
Li, Kai; Kevrekidis, P. G.; Malomed, Boris A.; Günther, Uwe
2012-11-01
We introduce four basic two-dimensional (2D) plaquette configurations with onsite cubic nonlinearities, which may be used as building blocks for 2D {PT}-symmetric lattices. For each configuration, we develop a dynamical model and examine its {P} {T}symmetry. The corresponding nonlinear modes are analyzed starting from the Hamiltonian limit, with zero value of the gain-loss coefficient, γ. Once the relevant waveforms have been identified (chiefly, in an analytical form), their stability is examined by means of linearization in the vicinity of stationary points. This reveals diverse and, occasionally, fairly complex bifurcations. The evolution of unstable modes is explored by means of direct simulations. In particular, stable localized modes are found in these systems, although the majority of identified solutions are unstable. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Lenaeus, Michael J; Burdette, Dylan; Wagner, Tobias; Focia, Pamela J; Gross, Adrian
2014-08-19
Potassium channels allow for the passive movement of potassium ions across the cell membrane and are instrumental in controlling the membrane potential in all cell types. Quaternary ammonium (QA) compounds block potassium channels and have long been used to study the functional and structural properties of these channels. Here we describe the interaction between three symmetrical hydrophobic QAs and the prokaryotic potassium channel KcsA. The structures demonstrate the presence of a hydrophobic pocket between the inner helices of KcsA and provide insight into the binding site and blocking mechanism of hydrophobic QAs. The structures also reveal a structurally hidden pathway between the central cavity and the outside membrane environment reminiscent of the lateral fenestration observed in sodium channels that can be accessed through small conformational changes in the pore wall. We propose that the hydrophobic binding pocket stabilizes the alkyl chains of long-chain QA molecules and may play a key role in hydrophobic drug binding in general. PMID:25093676
2015-01-01
Potassium channels allow for the passive movement of potassium ions across the cell membrane and are instrumental in controlling the membrane potential in all cell types. Quaternary ammonium (QA) compounds block potassium channels and have long been used to study the functional and structural properties of these channels. Here we describe the interaction between three symmetrical hydrophobic QAs and the prokaryotic potassium channel KcsA. The structures demonstrate the presence of a hydrophobic pocket between the inner helices of KcsA and provide insight into the binding site and blocking mechanism of hydrophobic QAs. The structures also reveal a structurally hidden pathway between the central cavity and the outside membrane environment reminiscent of the lateral fenestration observed in sodium channels that can be accessed through small conformational changes in the pore wall. We propose that the hydrophobic binding pocket stabilizes the alkyl chains of long-chain QA molecules and may play a key role in hydrophobic drug binding in general. PMID:25093676
Observation of Defect States in PT-Symmetric Optical Lattices
NASA Astrophysics Data System (ADS)
Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Näger, Jakob; Onishchukov, Georgy; Christodoulides, Demetrios N.; Peschel, Ulf
2013-05-01
We provide the first experimental demonstration of defect states in parity-time (PT) symmetric mesh-periodic potentials. Our results indicate that these localized modes can undergo an abrupt phase transition in spite of the fact that they remain localized in a PT-symmetric periodic environment. Even more intriguing is the possibility of observing a linearly growing radiation emission from such defects provided their eigenvalue is associated with an exceptional point that resides within the continuum part of the spectrum. Localized complex modes existing outside the band-gap regions are also reported along with their evolution dynamics.
An enzyme-centric approach for modelling non-linear biological complexity
2008-01-01
Background The current challenge of Systems Biology is to integrate high throughput data sets for simulating the complexity of biological networks, exploit the evolution of nature-designed networks that maintain the robustness of a biological system, and thereby generate novel, experimentally testable hypotheses. In order to simulate non-linear biological complexities, we have previously developed an Enzyme-Centric mechanistic modeling approach and validated it using metabolic network in E. coli. The idea is to use prior knowledge of catalytic and regulatory mechanisms of each enzyme within the metabolic network to build a dynamic model for investigating the network level regulation and thus understand the nature design principle behind the network. Results In this paper, we further demonstrate the application of complex enzyme catalytic and regulatory modules to simulate nonlinear network regulatory patterns vs. simple linear conversion model. We learned and validated that it is essential to incorporate prior knowledge from the literature to simulate non-linear biological complexities. The network expandability is demonstrated and validated with the complex amino acid biosynthetic network with multi-regulations. Also, we demonstrated the compatibility of mechanistic models within close species. Furthermore, the eukaryotic protein factory model for insuring steady mRNA production is simulated and the coupling of RNA transcription and splicing is validated by both mathematical simulation and experimental analysis. Conclusion We demonstrated the importance of modeling complex enzyme catalytic and regulatory mechanisms to further understand nonlinear network regulatory patterns. The simulations presented in this paper reveal how a living system maintains homeostasis and its robustness to continue functioning while facing environmental stresses or genetic mutations. PMID:18671883
NASA Astrophysics Data System (ADS)
Wang, Hu; Meng, Xiangmin; Fan, Chuanbin; Fan, Yuhua; Bi, Caifeng
2016-03-01
A new complex, Ni(C22H26N2O10S2)·2CH3OH, with a sexidentate (N2O4) symmetric bis-Schiff base ligand (C22H26N2O10S2 = 1,2-bis(2-methoxy-6-formylphenoxy)ethane-2-aminoethane-sulfonic acid) has been synthesized and characterized by physico-chemical and spectroscopic methods. The X-ray crystal structure shows that the Ni(II) atom of the complex is six-coordinated by two nitrogens from Cdbnd N groups, two oxygens from ether groups and two hydroxyl oxygens from sulfonic acid groups in the mono-ligand, forming a distorted octahedral geometry. Theoretical study of the complex is carried out by density functional theory (DFT) method and the B3LYP method employing the 6-3l+G* basis set. Moreover, the complex proved to be good candidate for the photocatalytic degradation of methylene blue.
The linear ubiquitin assembly complex (LUBAC) is essential for NLRP3 inflammasome activation
Rodgers, Mary A.; Bowman, James W.; Fujita, Hiroaki; Orazio, Nicole; Shi, Mude; Liang, Qiming; Amatya, Rina; Kelly, Thomas J.; Iwai, Kazuhiro; Ting, Jenny
2014-01-01
Linear ubiquitination is a newly discovered posttranslational modification that is currently restricted to a small number of known protein substrates. The linear ubiquitination assembly complex (LUBAC), consisting of HOIL-1L, HOIP, and Sharpin, has been reported to activate NF-κB–mediated transcription in response to receptor signaling by ligating linear ubiquitin chains to Nemo and Rip1. Despite recent advances, the detailed roles of LUBAC in immune cells remain elusive. We demonstrate a novel HOIL-1L function as an essential regulator of the activation of the NLRP3/ASC inflammasome in primary bone marrow–derived macrophages (BMDMs) independently of NF-κB activation. Mechanistically, HOIL-1L is required for assembly of the NLRP3/ASC inflammasome and the linear ubiquitination of ASC, which we identify as a novel LUBAC substrate. Consequently, we find that HOIL-1L−/− mice have reduced IL-1β secretion in response to in vivo NLRP3 stimulation and survive lethal challenge with LPS. Together, these data demonstrate that linear ubiquitination is required for NLRP3 inflammasome activation, defining the molecular events of NLRP3 inflammasome activation and expanding the role of LUBAC as an innate immune regulator. Furthermore, our observation is clinically relevant because patients lacking HOIL-1L expression suffer from pyogenic bacterial immunodeficiency, providing a potential new therapeutic target for enhancing inflammation in immunodeficient patients. PMID:24958845
Localized PT -symmetric directionally invisible scatterers
NASA Astrophysics Data System (ADS)
Hurwitz, Elisa; Gbur, Greg
2016-04-01
We demonstrate how to create localized PT -symmetric directionally invisible scatterers directly from a governing wave equation. Moreover, we can construct general non-PT -symmetric objects which exhibit directional invisibility, though such an effect is typically associated with PT -symmetric objects. Whereas previously the determining condition for an optical PT -symmetric device was a PT -symmetric complex refractive index, we show that a broader condition, requiring only the scattering potential to be PT -symmetric, leads to the same behavior. This enables the construction of PT -symmetric objects without a PT -symmetric complex refractive index, effectively doubling the number of possible invisible objects. Consequently, the set of gain-loss invisible objects is much broader than previously realized, and several examples are shown.
NASA Astrophysics Data System (ADS)
Gosálvez, Miguel A.; Otrokov, Mikhail M.; Ferrando, Nestor; Ryabishchenkova, Anastasia G.; Ayuela, Andres; Echenique, Pedro M.; Chulkov, Evgueni V.
2016-02-01
This is the first of two papers that introduce a general expression for the tracer diffusivity in complex, periodic energy landscapes with M distinct hop rates in one-, two-, and three-dimensional diluted systems (low-coverage, single-tracer limit). The present report focuses on the analysis of diffusion in systems where the end sites of the hops are located symmetrically with respect to the hop origins (symmetric hops), as encountered in many ideal surfaces and bulk materials. For diffusion in two dimensions, a number of formulas are presented for complex combinations of the different hops in systems with triangular, rectangular, and square symmetry. The formulas provide values in excellent agreement with kinetic Monte Carlo simulations, concluding that the diffusion coefficient can be directly determined from the proposed expressions without performing the simulations. Based on the diffusion barriers obtained from first-principles calculations and a physically meaningful estimate of the attempt frequencies, the proposed formulas are used to analyze the diffusion of Cu, Ag, and Rb adatoms on the surface and within the van der Waals (vdW) gap of a model topological insulator, Bi2Se3 . Considering the possibility of adsorbate intercalation from the terraces to the vdW gaps at morphological steps, we infer that, at low coverage and room temperature, (i) a majority of the Rb atoms bounce back at the steps and remain on the terraces, (ii) Cu atoms mostly intercalate into the vdW gap, the remaining fraction staying at the steps, and (iii) Ag atoms essentially accumulate at the steps and gradually intercalate into the vdW gap. These conclusions are in good qualitative agreement with previous experiments. The companion report (M. A. Gosálvez et al., Phys. Rev. B, submitted] extends the present study to the description of systems that contain asymmetric hops.
Boussie, T.R.
1991-10-01
A reproducible, high-yield synthesis of mono([8]annulene)uranium(4)dichloride (1) is reported, along with the X-ray crystal structural of the bis(pyridine) adduct. Metathesis reactions of the half-sandwich complex 1 with a variety of simple alkyl and alkoxy reagents failed to generate any isolable mono-ring complexes. Reactions of 1 with polydentate, delocalized anions did produce stable derivatives, including mono([8]annulene)uranium(4)bis(acetylacetonate) (4). An X-ray crystal structure of 4 is reported.
Boussie, T.R.
1991-10-01
A reproducible, high-yield synthesis of mono((8)annulene)uranium(4)dichloride (1) is reported, along with the X-ray crystal structural of the bis(pyridine) adduct. Metathesis reactions of the half-sandwich complex 1 with a variety of simple alkyl and alkoxy reagents failed to generate any isolable mono-ring complexes. Reactions of 1 with polydentate, delocalized anions did produce stable derivatives, including mono((8)annulene)uranium(4)bis(acetylacetonate) (4). An X-ray crystal structure of 4 is reported.
Cotton, Stephen J; Miller, William H
2016-03-01
In a recent series of papers, it has been illustrated that a symmetrical quasi-classical (SQC) windowing model applied to the Meyer-Miller (MM) classical vibronic Hamiltonian provides an excellent description of a variety of electronically non-adiabatic benchmark model systems for which exact quantum results are available for comparison. In this paper, the SQC/MM approach is used to treat energy transfer dynamics in site-exciton models of light-harvesting complexes, and in particular, the well-known 7-state Fenna-Mathews-Olson (FMO) complex. Again, numerically "exact" results are available for comparison, here via the hierarchical equation of motion (HEOM) approach of Ishizaki and Fleming, and it is seen that the simple SQC/MM approach provides very reasonable agreement with the previous HEOM results. It is noted, however, that unlike most (if not all) simple approaches for treating these systems, because the SQC/MM approach presents a fully atomistic simulation based on classical trajectory simulation, it places no restrictions on the characteristics of the thermal baths coupled to each two-level site, e.g., bath spectral densities (SD) of any analytic functional form may be employed as well as discrete SD determined experimentally or from MD simulation (nor is there any restriction that the baths be harmonic), opening up the possibility of simulating more realistic variations on the basic site-exciton framework for describing the non-adiabatic dynamics of photosynthetic pigment complexes. PMID:26761191
Armieri, Albert; Holmes, Jeffrey D; Spaulding, Sandi J; Jenkins, Mary E; Johnson, Andrew M
2009-02-01
The ability to execute and maintain gait while performing simultaneous cognitive, verbal, or motor tasks ('dual-tasking') is beneficial in many ways. It is well-documented, however, that dual-tasking can result in cognitive or motoric interference that results in diminished gait performance, and impaired secondary task performance. When manipulating cognitive load, it is common to have participants respond verbally to stimuli. While this is an ecologically valid way to measure the effects of cognitive load on gait, it ignores the additional demands inherent in the verbal aspect of the task. In the present study, we manipulated complexity and articulation within a single working memory task, in order to examine their relative impact on continuous spatiotemporal gait parameters. Fourteen healthy young adults (11 women) aged 18-30 (M=22.14, S.D.=2.28) were asked to memorize a random, non-repeating, sequence of three, five, or seven digits. Articulation was manipulated by either having participants rehearse the digits aloud, or rehearse the digits silently during the performance of the gait task. Gait parameters were quantified with a GAITRite instrumented carpet. Velocity, step time, swing time, and stance time demonstrated a significant (p<0.05) interaction between complexity and articulation, with articulation having a greater effect at higher levels of complexity. These results suggest that verbal secondary tasks may actually create a 'triple-task' in which the cognitive complexity of the task interacts with both the articulatory demands of the response modality, and the motoric demands of the gait task. PMID:18951799
ERIC Educational Resources Information Center
de Villiers, Michael
2011-01-01
Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…
ERIC Educational Resources Information Center
de Villiers, Michael
2011-01-01
Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and
NASA Astrophysics Data System (ADS)
Derouich, M.; Barklem, P. S.
2007-02-01
Aims: We develop an accurate and general semi-classical formalism that deals with the definition and the calculation of the collisional depolarizing constants of the levels of simple and complex singly-ionized atoms in arbitrary s-states perturbed by collisions with hydrogen atoms. The case of ions with hyperfine structure is investigated fully. Methods: We obtain potential energy curves based on the MSMA exchange perturbation theory by employing the Unsöld approximation. These potentials enter the Schrödinger equation to determine the collisional T-matrix elements in a semi-classical description. We use the T-matrix elements for the calculation of the collisional depolarization rates of simple atoms. Then, we use these rates to calculate the collisional coefficients in cases of ions with hyperfine structure. Results: We evaluate the collisional depolarization and polarization transfer rates of the ground levels of the ionized alkaline earth metals Be II, Mg II, Ca II, Sr II, and Ba II. We study the variation of the collisional rates with effective principal quantum number n* characterizing an arbitrary s-state of a perturbed simple ion. We find that the collisional rates for simple ions obey simple power laws as a function of n^*. We present direct and indirect formulations of the problem of the calculation of the depolarization and polarization transfer rates of levels of complex atoms and hyperfine levels from those for simple atoms. In particular, the indirect method allows a quick and simple calculation with its simple power-law relations. For the state 4s ^2S{1/2} of Ca II, our computed rate of the destruction of orientation differs from existing quantum chemistry calculations by only 4% at T=5000 K.
Leiger, Kristjan; Freiberg, Arvi
2016-01-01
Weak up-converted fluorescence related to bacteriochlorophyll a was recorded from various detergent-isolated and membrane-embedded light-harvesting pigment-protein complexes as well as from the functional membranes of photosynthetic purple bacteria under continuous-wave infrared laser excitation at 1064 nm, far outside the optically allowed singlet absorption bands of the chromophore. The fluorescence increases linearly with the excitation power, distinguishing it from the previously observed two-photon excited fluorescence upon femtosecond pulse excitation. Possible mechanisms of this excitation are discussed. PMID:25764015
Poulos, S.G.
1987-05-12
A high symmetry intake manifold is described for an internal combustion engine. The manifold comprises: an inlet plenum with a flat floor extending along an inlet plane and outlet means defining an outlet plane, the planes being spaced on a common axis normal to both; and equal length runners connecting inlet openings in the floor and lying along the inlet plane with linearly equidistant outlet openings in outlet means and lying along the outlet plane. The inlet openings are spaced in the floor on a circle centered on the axis and the outlet openings are linearly aligned in the outlet means with the outlet axis intersecting the plane at the midpoint between outer most ones of the outlet openings.
Linear Superposition and Prediction of Bacterial Promoter Activity Dynamics in Complex Conditions
Rothschild, Daphna; Dekel, Erez; Hausser, Jean; Bren, Anat; Aidelberg, Guy; Szekely, Pablo; Alon, Uri
2014-01-01
Bacteria often face complex environments. We asked how gene expression in complex conditions relates to expression in simpler conditions. To address this, we obtained accurate promoter activity dynamical measurements on 94 genes in E. coli in environments made up of all possible combinations of four nutrients and stresses. We find that the dynamics across conditions is well described by two principal component curves specific to each promoter. As a result, the promoter activity dynamics in a combination of conditions is a weighted average of the dynamics in each condition alone. The weights tend to sum up to approximately one. This weighted-average property, called linear superposition, allows predicting the promoter activity dynamics in a combination of conditions based on measurements of pairs of conditions. If these findings apply more generally, they can vastly reduce the number of experiments needed to understand how E. coli responds to the combinatorially huge space of possible environments. PMID:24809350
A non-canonical UBAUBL interaction forms the linear-ubiquitin-chain assembly complex
Yagi, Hirokazu; Ishimoto, Kazuhiro; Hiromoto, Takeshi; Fujita, Hiroaki; Mizushima, Tsunehiro; Uekusa, Yoshinori; Yagi-Utsumi, Maho; Kurimoto, Eiji; Noda, Masanori; Uchiyama, Susumu; Tokunaga, Fuminori; Iwai, Kazuhiro; Kato, Koichi
2012-01-01
HOIL-1L and its binding partner HOIP are essential components of the E3-ligase complex that generates linear ubiquitin (Ub) chains, which are critical regulators of NF-?B activation. Using crystallographic and mutational approaches, we characterize the unexpected structural basis for the specific interaction between the Ub-like domain (UBL) of HOIL-1L and the Ub-associated domain (UBA) of HOIP. Our data indicate the functional significance of this non-canonical mode of UBAUBL interaction in E3 complex formation and subsequent NF-?B activation. This study highlights the versatility and specificity of proteinprotein interactions involving Ub/UBLs and their cognate proteins. PMID:22430200
Yang, Yibin; Schmitz, Roland; Mitala, Joseph; Whiting, Amanda; Xiao, Wenming; Ceribelli, Michele; Wright, George W.; Zhao, Hong; Yang, Yandan; Xu, Weihong; Rosenwald, Andreas; Ott, German; Gascoyne, Randy D.; Connors, Joseph M.; Rimsza, Lisa M.; Campo, Elias; Jaffe, Elaine S.; Delabie, Jan; Smeland, Erlend B.; Braziel, Rita M.; Tubbs, Raymond R.; Cook, James. R.; Weisenburger, Dennis D.; Chan, Wing C.; Wiestner, Adrian; Kruhlak, Michael J.; Iwai, Kazuhiro; Bernal, Federico; Staudt, Louis M.
2014-01-01
Constitutive activation of NF-κB is a hallmark of the activated B cell-like (ABC) subtype of diffuse large B cell lymphoma (DLBCL), owing to upstream signals from the B cell receptor (BCR) and MyD88 pathways. The linear polyubiquitin chain assembly complex (LUBAC) attaches linear polyubiquitin chains to IκB kinase γ, a necessary event in some pathways that engage NF-κB. Two germ line polymorphisms affecting the LUBAC subunit RNF31 are rare among healthy individuals (~1%) but enriched in ABC DLBCL (7.8%). These polymorphisms alter RNF31 α helices that mediate binding to the LUBAC subunit RBCK1, thereby increasing RNF31-RBCK1 association, LUBAC enzymatic activity, and NF-κB engagement. In the BCR pathway, LUBAC associates with the CARD11/MALT1/BCL10 adapter complex and is required for ABC DLBCL viability. A stapled RNF31 α-helical peptide based on the ABC DLBCL-associated Q622L polymorphism inhibited RFN31-RBCK1 binding, decreased NF-κB and killed ABC DLBCL cells, credentialing this protein-protein interface as a therapeutic target. PMID:24491438
Baral, Minati; Gupta, Amit; Kanungo, B K
2016-06-01
The design, synthesis and physicochemical characterization of a C3-symmetry Benzene-1,3,5-tricarbonylhydroxamate tripod, noted here as BTHA, are described. The chelator was built from a benzene as an anchor, symmetrically extended by three hydroxamate as ligating moieties, each bearing O, O donor sites. A combination of absorption spectrophotometry, potentiometry and theoretical investigations are used to explore the complexation behavior of the ligand with some trivalent metal ions: Fe(III), Cr(III), and Al(III). Three protonation constants were calculated for the ligand in a pH range of 2-11 in a highly aqueous medium (9:1 H2O: DMSO). A high rigidity in the molecular structure restricts the formation of 1:1 (M/L) metal encapsulation but shows a high binding efficiency for a 3:1 metal ligand stoichiometry giving formation constant (in β unit) 28.73, 26.13 and 19.69 for [M3L]; MFe(III), Al(III) and Cr(III) respectively, and may be considered as an efficient Fe-carrier. The spectrophotometric study reveals of interesting electronic transitions occurred during the complexation. BTHA exhibits a peak at 238nm in acidic pH and with the increase of pH, a new peak appeared at 270nm. A substantial shifting in both of the peaks in presence of the metal ions implicates a s coordination between ligand and metal ions. Moreover, complexation of BTHA with iron shows three distinct colors, violet, reddish orange and yellow in different pH, enables the ligand to be considered for the use as colorimetric sensor. PMID:26970809
NASA Astrophysics Data System (ADS)
Baral, Minati; Gupta, Amit; Kanungo, B. K.
2016-06-01
The design, synthesis and physicochemical characterization of a C3-symmetry Benzene-1,3,5-tricarbonylhydroxamate tripod, noted here as BTHA, are described. The chelator was built from a benzene as an anchor, symmetrically extended by three hydroxamate as ligating moieties, each bearing O, O donor sites. A combination of absorption spectrophotometry, potentiometry and theoretical investigations are used to explore the complexation behavior of the ligand with some trivalent metal ions: Fe(III), Cr(III), and Al(III). Three protonation constants were calculated for the ligand in a pH range of 2-11 in a highly aqueous medium (9:1 H2O: DMSO). A high rigidity in the molecular structure restricts the formation of 1:1 (M/L) metal encapsulation but shows a high binding efficiency for a 3:1 metal ligand stoichiometry giving formation constant (in β unit) 28.73, 26.13 and 19.69 for [M3L]; Mdbnd Fe(III), Al(III) and Cr(III) respectively, and may be considered as an efficient Fe-carrier. The spectrophotometric study reveals of interesting electronic transitions occurred during the complexation. BTHA exhibits a peak at 238 nm in acidic pH and with the increase of pH, a new peak appeared at 270 nm. A substantial shifting in both of the peaks in presence of the metal ions implicates a s coordination between ligand and metal ions. Moreover, complexation of BTHA with iron shows three distinct colors, violet, reddish orange and yellow in different pH, enables the ligand to be considered for the use as colorimetric sensor.
NASA Astrophysics Data System (ADS)
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
2013-01-01
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]·2H2O and [CoLCl2]CH3OH·0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base.
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
2013-01-15
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]·2H2O and [CoLCl2]CH3OH·0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base. PMID:23099161
NASA Astrophysics Data System (ADS)
Cattabiani, Alessandro; Barbarulo, Andrea; Riou, Hervé; Ladevèze, Pierre
2015-12-01
Recently, interest of aerospace and automotive industries on medium-frequency vibrational behavior of composite shell structures has grown due to their high specific stiffness and fatigue resistance. Conventional methods such as the finite element method and the statistical energy analysis are not suitable for the medium-frequency bandwidth. Conversely, the variational theory of complex rays (VTCR) is taking place as an ad-hoc technique to tackle such frequency band. It is a Trefftz method based on a weak variational formulation. Equilibrium equations are met using exact solutions as shape functions. The variational problem imposes boundary conditions in weak form. The present paper extends VTCR to orthotropic shell structures. Moreover, several new enhancements are introduced. Now, we use a quasi-symmetric ray distribution which can greatly reduce computational costs, and addresses in-plane inertia which was neglected in previous works. Some relevant numerical examples are presented to show the strategy and results are compared with a FEM reference to study performances.
Linear complexity integral-equation based methods for large-scale electromagnetic analysis
NASA Astrophysics Data System (ADS)
Chai, Wenwen
In general, to solve problems with N parameters, the optimal computational complexity is linear complexity O( N). However, for most computational electromagnetic methods, the complexity is higher than O(N). In this work, we introduced and further developed the H - and H2 -matrix based mathematical framework to break the computational barrier of existing integral-equation (IE)-based methods for large-scale electromagnetic analysis. Our significant contributions include the first-time dense matrix inversion and LU factorization of O(N) complexity for large-scale 3-D circuit extraction and a fast direct integral equation solver that outperforms existing direct solvers for large-scale electrodynamic analysis having millions of unknowns and ˜100 wavelengths. The major contributions of this work are: (1) Direct Matrix Solution of Linear Complexity for 3-D Integrated Circuit (IC) and Package Extraction • O(N) complexity dense matrix inversion and LU factorization algorithms and their applications to capacitance extraction and impedance extraction of large-scale 3-D circuits • O(N) direct matrix solution of highly irregular matrices consisting of both dense and sparse matrix blocks arising from full-wave analysis of general 3-D circuits with lossy conductors in multiple dielectrics. (2) Fast H - and H2 -Based IE Solvers for Large-Scale Electrodynamic Analysis • theoretical proof on the error bounded low-rank representation of electrodynamic integral operators • fast H2 -based iterative solver with O(N) computational cost and controlled accuracy from small to tens of wavelengths • fast H -based direct solver with computational cost minimized based on accuracy • Findings on how to reduce the complexity of H - and H2 -based methods for electrodynamic analysis, which are also applicable to many other fast IE solvers. (3) Fast Algorithms for Accelerating H - and H2 -Based Iterative and Direct Solvers • Optimal H -based representation and its applications from circuits to electrically large problems • Optimal H2 -based representation for dense matrices arising from IE-based analysis • Iterative as well as direct solvers significantly accelerated by optimal H - and H2 -based representations. (4) Advanced Mathematical Computing • The construction of a simple H2 -representation with Csp = 1 • Linear-time matrix-matrix multiplication with controlled accuracy. The proposed methods have successfully solved large-scale electromagnetic scattering problems having 100 wavelengths and integrated circuit problems involving millions of unknowns in fast CPU time, modest memory consumption, and without sacrificing accuracy. Comparisons with state-of-the-art solvers have demonstrated the clear advantages of the proposed methods. The proposed methods have important applications in a wide range of areas such as electromagnetics, optics, acoustics, plasmonics, etc.
Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen
2012-06-15
Highlights: Black-Right-Pointing-Pointer Inexact piecewise-linearization-based fuzzy flexible programming is proposed. Black-Right-Pointing-Pointer It's the first application to waste management under multiple complexities. Black-Right-Pointing-Pointer It tackles nonlinear economies-of-scale effects in interval-parameter constraints. Black-Right-Pointing-Pointer It estimates costs more accurately than the linear-regression-based model. Black-Right-Pointing-Pointer Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities.
Mixed Linear Model Approaches of Association Mapping for Complex Traits Based on Omics Variants.
Zhang, Fu-Tao; Zhu, Zhi-Hong; Tong, Xiao-Ran; Zhu, Zhi-Xiang; Qi, Ting; Zhu, Jun
2015-01-01
Precise prediction for genetic architecture of complex traits is impeded by the limited understanding on genetic effects of complex traits, especially on gene-by-gene (GxG) and gene-by-environment (GxE) interaction. In the past decades, an explosion of high throughput technologies enables omics studies at multiple levels (such as genomics, transcriptomics, proteomics, and metabolomics). The analyses of large omics data, especially two-loci interaction analysis, are very time intensive. Integrating the diverse omics data and environmental effects in the analyses also remain challenges. We proposed mixed linear model approaches using GPU (Graphic Processing Unit) computation to simultaneously dissect various genetic effects. Analyses can be performed for estimating genetic main effects, GxG epistasis effects, and GxE environment interaction effects on large-scale omics data for complex traits, and for estimating heritability of specific genetic effects. Both mouse data analyses and Monte Carlo simulations demonstrated that genetic effects and environment interaction effects could be unbiasedly estimated with high statistical power by using the proposed approaches. PMID:26223539
Farias, R. L. S.; Ramos, Rudnei O.; Krein, G.
2008-09-15
The thermodynamics of a scalar field with a quartic interaction is studied within the linear {delta} expansion (LDE) method. Using the imaginary-time formalism the free energy is evaluated up to second order in the LDE. The method generates nonperturbative results that are then used to obtain thermodynamic quantities like the pressure. The phase transition pattern of the model is fully studied, from the broken to the symmetry restored phase. The results are compared with those obtained with other nonperturbative methods and also with ordinary perturbation theory. The results coming from the two main optimization procedures used in conjunction with the LDE method, the principle of minimal sensitivity (PMS) and the fastest apparent convergence (FAC) are also compared with each other and studied in which cases they are applicable or not. The optimization procedures are applied directly to the free energy.
Zhang, Xuepeng; Zheng, Xiaowei; Phillips, David Lee; Zhao, Cunyuan
2014-11-21
Density functional theory (DFT) was utilized to investigate the hydrolysis reaction mechanisms of phosphodiester BNPP (BNPP = bis(4-nitrophenyl)phosphate) catalyzed by a symmetrical oxyimine-based macrocyclic dinuclear zinc(ii) complex. We examined the nature of the nucleophilic reagent and the active form of the catalyst. The coordination and binding models of the catalyst-substrate complex were explored and we investigated two catalyst configurations (a ridge configuration and a plane configuration), four basic catalyst-substrate binding models (a mono-point-binding model, a dual-point-binding model, an OH-bridging model and a mono-center-dual-binding model) and two alternate roles for the metal-coordinated hydroxide ion (whether it acts as a nucleophile or as a general base to facilitate the deprotonation of a solvent molecule). The one-point-binding mode was found to be preferred to construct a starting reactant. Nine plausible reaction mechanisms were proposed and investigated. Mechanism 1, a stepwise SN2-type addition-substitution reaction involving a para-position nucleophilic attack and the configuration inversion of the phosphate, was found to be the most favorable pathway. All of the proposed pathways are derived from alternate mechanisms such as a ping-pong mechanism and an AP mechanism. The ping-pong mechanism in combination with the role of the metal-coordinated hydroxide ion acting as a nucleophile was found to be more competitive than the other mechanisms examined. Results reported in this paper are consistent with, and can be utilized to systematically interpret, the experimental observations in the literature. PMID:25141046
Fleischmann, Martin; Dütsch, Luis; Elsayed Moussa, Mehdi; Balázs, Gábor; Kremer, Werner; Lescop, Christophe; Scheer, Manfred
2016-03-21
This study describes the selective synthesis of linear, trinuclear, halide-bridged Cu(I) complexes [Cu3(μ-X)2(μ-dpmp)2(MeCN)2](+) (1a: X = Cl; 1b: X = Br; 1c: X = I) stabilized by the tridentate dpmp ligand obtained by self-assembly reactions in THF/MeCN. Upon drying, the MeCN ligands can be removed and the complexes are transformed to the reactive parent trinuclear [Cu3(μ-X)2(μ-dpmp)2](+) (2a-c) building blocks with two vacant coordination sites on the terminal Cu atoms. Another synthesis in CH2Cl2 directly yields 2a-c. Additionally, two related isomeric compounds, 2a* and 2c*, and two CH2Cl2-ligated complexes, [Cu3(μ-X)2(μ-dpmp)2(CH2Cl2)2](+) (X = Br (3b), I (3c)), were structurally characterized. The frameworks of the cationic [Cu3(μ-X)2(μ-dpmp)2](+) complexes are stable in solution at low temperatures and show dynamic coordination behavior at elevated temperatures, indicated by new signals arising in the (31)P{(1)H} NMR spectra. This evolution cannot be shifted back by decreasing the temperature again. However, cationic [Cu3(μ-X)2(μ-dpmp)2](+) (X = Cl, Br, I) complexes can be obtained selectively in the solid state upon crystallization. Although reactions of 2a-c with complexes [{CpMo(CO)2}2(μ,η(2):η(2)-E2)] (E = P (A1), As (A2)) led to unsymmetrically substituted [Cu3(μ-X)2(μ-dpmp)2(η(1)-L)](+) (4a-c: X = Cl-I, L = A1; 5: X = Cl, L = A2) complexes, reactions with the cyclo-P3 complex [CpMo(CO)2(η(3)-P3)] (B) afforded zigzag chain polymers [Cu3(μ-X)2(μ-dpmp)2(μ,η(1):η(1)-B)]n[BF4]n (6a: X = Cl; 6b: X = Br) and symmetrically substituted complex [Cu3(μ-I)2(μ-dpmp)2(η(1)-B)2](+) (7). Reactions of 2a-c with cyclo-E5 complexes [Cp*Fe(η(5)-E5)] (E = P (C1), As (C2)) led to the isolation of one-dimensional coordination polymers [Cu3(μ-X)2(μ-dpmp)2(μ,η(1):η(1)-L)]n[BF4]n (8a-b: X = Cl-Br, L = C1; 9: X = Cl, L = C2) and symmetrically substituted complex [Cu3(μ-I)2(μ-dpmp)2(η(1)-C1)2](+) (10). All products exhibit a trinuclear, cationic [Cu3(μ-X)2(μ-dpmp)2](+) complex as the central structural motif. Variation of the intramolecular Cu-Cu distances inside the Cu3 complexes is discussed, and supporting DFT computations for the model complex [Cu3(μ-Cl)2(dmmp)2{(η(1)-A1)}](+) (4a') are presented. PMID:26950219
FORTRAN subroutines for out-of-core solutions of large complex linear systems
NASA Technical Reports Server (NTRS)
Yip, E. L.
1979-01-01
The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems.
Complexity transitions in global algorithms for sparse linear systems over finite fields
NASA Astrophysics Data System (ADS)
Braunstein, A.; Leone, M.; Ricci-Tersenghi, F.; Zecchina, R.
2002-09-01
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois field modulo q. Using tools from statistical mechanics we are able to identify phase transitions in the structure of the solution space and to connect them to the changes in the performance of a global algorithm, namely Gaussian elimination. Crossing phase boundaries produces a dramatic increase in memory and CPU requirements necessary for the algorithms. In turn, this causes the saturation of the upper bounds for the running time. We illustrate the results on the specific problem of integer factorization, which is of central interest for deciphering messages encrypted with the RSA cryptosystem.
Preparation, linear and NLO properties of DNA-CTMA-SBE complexes
NASA Astrophysics Data System (ADS)
Manea, Ana-Maria; Rau, Ileana; Kajzar, Francois; Meghea, Aurelia
2013-10-01
Synthesis of deoxyribonucleic acid (DNA) - was cetyltrimethylammonium (CTMA) - sea buckthorn extract (SBE) at different concentrations is decribed. The complexes were processed into good optical quality thin films by spin coating on different substrates such as: glass, silica and ITO covered glass substrates. SBE contains many bioactive substances that can be used in the treatment of several diseases, such as cardiovascular disease, cancer, and acute mountain sickness. The obtained thin films were characterized for their spectroscopic, fluorescent, linear and nonlinear optical properties as function of SBE concentration. The third-order nonlinear optical (NLO) properties of thin films were determined by the optical third-harmonic generation technique at 1 064.2 nm fundamental wavelength.
NASA Technical Reports Server (NTRS)
Ma, Q.; Boulet, C.; Tipping, R. H.
2014-01-01
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Ma, Q.; Tipping, R. H.
2014-03-14
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters’ two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
A new ion mobility-linear ion trap instrument for complex mixture analysis.
Donohoe, Gregory C; Maleki, Hossein; Arndt, James R; Khakinejad, Mahdiar; Yi, Jinghai; McBride, Carroll; Nurkiewicz, Timothy R; Valentine, Stephen J
2014-08-19
A new instrument that couples a low-pressure drift tube with a linear ion trap mass spectrometer is demonstrated for complex mixture analysis. The combination of the low-pressure separation with the ion trapping capabilities provides several benefits for complex mixture analysis. These include high sensitivity, unique ion fragmentation capabilities, and high reproducibility. Even though the gas-phase separation and the mass measurement steps are each conducted in an ion filtering mode, detection limits for mobility-selected peptide ions are in the tens of attomole range. In addition to ion separation, the low-pressure drift tube can be used as an ion fragmentation cell yielding mobility-resolved fragment ions that can be subsequently analyzed by multistage tandem mass spectrometry (MS(n)) methods in the ion trap. Because of the ion trap configuration, these methods can be comprised of any number (limited by ion signal) of collision-induced dissociation (CID) and electron transfer dissociation (ETD) processes. The high reproducibility of the gas-phase separation allows for comparison of two-dimensional ion mobility spectrometry (IMS)-MS data sets in a pixel-by-pixel fashion without the need for data set alignment. These advantages are presented in model analyses representing mixtures encountered in proteomics and metabolomics experiments. PMID:25068446
Slow magnetic relaxation of light lanthanide-based linear LnZn2 trinuclear complexes.
Takehara, Chika; Then, Poh Ling; Kataoka, Yumiko; Nakano, Motohiro; Yamamura, Tomoo; Kajiwara, Takashi
2015-11-01
Four isostructural LnZn2 trinuclear complexes, [Ln(NO3){Zn(L)(SCN)}2] (H2L is a Schiff base ligand derived from o-vanillin and ethylenediamine), were synthesized, which include light lanthanide ions as spin carriers (Ln = Ce 1, Pr 2, Nd 3, and Sm 4). These complexes involve a linear Zn(ii)-Ln(iii)-Zn(ii) array, which leads to an axially stressed ligand field and can also cause single-moleluce magnet (SMM) behavior in oblate-type electronic distributions of ground sublevels found in Ce(iii), Pr(iii), and Nd(iii). Slow magnetic relaxation behavior was observed in 1 and 3 under an applied bias dc field of 1000 Oe, whereas such a slow relaxation was not observed in 2 and 4. The appearance of field-induced SMM behavior in 1 and 3 was correlated with the even-numbered Jz sublevels of Ce(iii) and Nd(iii) ions known as the Kramers system. PMID:26435181
NASA Astrophysics Data System (ADS)
Laxalde, Denis; Thouverez, Fabrice
2009-05-01
A method for modal analysis of non-linear and non-conservative mechanical systems is proposed. In particular, dry-friction nonlinearities are considered although the method is not restricted to these. Based on the concept of complex nonlinear modes, eigensolutions are written as generalized Fourier series and the eigenproblem is then formulated in the frequency-domain. An alternating frequency-time domain method is used for the calculation of implicit nonlinear forces. A two degrees-of-freedom example featuring dry-friction illustrates the method and highlights the effects of dissipation on modal parameters. The stabilizing effects of friction in presence of negative damping in the system are also addressed. Then an application on a large-scale nonlinear system consisting of a turbomachinery blade, with dry-friction interfaces is proposed. In the latter, an original framework for the description of two-dimensional frictional motions by complex variables is proposed and applied, in particular, to a Dahl model. Effects of friction parameters and models on the blade's modal characteristics are investigated.
Matsuura, Noriyuki; Igashira-Kamiyama, Asako; Kawamoto, Tatsuya; Konno, Takumi
2006-01-01
Treatment of [RuCl(2)(DMSO)(4)] with 2-aminoethanethiol (Haet) in ethanol gave a dicationic triruthenium complex, [Ru[Ru(aet)(3)](2)]Cl(2) ([1]Cl(2)). Complex [1]Cl(2) was also obtained by treatment of RuCl(3).nH(2)O with excess Haet in water. When [1](2+) was chromatographed on a cation-exchange column of SP-Sephadex C-25, meso (DeltaLambda) and racemic (DeltaDelta/LambdaLambda) isomers of the corresponding tricationic complex, [Ru[Ru(aet)(3)](2)](3+) ([2](3+)), were eluted with aqueous NaNO(3). The racemic isomer of [2](3+) was optically resolved into DeltaDelta and LambdaLambda isomers by using [Sb(2)(R,R-tartrato)(2)](2-) as a resolving agent. The molecular structures of DeltaLambda- and DeltaDelta/LambdaLambda-[2](NO(3))(3) were determined by X-ray crystallography. In these complexes, the central Ru atom is coordinated by six thiolato groups from two terminal fac-(S)-[Ru(aet)(3)] units in an octahedral geometry, forming a linear-type S-bridged triruthenium structure. The spectroelectrochemical studies on the electronic absorption and CD spectra, together with the electrochemical studies, demonstrated that [1](2+) and [2](3+) are interconvertible with each other through a one-electron redox process, retaining the chirality of the triruthenium structure. Their electronic structures were investigated on the basis of EPR and magnetic susceptibility measurements, which indicated that [1](2+) and [2](3+) have spin ground states of S(t) = 0 and S(t) = 1/2, respectively. The corresponding L-cysteinato complex, [Ru[Ru(L-cys-N,S)(3)](2)](3-), which was formed from RuCl(3).nH(2)O and excess L-cysteine (L-H(2)cys) in water followed by air oxidation, is also presented. PMID:16390081
Probabilistic cloning of three symmetric states
Jimenez, O.; Bergou, J.; Delgado, A.
2010-12-15
We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating M copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and M copies of symmetric states.
Minimally symmetric Higgs boson
NASA Astrophysics Data System (ADS)
Low, Ian
2015-06-01
Models addressing the naturalness of a light Higgs boson typically employ symmetries, either bosonic or fermionic, to stabilize the Higgs mass. We consider a setup with the minimal amount of symmetries: four shift symmetries acting on the four components of the Higgs doublet, subject to the constraints of linearly realized S U (2 )L×U (1 )Y electroweak symmetry. Up to terms that explicitly violate the shift symmetries, the effective Lagrangian can be derived, irrespective of the spontaneously broken group G in the ultraviolet, and is universal among all models where the Higgs arises as a pseudo-Nambu-Goldstone boson. Very high energy scatterings of vector bosons could provide smoking gun signals of a minimally symmetric Higgs boson.
Deciphering landscape complexity to predict (non)linear responses to extreme climatic events
NASA Astrophysics Data System (ADS)
Peters, D. P.; Yao, J.; Duniway, M.; Peters, S.; Huang, H.
2012-12-01
Extreme events are increasing in frequency and magnitude for many landscapes globally. Ecologically, most of the focus on extreme climatic events has been on effects of either short-term pulses (floods, freezes) or long-term drought. Multi-year increases in precipitation are also occurring with little known consequences, in particular for landscapes with high spatial variation in soils, geomorphology, and vegetation. We used long-term data from the Chihuahuan Desert in North America to compare ecosystem responses to precipitation in dry, average, and wet periods for a landscape consisting of five major ecosystem types. These types are dominated by one of two life forms (grasses or shrubs) that are located on different soils and topographic positions. We then used a process-based simulation model integrated with additional long-term data to identify the processes driving dynamics in each climatic period for different landscape locations. For some ecosystem types, ecological responses in average and dry periods could be linearly extrapolated to predict responses in an extended wet period, and the same set of processes occurred regardless of climatic period. However, for much of the landscape, a different set of biotic-abiotic processes and their feedbacks became operative in a wet period. This sequence of processes led to nonlinear dynamics through time. Our results show that dynamics of complex landscapes can be deciphered given information and long-term data on linked biotic-abiotic processes across spatial and temporal scales. Understanding the role of sequential processes and landscape complexity in ecosystem responses to multi-year climatic patterns is needed to improve predictions of landscape-scale responses to climate.
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.
2013-01-01
We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with groundbased, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.
NASA Astrophysics Data System (ADS)
Leslie, L. M.; Abbey, R. F., Jr.
Forecasting the tracks of hurricanes is a problem of immense importance. It is a major scientific exercise in solving the complicated set of mathematical equations that govern the behavior of atmospheric flow in general and hurricanes in particular. Moreover, hurricanes rank as the most devastating of all natural phenomena, in terms of loss of life and destruction of property. Hitherto, unlike many other atmospheric and oceanic systems, hurricanes have defied rapid advances in prediction of their motion, and progress has been of the order of a mere one percent or so reduction per annum in mean 48hour forecast position errors over the past two decades. A research program aimed at estimating inherent and actual mean absolute forecast position errors, has produced an apparent paradox. Despite the fact that the equations governing hurricane motion are a complex, coupled, nonlinear set of dynamical equations, there is very strong evidence for the existence of an underlying simple, linear, invariant behavior. The original aim of the research program was to determine the lower limits of mean hurricane forecast position errors and to quantify them out to 72hour leadtime. The appearance of the paradox meant that the focus shifted first to examining and explaining the paradox. Attention then turns to showing that the mean forecasts errors are still a very large 40 to 50 percent lower than the mean position errors currently being achieved in practice by state-of-the-art models numerical weather prediction (NWP) models.
NASA Astrophysics Data System (ADS)
Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.
2013-07-01
We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with ground-based, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.
Bhattacharjee, Saurav Das, Nilakshi
2015-10-15
A systematic theoretical investigation has been carried out on the role of dust charging dynamics on the nature and stability of DIA (Dust Ion Acoustic) mode in complex plasma. The study has been made for both linear and non-linear scale regime of DIA mode. The observed results have been characterized in terms of background plasma responses towards dust surface responsible for dust charge fluctuation, invoking important dusty plasma parameters, especially the ion flow speed and dust size. The linear analyses confirm the nature of instability in DIA mode in presence of dust charge fluctuation. The instability shows a damping of DIA mode in subsonic flow regime followed by a gradual growth in instability in supersonic limit of ion flow. The strength of non-linearity and their existence domain is found to be driven by different dusty plasma parameters. As dust is ubiquitous in interstellar medium with plasma background, the study also addresses the possible effect of dust charging dynamics in gravito-electrostatic characterization and the stability of dust molecular clouds especially in proto-planetary disc. The observations are influential and interesting towards the understanding of dust settling mechanism and formation of dust environments in different regions in space.
Efficient spectral simulations of complex non-linear and time-dependent flows
NASA Astrophysics Data System (ADS)
Dimitropoulos, Costas Dimitrios
2000-06-01
In this work we developed highly accurate and efficient (linearly scalable with the number of unknowns) spectral methods with applications in multidimensional time-dependent flows of complex fluids in various geometries, such as free-surface flows with surfactants, turbulent flows and viscoelastic flows. A pseudospectral method was developed for incompressible flow simulations in two-dimensional channels with significant boundary deformations, utilizing pseudoconformal mapping, second-order explicit/implicit time-splitting, the influence matrix method to enforce continuity and a spectrally preconditioned biconjugate gradient iterative solver for nonseparable elliptic equations. It was further extended for time-dependent free-surface flows in the presence of an insoluble surfactant, using fully implicit time-integration to accommodate the highly nonlinear free-surface motion. Transverse wave simulations are in excellent agreement with linear theory. Furthermore, longitudinal waves simulated with the specific flow conditions in this work showed sensitivity to the initial guess, evolving at long times to superimposed longitudinal and transverse waves. The implicit time-integration scheme is also advantageous in direct numerical simulation (DNS) of turbulent channel flow of fluids with internal microstructure, where highly nonlinear constitutive equations are utilized. DNS were used to study polymer-induced drag reduction using the FENE-P and Giesekus models. All results for different values of the molecular extensibility and the solvent viscosity ratio are consistent with experiments and proposed mechanisms for drag reduction based on a substantially increased extensional viscosity compared to the shear viscosity. Large magnitudes of drag reduction were observed with increasing extensional viscosity and all flow statistics show consistent trends. A critical range of the onset Weissenberg number, independent of the model and the chain extensibility, was identified. Giesekus model simulations demonstrate that the second normal-stress coefficient induces additional drag reduction. Reynolds stress, turbulent kinetic energy and streamwise enstrophy budgets for the FENE-P fluid demonstrated that as the extensional viscosity increases all components of the production of Reynolds stress, the pressure-velocity gradient, as well as other terms in the budgets decrease. The decrease in streamwise enstrophy production is consistent with the inhibition of vortex stretching by a large extensional viscosity.
Optimal symmetric flight studies
NASA Technical Reports Server (NTRS)
Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.
1985-01-01
Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.
Two-dimensional linear modes and solitons in parity-time symmetry bessel complex-valued potential
NASA Astrophysics Data System (ADS)
Chen, Haibo; Hu, Sumei
2015-11-01
We study the optical properties of two-dimensional linear modes and solitons in parity-time (PT) symmetry Bessel complex-valued potential. The PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of two-dimensional PT symmetry Bessel complex potential are obtained numerically. The PT-breaking points increase linearly with increasing the real part of the modulated depths of PT potential. The existence of fundamental and dipole solitons are studied in self-focusing and self-defocusing media. The eigenvalue for linear case is equal to the critical propagation constant bc of the existing soliton. The fundamental solitons are stable in both the self-focusing and self-defocusing media, and the dipole solitons are stable in the self-defocusing media but unstable in the self-focusing media.
Modifications to Axially Symmetric Simulations Using New DSMC (2007) Algorithms
NASA Technical Reports Server (NTRS)
Liechty, Derek S.
2008-01-01
Several modifications aimed at improving physical accuracy are proposed for solving axially symmetric problems building on the DSMC (2007) algorithms introduced by Bird. Originally developed to solve nonequilibrium, rarefied flows, the DSMC method is now regularly used to solve complex problems over a wide range of Knudsen numbers. These new algorithms include features such as nearest neighbor collisions excluding the previous collision partners, separate collision and sampling cells, automatically adaptive variable time steps, a modified no-time counter procedure for collisions, and discontinuous and event-driven physical processes. Axially symmetric solutions require radial weighting for the simulated molecules since the molecules near the axis represent fewer real molecules than those farther away from the axis due to the difference in volume of the cells. In the present methodology, these radial weighting factors are continuous, linear functions that vary with the radial position of each simulated molecule. It is shown that how one defines the number of tentative collisions greatly influences the mean collision time near the axis. The method by which the grid is treated for axially symmetric problems also plays an important role near the axis, especially for scalar pressure. A new method to treat how the molecules are traced through the grid is proposed to alleviate the decrease in scalar pressure at the axis near the surface. Also, a modification to the duplication buffer is proposed to vary the duplicated molecular velocities while retaining the molecular kinetic energy and axially symmetric nature of the problem.
Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models.
Fan, Ruzong; Wang, Yifan; Chiu, Chi-Yang; Chen, Wei; Ren, Haobo; Li, Yun; Boehnke, Michael; Amos, Christopher I; Moore, Jason H; Xiong, Momiao
2016-02-01
We developed generalized functional linear models (GFLMs) to perform a meta-analysis of multiple case-control studies to evaluate the relationship of genetic data to dichotomous traits adjusting for covariates. Unlike the previously developed meta-analysis for sequence kernel association tests (MetaSKATs), which are based on mixed-effect models to make the contributions of major gene loci random, GFLMs are fixed models; i.e., genetic effects of multiple genetic variants are fixed. Based on GFLMs, we developed chi-squared-distributed Rao's efficient score test and likelihood-ratio test (LRT) statistics to test for an association between a complex dichotomous trait and multiple genetic variants. We then performed extensive simulations to evaluate the empirical type I error rates and power performance of the proposed tests. The Rao's efficient score test statistics of GFLMs are very conservative and have higher power than MetaSKATs when some causal variants are rare and some are common. When the causal variants are all rare [i.e., minor allele frequencies (MAF) < 0.03], the Rao's efficient score test statistics have similar or slightly lower power than MetaSKATs. The LRT statistics generate accurate type I error rates for homogeneous genetic-effect models and may inflate type I error rates for heterogeneous genetic-effect models owing to the large numbers of degrees of freedom and have similar or slightly higher power than the Rao's efficient score test statistics. GFLMs were applied to analyze genetic data of 22 gene regions of type 2 diabetes data from a meta-analysis of eight European studies and detected significant association for 18 genes (P < 3.10 × 10(-6)), tentative association for 2 genes (HHEX and HMGA2; P ≈ 10(-5)), and no association for 2 genes, while MetaSKATs detected none. In addition, the traditional additive-effect model detects association at gene HHEX. GFLMs and related tests can analyze rare or common variants or a combination of the two and can be useful in whole-genome and whole-exome association studies. PMID:26715663
Three PT-symmetric Hamiltonians with completely different spectra
NASA Astrophysics Data System (ADS)
Fernndez, Francisco M.; Garcia, Javier
2015-12-01
We discuss three Hamiltonians, each with a central-field part H0 and a PT-symmetric perturbation igz. When H0 is the isotropic Harmonic oscillator the spectrum is real for all g because H is isospectral to H0 +g2 / 2. When H0 is the Hydrogen atom then infinitely many eigenvalues are complex for all g. If the potential in H0 is linear in the radial variable r then the spectrum of H exhibits real eigenvalues for 0 < g
NASA Astrophysics Data System (ADS)
Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui
2014-07-01
The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.
Conformally symmetric traversable wormholes
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
2007-10-15
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
Bis(arene) Actinide Sandwich Complexes, (eta6-C6H3R3)2An: Linear or bent?
Li, Jun; Bursten, Bruce E.
1999-11-03
The syntheses of the sandwich complexes ferrocene, (n5-C5H5)2-Fe, in 1951 and uranocene, (n8-C8H8)2U, in 1968 ushered in the modern eras of organotransition metal and organoactinide chemistry, respectively. Ferrocene and uranocene are examples of linear sandwich complexes, that is, those in which the (ring centroid)-M-(ring centroid) angle (denoted 0) is 180 degrees. In the case of (n5-C5H5)2M chemistry, a number of bent (0 < 180 degrees) complexes are known when M is a main-group or rare-earth element. The explanation for the bent structures of these complexes has been the subject of some debate concerning the relative importance of covalent, electrostatic, and steric interactions.
Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth
ERIC Educational Resources Information Center
Jeon, Minjeong
2012-01-01
Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…
Inhibiting complex IL-17A and IL-17RA interactions with a linear peptide.
Liu, Shenping; Desharnais, Joel; Sahasrabudhe, Parag V; Jin, Ping; Li, Wei; Oates, Bryan D; Shanker, Suman; Banker, Mary Ellen; Chrunyk, Boris A; Song, Xi; Feng, Xidong; Griffor, Matt; Jimenez, Judith; Chen, Gang; Tumelty, David; Bhat, Abhijit; Bradshaw, Curt W; Woodnutt, Gary; Lappe, Rodney W; Thorarensen, Atli; Qiu, Xiayang; Withka, Jane M; Wood, Lauren D
2016-01-01
IL-17A is a pro-inflammatory cytokine that has been implicated in autoimmune and inflammatory diseases. Monoclonal antibodies inhibiting IL-17A signaling have demonstrated remarkable efficacy, but an oral therapy is still lacking. A high affinity IL-17A peptide antagonist (HAP) of 15 residues was identified through phage-display screening followed by saturation mutagenesis optimization and amino acid substitutions. HAP binds specifically to IL-17A and inhibits the interaction of the cytokine with its receptor, IL-17RA. Tested in primary human cells, HAP blocked the production of multiple inflammatory cytokines. Crystal structure studies revealed that two HAP molecules bind to one IL-17A dimer symmetrically. The N-terminal portions of HAP form a β-strand that inserts between two IL-17A monomers while the C-terminal section forms an α helix that directly blocks IL-17RA from binding to the same region of IL-17A. This mode of inhibition suggests opportunities for developing peptide antagonists against this challenging target. PMID:27184415
Laaser, Jennifer E; Jiang, Yaming; Petersen, Shannon R; Reineke, Theresa M; Lodge, Timothy P
2015-12-31
The complexation of poly(dimethylaminoethyl methacrylate)-block-poly(styrene) micelles with poly(styrenesulfonate) homopolymers was investigated in aqueous buffer at pH 4.5 as a function of ionic strength. The complexation process was monitored by turbidimetric titration, and the structure and stability of the complexes were assessed by dynamic light scattering (DLS), cryogenic transmission electron microscopy (cryoTEM), and small-angle X-ray scattering. When complexes were formed by slow titration of one polyelectrolyte solution into the other, soluble complexes could be formed with either polyelectrolyte in excess as long as the mixture did not pass through the charge-neutral point. The initial complexes exhibited bimodal size distributions by DLS, with one population similar in size to or slightly smaller than the bare micelles, and the other significantly larger. The former correspond to individual micelles with complexed polyelectrolytes leading to a contracted corona; the latter reflect multimicelle aggregates that were directly observed by cryoTEM. At low ionic strength (e.g., 10 mM), these aggregates were stable on weeks-to-months time scales, but at high ionic strength (e.g., 500 mM), the aggregates rapidly annealed toward structures whose size and solubility depended on which polyelectrolyte was present in excess. These results are discussed in terms of the kinetics and thermodynamics of the polyelectrolyte complexation process and allow a detailed description of the interplay between kinetic and thermodynamic factors in this system. This work will inform design of polyelectrolyte complexes with tunable structure and stability for future applications. PMID:26677867
Viscosity in spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Ray, Arnab K.
2003-10-01
The influence of viscosity on the flow behaviour in spherically symmetric accretion has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length scale has been compared with the conventional understanding of the so-called `accretion radius' for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions - an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system than has been seen for the case of inviscid spherically symmetric inflows.
Kim, Inhae; Lee, Heetak; Han, Seong Kyu; Kim, Sanguk
2014-01-01
The modular architecture of protein-protein interaction (PPI) networks is evident in diverse species with a wide range of complexity. However, the molecular components that lead to the evolution of modularity in PPI networks have not been clearly identified. Here, we show that weak domain-linear motif interactions (DLIs) are more likely to connect different biological modules than strong domain-domain interactions (DDIs). This molecular division of labor is essential for the evolution of modularity in the complex PPI networks of diverse eukaryotic species. In particular, DLIs may compensate for the reduction in module boundaries that originate from increased connections between different modules in complex PPI networks. In addition, we show that the identification of biological modules can be greatly improved by including molecular characteristics of protein interactions. Our findings suggest that transient interactions have played a unique role in shaping the architecture and modularity of biological networks over the course of evolution. PMID:25299147
Predictive non-linear modeling of complex data by artificial neural networks.
Almeida, Jonas S
2002-02-01
An artificial neural network (ANN) is an artificial intelligence tool that identifies arbitrary nonlinear multiparametric discriminant functions directly from experimental data. The use of ANNs has gained increasing popularity for applications where a mechanistic description of the dependency between dependent and independent variables is either unknown or very complex. This machine learning technique can be roughly described as a universal algebraic function that will distinguish signal from noise directly from experimental data. The application of ANNs to complex relationships makes them highly attractive for the study of biological systems. Recent applications include the analysis of expression profiles and genomic and proteomic sequences. PMID:11849962
Tandon, Santokh S; Dawe, Louise N; Milway, Victoria A; Collins, Julie L; Thompson, Laurence K
2007-05-21
Tritopic 2,6-picolyl-bis-hydrazone ligands with bulky terminal groups derived from phenyl-pyridyl ketone do not form the expected [3 x 3] grids on reaction with copper(II), but instead form Cu8 'pinwheels', and in the present case linear trinuclear, pentanuclear and chain structures also. Direct bridging between copper ions occurs through micro2-N-N diazine groups, and longer O-C-N hydrazone connections, leading to moderately strong antiferromagnetic exchange between adjacent metal centres. Structural and magnetic properties are discussed in the context of specific orthogonal and non-orthogonal bridges, which can be distinguished and quantified. PMID:17702175
Panprasitwech, Oranit; Laohakosol, Vichian; Chaichana, Tuangrat
2010-11-11
Explicit formulae for continued fractions with symmetric patterns in their partial quotients are constructed in the field of formal power series. Similar to the work of Cohn in 1996, which generalized the so-called folding lemma to {kappa}-fold symmetry, the notion of {kappa}-duplicating symmetric continued fractions is investigated using a modification of the 1995 technique due to Clemens, Merrill and Roeder.
NASA Astrophysics Data System (ADS)
Azaña, José; Park, Yongwoo; Li, Fangxin
2011-07-01
This paper reviews recent work on a new group of linear and self-referenced techniques for full (amplitude and phase) characterization of fast optical signals based upon the concept of photonic differentiation, generally referred to as 'phase reconstruction using optical ultrafast differentiation' (PROUD). These techniques are particularly well adapted for applications in the context of fiber-optics telecommunications. PROUD methods can be implemented using simple and practical optical fiber-based setups and they rely on a direct, non-iterative phase recovery numerical algorithm. They can be used over a very wide range of pulse time durations, from the sub-picosecond to the nanosecond regime, and they can provide measurements in a single shot and in real time with power sensitivities down to the microwatt level. Previously reported PROUD methods are treated here under a unified, single framework, facilitating their analysis and comparison.
NASA Astrophysics Data System (ADS)
Rasulov, R. Ya.; Rasulov, V. R.; Eshboltaev, I.
2016-04-01
Matrix elements of optical transitions occuring between the subbands of the valence band of a p-GaAs type semiconductor are calculated. Transitions associated with the non-simultaneous absorption of single photons and simultaneous absorption of two photons are taken into account. The expressions are obtained for the average values of the square modulus of matrix elements calculated with respect to the solid angle of the wave vector of holes. Linear-circular dichroism of four-photon absorption of light in semiconductors with a complex valence band is theoretically studied.
NASA Technical Reports Server (NTRS)
Bogdanoff, J. L.; Kayser, K.; Krieger, W.
1977-01-01
The paper describes convergence and response studies in the low frequency range of complex systems, particularly with low values of damping of different distributions, and reports on the modification of the relaxation procedure required under these conditions. A new method is presented for response estimation in complex lumped parameter linear systems under random or deterministic steady state excitation. The essence of the method is the use of relaxation procedures with a suitable error function to find the estimated response; natural frequencies and normal modes are not computed. For a 45 degree of freedom system, and two relaxation procedures, convergence studies and frequency response estimates were performed. The low frequency studies are considered in the framework of earlier studies (Kayser and Bogdanoff, 1975) involving the mid to high frequency range.
Milway, Victoria A; Niel, Virginie; Abedin, Tareque S M; Xu, Zhiqiang; Thompson, Laurence K; Grove, Hilde; Miller, David O; Parsons, Stewart R
2004-03-22
The structures and magnetic properties of self-assembled copper(II) clusters and grids with the "tritopic" ligands 2poap (a), Cl2poap (b), m2poap (c), Cl2pomp (d), and 2pomp (e) are described [ligands derived by reaction of 4-R-2,6-pyridinedicarboxylic hydrazide (R = H, Cl, MeO) with 2-pyridinemethylimidate (a-c, respectively) or 2-acetylpyridine (d, R = Cl; e, R = H)]. Cl2poap and Cl2pomp self-assemble with Cu(NO(3))(2) to form octanuclear "pinwheel" cluster complexes [Cu(8)(Cl2poap-2H)(4)(NO(3))(8)].20H(2)O (1) and [Cu(8)(Cl2pomp-2H)(4)(NO(3))(8)].15H(2)O (2), built on a square [2 x 2] grid with four pendant copper arms, using "mild" reaction conditions. Similar reactions of Cl2pomp and 2pomp with Cu(ClO(4))(2) produce pinwheel clusters [Cu(8)(Cl2pomp-2H)(4)(H(2)O)(8)](ClO(4))(8).7H(2)O (3) and [Cu(8)(2pomp-2H)(4)(H(2)O)(8)](ClO(4))(8) (4), respectively. Heating a solution of 1 in MeOH/H(2)O produces a [3 x 3] nonanuclear square grid complex, [Cu(9)(Cl2poap-H)(3)(Cl2poap-2H)(3)](NO(3))(9).18H(2)O (5), which is also produced by direct reaction of the ligand and metal salt under similar conditions. Reaction of m2poap with Cu(NO(3))(2) produces only the [3 x 3] grid [Cu(9)(m2poap-H)(2)(m2poap-2H)(4)](NO(3))(8).17H(2)O (6) under similar conditions. Mixing the tritopic ligand 2poap with pyridine-2,6-dicarboxylic acid (picd) in the presence of Cu(NO(3))(2) produces a remarkable mixed ligand, nonanuclear grid complex [Cu(9)(2poap-H)(4)(picd-H)(3)(picd-2H)](NO(3))(9).9H(2)O (7), in which aromatic pi-stacking interactions are important in stabilizing the structure. Complexes 1-3 and 5-7 involve single oxygen atom (alkoxide) bridging connections between adjacent copper centers, while complex 4 has an unprecedented mixed micro-(N-N) and micro-O metal ion connectivity. Compound 1 (C(76)H(92)N(44)Cu(8)O(50)Cl(4)) crystallizes in the tetragonal system, space group I, with a = 21.645(1) A, c = 12.950(1) A, and Z = 2. Compound 2 (C(84)H(88)N(36)O(44)Cl(4)Cu(8)) crystallizes in the tetragonal system, space group I, with a = 21.2562(8) A, c = 12.7583(9) A, and Z = 2. Compound 4 (C(84)H(120)N(28)O(66)Cl(8)Cu(8)) crystallizes in the tetragonal system, space group I4(1)/a, with a = 20.7790(4) A, c = 32.561(1) A, and Z = 4. Compound 7(C(104)H(104)N(46)O(56)Cu(9)) crystallizes in the triclinic system, space group P, with a = 15.473(1) A, b = 19.869(2) A, c = 23.083(2) A, alpha = 88.890(2) degrees, beta = 81.511(2) degrees, gamma = 68.607(1) degrees, and Z = 2. All complexes exhibit dominant intramolecular ferromagnetic exchange coupling, resulting from an orthogonal bridging arrangement within each polynuclear structure. PMID:15018506
Multi-Party Privacy-Preserving Set Intersection with Quasi-Linear Complexity
NASA Astrophysics Data System (ADS)
Cheon, Jung Hee; Jarecki, Stanislaw; Seo, Jae Hong
Secure computation of the set intersection functionality allows n parties to find the intersection between their datasets without revealing anything else about them. An efficient protocol for such a task could have multiple potential applications in commerce, health care, and security. However, all currently known secure set intersection protocols for n>2 parties have computational costs that are quadratic in the (maximum) number of entries in the dataset contributed by each party, making secure computation of the set intersection only practical for small datasets. In this paper, we describe the first multi-party protocol for securely computing the set intersection functionality with both the communication and the computation costs that are quasi-linear in the size of the datasets. For a fixed security parameter, our protocols require O(n2k) bits of communication and Õ(n2k) group multiplications per player in the malicious adversary setting, where k is the size of each dataset. Our protocol follows the basic idea of the protocol proposed by Kissner and Song, but we gain efficiency by using different representations of the polynomials associated with users' datasets and careful employment of algorithms that interpolate or evaluate polynomials on multiple points more efficiently. Moreover, the proposed protocol is robust. This means that the protocol outputs the desired result even if some corrupted players leave during the execution of the protocol.
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
NASA Astrophysics Data System (ADS)
Guy, Capdeville
2013-10-01
We present a new HLL-type approximate Riemann solver that aims at capturing any isolated discontinuity without necessitating extensive characteristic analysis of governing partial differential equations. This property is especially attractive for complex hyperbolic systems with more than two equations. Following Linde's (2002) approach [6], we introduce a generic middle wave into the classical two-state HLL solver. The property of this third wave is typified by the way of a "strength indicator" that is derived from polynomial considerations. The polynomial that constitutes the basis of the procedure is made non-oscillatory by an adapted fourth-order WENO algorithm (CWENO4). This algorithm makes it possible to derive an expression for the strength indicator. According to the size of this latter parameter, the resulting solver (HLL-RH), either computes the multi-dimensional Rankine-Hugoniot equations if an isolated discontinuity appears in the Riemann fan, or asymptotically tends towards the two-state HLL solver if the solution is locally smooth. The asymptotic version of the HLL-RH solver is demonstrated to be positively conservative and entropy satisfying in its first-order multi-dimensional form provided that a relevant and not too restrictive CFL condition is considered; specific limitations of the conservative increments of the numerical solution and a suited entropy condition enable to maintain these properties in its high-order version. With a monotonicity-preserving algorithm for the time integration, the numerical method so generated, is third order in time and fourth-order accurate in space for the smooth part of the solution; moreover, the scheme is stable and accurate when capturing a shock wave, whatever the complexity of the underlying differential system. Extensive numerical tests for the one- and two-dimensional Euler equation of gas dynamics and comparisons with classical Godunov-type methods help to point out the potentialities and insufficiencies of the method.
Cylindrically symmetric electrohydrodynamic patterning.
Deshpande, Paru; Pease, Leonard F; Chen, Lei; Chou, Stephen Y; Russel, William B
2004-10-01
Cylindrically symmetric structures such as concentric rings and rosettes arise out of thin polymeric films subjected to strong electric fields. Experiments that formed concentric rings and theory capable of explaining these and other cylindrical structures are presented. These rings represent an additional member of a class of structures, including pillars and holes, formed by electrohydrodynamic patterning of thin films, occasionally referred to as lithographically induced self-assembly. Fabrication of a set of concentric rings begins by spin coating a thin poly(methyl methacrylate) film onto a silicon wafer. A mask is superimposed parallel to the film leaving a similarly thin air gap. Electric fields, acting in opposition to surface tension, destabilize the free interface when raised above the glass transition temperature. Central pillars nucleate under small cylindrical protrusions patterned on the mask. Rings then emerge sequentially, with larger systems having as many as 10 fully formed rings. Ring-to-ring spacings and annular widths, typically on the order of a micron, are approximately constant within a concentric cluster. The formation rate is proportional to the viscosity and, consequently, has the expected Williams-Landel-Ferry dependence on temperature. In light of these developments we have undertaken a linear stability analysis in cylindrical coordinates to describe these rings and ringlike structures. The salient feature of this analysis is the use of perturbations that incorporate their radial dependence in terms of Bessel functions as opposed to the traditional sinusoids of Cartesian coordinates. The theory predicts approximately constant ring-to-ring spacings, constant annular widths, and growth rates that agree with experiment. A secondary instability is observed at higher temperatures, which causes the rings to segment into arcs or pillar arrays. The cylindrical theory may be generalized to describe hexagonal pillar/hole packing, gratings, and rosettes with the first being of particular importance given the ubiquitous observation of hexagonal packing. The perturbation analysis presented here is relevant to any system with cylindrical symmetry, for which the radial dependence can be described in terms of Bessel functions. PMID:15600415
Werner, Tamas W; Reschke, Stephan; Bunzen, Hana; von Nidda, Hans-Albrecht Krug; Deisenhofer, Joachim; Loidl, Alois; Volkmer, Dirk
2016-02-01
The pentanuclear Co(II) complex [Co5Tp*4(Me2bta)6] containing N-donor ligands (5,6-dimethyl benzotriazolate; Me2bta6) and N-donor capping ligands (tris(3,5-dimethyl-1-pyrazolyl)borate; Tp*) was prepared by a simple and efficient ligand exchange reaction from [Co5Cl4(Me2bta)6] and tetra-n-butyl ammonium tris(3,5-dimethyl-1-pyrazolyl)borate. Compared to the precursor complex [Co5Cl4(Me2bta)6], which contains one Co(II) ion in octahedral and four Co(II) ions in tetrahedral coordination geometry, the title compound features all five Co(II) ions in an octahedral coordination environment while keeping a high complex symmetry. This results in modified properties including improved solubility and distinct magnetic behavior as compared to the precursor complex. The molecular structure and phase purity of the compound was verified by XRPD, UV-vis, ESI-MS, IR, and NMR measurements. Thermal stability of the compound was determined via TGA. The magnetic properties of here reported novel complex [Co5Tp*4(Me2bta)6] as well as its precursor [Co5Cl4(Me2bta)6] were examined in detail via ESR and SQUID measurements, which indicated weak anti-ferromagnetic exchange interactions between high-spin Co(II) centers at T < 20 and 50 K, respectively. PMID:26828949
Vieira, Erika M.; Snapper, Marc L.; Hoveyda, Amir H.
2011-01-01
A catalytic method for enantioselective synthesis of homoallylamides through Cu-catalyzed reactions of stable and easily accessible (pinacolato)allylborons with aryl-, heteroaryl-,alkyl- or alkenyl-substituted N-phosphinoylimines is disclosed. Transformations are promoted by 1–5 mol % of readily accessible NHC–Cu complexes, derived from C1-symmetric imidazolinium salts, which can be prepared in multi-gram quantities in four steps from commercially available materials. Allyl additions deliver the desired products in up to quantitative yield and 98.5:1.5 enantiomeric ratio and are amenable to gram-scale operations. A mechanistic model accounting for the observed selectivity levels and trends is proposed. PMID:21341657
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
ERIC Educational Resources Information Center
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
ERIC Educational Resources Information Center
Uebelacker, James W.
This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)
Integrable nonlinear parity-time-symmetric optical oscillator
NASA Astrophysics Data System (ADS)
Hassan, Absar U.; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N.
2016-04-01
The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
The complex viewpoint for transverse impasse points of quasi-linear differential equations
NASA Astrophysics Data System (ADS)
Thomas, Gabriel
2016-01-01
The main purpose of this paper is to show that the singularities called impasse points of real implicit ordinary differential equations are generically branch points of the solution, using a complex viewpoint. This research starts from a result asserting that the real solution in most cases behaves like ±√{ x -x0 } at an impasse point (x0, y0). We extend the notion of regular impasse point defined in previous works, and consider instead transverse impasse point, where the underlying vector field is transverse to the singular locus, even in the case when this hypersurface is not a manifold locally. Here we make use of Puiseux expansions and we show that, under generic hypotheses, the solution is multivalued at such a point. We prove that the Puiseux exponent is related simply to the multiplicity of the impasse point in the singular locus: if M is the total multiplicity of the singularity (z0, y0), there is a unique solution at this point and it is M + 1-valued.
Toppi, J; Babiloni, F; Vecchiato, G; De Vico Fallani, F; Mattia, D; Salinari, S; Milde, T; Leistritz, L; Witte, H; Astolfi, L
2012-01-01
One of the main limitations of the brain functional connectivity estimation methods based on Autoregressive Modeling, like the Granger Causality family of estimators, is the hypothesis that only stationary signals can be included in the estimation process. This hypothesis precludes the analysis of transients which often contain important information about the neural processes of interest. On the other hand, previous techniques developed for overcoming this limitation are affected by problems linked to the dimension of the multivariate autoregressive model (MVAR), which prevents from analysing complex networks like those at the basis of most cognitive functions in the brain. The General Linear Kalman Filter (GLKF) approach to the estimation of adaptive MVARs was recently introduced to deal with a high number of time series (up to 60) in a full multivariate analysis. In this work we evaluated the performances of this new method in terms of estimation quality and adaptation speed, by means of a simulation study in which specific factors of interest were systematically varied in the signal generation to investigate their effect on the method performances. The method was then applied to high density EEG data related to an imaginative task. The results confirmed the possibility to use this approach to study complex connectivity networks in a full multivariate and adaptive fashion, thus opening the way to an effective estimation of complex brain connectivity networks. PMID:23367343
Lang, Weeranuch; Kumagai, Yuya; Sadahiro, Juri; Maneesan, Janjira; Okuyama, Masayuki; Mori, Haruhide; Sakairi, Nobuo; Kimura, Atsuo
2014-10-01
Intermolecular interaction of linear-type ?-(1 ? 6)-glucosyl megalosaccharide rich (L-IMS) and water-insoluble anionic ethyl red was firstly characterized in a comparison with inclusion complexation by cyclodextrins (CDs) to overcome the problem of poor solubility and bioavailability. Phase solubility studies indicated an enhancement of 3- and 9-fold over the solubility in water upon the presence of L-IMS and ?-CD, respectively. (1)H NMR and circular dichrosim spectra revealed the dye forms consisted of 1:1 stoichiometric inclusion complex within the ?-CD cavity, whereas they exhibited non-specific hydrophobic interaction, identified by solvent polarity changes, with L-IMS. The inclusion complex delivered by ?-CD showed an uncompetitive inhibitory-type effect to azoreductase, particularly with high water content that did not promote dye liberation. Addition of the solid dye dispersed into coupled-enzyme reaction system supplied by L-IMS as the dye solubilizer provided usual degradation rate. The dye intermission in series exhibited successful removal with at least 5 cycles was economically feasible. PMID:25087215
Braids, shuffles and symmetrizers
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2009-07-01
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined. Dedicated to the memory of Aleosha Zamolodchikov.
Sato, Atsuko; Shimeld, Sebastian M; Bishop, John D D
2014-06-01
The sea squirt Ciona intestinalis species complex is a widely used model system for genomics and developmental biology, as well as ecology. Contrary to previous reports, here we show no difference in the success of development and hatching between hybrid and conspecific crosses between the two species within this complex known as types A and B, from a region in the English Channel where they are sympatric. We grew laboratory hybrids in the field for three months, and successfully obtained reproductive adults. In back-crosses of F1 laboratory hybrids to parental types, normal larvae were obtained. We conclude that hybrid crosses generate viable offspring and the resulting hybrids are interfertile with types A and B. However we also show that introgression in the natural sympatric population remains low. We discuss possible pre-zygotic and post-zygotic mechanisms which reproductively isolate these species. PMID:24882097
Souza Dutra, A. de; Santos, V. G. C. S. dos; Amaro de Faria, A. C. Jr.
2007-06-15
Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.
Xu, Songchen; Magoon, Yitzhak; Reinig, Regina R.; Schmidt, Bradley M.; Ellern, Arkady; Sadow, Aaron D.
2015-07-16
A bulky, optically active monoanionic scorpionate ligand, tris(4S-isopropyl-5,5-dimethyl-2-oxazolinyl)phenylborate (ToP*), is synthesized from the naturally occurring amino acid l-valine as its lithium salt, Li[ToP*] (1). That compound is readily converted to the thallium complex Tl[ToP*] (2) and to the acid derivative H[ToP*] (3). Group 7 tricarbonyl complexes ToP*M(CO)3 (M = Mn (4), Re (5)) are synthesized by the reaction of MBr(CO)5 and Li[ToP*] and are crystallographically characterized. The νCO bands in their infrared spectra indicate that π back-donation in the rhenium compounds is greater with ToP* than with non-methylated tris(4S-isopropyl-2-oxazolinyl)phenylborate (ToP). The reaction of H[ToP*] and ZnEt2 gives ToP*ZnEt (6), whilemore » ToP*ZnCl (7) is synthesized from Li[ToP*] and ZnCl2. The reaction of ToP*ZnCl and KOtBu followed by addition of PhSiH3 provides the zinc hydride complex ToP*ZnH (8). In this study, compound 8 is the first example of a crystallographically characterized optically active zinc hydride. We tested its catalytic reactivity in the cross-dehydrocoupling of silanes and alcohols, which provided Si-chiral silanes with moderate enantioselectivity.« less
Plotzitzka, Jacqueline; Kleeberg, Christian
2016-05-16
A series of complexes of the type [(NHC)Cu-ER3] (NHC = IDipp, IMes, ItBu, Me2IMe, and ER3 = SiMe2Ph, SiPh3, SnMe3) and [(NHC)Cu-R'] (NHC = IDipp, Me2IMe and R' = Ph, C≡CPh) was synthesized in good yields by the reaction of the corresponding [(NHC)Cu-OtBu] complex with the respective silylborane pinB-ER3 (pin = OCMe2CMe2O; ER3 = SiMe2Ph, SiPh3), the stannylborane ((C2H4)(iPrN)2)B-SnMe3, or a boronic acid ester pinB-R' (R' = Ph, C≡CPh). Solid structures of all complexes were systematically studied by X-ray diffraction analysis. The solid state structures of the complexes [(NHC)Cu-ER3] show a dependence of the structural motif from the steric properties of the NHC ligand. The sterically demanding NHC ligands (IDipp, IMes, ItBu) lead to monomeric, linear complexes [(NHC)Cu-ER3], while with the less demanding Me2IMe ligand, polynuclear, μ-ER3-bridged complexes with ultrashort Cu···Cu distances are observed. For the related complexes [(NHC)Cu-R'] no analogous complexes with bridging anionic ligands are realized. Instead, irrespective of the NHC ligand, linear coordinated copper complexes of different types are formed. (29)Si heteronuclear solution NMR spectroscopic data on [(NHC)Cu(I)-SiR3] exhibit distinctly different chemical shifts for the (in the solid state) monomeric and dimeric complexes suggesting different structure types also in solution. This agrees well with the observation of a trinuclear complex [(Me2IMe)Cu-SnMe3]3 both in the solid state and in solution. Initial catalytic studies suggest that [(NHC)Cu-OtBu] complexes (NHC = ItBu, Me2IMe) are, in addition to the established [(IDipp)Cu-OtBu] complex, efficient precatalysts for the silylation of aldehydes and α,β-unsaturated ketones with pinB-SiMe2Ph. PMID:27145039
Resonances for Symmetric Two-Barrier Potentials
ERIC Educational Resources Information Center
Fernandez, Francisco M.
2011-01-01
We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the Siegert approximation, the complex scaling method and the box-stabilization method. A comparison of the…
Non-linear model for the kinetics of 10B in blood after BPA-fructose complex infusion
NASA Astrophysics Data System (ADS)
Ryynänen, Päivi; Kangasmäki, Aki; Hiismäki, Pekka; Coderre, Jeffrey; Diaz, Aidnag Z.; Kallio, Merja; Laakso, Juha; Kulvik, Martti; Savolainen, Sauli
2002-03-01
A numerical model with a memory effect was created to describe the kinetics of 10B in blood after a single 4-dihydroxyborylphenylalanine-fructose complex (BPA-F) infusion in boron neutron capture therapy (BNCT). The model formulation was based on the averaged data from 10 glioma patients from the Brookhaven National Laboratory (BNL) BNCT-trials. These patients received a 2 h i.v. infusion of a BPA-fructose complex that delivered 290 mg BPA/kg body weight. The model was validated by fitting the original BNL patient data and new patient data from the Finnish BNCT-trials. The new 3-parameter non-linear model provided mean absolute differences between the measured and estimated 10B concentrations in blood that were less than 3.9% when used to simulate actual patient irradiations that comprised two irradiation fields separated by a break to reposition the patient. The flexibility of the model was successfully tested with two different infusion protocols. The patient data were modelled with a two-compartment model and a bi-exponential fit for comparison. The 3-parameter model is better than previously described models in predicting the time course of blood 10B concentration after cessation of intravenous infusion of BPA-fructose.
NASA Astrophysics Data System (ADS)
Carbonaro, Richard F.; Atalay, Yasemin B.; Di Toro, Dominic M.
2011-05-01
Stability constants for metal complexation to bidentate ligands containing negatively-charged oxygen donor atoms can be estimated from the following linear free energy relationship (LFER): log KML = χOO( αO log KHL,1 + αO log KHL,2) where KML is the metal-ligand stability constant for a 1:1 complex, KHL,1 and KHL,2 are the proton-ligand stability constants (the ligand p Ka values), and αO is the Irving-Rossotti slope. The parameter χOO is metal specific and has slightly different values for five and six membered chelate rings. LFERs are presented for 21 different metal ions and are accurate to within approximately 0.30 log units in predictions of log KML values. Ligands selected for use in LFER development include dicarboxylic acids, carboxyphenols, and ortho-diphenols. For ortho-hydroxybenzaldehydes, α-hydroxycarboxylic acids, and α-ketocarboxylic acids, a modification of the LFER where log KHL,2 is set equal to zero is required. The chemical interpretation of χOO is that it accounts for the extra stability afforded to metal complexes by the chelate effect. Cu-NOM binding constants calculated from the bidentate LFERs are similar in magnitude to those used in WHAM 6. This LFER can be used to make log KML predictions for small organic molecules. Since natural organic matter (NOM) contains many of the same functional groups (i.e. carboxylic acids, phenols, alcohols), the LFER log KML predictions shed light on the range of appropriate values for use in modeling metal partitioning in natural systems.
Carbonaro, Richard F.; Atalay, Yasemin B.; Di Toro, Dominic M.
2011-01-01
Stability constants for metal complexation to bidentate ligands containing negatively-charged oxygen donor atoms can be estimated from the following linear free energy relationship (LFER): log KML = χOO(αO log KHL,1 + αO log KHL,2) where KML is the metal-ligand stability constant for a 1:1 complex, KHL,1 and KHL,2 are the proton-ligand stability constants (the ligand pKa values), and αO is the Irving-Rossotti slope. The parameter χOO is metal specific and has slightly different values for 5 and 6 membered chelate rings. LFERs are presented for 21 different metal ions and are accurate to within approximately 0.30 log units in predictions of log KML values. Ligands selected for use in LFER development include dicarboxylic acids, carboxyphenols, and ortho-diphenols. For ortho-hydroxybenzaldehydes, α-hydroxycarboxylic acids, and α-ketocarboxylic acids, a modification of the LFER where log KHL,2 is set equal to zero is required. The chemical interpretation of χOO is that it accounts for the extra stability afforded to metal complexes by the chelate effect. Cu-NOM binding constants calculated from the bidentate LFERs are similar in magnitude to those used in WHAM 6. This LFER can be used to make log KML predictions for small organic molecules. Since natural organic matter (NOM) contains many of the same functional groups (i.e. carboxylic acids, phenols, alcohols), the LFER log KML predictions shed light on the range of appropriate values for use in modeling metal partitioning in natural systems. PMID:21833149
Integrability of PT-symmetric dimers
NASA Astrophysics Data System (ADS)
Pickton, J.; Susanto, H.
2013-12-01
The coupled discrete linear and Kerr nonlinear Schrödinger equations with gain and loss describing transport on dimers with parity-time (PT)-symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT-symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase portraits of the system. A pendulum equation with a linear potential and a constant force for the phase difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behavior of all solutions of the system, including changes in the topological structure of the phase plane, is then discussed.
Rome, J.A.; Harris, J.H.
1984-01-01
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
Condorelli, Rosalia
2016-01-01
Can we share even today the same vision of modernity which Durkheim left us by its suicide analysis? or can society 'surprise us'? The answer to these questions can be inspired by several studies which found that beginning the second half of the twentieth century suicides in western countries more industrialized and modernized do not increase in a constant, linear way as modernization and social fragmentation process increases, as well as Durkheim's theory seems to lead us to predict. Despite continued modernizing process, they found stabilizing or falling overall suicide rate trends. Therefore, a gradual process of adaptation to the stress of modernization associated to low social integration levels seems to be activated in modern society. Assuming this perspective, the paper highlights as this tendency may be understood in the light of the new concept of social systems as complex adaptive systems, systems which are able to adapt to environmental perturbations and generate as a whole surprising, emergent effects due to nonlinear interactions among their components. So, in the frame of Nonlinear Dynamical System Modeling, we formalize the logic of suicide decision-making process responsible for changes at aggregate level in suicide growth rates by a nonlinear differential equation structured in a logistic way, and in so doing we attempt to capture the mechanism underlying the change process in suicide growth rate and to test the hypothesis that system's dynamics exhibits a restrained increase process as expression of an adaptation process to the liquidity of social ties in modern society. In particular, a Nonlinear Logistic Map is applied to suicide data in a modern society such as the Italian one from 1875 to 2010. The analytic results, seeming to confirm the idea of the activation of an adaptation process to the liquidity of social ties, constitutes an opportunity for a more general reflection on the current configuration of modern society, by relating the Durkheimian Theory with the Halbwachs' Theory and most current visions of modernity such as the Baumanian one. Complexity completes the interpretative framework by rooting the generating mechanism of adaptation process in the precondition of a new General Theory of Systems making the non linearity property of social system's interactions and surprise the functioning and evolution rule of social systems. PMID:27065077
Müh, Frank; Renger, Thomas
2012-08-01
Linear optical spectra of solubilized trimers and small lamellar aggregates of the major light-harvesting complex II (LHCII) of higher plants are simulated employing excitonic couplings and site energies of chlorophylls (Chls) computed on the basis of the two crystal structures by a combined quantum chemical/electrostatic approach. A good agreement between simulation and experiment is achieved (except for the circular dichroism in the Chl b region), if vibronic transitions of Chls are taken into account. Site energies are further optimized by refinement fits of optical spectra. The differences between refined and directly calculated values are not significant enough to decide, whether the crystal structures are closer to trimers or aggregates. Changes in the linear dichroism spectrum upon aggregation are related to site energy shifts of Chls b601, b607, a603, a610, and a613, and are interpreted in terms of conformational changes of violaxanthin and the two luteins involving their ionone rings. Chl a610 is the energy sink at 77K in both conformations. An analysis of absorption spectra of trimers perpendicular and parallel to the C(3)-axis (van Amerongen et al. Biophys. J. 67 (1994) 837-847) shows that only Chl a604 close to neoxanthin is significantly reoriented in trimers compared to the crystal structures. Whether this pigment is orientated in aggregates as in the crystal structures, can presently not be determined faithfully. To finally decide about pigment reorientations that could be of relevance for non-photochemical quenching, further polarized absorption and fluorescence measurements of aggregates or detergent-depleted LHCII would be helpful. This article is part of a Special Issue entitled: Photosynthesis Research for Sustainability: from Natural to Artificial. PMID:22387396
Chilton, Nicholas F; Lei, Hao; Bryan, Aimee M; Grandjean, Fernande; Long, Gary J; Power, Philip P
2015-06-28
The 2 to 300 K magnetic susceptibilities of Fe{N(SiMe2Ph)2}2, 1, Fe{N(SiMePh2)2}2, 2, and the diaryl complex Fe(Ar(Pr(i)4))2, 3, where Ar(Pr(i)4) is C6H3-2,6(C6H3-2,6-Pr(i)2)2 have been measured. Initial fits of these properties in the absence of an independent knowledge of their ligand field splitting have proven problematic. Ab initio calculations of the CASSCF/RASSI/SINGLE-ANISO type have indicated that the orbital energies of the complexes, as well as those of Fe(Ar(Me6))2, 4, where Ar(Me6) is C6H3-2,6(C6H2-2,4,6-Me3)2), are in the order d(xy)≈ d(x(2)-y(2)) < d(xz) ≈ d(yz) < d(z(2)), and the iron(II) complexes in this ligand field have the (d(xy), d(x(2)-y(2)))(3)(d(xz), d(yz))(2)(d(z(2)))(1) ground electronic configuration with a substantial orbital contribution to their effective magnetic moments. An ab initio-derived ligand field and spin-orbit model is found to yield an excellent simulation of the observed magnetic properties of 1-3. The calculated ligand field strengths of these ligands are placed in the broader context of common coordination ligands in hypothetical two-coordinate linear iron(ii) complexes. This yields the ordering I(-) < H(-) < Br(-)≈ PMe3 < CH3(-) < Cl(-)≈ C(SiMe3)3(-) < CN(-)≈ SAr(Pr(i)6-) < Ar(Pr(i)4-) < Ar(Me6-)≈ N3(-) < NCS(-)≈ NCSe(-)≈ NCBH3(-)≈ MeCN ≈ H2O ≈ NH3 < NO3(-)≈ THF ≈ CO ≈ N(SiMe2Ph)2(-)≈ N(SiMePh2)2(-) < F(-)≈ N(H)Ar(Pr(i)6-)≈ N(SiMe3)Dipp(-) < OAr(Pr(i)4-). The magnetic susceptibility of the bridged dimer, [Fe{N(SiMe3)2}2]2, 5, has also been measured between 2 and 300 K and a fit of χMT with the isotropic Heisenberg Hamiltonian, Ĥ = -2JŜ1·Ŝ2 yields an antiferromagnetic exchange coupling constant, J, of -131(2) cm(-1). PMID:26006177
Ewert, Kai K; Kotamraju, Venkata Ramana; Majzoub, Ramsey N; Steffes, Victoria M; Wonder, Emily A; Teesalu, Tambet; Ruoslahti, Erkki; Safinya, Cyrus R
2016-03-15
Because nucleic acids (NAs) have immense potential value as therapeutics, the development of safe and effective synthetic NA vectors continues to attract much attention. In vivo applications of NA vectors require stabilized, nanometer-scale particles, but the commonly used approaches of steric stabilization with a polymer coat (e.g., PEGylation; PEG=poly(ethylene glycol)) interfere with attachment to cells, uptake, and endosomal escape. Conjugation of peptides to PEG-lipids can improve cell attachment and uptake for cationic liposome-DNA (CL-DNA) complexes. We present several synthetic approaches to peptide-PEG-lipids and discuss their merits and drawbacks. A lipid-PEG-amine building block served as the common key intermediate in all synthetic routes. Assembling the entire peptide-PEG-lipid by manual solid phase peptide synthesis (employing a lipid-PEG-carboxylic acid) allowed gram-scale synthesis but is mostly applicable to linear peptides connected via their N-terminus. Conjugation via thiol-maleimide or strain-promoted (copper-free) azide-alkyne cycloaddition chemistry is highly amenable to on-demand preparation of peptide-PEG-lipids, and the appropriate PEG-lipid precursors are available in a single chemical step from the lipid-PEG-amine building block. Azide-alkyne cycloaddition is especially suitable for disulfide-bridged peptides such as iRGD (cyclic CRGDKGPDC). Added at 10mol% of a cationic/neutral lipid mixture, the peptide-PEG-lipids stabilize the size of CL-DNA complexes. They also affect cell attachment and uptake of nanoparticles in a peptide-dependent manner, thereby providing a platform for preparing stabilized, affinity-targeted CL-DNA nanoparticles. PMID:26874401
Brennan, D. P.; Finn, J. M.
2014-10-15
Feedback stabilization of magnetohydrodynamic (MHD) modes in a tokamak is studied in a cylindrical model with a resistive wall, plasma resistivity, viscosity, and toroidal rotation. The control is based on a linear combination of the normal and tangential components of the magnetic field just inside the resistive wall. The feedback includes complex gain, for both the normal and for the tangential components, and it is known that the imaginary part of the feedback for the former is equivalent to plasma rotation [J. M. Finn and L. Chacon, Phys. Plasmas 11, 1866 (2004)]. The work includes (1) analysis with a reduced resistive MHD model for a tokamak with finite β and with stepfunction current density and pressure profiles, and (2) computations with a full compressible visco-resistive MHD model with smooth decreasing profiles of current density and pressure. The equilibria are stable for β = 0 and the marginal stability values β{sub rp,rw} < β{sub rp,iw} < β{sub ip,rw} < β{sub ip,iw} (resistive plasma, resistive wall; resistive plasma, ideal wall; ideal plasma, resistive wall; and ideal plasma, ideal wall) are computed for both models. The main results are: (a) imaginary gain with normal sensors or plasma rotation stabilizes below β{sub rp,iw} because rotation suppresses the diffusion of flux from the plasma out through the wall and, more surprisingly, (b) rotation or imaginary gain with normal sensors destabilizes above β{sub rp,iw} because it prevents the feedback flux from entering the plasma through the resistive wall to form a virtual wall. A method of using complex gain G{sub i} to optimize in the presence of rotation in this regime with β > β{sub rp,iw} is presented. The effect of imaginary gain with tangential sensors is more complicated but essentially destabilizes above and below β{sub rp,iw}.
Zang, Limin; Dai, Wei; Zheng, Limin; Duan, Chuanxi; Lu, Yunpeng; Yang, Minghui
2014-03-21
Theoretical studies of the potential energy surfaces (PESs) and bound states are performed for rare gas-carbon disulfide complexes, He-CS2, Ne-CS2, and Ar-CS2. Three two-dimensional intermolecular PESs are constructed from ab initio data points which are calculated at the CCSD(T) level with aug-cc-pVTZ basis set supplemented with bond functions. We find that the three PESs have very similar features and each PES can be characterized by a global T-shaped minimum, two equivalent local linear minima, and the saddle points between them. The T-shaped isomer is energetically more stable than the linear isomer for each complex. The linear isomers, which have not been observed in experiment so far, are predicted from our PESs and further identified by bound state calculations. Moreover, we assign several intermolecular vibrational states for both the T-shaped and linear isomers of the three complexes via the analysis of wavefunctions. The corresponding vibrational frequencies are calculated from the bound state energies for these assigned states. These frequencies could be helpful for further experimental studies, especially for the linear isomers. We also calculate the rovibrational transition frequencies for the three T-shaped isomers and the pure rotational transition frequencies for the linear isomers, respectively. The accuracy of the PESs is validated by the good agreement between theoretical and experimental results for the rovibrational transition frequencies and spectroscopic parameters. PMID:24655183
Solution of the embedding problem and decomposition of symmetric matrices.
Sippl, M J; Scheraga, H A
1985-01-01
A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a general distance matrix by a one-to-one transformation. Embedding of a distance matrix yields a decomposition of the associated symmetric matrix in the form of a sum over outer products of a linear independent system of coordinate vectors. It is shown that such a decomposition exists for every symmetric matrix and that it is numerically stable. From this decomposition, the rank and the numbers of positive, negative, and zero eigenvalues of the symmetric matrix are obtained directly. PMID:3857574
Construction of dynamics and time-ordered exponential for unbounded non-symmetric Hamiltonians
Futakuchi, Shinichiro; Usui, Kouta
2014-06-15
We prove under certain assumptions that there exists a solution of the Schrödinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not normal. We also prove that, under the same assumptions, there exists a time evolution operator in the interaction picture and that the evolution operator enjoys a useful series expansion formula. This expansion is considered to be one of the mathematically rigorous realizations of so-called “time-ordered exponential,” which is familiar in the physics literature. We apply the general theory to prove the existence of dynamics for the mathematical model of Quantum Electrodynamics quantized in the Lorenz gauge, the interaction Hamiltonian of which is not even symmetric or normal.
Koyama, Yoshiyuki; Sugiura, Kikuya; Yoshihara, Chieko; Inaba, Toshio; Ito, Tomoko
2015-01-01
We have reported that ternary complexes of plasmid DNA with conventional linear polyethylenimine (l-PEI) and certain polyanions were very stably dispersed, and, with no cryoprotectant, they could be freeze-dried and re-hydrated without the loss of transfection ability. These properties enabled the preparation of a concentrated suspension of very small pDNA complex, by preparing the complexes at highly diluted conditions, followed by condensation via lyophilization-and-rehydration procedure. Recently, a high potency linear polyethylenimine having no residual protective groups, i.e., Polyethylenimine “Max” (PEI “Max”), is available, which has been reported to induce much higher gene expression than conventional l-PEI. We tried to prepare the small DNA/PEI “Max”/polyanion complexes by a similar freeze-drying method. Small complex particles could be obtained without apparent aggregation, but transfection activity of the rehydrated complexes was severely reduced. Complex-preparation conditions were investigated in details to achieve the freeze-dried DNA/PEI “Max”/polyanion small ternary complexes with high transfection efficiency. DNA/PEI “Max”/polyanion complexes containing cytokine-coding plasmids were then prepared, and their anti-tumor therapeutic efficacy was examined in tumor-bearing mice. PMID:26213961
Keith, Scott W.; Allison, David B.
2014-01-01
This paper details the design, evaluation, and implementation of a framework for detecting and modeling non-linearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples. The framework provides familiar-looking parameterizations of output in terms of linear slope coefficients and odds ratios. Estimation methods focus on maximum likelihood optimization of piecewise linear free-knot splines formulated as B-splines. Correctly specifying the optimal number and positions of the knots improves the model, but is marked by computational intensity and numerical instability. Our inference methods utilize both parametric and non-parametric bootstrapping. Unlike other non-linear modeling packages, this framework is designed to incorporate multistage survey sample designs common to nationally representative datasets. We illustrate the approach and evaluate its performance in specifying the correct number of knots under various conditions with an example using body mass index (BMI, kg/m2) and the complex multistage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic non-linear sample-weighted risk associations with BMI. BMI and mortality data provide a particularly apt example and area of application since BMI is commonly recorded in large health surveys with complex designs, often categorized for modeling, and non-linearly related to mortality. When complex sample design considerations were ignored, our method was generally similar to or more accurate than two common model selection procedures, Schwarz’s Bayesian Information Criterion (BIC) and Akaike’s Information Criterion (AIC), in terms of correctly selecting the correct number of knots. Our approach provided accurate knot selections when complex sampling weights were incorporated, while AIC and BIC were not effective under these conditions. PMID:25610831
Symmetrization for redundant channels
NASA Technical Reports Server (NTRS)
Tulplue, Bhalchandra R. (Inventor); Collins, Robert E. (Inventor)
1988-01-01
A plurality of redundant channels in a system each contain a global image of all the configuration data bases in each of the channels in the system. Each global image is updated periodically from each of the other channels via cross channel data links. The global images of the local configuration data bases in each channel are separately symmetrized using a voting process to generate a system signal configuration data base which is not written into by any other routine and is available for indicating the status of the system within each channel. Equalization may be imposed on a suspect signal and a number of chances for that signal to heal itself are provided before excluding it from future votes. Reconfiguration is accomplished upon detecting a channel which is deemed invalid. A reset function is provided which permits an externally generated reset signal to permit a previously excluded channel to be reincluded within the system. The updating of global images and/or the symmetrization process may be accomplished at substantially the same time within a synchronized time frame common to all channels.
NASA Astrophysics Data System (ADS)
Rai, Durgesh K.; Beaucage, Gregory; Ratkanthwar, Kedar; Beaucage, Peter; Ramachandran, Ramnath; Hadjichristidis, Nikos
2015-07-01
Star polymers provide model architectures to understand the dynamic and rheological effects of chain confinement for a range of complex topological structures like branched polymers, colloids, and micelles. It is important to describe the structure of such macromolecular topologies using small-angle neutron and x-ray scattering to facilitate understanding of their structure-property relationships. Modeling of scattering from linear, Gaussian polymers, such as in the melt, has applied the random phase approximation using the Debye polymer scattering function. The Flory-Huggins interaction parameter can be obtained using neutron scattering by this method. Gaussian scaling no longer applies for more complicated chain topologies or when chains are in good solvents. For symmetric star polymers, chain scaling can differ from ν =0.5 (df=2 ) due to excluded volume, steric interaction between arms, and enhanced density due to branching. Further, correlation between arms in a symmetric star leads to an interference term in the scattering function first described by Benoit for Gaussian chains. In this work, a scattering function is derived which accounts for interarm correlations in symmetric star polymers as well as the polymer-solvent interaction parameter for chains of arbitrary scaling dimension using a hybrid Unified scattering function. The approach is demonstrated for linear, four-arm and eight-arm polyisoprene stars in deuterated p -xylene.
Rai, Durgesh K; Beaucage, Gregory; Ratkanthwar, Kedar; Beaucage, Peter; Ramachandran, Ramnath; Hadjichristidis, Nikos
2015-07-01
Star polymers provide model architectures to understand the dynamic and rheological effects of chain confinement for a range of complex topological structures like branched polymers, colloids, and micelles. It is important to describe the structure of such macromolecular topologies using small-angle neutron and x-ray scattering to facilitate understanding of their structure-property relationships. Modeling of scattering from linear, Gaussian polymers, such as in the melt, has applied the random phase approximation using the Debye polymer scattering function. The Flory-Huggins interaction parameter can be obtained using neutron scattering by this method. Gaussian scaling no longer applies for more complicated chain topologies or when chains are in good solvents. For symmetric star polymers, chain scaling can differ from ν=0.5(d(f)=2) due to excluded volume, steric interaction between arms, and enhanced density due to branching. Further, correlation between arms in a symmetric star leads to an interference term in the scattering function first described by Benoit for Gaussian chains. In this work, a scattering function is derived which accounts for interarm correlations in symmetric star polymers as well as the polymer-solvent interaction parameter for chains of arbitrary scaling dimension using a hybrid Unified scattering function. The approach is demonstrated for linear, four-arm and eight-arm polyisoprene stars in deuterated p-xylene. PMID:26274195
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2016-06-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Symmetric Waveguide Orthomode Junctions
NASA Technical Reports Server (NTRS)
Wollack, E. J.; Grammer, W.
2003-01-01
Imaging applications at millimeter and submillimeter wavelengths demand precise characterization of the amplitude, spectrum, and polarization of the electromagnetic radiation. The use of a waveguide orthomode transducer (OMT) can help achieve these goals by increasing spectral coverage and sensitivity while reducing exit aperture size, optical spill, instrumental polarization offsets, and lending itself to integration in focal plane arrays. For these reasons, four-fold symmetric OMTs are favored over a traditional quasi-optical wire grid for focal plane imaging arrays from a systems perspective. The design, fabrication, and test of OMTs realized with conventional split-block techniques for millimeter wave-bands are described. The design provides a return loss is -20 dB over a full waveguide band (40% bandwidth), and the cross-polarization and isolation are greater than -40 dB for tolerances readily achievable in practice. Prototype examples realized in WR10.0 and WR3.7 wavebands will be considered in detail.
Symmetric Waveguide Orthomode Junctions
NASA Technical Reports Server (NTRS)
Wollack, E. J.; Grammer, W.
2003-01-01
Imaging applications at millimeter and submillimeter wavelengths demand precise characterization of the amplitude, spectrum, and polarization of the electromagnetic radiation. The use of a waveguide orthomode transducer (OMT) can help achieve these goals by increasing spectral coverage and sensitivity while reducing exit aperture size, optical spill, instrumental polarization offsets, and lending itself to integration in focal plane arrays. For these reasons, four-old symmetric OMTs are favored over a traditional quasi-optical wire grid for focal plane imaging arrays from a systems perspective. The design, fabrication, and test of OMTs realized with conventional split-block techniques for millimeter wave-bands are described. The design provides a return loss is -20 dB over a full waveguide band (40% bandwidth), and the cross-polarization and isolation are greater than -40 dB for tolerances readily achievable in practice. Prototype examples realized in WR10.0 and WR3.7 wavebands will be considered in detail.
Chen, Yong; Yan, Zhenya
2016-01-01
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543
Chen, Yong; Yan, Zhenya
2016-01-01
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543
NASA Astrophysics Data System (ADS)
Chen, Yong; Yan, Zhenya
2016-03-01
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.
Novel linear piezoelectric motor for precision position stage
NASA Astrophysics Data System (ADS)
Chen, Chao; Shi, Yunlai; Zhang, Jun; Wang, Junshan
2016-03-01
Conventional servomotor and stepping motor face challenges in nanometer positioning stages due to the complex structure, motion transformation mechanism, and slow dynamic response, especially directly driven by linear motor. A new butterfly-shaped linear piezoelectric motor for linear motion is presented. A two-degree precision position stage driven by the proposed linear ultrasonic motor possesses a simple and compact configuration, which makes the system obtain shorter driving chain. Firstly, the working principle of the linear ultrasonic motor is analyzed. The oscillation orbits of two driving feet on the stator are produced successively by using the anti-symmetric and symmetric vibration modes of the piezoelectric composite structure, and the slider pressed on the driving feet can be propelled twice in only one vibration cycle. Then with the derivation of the dynamic equation of the piezoelectric actuator and transient response model, start-upstart-up and settling state characteristics of the proposed linear actuator is investigated theoretically and experimentally, and is applicable to evaluate step resolution of the precision platform driven by the actuator. Moreover the structure of the two-degree position stage system is described and a special precision displacement measurement system is built. Finally, the characteristics of the two-degree position stage are studied. In the closed-loop condition the positioning accuracy of plus or minus <0.5 μm is experimentally obtained for the stage propelled by the piezoelectric motor. A precision position stage based the proposed butterfly-shaped linear piezoelectric is theoretically and experimentally investigated.
Tensor species and symmetric functions.
Méndez, M
1991-01-01
An equivariant representation of the symmetric group Sn (equivariant representation from here on) is defined as a particular type of tensor species. For any tensor species R the characteristic generating function of R is defined in a way that generalizes the Frobenius characters of representations of the symmetric groups. If R is an equivariant representation, then the characteristic is a homogeneous symmetric function. The combinatorial operations on equivariant representations correspond to formal operations on the respective characteristic functions. In particular, substitution of equivariant representations corresponds to plethysm of symmetric functions. Equivariant representations are constructed that have as characteristic the elementary, complete, and Schur functions. Bijective proofs are given for the formulas that connect them with the monomial symmetric functions. PMID:11607233
Larsson, Göran; Schleucher, Jürgen; Onions, Jacqueline; Hermann, Stefan; Grundström, Thomas; Wijmenga, Sybren S
2005-08-01
Calmodulin (CaM) interacts specifically as a dimer with some dimeric basic-Helix-Loop-Helix (bHLH) transcription factors via a novel high affinity binding mode. Here we report a study of the backbone dynamics by (15)N-spin relaxation on the CaM dimer in complex with a dimeric peptide that mimics the CaM binding region of the bHLH transcription factor SEF2-1. The relaxation data were measured at multiple magnetic fields, and analyzed in a model-free manner using in-house written software designed to detect nanosecond internal motion. Besides picosecond motions, all residues also experience internal motion with an effective correlation time of approximately 2.5 ns with squared order parameter (S(2)) of approximately 0.75. Hydrodynamic calculations suggest that this can be attributed to motions of the N- and C-terminal domains of the CaM dimer in the complex. Moreover, residues with significant exchange broadening are found. They are clustered in the CaM:SEF2-1mp binding interface, the CaM:CaM dimer interface, and in the flexible helix connecting the CaM N- and C-terminal domains, and have similar exchange times (approximately 50 micros), suggesting a cooperative mechanism probably caused by protein:protein interactions. The dynamic features presented here support the conclusion that the conformationally heterogeneous bHLH mimicking peptide trapped inside the CaM dimer exchanges between different binding sites on both nanosecond and microsecond timescales. Nature has thus found a way to specifically recognize a relatively ill-fitting target. This novel mode of target-specific binding, which neither belongs to lock-and-key nor induced-fit binding, is characterized by dimerization and continuous exchange between multiple flexible binding alternatives. PMID:15894636
Note on free symmetric rigid body motion
NASA Astrophysics Data System (ADS)
Dragović, Vladimir; Gajić, Borislav; Jovanović, Božidar
2015-05-01
We consider the Euler equations of motion of a free symmetric rigid body around a fixed point, restricted to the invariant subspace given by the zero values of the corresponding linear Noether integrals. In the case of the SO( n - 2)-symmetry, we show that almost all trajectories are periodic and that the motion can be expressed in terms of elliptic functions. In the case of the SO( n - 3)-symmetry, we prove the solvability of the problem by using a recent Kozlov's result on the Euler-Jacobi-Lie theorem.
Stability analysis of axial reflection symmetric spacetime
NASA Astrophysics Data System (ADS)
Sharif, M.; Bhatti, M. Zaeem Ul Haq
2016-01-01
In this paper, we explore instability regions of non-static axial reflection symmetric spacetime with anisotropic source in the interior. We impose linear perturbation on the Einstein field equations and dynamical equations to establish the collapse equation. The effects of different physical factors like energy density and anisotropic stresses on the instability regions are studied under Newtonian and post-Newtonian limits. We conclude that stiffness parameter has a significant role in this analysis while the reflection terms increase instability ranges of non-static axial collapse.
Symmetric multilayer megampere X-pinch
Shelkovenko, T. A.; Pikuz, S. A.; McBride, R. D.; Knapp, P. F.; Wilhelm, G.; Sinars, D. B.; Hammer, D. A.; Orlov, N. Yu.
2010-01-15
Raising the power of X-ray emission from an X-pinch by increasing the pinch current to the megampere level requires the corresponding increase in the initial linear mass of the load. This can be achieved by increasing either the number of wires or their diameter. In both cases, special measures should be undertaken to prevent the formation of a complicated configuration with an uncontrolled spatial structure in the region of wire crossing, because such a structure breaks the symmetry of the neck formed in the crossing region, destabilizes plasma formation, and degrades X-ray generation. To improve the symmetry of the wire crossing region, X-pinch configurations with a regular multilayer arrangement of wires in this region were proposed and implemented. The results of experiments with various symmetric X-pinch configurations on the COBRA facility at currents of {approx}1MA are presented. It is shown that an X-pinch with a symmetric crossing region consisting of several layers of wires made of different materials can be successfully used in megampere facilities. The most efficient combinations of wires in symmetric multilayer X-pinches are found in which only one hot spot forms and that are characterized by a high and stable soft X-ray yield.
Šebest, Peter; Brázdová, Marie; Fojta, Miroslav; Pivoňková, Hana
2015-01-01
A study of the effects of salt conditions on the association and dissociation of wild type p53 with different ~3 kbp long plasmid DNA substrates (supercoiled, relaxed circular and linear, containing or lacking a specific p53 binding site, p53CON) using immunoprecipitation at magnetic beads is presented. Salt concentrations above 200 mM strongly affected association of the p53 protein to any plasmid DNA substrate. Strikingly different behavior was observed when dissociation of pre-formed p53-DNA complexes in increased salt concentrations was studied. While contribution from the p53CON to the stability of the p53-DNA complexes was detected between 100 and 170 mM KCl, p53 complexes with circular DNAs (but not linear) exhibited considerable resistance towards salt treatment for KCl concentrations as high as 2 M provided that the p53 basic C-terminal DNA binding site (CTDBS) was available for DNA binding. On the contrary, when the CTDBS was blocked by antibody used for immunoprecipitation, all p53-DNA complexes were completely dissociated from the p53 protein in KCl concentrations ≥200 mM under the same conditions. These observations suggest: (a) different ways for association and dissociation of the p53-DNA complexes in the presence of the CTDBS; and (b) a critical role for a sliding mechanism, mediated by the C-terminal domain, in the dissociation process. PMID:25647416
Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application
NASA Astrophysics Data System (ADS)
Ueda, Yoshihiro; Duan, Renjun; Kawashima, Shuichi
2012-07-01
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima-Shizuta stability condition formulated in Umeda et al. (Jpn J Appl Math 1:435-457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249-275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko system and the Euler-Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375-413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647-667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001-1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima-Shizuta condition, and to analyze the weak dissipative structure for general systems with non-symmetric relaxation.
Lokstein, Heiko; Krikunova, Maria; Teuchner, Klaus; Voigt, Bernd
2011-08-15
Photosynthetically active pigments are usually organized into pigment-protein complexes. These include light-harvesting antenna complexes (LHCs) and reaction centers. Site energies of the bound pigments are determined by interactions with their environment, i.e., by pigment-protein as well as pigment-pigment interactions. Thus, resolution of spectral substructures of the pigment-protein complexes may provide valuable insight into structure-function relationships. By means of conventional (linear) and time-resolved spectroscopic techniques, however, it is often difficult to resolve the spectral substructures of complex pigment-protein assemblies. Nonlinear polarization spectroscopy in the frequency domain (NLPF) is shown to be a valuable technique in this regard. Based on initial experimental work with purple bacterial antenna complexes as well as model systems NLPF has been extended to analyse the substructure(s) of very complex spectra, including analyses of interactions between chlorophylls and "optically dark" states of carotenoids in LHCs. The paper reviews previous work and outlines perspectives regarding the application of NLPF spectroscopy to disentangle structure-function relationships in pigment-protein complexes. PMID:21316796
NASA Technical Reports Server (NTRS)
Kasami, Tadao; Takata, Toyoo; Fujiwara, Toru; Lin, Shu
1993-01-01
It was shown earlier that for a punctured Reed-Muller (RM) code or a primitive BCH code, which contains a punctured RM code of the same minimum distance as a large subcode, the state complexity of the minimal trellis diagram is much greater than that for an equivalent code obtained by a proper permutation on the bit positions. To find a permutation on the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is an interesting and challenging problem. This permutation problem is related to the generalized Hamming weight hierarchy of a code, and is shown that for RM codes, the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to Wei. The state complexity of trellis diagram for the extended and permuted (64, 24) BCH code is discussed.
Sampling and error analysis of radial symmetric interpolation for fast hologram generation.
Lee, Seok; Chang, Hyunsung; Wey, Hocheon; Nam, Dongkyung
2016-01-20
In this paper, we present a fast hologram pattern generation method by radial symmetric interpolation, which exploits concentric redundancy of a point hologram pattern to reduce computational complexity in hologram pattern calculation, and analyze the quality degradation sources in the proposed method. Compared to the analytic method in which phase and amplitude information is directly calculated from a wave equation, in our method a Fresnel zone plate is periodically sampled along a diagonal line and the wave information of a point hologram is calculated by linear interpolation. During these sampling and interpolation processes, the wave information can be modified from the original signal and the reconstruction quality can be degraded compared to the analytic pattern calculation method. The effects of sampling and linear interpolation are investigated in spatial and frequency domains. PMID:26835941
NASA Astrophysics Data System (ADS)
Shanmugakala, R.; Tharmaraj, P.; Sheela, C. D.
2014-11-01
A series of transition metal complexes of type [ML] and [ML2]Cl2 (where M = Cu(II), Ni(II), Co(II) have synthesized from 2-phenylamino-4,6-dichloro-s-triazine and 3,5-dimethyl pyrazole; their characteristics have been investigated by means of elemental analyses, magnetic susceptibility, molar conductance, IR, UV-Vis, Mass, NMR and ESR spectra. The electrochemical behavior of copper(II) complexes we have studied, by using cyclic voltammetry. The ESR spectra of copper(II) complexes are recorded at 300 K and 77 K and their salient features are appropriately reported. Spectral datas, we found, show that the ligand acts as a neutral tridentate, and coordinates through the triazine ring nitrogen and pyrazolyl ring nitrogen atoms to the metal ion. Evident from our findings, the metal(II) complexes of [ML] type exhibit square pyramidal geometry, and that of [ML2]Cl2 exhibit octahedral geometry. The in vitro antimicrobial activities of the ligand and its complexes are evaluated against Bacillus subtilis, Micrococcus luteus, Staphylococcus aureus, Staphylococcus epidermidis, Streptococcus mutans, Escherichia coli, Enterobacter aerogenes, Klebsiella pneumoniae, Proteus vulgaris, Cryptococcus neoformans, Pseudomonas aeruginosa, Salmonella typhi, Serratia marcescens, Shigella flexneri, Vibrio cholera, Vibris parahaemolyticus, Aspergillus niger, Candida albicans and Penicillium oxalicum by well-diffusion method. The second harmonic generation efficiency of the ligand and its complexes are determined and compared with urea and KDP.
Conditional symmetric instability and mesoscale rainbands
NASA Technical Reports Server (NTRS)
Xu, Q.
1986-01-01
The linear theory of conditional symmetric instability (CSI) is re-examined in a rigorous framework. In comparison with symmetric instability a new feature of CSI is that the moist updraught tends to be narrow, as with conditional buoyancy instability (CBI). As the width of the moist updraught varies from its tolerance maximum to infinitesimal, the inviscid growth rate increases from zero to its maximum and the slope of the moist updraught increases from the absolute momentum surface to the moist most unstable surface. The fact that CSI circulations absorb energy from the basic shear and moist thermal field but lose energy to the dry basic thermal field is responsible for the narrow and slant feature of the moist updraught. When a bulk viscosity is accounted for, the most rapidly growing CSI modes bear a qualitative resemblance to some observed rainbands. The stability criterion of viscous CSI also shows a better comparison with observational data than inviscid CSI. The linear CSI theory here predicts that the isolated mode is preferred to other non-isolated (periodic or irregular spacing) modes. The preference of non-isolated modes is speculated to occur in the nonlinear stage.
NASA Astrophysics Data System (ADS)
Metzger, Bernd; Hentschel, Mario; Nesterov, Maxim; Schumacher, Thorsten; Lippitz, Markus; Giessen, Harald
2016-04-01
We investigate the polarization-resolved linear and third-order optical response of plasmonic nanostructure arrays that consist of orthogonally coupled gold nanoantennas. By rotating the incident light polarization direction, either one of the two eigenmodes of the coupled system or a superposition of the eigenmodes can be excited. We find that when an eigenmode is driven by the external light field, the generated third-harmonic signals exhibit the same polarization direction as the fundamental field. In contrast, when a superposition of the two eigenmodes is excited, third-harmonic can efficiently be radiated at the perpendicular polarization direction. Furthermore, the interference of the coherent third-harmonic signals radiated from both nanorods proves that the phase between the two plasmonic oscillators changes in the third-harmonic signal over 3π when the laser is spectrally tuned over the resonance, rather than over π as in the case of the fundamental field. Finally, almost all details of the linear and the nonlinear spectra can be described by an anharmonic coupled oscillator model, which we discuss in detail and which provides deep insight into the linear and the nonlinear optical response of coupled plasmonic nanoantennas.
Progressive symmetrical erythrokeratodermia - Case report*
Guaraldi, Bianca de Mello; Jaime, Thaís Jerez; Guaraldi, Rafael de Mello; Melo, Daniel Fernandes; Nogueira, Osvania Maris; Rodrigues, Nilton
2013-01-01
Progressive symmetrical erythrokeratodermia is a rare autosomal dominant genodermatosis with variable penetrance described by Darier in 1911. It is characterized by erythematous and keratotic plaques, sharply defined and symmetrically distributed along the extremities, buttocks and, more rarely, on the face. We report a case of a 55-year-old patient with lesions on the dorsum of the hands, interphalangeal pads, wrists, groin and back feet. This case demonstrates a rare and late diagnosis, clinical profusion and presence of familiar involvement. PMID:23539014
Symmetric Composite Laminate Stress Analysis
NASA Technical Reports Server (NTRS)
Wang, T.; Smolinski, K. F.; Gellin, S.
1985-01-01
It is demonstrated that COSMIC/NASTRAN may be used to analyze plate and shell structures made of symmetric composite laminates. Although general composite laminates cannot be analyzed using NASTRAN, the theoretical development presented herein indicates that the integrated constitutive laws of a symmetric composite laminate resemble those of a homogeneous anisotropic plate, which can be analyzed using NASTRAN. A detailed analysis procedure is presented, as well as an illustrative example.
Taming the Exceptional Points of Parity-Time Symmetric Acoustics
NASA Astrophysics Data System (ADS)
Dubois, Marc; Shi, Chengzhi; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
Parity-time (PT) symmetric concept and development lead to a wide range of applications including coherent perfect absorbers, single mode lasers, unidirectional cloaking and sensing, and optical isolators. These new applications and devices emerge from the existence of a phase transition in PT symmetric complex-valued potential obtained by balancing gain and loss materials. However, the systematic extension of such devices is adjourned by the key challenge in the management of the complex scattering process within the structure in order to engineer PT phase and exceptional points. Here, based on active acoustic elements, we experimentally demonstrate the simultaneous control of complex-valued potentials and multiple interference inside the structure at any given frequency. This method broadens the scope of applications for PT symmetric devices in many fields including optics, microwaves, electronics, which are crucial for sensing, imaging, cloaking, lasing, absorbing, etc.
Gitsov, Ivan; Hamzik, James; Ryan, Joseph; Simonyan, Arsen; Nakas, James P; Omori, Shigetoshi; Krastanov, Albert; Cohen, Tomer; Tanenbaum, Stuart W
2008-03-01
We describe the construction of enzymatic nanoreactors through noncovalent envelopment of a glycoprotein by amphiphilic linear-dendritic AB or ABA copolymers. The synthetic procedure is based on the regioselective adsorption of dendritic poly(benzyl ether)-block-linear poly(ethylene glycol)-block-dendritic poly(benzyl ether) or linear poly(ethylene oxide)-block-dendritic poly(benzyl ether) copolymers onto the oxidative enzyme laccase from Trametes versicolor in aqueous medium. The complexes formed have improved catalytic activity compared with the native enzyme (77-85 nkat/mL vs 60 nkat/mL, respectively) and are more stable at elevated temperatures up to 70 degrees C. Experiments with deglycosylated laccase confirm that the glycoside fragments in the native enzyme serve as the anchor sites for the linear-dendritic copolymers. The enzymatic nanoreactors are able to effectively oxidize series of substrates: phenolic compounds (syringaldazine) and hydrophobic polyaromatic hydrocarbons (anthracene and benzo[a]pyrene) under "green" chemistry conditions. PMID:18257555
Oskrochi, Gholamreza; Lesaffre, Emmanuel; Oskrochi, Youssof; Shamley, Delva
2016-01-01
In this study, four major muscles acting on the scapula were investigated in patients who had been treated in the last six years for unilateral carcinoma of the breast. Muscle activity was assessed by electromyography during abduction and adduction of the affected and unaffected arms. The main principal aim of the study was to compare shoulder muscle activity in the affected and unaffected shoulder during elevation of the arm. A multivariate linear mixed model was introduced and applied to address the principal aims. The result of fitting this model to the data shows a huge improvement as compared to the alternatives. PMID:26950134
Oskrochi, Gholamreza; Lesaffre, Emmanuel; Oskrochi, Youssof; Shamley, Delva
2016-01-01
In this study, four major muscles acting on the scapula were investigated in patients who had been treated in the last six years for unilateral carcinoma of the breast. Muscle activity was assessed by electromyography during abduction and adduction of the affected and unaffected arms. The main principal aim of the study was to compare shoulder muscle activity in the affected and unaffected shoulder during elevation of the arm. A multivariate linear mixed model was introduced and applied to address the principal aims. The result of fitting this model to the data shows a huge improvement as compared to the alternatives. PMID:26950134
Hydrogen Bond Symmetrization in Glycinium Oxalate under Pressure.
Bhatt, Himal; Murli, Chitra; Mishra, A K; Verma, Ashok K; Garg, Nandini; Deo, M N; Chitra, R; Sharma, Surinder M
2016-02-01
The study of hydrogen bonds near symmetrization limit at high pressures is of importance to understand proton dynamics in complex bio-geological processes. We report here the evidence of hydrogen bond symmetrization in the simplest amino acid-carboxylic acid complex, glycinium oxalate, at moderate pressures of 8 GPa using in-situ infrared and Raman spectroscopic investigations combined with first-principles simulations. The dynamic proton sharing between semioxalate units results in covalent-like infinite oxalate chains. At pressures above 12 GPa, the glycine units systematically reorient with pressure to form hydrogen-bonded supramolecular assemblies held together by these chains. PMID:26730739
NASA Astrophysics Data System (ADS)
Ott, Peter
2005-06-01
An efficient two-dimensional matrix method is presented that facilitates the design of optical systems with tilted surfaces for which the requirement or knowledge of the orientation of the image plane is necessary, i.e., for which a generalized Scheimpflug condition is needed. In more general terms, the method results in imaging properties of second-order expansion, but the method is linear. Therefore the complexity of the design process is considerably reduced. The strength of the design method is demonstrated in detail for a novel application in which a reflective optical system of several surfaces is required for rotationally symmetric triangulation.
Koontz, J L; Moffitt, R D; Marcy, J E; O'Keefe, S F; Duncan, S E; Long, T E
2010-11-01
Polymer additive migration into a food product is dependent upon numerous factors including the original concentration of the additive in the polymer, its solubility in the food, its diffusion coefficient in the polymer, its partition coefficient between the polymer and food, temperature, and time. The limited solubility of quercetin in linear low-density polyethylene (LLDPE) did not allow release from the film due to phase segregation of the quercetin in the bulk polymer. Increasing the molecular weight of α-tocopherol by β-cyclodextrin inclusion complexation can greatly reduce its diffusion coefficient in LLDPE. Ziegler-Natta and metallocene LLDPE contain different crystalline structure morphologies and diffusion path networking arrangements that allow for differences in additive release rates. Effective controlled-release packaging should combine β-cyclodextrin complexation of additives and polymer morphology control to target delivery of an optimal antioxidant concentration to achieve prolonged activity, resulting in extended shelf life foods. PMID:20672204
Pohle, W; Rim, T
1989-01-01
Infrared linear dichroism and X-ray diffraction analysis on oriented films and fibres, respectively, were used simultaneously to elucidate structural characteristics of a DNA-drug complex (the drug was the anticancer antibiotic violamycin BI, an anthracycline derivative). First, the parameters accessible by the two methods are briefly explained; then, attempts to inter-correlate the data from both lines of investigations are made, which demonstrate that they support and supplement each other favourably concerning several structural aspects. This holds, in particular, for results regarding the conformational flexibility of DNA in complexes and the relative amounts of intercalated and outside-bound drug molecules. Thus, the study represents an example for a successful combined application of two physical methods to one biochemical problem. PMID:2803279
NASA Astrophysics Data System (ADS)
Ushenko, V. A.; Gorsky, M. P.
2013-08-01
We present theoretical fundamentals of polarization and correlation analysis of the optical anisotropy of biological tissues. Results of measurements of coordinate distributions of the complex degree of mutual anisotropy (CDMA) that are formed by birefringent structures of the prostate tissue with benign and malignant changes are compared. Magnitudes and ranges of variation of statistical (the firstto fourth-order distribution moments) and correlation (excess of autocorrelation functions) parameters of the coordinate CDMA distributions of histological sections of the prostate postoperative bioptic material are studied. Objective criteria of the diagnostics of the appearance of pathology and of the differentiation of the degree of its severity are determined.
2014-01-01
A simple and robust nanolithographic method that allows sub-100 nm chemical patterning on a range of oxide surfaces was developed in order to fabricate nanoarrays of plant light-harvesting LHCII complexes. The site-specific immobilization and the preserved functionality of the LHCII complexes were confirmed by fluorescence emission spectroscopy. Nanopatterned LHCII trimers could be reversibly switched between fluorescent and quenched states by controlling the detergent concentration in the imaging buffer. A 3-fold quenching of the average fluorescence intensity was accompanied by a decrease in the average (amplitude-weighted) fluorescence lifetime from approximately 2.24 ns to approximately 0.4 ns, attributed to the intrinsic ability of LHCII to switch between fluorescent and quenched states upon changes in its conformational state. The nanopatterning methodology was extended by immobilizing a second protein, the enhanced green fluorescent protein (EGFP), onto LHCII-free areas of the chemically patterned surfaces. This very simple surface chemistry, which allows simultaneous selective immobilization and therefore sorting of the two types of protein molecules on the surface, is a key underpinning step toward the integration of LHCII into switchable biohybrid antenna constructs. PMID:24988144
Looking for symmetric Bell inequalities
NASA Astrophysics Data System (ADS)
Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano
2010-09-01
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.
Numerical study of two-dimensional moist symmetric instability
NASA Astrophysics Data System (ADS)
Fantini, M.; Malguzzi, P.
2008-06-01
The 2-D version of the non-hydrostatic fully compressible model MOLOCH developed at ISAC-CNR was used in idealized set-up to study the start-up and finite amplitude evolution of symmetric instability. The unstable basic state was designed by numerical integration of the equation which defines saturated equivalent potential vorticity qe*. We present the structure and growth rates of the linear modes both for a supersaturated initial state ("super"-linear mode) and for a saturated one ("pseudo"-linear mode) and the modifications induced on the base state by their finite amplitude evolution.
Thin-shell wormholes: Linearization stability
Poisson, E.; Visser, M.
1995-12-15
The class of spherically symmetric thin-shell wormholes provides a particularly elegant collection of exemplars for the study of traversable Lorentzian wormholes. In the present paper we consider linearized (spherically symmetric) perturbations around some assumed static solution of the Einstein field equations. This permits us to relate stability issues to the (linearized) equation of state of the exotic matter which is located at the wormhole throat. {copyright} 1995 The American Physical Society.
Small acoustically forced symmetric bodies in viscous fluids.
Nadal, François; Lauga, Eric
2016-03-01
The total force exerted on a small rigid body by an acoustic field in a viscous fluid is addressed analytically in the limit where the typical size of the particle is smaller than both the viscous diffusion length scale and the acoustic wavelength. In this low-frequency limit, such a force can be calculated provided the effect of the acoustic steady streaming is negligible. Using the Eulerian linear expansion of Lagrangian hydrodynamic quantities (velocity and pressure), the force on a small solid sphere free to move in an acoustic field is first calculated in the case of progressive and standing waves, and it is compared to past results. The proposed method is then extended to the case of more complex shapes with three planes of symmetry. For a symmetric body oriented with one of its axis along the wave direction, the acoustic force exerted by a progressive wave is affected by the particle shape at leading order. In contrast, for a standing wave (with the same orientation), the force experienced by the particle at leading order is the same as the one experienced by a sphere of same volume and density. PMID:27036245
APPROXIMATING SYMMETRIC POSITIVE SEMIDEFINITE TENSORS OF EVEN ORDER*
BARMPOUTIS, ANGELOS; JEFFREY, HO; VEMURI, BABA C.
2012-01-01
Tensors of various orders can be used for modeling physical quantities such as strain and diffusion as well as curvature and other quantities of geometric origin. Depending on the physical properties of the modeled quantity, the estimated tensors are often required to satisfy the positivity constraint, which can be satisfied only with tensors of even order. Although the space P02m of 2mth-order symmetric positive semi-definite tensors is known to be a convex cone, enforcing positivity constraint directly on P02m is usually not straightforward computationally because there is no known analytic description of P02m for m > 1. In this paper, we propose a novel approach for enforcing the positivity constraint on even-order tensors by approximating the cone P02m for the cases 0 < m < 3, and presenting an explicit characterization of the approximation ?2m ? ?2m for m ? 1, using the subset ?2m?P02m of semi-definite tensors that can be written as a sum of squares of tensors of order m. Furthermore, we show that this approximation leads to a non-negative linear least-squares (NNLS) optimization problem with the complexity that equals the number of generators in ?2m. Finally, we experimentally validate the proposed approach and we present an application for computing 2mth-order diffusion tensors from Diffusion Weighted Magnetic Resonance Images. PMID:23285313
Koka, Kanthaiah; Tollin, Daniel J.
2014-01-01
The interaural level difference (ILD) cue to sound location is first encoded in the lateral superior olive (LSO). ILD sensitivity results because the LSO receives excitatory input from the ipsilateral cochlear nucleus and inhibitory input indirectly from the contralateral cochlear nucleus via glycinergic neurons of the ipsilateral medial nucleus of the trapezoid body (MNTB). It is hypothesized that in order for LSO neurons to encode ILDs, the sound spectra at both ears must be accurately encoded via spike rate by their afferents. This spectral-coding hypothesis has not been directly tested in MNTB, likely because MNTB neurons have been mostly described and studied recently in regards to their abilities to encode temporal aspects of sounds, not spectral. Here, we test the hypothesis that MNTB neurons and their inputs from the cochlear nucleus and auditory nerve code sound spectra via discharge rate. The Random Spectral Shape (RSS) method was used to estimate how the levels of 100-ms duration spectrally stationary stimuli were weighted, both linearly and non-linearly, across a wide band of frequencies. In general, MNTB neurons, and their globular bushy cell inputs, were found to be well-modeled by a linear weighting of spectra demonstrating that the pathways through the MNTB can accurately encode sound spectra including those resulting from the acoustical cues to sound location provided by head-related directional transfer functions (DTFs). Together with the anatomical and biophysical specializations for timing in the MNTB-LSO complex, these mechanisms may allow ILDs to be computed for complex stimuli with rapid spectrotemporally-modulated envelopes such as speech and animal vocalizations and moving sound sources. PMID:25565971
Choi, Byung-Moon; Shin, Da-Huin; Noh, Moon-Ho; Kim, Young-Hac; Jeong, Yong-Bo; Lee, Soo-Han; Lee, Eun-Kyung; Noh, Gyu-Jeong
2011-01-01
AIMS Previously, electroencephalographic approximate entropy (ApEn) effectively described both depression of central nervous system (CNS) activity and rebound during and after remifentanil infusion. ApEn is heavily dependent on the record length. Linear mode complexity, which is algorithmatically independent of the record length, was investigated to characterize the effect of remifentanil on the CNS using the combined effect and tolerance, feedback and sigmoid Emax models. METHODS The remifentanil blood concentrations and electroencephalographic data obtained in our previous study were used. With the recording of the electroencephalogram, remifentanil was infused at a rate of 1, 2, 3, 4, 5, 6, 7 or 8 µg kg−1 min−1 for 15–20 min. The areas below (AUCeffect) or above (AACrebound) the effect vs. time curve of temporal linear mode complexity (TLMC) and ApEn were calculated to quantitate the decrease of the CNS activity and rebound. The coefficients of variation (CV) of median baseline (E0), maximal (Emax), and individual median E0 minus Emaxvalues of TLMC were compared with those of ApEn. The concentration–TLMC relationship was characterized by population analysis using non-linear mixed effects modelling. RESULTS Median AUCeffectand AACreboundwere 1016 and 5.3 (TLMC), 787 and 4.5 (ApEn). The CVs of individual median E0 minus Emax were 35.6, 32.5% (TLMC, ApEn). The combined effect and tolerance model demonstrated the lowest Akaike information criteria value and the highest positive predictive value of rebound in tolerance. CONCLUSIONS The combined effect and tolerance model effectively characterized the time course of TLMC as a surrogate measure of the effect of remifentanil on the CNS. PMID:21223358
Staggered parity-time-symmetric ladders with cubic nonlinearity
NASA Astrophysics Data System (ADS)
D'Ambroise, Jennie; Kevrekidis, P. G.; Malomed, Boris A.
2015-03-01
We introduce a ladder-shaped chain with each rung carrying a parity-time- (PT -) symmetric gain-loss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gain-loss and loss-gain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system PT -symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton's method for continuation of the solutions with the increase of the inter-rung coupling, we construct families of PT -symmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung and double ones are identified. Dynamics of unstable solitons is investigated too.
Staggered parity-time-symmetric ladders with cubic nonlinearity.
D'Ambroise, Jennie; Kevrekidis, P G; Malomed, Boris A
2015-03-01
We introduce a ladder-shaped chain with each rung carrying a parity-time- (PT-) symmetric gain-loss dimer. The polarity of the dimers is staggered along the chain, meaning alternation of gain-loss and loss-gain rungs. This structure, which can be implemented as an optical waveguide array, is the simplest one which renders the system PT-symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from the analytically tractable anticontinuum limit of uncoupled rungs and using the Newton's method for continuation of the solutions with the increase of the inter-rung coupling, we construct families of PT-symmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung and double ones are identified. Dynamics of unstable solitons is investigated too. PMID:25871238
Plane symmetric thin-shell wormholes: Solutions and stability
Lemos, Jose P. S.; Lobo, Francisco S. N.
2008-08-15
Using the cut-and-paste procedure, we construct static and dynamic, plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes can be interpreted as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around static solutions is also explored. It is found that thin-shell wormholes made of a dark energy fluid or of a cosmological constant fluid are stable, while thin-shell wormholes made of phantom energy are unstable.
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali; Roychoudhury, Rajkumar
2014-02-15
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Bumblebee preference for symmetrical flowers.
Møller, A P
1995-01-01
Fluctuating asymmetry, which represents small random deviations from otherwise bilateral symmetry, is a measure of the phenotypic quality of individuals indicating the ability of controlled development under given environmental and genetic conditions. I tested whether floral symmetry reliably reflects phenotypic quality measured in terms of pollinator rewards and whether pollinators respond to floral symmetry in a series of observations and experiments on Epilobium angustifolium (Onagraceae). Lower petal asymmetry was negatively related to mean lower petal length, whereas asymmetry in leaf width was positively related to mean leaf width. Flowers visited by bumblebees were larger and more symmetrical than the nearest neighboring flower. This relationship between pollinator preference for large and symmetrical flowers was demonstrated to be causal in experiments in which the lower petals were manipulated symmetrically or asymmetrically. Nectar production was larger in symmetrical flowers, and this may explain the bumblebee preference for flower symmetry. Floral symmetry therefore reliably reflects nectar production and hence enhances pollen transport. Extensive embryo abortion has been documented in E. angustifolium and other outcrossing plant species. Floral fluctuating asymmetry, which reflects general developmental homeostasis, may explain such developmental selection in these plants. PMID:11607519
Benign symmetric lipomatosis (Madelung's disease).
Economides, N G; Liddell, H T
1986-08-01
A black man with benign symmetrical lipomatosis had extensive complete surgical removal of lipomas in the neck and shoulder regions, with an excellent functional result. Despite previous reports advocating conservative surgical debulking, we believe that adequate excision under direct exposure can produce a permanent cure of these tumors. PMID:3738576
Parametric separation of symmetric pure quantum states
NASA Astrophysics Data System (ADS)
Solís-Prosser, M. A.; Delgado, A.; Jiménez, O.; Neves, L.
2016-01-01
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or independent quantum states. We obtained analytical solutions for the success probability of the maps—which is shown to be optimal—as well as explicit constructions in terms of positive operator valued measures. Our results can be used for state discrimination strategies interpolating continuously between minimum-error and unambiguous (or maximum-confidence) discrimination, which, in turn, have many applications in quantum information protocols. As an example, we show that quantum teleportation through a nonmaximally entangled quantum channel can be accomplished with higher probability than the one provided by unambiguous (or maximum-confidence) discrimination and with higher fidelity than the one achievable by minimum-error discrimination. Finally, an optical network is proposed for implementing parametric state separation.
A symmetric bipolar nebula around MWC 922.
Tuthill, P G; Lloyd, J P
2007-04-13
We report regular and symmetric structure around dust-enshrouded Be star MWC 922 obtained with infrared imaging. Biconical lobes that appear nearly square in aspect, forming this "Red Square" nebula, are crossed by a series of rungs that terminate in bright knots or "vortices," and an equatorial dark band crossing the core delimits twin hyperbolic arcs. The intricate yet cleanly constructed forms that comprise the skeleton of the object argue for minimal perturbation from global turbulent or chaotic effects. We also report the presence of a linear comb structure, which may arise from optically projected shadows of a periodic feature in the inner regions, such as corrugations in the rim of a circumstellar disk. The sequence of nested polar rings draws comparison with the triple-ring system seen around the only naked-eye supernova in recent history: SN1987A. PMID:17431173
SymmRef: a Flexible Refinement Method for Symmetric Multimers
Mashiach-Farkash, Efrat; Nussinov, Ruth; Wolfson, Haim J.
2011-01-01
Symmetric protein complexes are abundant in the living cell. Predicting their atomic structure can shed light on the mechanism of many important biological processes. Symmetric docking methods aim to predict the structure of these complexes given the unbound structure of a single monomer, or its model. Symmetry constraints reduce the search-space of these methods and make the prediction easier compared to asymmetric protein-protein docking. However the challenge of modeling the conformational changes that the monomer might undergo is a major obstacle. In this paper we present SymmRef, a novel method for refinement and re-ranking of symmetric docking solutions. The method models backbone and side-chain movements and optimizes the rigid-body orientations of the monomers. The backbone movements are modeled by normal modes minimization and the conformations of the side-chains are modeled by selecting optimal rotamers. Since solved structures of symmetric multimers show asymmetric side-chain conformations, we do not use symmetry constraints in the side-chain optimization procedure. The refined models are re-ranked according to an energy score. We tested the method on a benchmark of unbound docking challenges. The results show that the method significantly improves the accuracy and the ranking of symmetric rigid docking solutions. SymmRef is available for download at http://bioinfo3d.cs.tau.ac.il/SymmRef/download.html. PMID:21721046
NASA Astrophysics Data System (ADS)
Sanchez-Vila, X.; Rubol, S.; Fernandez-Garcia, D.
2011-12-01
Despite the fact that the prognoses on the availability of resources related to different climate scenarios have been already formulated, the complex hydrological and biogeochemical reactions taking place in different compartments in natural environmental media are poorly understood, especially regarding the interactions between water bodies, and the reactions taking place at soil-water interfaces. Amongst them, the inter-relationship between hydrology, chemistry and biology has important implications in natural (rivers, lakes) and man-made water facilities (lagoons, artificial recharge pounds, reservoirs, slow infiltration systems, etc). The consequences involve environment, economic, social and health-risk aspects. At the current stage, only limited explanations are available to understand the implications of these relationships on ecosystem services, water quality and water quantity. Therefore, there is an urgent need to seek a full understanding of these physical-biogeochemical processes in water-bodies, sediments and biota and its implications in ecological and health risk. We present a soil column experiment and a mathematical model which aim to study the mutual interplay between water and bacteria activity in porous media, the corresponding dynamics and the feedback on nutrient cycling by using a multidisciplinary approach.
Li, J.; Bursten, B.E.
1999-11-03
The syntheses of the sandwich complexes ferrocene, ({eta}{sup 5}-C{sub 5}H{sub 5}){sub 2}-Fe, in 1951 and uranocene, ({eta}{sup 8}-C{sub 8}H{sub 8}){sub 2}U, in 1968 ushered in the modern eras of organotransition metal and organoactinide chemistry, respectively. Ferrocene and uranocene are examples of linear sandwich complexes, that is, those in which the (ring centroid)-M-(ring centroid) angle (denoted {theta}) is 180{degree}. In the case of ({eta}{sup 5}-C{sub 5}H{sub 5}){sub 2}M chemistry, a number of bent ({theta} < 180{degree}) complexes are known when M is a main-group or rare-earth element. The explanation for the bent structures of these complexes has been the subject of some debate concerning the relative importance of covalent, electrostatic, and steric interactions. The authors report optimized geometries of Bz{sub 2}An (An = Th-Am) and ({eta}{sup 6}-C{sub 6}H{sub 3}R{sub 3}){sub 2}An (An = Th, U, Pu; R = Me, {sup t}Bu) obtained by using local density approximation (LDA) and Perdew-Wang (PW91) gradient-corrected relativistic density functional theory (DFT) methods. These DFT methods are found to be able to reproduce the experimental geometries and vibrational frequencies of organoactinide complexes with satisfactory accuracy. The (TTB){sub 2}An calculations that are reported here are, to date, the largest full geometry optimizations to be carried out on an actinide system.
Das, Sourav; Dey, Atanu; Kundu, Subrata; Biswas, Sourav; Mota, A J; Colacio, Enrique; Chandrasekhar, Vadapalli
2014-07-01
Sequential reaction of a multisite LH(4) ligand {2-[2-hydroxy-3-(hydroxymethyl)-5-methylbenzylideneamino]-2-methylpropane-1,3-diol} with appropriate lanthanide salts followed by the addition of Ni(NO(3))(2)⋅6 H(2)O in a 4:1:2 stoichiometric ratio in the presence of triethylamine afforded four heterobimetallic trinuclear complexes [Ni(2)Gd(LH(3))(4)]⋅3NO(3)⋅3 MeOH⋅H(2)O⋅CH(3)CN (1), [Ni(2)Tb(LH(3))(4)]⋅(3 )NO(3)⋅3 MeOH⋅CH(3)CN (2), [Ni(2)Dy(LH(3))(4)]⋅3 NO(3)⋅3 MeOH⋅H(2)O⋅CH(3)CN (3), and [Ni(2)Ho(LH(3))(4)]⋅3 NO(3)⋅3 MeOH⋅H(2)O⋅CH(3)CN (4). Complexes 1-4 possess linear trimetallic cores with a central lanthanide ion. Magnetic studies revealed a predominant ferromagnetic interaction between the Ni and Ln centers. Alternating current susceptibility measurements of complex 3 showed a small frequency dependence of the out-of-phase signal, χ''(M), under zero direct current field, but without achieving a net maximum above 2 K. Magnetic studies on 1 revealed that it has a significant magnetocaloric effect. PMID:24817615
Linear electric field mass spectrometry
McComas, David J.; Nordholt, Jane E.
1992-01-01
A mass spectrometer and methods for mass spectrometry. The apparatus is compact and of low weight and has a low power requirement, making it suitable for use on a space satellite and as a portable detector for the presence of substances. High mass resolution measurements are made by timing ions moving through a gridless cylindrically symmetric linear electric field.
Linear electric field mass spectrometry
McComas, D.J.; Nordholt, J.E.
1992-12-01
A mass spectrometer and methods for mass spectrometry are described. The apparatus is compact and of low weight and has a low power requirement, making it suitable for use on a space satellite and as a portable detector for the presence of substances. High mass resolution measurements are made by timing ions moving through a gridless cylindrically symmetric linear electric field. 8 figs.
Benign symmetric lipomatosis (Madelung's disease).
Smith, P D; Stadelmann, W K; Wassermann, R J; Kearney, R E
1998-12-01
Benign symmetric lipomatosis, also known as Madelung's disease, is a rare condition characterized by massive fatty deposits arranged symmetrically around the neck, shoulders, and arms. These patients might present for liposuction and body contouring. Although infrequently encountered in the average plastic surgeon's practice, this condition should be considered when evaluating candidates for these procedures. The deformity is associated with chronic alcohol use and also with malignant tumors of the upper airways. The deformity is prone to recurrence and its surgical treatment often results in less than optimal aesthetic outcomes. Despite this fact, surgical removal via either direct excision or suction-assisted lipectomy provides the only real hope of palliation. This report describes a patient with this deformity and a review of the literature. PMID:9869144
Jing, Hui; zdemir, S K; L, Xin-You; Zhang, Jing; Yang, Lan; Nori, Franco
2014-08-01
By exploiting recent developments associated with coupled microcavities, we introduce the concept of the PT-symmetric phonon laser with balanced gain and loss. This is accomplished by introducing gain to one of the microcavities such that it balances the passive loss of the other. In the vicinity of the gain-loss balance, a strong nonlinear relation emerges between the intracavity-photon intensity and the input power. This then leads to a giant enhancement of both optical pressure and mechanical gain, resulting in a highly efficient phonon-lasing action. These results provide a promising approach for manipulating optomechanical systems through PT-symmetric concepts. Potential applications range from enhancing mechanical cooling to designing phonon-laser amplifiers. PMID:25126921
NASA Astrophysics Data System (ADS)
De Lope Amigo, Santiago; Blechman, Andrew E.; Fox, Patrick J.; Poppitz, Erich
2009-01-01
We present a version of Gauge Mediated Supersymmetry Breaking which preserves an R-symmetrythe gauginos are Dirac particles, the A-terms are zero, and there are four Higgs doublets. This offers an alternative way for gauginos to acquire mass in the supersymmetry-breaking models of Intriligator, Seiberg, and Shih. We investigate the possibility of using R-symmetric gauge mediation to realize the spectrum and large sfermion mixing of the model of Kribs, Poppitz, and Weiner.
NASA Astrophysics Data System (ADS)
Papac, Joseph; Gibou, Frédéric; Ratsch, Christian
2010-02-01
We present a novel and efficient method for solving the Poisson equation, the heat equation, and Stefan-type problems with Robin boundary conditions over potentially moving, arbitrarily-shaped domains. The method utilizes a level set framework, thus it has all of the benefits of a sharp, implicitly-represented interface such as the ease of handling complex topological changes. This method is straightforward to implement and leads to a linear system that is symmetric and positive definite, which can be inverted efficiently with standard iterative methods. This approach is second-order accurate for both the Poisson and heat equations, and first-order accurate for the Stefan problem. We demonstrate the accuracy in the L1 and L∞ norms.
Accessing the exceptional points of parity-time symmetric acoustics.
Shi, Chengzhi; Dubois, Marc; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
2016-01-01
Parity-time (PT) symmetric systems experience phase transition between PT exact and broken phases at exceptional point. These PT phase transitions contribute significantly to the design of single mode lasers, coherent perfect absorbers, isolators, and diodes. However, such exceptional points are extremely difficult to access in practice because of the dispersive behaviour of most loss and gain materials required in PT symmetric systems. Here we introduce a method to systematically tame these exceptional points and control PT phases. Our experimental demonstration hinges on an active acoustic element that realizes a complex-valued potential and simultaneously controls the multiple interference in the structure. The manipulation of exceptional points offers new routes to broaden applications for PT symmetric physics in acoustics, optics, microwaves and electronics, which are essential for sensing, communication and imaging. PMID:27025443
Accessing the exceptional points of parity-time symmetric acoustics
Shi, Chengzhi; Dubois, Marc; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
2016-01-01
Parity-time (PT) symmetric systems experience phase transition between PT exact and broken phases at exceptional point. These PT phase transitions contribute significantly to the design of single mode lasers, coherent perfect absorbers, isolators, and diodes. However, such exceptional points are extremely difficult to access in practice because of the dispersive behaviour of most loss and gain materials required in PT symmetric systems. Here we introduce a method to systematically tame these exceptional points and control PT phases. Our experimental demonstration hinges on an active acoustic element that realizes a complex-valued potential and simultaneously controls the multiple interference in the structure. The manipulation of exceptional points offers new routes to broaden applications for PT symmetric physics in acoustics, optics, microwaves and electronics, which are essential for sensing, communication and imaging. PMID:27025443
Accessing the exceptional points of parity-time symmetric acoustics
NASA Astrophysics Data System (ADS)
Shi, Chengzhi; Dubois, Marc; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
2016-03-01
Parity-time (PT) symmetric systems experience phase transition between PT exact and broken phases at exceptional point. These PT phase transitions contribute significantly to the design of single mode lasers, coherent perfect absorbers, isolators, and diodes. However, such exceptional points are extremely difficult to access in practice because of the dispersive behaviour of most loss and gain materials required in PT symmetric systems. Here we introduce a method to systematically tame these exceptional points and control PT phases. Our experimental demonstration hinges on an active acoustic element that realizes a complex-valued potential and simultaneously controls the multiple interference in the structure. The manipulation of exceptional points offers new routes to broaden applications for PT symmetric physics in acoustics, optics, microwaves and electronics, which are essential for sensing, communication and imaging.
Linear analysis of a force reflective teleoperator
NASA Technical Reports Server (NTRS)
Biggers, Klaus B.; Jacobsen, Stephen C.; Davis, Clark C.
1989-01-01
Complex force reflective teleoperation systems are often very difficult to analyze due to the large number of components and control loops involved. One mode of a force reflective teleoperator is described. An analysis of the performance of the system based on a linear analysis of the general full order model is presented. Reduced order models are derived and correlated with the full order models. Basic effects of force feedback and position feedback are examined and the effects of time delays between the master and slave are studied. The results show that with symmetrical position-position control of teleoperators, a basic trade off must be made between the intersystem stiffness of the teleoperator, and the impedance felt by the operator in free space.
Draber, Peter; Kupka, Sebastian; Reichert, Matthias; Draberova, Helena; Lafont, Elodie; de Miguel, Diego; Spilgies, Lisanne; Surinova, Silvia; Taraborrelli, Lucia; Hartwig, Torsten; Rieser, Eva; Martino, Luigi; Rittinger, Katrin; Walczak, Henning
2015-01-01
Summary Ubiquitination and deubiquitination are crucial for assembly and disassembly of signaling complexes. LUBAC-generated linear (M1) ubiquitin is important for signaling via various immune receptors. We show here that the deubiquitinases CYLD and A20, but not OTULIN, are recruited to the TNFR1- and NOD2-associated signaling complexes (TNF-RSC and NOD2-SC), at which they cooperate to limit gene activation. Whereas CYLD recruitment depends on its interaction with LUBAC, but not on LUBAC’s M1-chain-forming capacity, A20 recruitment requires this activity. Intriguingly, CYLD and A20 exert opposing effects on M1 chain stability in the TNF-RSC and NOD2-SC. While CYLD cleaves M1 chains, and thereby sensitizes cells to TNF-induced death, A20 binding to them prevents their removal and, consequently, inhibits cell death. Thus, CYLD and A20 cooperatively restrict gene activation and regulate cell death via their respective activities on M1 chains. Hence, the interplay between LUBAC, M1-ubiquitin, CYLD, and A20 is central for physiological signaling through innate immune receptors. PMID:26670046
Aukema, Sietse M; Theil, Laura; Rohde, Marius; Bauer, Benedikt; Bradtke, Jutta; Burkhardt, Birgit; Bonn, Bettina R; Claviez, Alexander; Gattenlhner, Stefan; Makarova, Olga; Nagel, Inga; Oschlies, Ilske; Pott, Christiane; Szczepanowski, Monika; Traulsen, Arne; Kluin, Philip M; Klapper, Wolfram; Siebert, Reiner; Murga Penas, Eva M
2015-09-01
Typical Burkitt lymphoma is characterized by an IG-MYC translocation and overall low genomic complexity. Clinically, Burkitt lymphoma has a favourable prognosis with very few relapses. However, the few patients experiencing disease progression and/or relapse have a dismal outcome. Here we report cytogenetic findings of seven cases of Burkitt lymphoma in which sequential karyotyping was performed at time of diagnosis and/or disease progression/relapse(s). After case selection, karyotype re-review and additional molecular analyses were performed in six paediatric cases, treated in Berlin-Frankfurt-Mnster-Non-Hodgkin lymphoma study group trials, and one additional adult patient. Moreover, we analysed 18 cases of Burkitt lymphoma from the Mitelman database in which sequential karyotyping was performed. Our findings show secondary karyotypes to have a significant increase in load of cytogenetic aberrations with a mean number of 2, 5 and 8 aberrations for primary, secondary and third investigations. Importantly, this increase in karyotype complexity seemed to result from recurrent secondary chromosomal changes involving mainly trisomy 21, gains of 1q and 7q, losses of 6q, 11q, 13q, and 17p. In addition, our findings indicate a linear clonal evolution to be the predominant manner of cytogenetic evolution. Our data may provide a biological framework for the dismal outcome of progressive and relapsing Burkitt lymphoma. PMID:26104998
Abusam, A; Keesman, K J; van Straten, G; Spanjers, H; Meinema, K
2001-01-01
When applied to large simulation models, the process of parameter estimation is also called calibration. Calibration of complex non-linear systems, such as activated sludge plants, is often not an easy task. On the one hand, manual calibration of such complex systems is usually time-consuming, and its results are often not reproducible. On the other hand, conventional automatic calibration methods are not always straightforward and often hampered by local minima problems. In this paper a new straightforward and automatic procedure, which is based on the response surface method (RSM) for selecting the best identifiable parameters, is proposed. In RSM, the process response (output) is related to the levels of the input variables in terms of a first- or second-order regression model. Usually, RSM is used to relate measured process output quantities to process conditions. However, in this paper RSM is used for selecting the dominant parameters, by evaluating parameters sensitivity in a predefined region. Good results obtained in calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch proved that the proposed procedure is successful and reliable. PMID:11385868
Shimizu, Satoshi; Fujita, Hiroaki; Sasaki, Yoshiteru; Tsuruyama, Tatsuaki; Fukuda, Kazuhiko; Iwai, Kazuhiro
2016-05-15
The linear ubiquitin chain assembly complex (LUBAC) participates in NF-κB activation and cell death protection. Loss of any of the three LUBAC subunits (catalytic HOIP, accessory HOIL-1L, or accessory SHARPIN subunit) leads to distinct phenotypes in mice and human. cpdm mice (chronic proliferative dermatitis in mice [cpdm]) that lack SHARPIN exhibit chronic inflammatory phenotypes, whereas HOIL-1L knockout mice exhibit no overt phenotypes, despite sharing highly homologous ubiquitin-like (UBL) and Npl4 zinc finger (NZF) domains. Here, we intercrossed mice lacking HOIL-1L and SHARPIN and found that reduction of HOIL-1L in cpdm mice exacerbated inflammatory phenotypes without affecting characteristic features of cpdm disease, whereas reduction of SHARPIN in HOIL-1L knockout mice provoked no overt phenotypes. Hence, loss of SHARPIN and reduction of LUBAC triggers cpdm phenotypes. We found that the NZF domain of SHARPIN, but not that of HOIL-1L, is critical for effective protection from programmed cell death by enhancing the recruitment of LUBAC to the activated TNFR complex. The binding activity to K63-linked ubiquitin chains that the NZF domain of SHARPIN, but not that of HOIL-1L, possesses appears to be involved in the recruitment. Thus, selective recognition of ubiquitin chains by NZFs in LUBAC underlies the regulation of LUBAC function. PMID:26976635
van Rahden, Vanessa A.; Fernandez-Vizarra, Erika; Alawi, Malik; Brand, Kristina; Fellmann, Florence; Horn, Denise; Zeviani, Massimo; Kutsche, Kerstin
2015-01-01
Microphthalmia with linear skin defects (MLS) syndrome is an X-linked male-lethal disorder also known as MIDAS (microphthalmia, dermal aplasia, and sclerocornea). Additional clinical features include neurological and cardiac abnormalities. MLS syndrome is genetically heterogeneous given that heterozygous mutations in HCCS or COX7B have been identified in MLS-affected females. Both genes encode proteins involved in the structure and function of complexes III and IV, which form the terminal segment of the mitochondrial respiratory chain (MRC). However, not all individuals with MLS syndrome carry a mutation in either HCCS or COX7B. The majority of MLS-affected females have severe skewing of X chromosome inactivation, suggesting that mutations in HCCS, COX7B, and other as-yet-unidentified X-linked gene(s) cause selective loss of cells in which the mutated X chromosome is active. By applying whole-exome sequencing and filtering for X-chromosomal variants, we identified a de novo nonsense mutation in NDUFB11 (Xp11.23) in one female individual and a heterozygous 1-bp deletion in a second individual, her asymptomatic mother, and an affected aborted fetus of the subject’s mother. NDUFB11 encodes one of 30 poorly characterized supernumerary subunits of NADH:ubiquinone oxidoreductase, known as complex I (cI), the first and largest enzyme of the MRC. By shRNA-mediated NDUFB11 knockdown in HeLa cells, we demonstrate that NDUFB11 is essential for cI assembly and activity as well as cell growth and survival. These results demonstrate that X-linked genetic defects leading to the complete inactivation of complex I, III, or IV underlie MLS syndrome. Our data reveal an unexpected role of cI dysfunction in a developmental phenotype, further underscoring the existence of a group of mitochondrial diseases associated with neurocutaneous manifestations. PMID:25772934
Symmetric and antisymmetric nonlinear modes supported by dual local gain in lossy lattices
NASA Astrophysics Data System (ADS)
Chow, K. W.; Ding, Edwin; Malomed, B. A.; Tang, A. Y. S.
2014-01-01
We introduce a discrete lossy system, into which a double "hot spot" (HS) is inserted, i.e., two mutually symmetric sites carrying linear gain and cubic nonlinearity. The system can be implemented as an array of optical or plasmonic waveguides, with a pair of amplified nonlinear cores embedded into it. We focus on the case of self-defocusing nonlinearity and cubic losses acting at the HSs. Symmetric localized modes pinned to the double HS are constructed in an implicit analytical form, which is done separately for the cases of odd and even numbers of intermediate sites between the HSs. In the former case, some stationary solutions feature a W-like shape, with a low peak at the central site, added to tall peaks at the positions of the embedded HSs. The special case of two adjacent HSs is considered too. Stability of the solution families against small perturbations is investigated in a numerical form, which reveals stable and unstable subfamilies. The instability generated by an isolated positive eigenvalue leads to a spontaneous transformation into a co-existing stable antisymmetric mode, while a pair of complex-conjugate eigenvalues gives rise to persistent breathers. This article is a contribution to the volume dedicated to Professor Helmut Brand on the occasion of his 60th birhday.
Giribet, Claudia G; Aza, Martn C Ruiz de
2008-05-01
The cooperative effects on NMR indirect nuclear coupling constants are analyzed by means of the IPPP-CLOPPA approach (where CLOPPA is the Contributions from Localized Orbitals within the Polarization Propagator Approach and IPPP is the Inner Projections of the Polarization Propagator). The decomposition of the J coupling allows one to classify these effects as those due to changes in the geometric structure and those that directly involve the transmission mechanisms. This latter contribution admits a further classification, taking into account its electronic origin. As an example, the cooperative effects on intermolecular 2hJ(N,C) couplings of the linear complexes (CNH)n (n = 2, 3, 4) are discussed. PMID:18410158
Postural stability in symmetrical gaits.
Zielińska, Teresa; Trojnacki, Maciej
2009-01-01
In this paper the method of stability analysis of dynamic symmetrical gaits is discussed. The problem of dynamic postural equilibrium, taking into account the role of compliant feet, is solved. The equilibrium conditions are split between the foot attachment points and the points within the foot-end area. The present method is useful for motion synthesis, taking into account robot parameters. It also helps in the robot foot design. As an illustrative example a four-legged diagonal gait is considered. The theoretical results were verified by implementing and observing the diagonal gait in four-legged machine with and without feet. PMID:19839558
Cycles in symmetric sequence processing
NASA Astrophysics Data System (ADS)
Metz, Fernando L.; Theumann, Walter K.
2007-02-01
The competition between pattern reconstruction and sequence processing is studied here in an exactly solvable feed-forward layered neural network model of binary units and patterns near saturation. We show results for both symmetric and asymmetric sequence processing, either one competing with pattern reconstruction represented by a Hebbian interaction, in order to compare these two kinds of sequence processing. Phase diagrams of stationary states are obtained and a new phase of cycles of period two is found for a weak Hebbian term in the case of symmetric sequence processing, independently of the number of condensed patterns c which have macroscopic overlaps with the states of the network. In contrast, the stability of these cycles depends strongly on c. These results are in contrast with those for the competition between a Hebbian interaction and an asymmetric sequence processing interaction, in which the period of the cycles is c and the stability of these solutions does not depend on c. The dynamics of the macroscopic overlaps in the stationary cyclic phase is analyzed in both models.
Odille, Fabrice G J; Jónsson, Stefán; Stjernqvist, Susann; Rydén, Tobias; Wärnmark, Kenneth
2007-01-01
A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab, and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4n5m as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the DeltaH degrees and DeltaS degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters. PMID:17868169
Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge
NASA Astrophysics Data System (ADS)
Cao, D. Q.; Song, M. T.; Zhu, W. D.; Tucker, R. W.; Wang, C. H.-T.
2012-12-01
The in-plane vibration of a complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern transverse and longitudinal vibrations of the cables and transverse vibrations of segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge are determined, and orthogonality relations of the mode shapes are established. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for various symmetrical and non-symmetrical bridge cases with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies when the bridge model is symmetrical and/or partially symmetrical, and the mode shapes tend to be more localized when the bridge model is less symmetrical. The relationships between the natural frequencies and mode shapes of the cable-stayed bridge and those of a single fixed-fixed cable and the single simply-supported deck beam are analyzed. The results, which are validated by commercial finite element software, demonstrate some complex classical resonance behavior of the cable-stayed bridge.
PT-symmetric phase in kagome-based photonic lattices.
Chern, Gia-Wei; Saxena, Avadh
2015-12-15
The kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing PT-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation. PMID:26670517
PT-symmetric phase in kagome-based photonic lattices
NASA Astrophysics Data System (ADS)
Chern, Gia-Wei; Saxena, Avadh
2015-12-01
Kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing $\\mathcal{PT}$-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a $\\mathcal{PT}$-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
Spatiotemporal localized modes in PT-symmetric optical media
Wang, Yue-Yue; Dai, Chao-Qing Wang, Xiao-Gang
2014-09-15
We firstly obtain spatiotemporal localized mode solutions of a (3+1)-dimensional nonlinear Schrödinger equation in PT-symmetric potentials, and then discuss the linear stability of LMs, which are also tested by means of direct simulations. Moreover, phase switches and transverse power-flow density associated with these localized modes have also been examined. At last, we investigate the dynamical behaviors of spatiotemporal LMs in three kinds of inhomogeneous media. - Highlights: • Spatiotemporal LMs of a (3+1)-dimensional NLSE in PT-symmetric potentials are obtained. • Phase switches and transverse power-flow density of LM are examined. • Dynamical behaviors of LMs in three kinds of inhomogeneous media are studied.
PT-symmetric dimer of coupled nonlinear oscillators
NASA Astrophysics Data System (ADS)
Cuevas, Jesús; Kevrekidis, Panayotis G.; Saxena, Avadh; Khare, Avinash
2013-09-01
We provide a systematic analysis of a prototypical nonlinear oscillator system respecting PT symmetry i.e., one of them has gain and the other an equal and opposite amount of loss. Starting from the linear limit of the system, we extend considerations to the nonlinear case for both soft and hard cubic nonlinearities identifying symmetric and antisymmetric breather solutions, as well as symmetry-breaking variants thereof. We propose a reduction of the system to a Schrödinger-type PT-symmetric dimer, whose detailed earlier understanding can explain many of the phenomena observed herein, including the PT phase transition. Nevertheless, there are also significant parametric as well as phenomenological potential differences between the two models and we discuss where these arise and where they are most pronounced. Finally, we also provide examples of the evolution dynamics of the different states in their regimes of instability.
Circular symmetrization of condensers on Riemann surfaces
NASA Astrophysics Data System (ADS)
Dubinin, V. N.
2015-01-01
We give a simplified definition of the new version of circular symmetrization which has previously been suggested by the author for solving extremal problems in geometric function theory. A proof of the symmetrization principle for the capacities of condensers on Riemann surfaces is presented. In addition, the class of condensers under consideration is extended and all the cases of equality in the symmetrization principle are found. Bibliography: 22 titles.
Open String on Symmetric Product
NASA Astrophysics Data System (ADS)
Fuji, Hiroyuki; Matsuo, Yutaka
We discuss some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete light-cone quantization (DLCQ). We first derive the consistent twisted boundary conditions for Annulus/Möbius/Klein Bottle diagrams and give the explicit form of the corresponding amplitude. They have the interpretation as the long open (or closed) string amplitude but the world sheet topology viewed from the short string and from the long string is in general different. Boundary (cross-cap) states of the short string are classified into three categories, the boundary (cross-cap) states of the long string and the "joint" state which connects two strings. The partition function has the typical structure of the string field theory in DLCQ. Tadpole condition is also analyzed and gives a reasonable gauge group SO(213).
Drift waves in helically symmetric stellarators
Rafiq, T.; Hegna, C.
2005-11-15
The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to be more affected by the normal curvature than by the geodesic curvature. The threshold of stability of the ITG modes in terms of {eta}{sub i} is found to be 2/3 in this fluid model consistent with the smallest threshold for toroidal geometry with adiabatic electrons. Optimization to favorable drift wave stability has small field line curvature, short connection lengths, the proper combination of geodesic curvature and local magnetic shear, large values of local magnetic shear, and the compression of flux surfaces in the unfavorable curvature region.
Strong orientational coordinates and orientational order parameters for symmetric objects
NASA Astrophysics Data System (ADS)
Haji-Akbari, Amir; Glotzer, Sharon C.
2015-12-01
Recent advancements in the synthesis of anisotropic macromolecules and nanoparticles have spurred an immense interest in theoretical and computational studies of self-assembly. The cornerstone of such studies is the role of shape in self-assembly and in inducing complex order. The problem of identifying different types of order that can emerge in such systems can, however, be challenging. Here, we revisit the problem of quantifying orientational order in systems of building blocks with non-trivial rotational symmetries. We first propose a systematic way of constructing orientational coordinates for such symmetric building blocks. We call the arising tensorial coordinates strong orientational coordinates (SOCs) as they fully and exclusively specify the orientation of a symmetric object. We then use SOCs to describe and quantify local and global orientational order, and spatiotemporal orientational correlations in systems of symmetric building blocks. The SOCs and the orientational order parameters developed in this work are not only useful in performing and analyzing computer simulations of symmetric molecules or particles, but can also be utilized for the efficient storage of rotational information in long trajectories of evolving many-body systems.
Xu, Songchen; Magoon, Yitzhak; Reinig, Regina R.; Schmidt, Bradley M.; Ellern, Arkady; Sadow, Aaron D.
2015-07-16
A bulky, optically active monoanionic scorpionate ligand, tris(4S-isopropyl-5,5-dimethyl-2-oxazolinyl)phenylborate (To^{P*}), is synthesized from the naturally occurring amino acid l-valine as its lithium salt, Li[To^{P*}] (1). That compound is readily converted to the thallium complex Tl[To^{P*}] (2) and to the acid derivative H[To^{P*}] (3). Group 7 tricarbonyl complexes To^{P*}M(CO)_{3} (M = Mn (4), Re (5)) are synthesized by the reaction of MBr(CO)_{5} and Li[To^{P*}] and are crystallographically characterized. The ν_{CO} bands in their infrared spectra indicate that π back-donation in the rhenium compounds is greater with To^{P*} than with non-methylated tris(4S-isopropyl-2-oxazolinyl)phenylborate (To^{P}). The reaction of H[To^{P*}] and ZnEt_{2} gives To^{P*}ZnEt (6), while To^{P*}ZnCl (7) is synthesized from Li[To^{P*}] and ZnCl_{2}. The reaction of To^{P*}ZnCl and KOtBu followed by addition of PhSiH_{3} provides the zinc hydride complex To^{P*}ZnH (8). In this study, compound 8 is the first example of a crystallographically characterized optically active zinc hydride. We tested its catalytic reactivity in the cross-dehydrocoupling of silanes and alcohols, which provided Si-chiral silanes with moderate enantioselectivity.
Critical binding and electron scattering by symmetric-top polar molecules
Garrett, W. R.
2014-10-28
Quantum treatments of electron interactions with polar symmetric-top rotor molecules show features not present in the treatment of the linear-polar-rotor model. For symmetric tops possessing non-zero angular momentum about the symmetry axis, a new critical dipole can be defined that guarantees an infinite set of dipole-bound states independent of the values of the components of the inertial tensor. Additionally, for this same class, the scattering cross section diverges for all nonzero values of dipole moments and inertial moments, similar to solutions for the fixed linear dipole. Additional predictions are presented for electron affinities and rotational resonances of these systems.
The generalized sidelobe canceller based on quaternion widely linear processing.
Tao, Jian-wu; Chang, Wen-xiu
2014-01-01
We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array's quaternion model, we propose the general expression of a quaternion semiwidely linear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array's gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal's direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC. PMID:24955425
The Generalized Sidelobe Canceller Based on Quaternion Widely Linear Processing
Tao, Jian-wu; Chang, Wen-xiu
2014-01-01
We investigate the problem of quaternion beamforming based on widely linear processing. First, a quaternion model of linear symmetric array with two-component electromagnetic (EM) vector sensors is presented. Based on array's quaternion model, we propose the general expression of a quaternion semiwidely linear (QSWL) beamformer. Unlike the complex widely linear beamformer, the QSWL beamformer is based on the simultaneous operation on the quaternion vector, which is composed of two jointly proper complex vectors, and its involution counterpart. Second, we propose a useful implementation of QSWL beamformer, that is, QSWL generalized sidelobe canceller (GSC), and derive the simple expressions of the weight vectors. The QSWL GSC consists of two-stage beamformers. By designing the weight vectors of two-stage beamformers, the interference is completely canceled in the output of QSWL GSC and the desired signal is not distorted. We derive the array's gain expression and analyze the performance of the QSWL GSC in the presence of one type of interference. The advantage of QSWL GSC is that the main beam can always point to the desired signal's direction and the robustness to DOA mismatch is improved. Finally, simulations are used to verify the performance of the proposed QSWL GSC. PMID:24955425
NASA Astrophysics Data System (ADS)
Sidorin, Anatoly
2010-01-01
In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.
Sidorin, Anatoly
2010-01-05
In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.
Continuity and Separation in Symmetric Topologies
ERIC Educational Resources Information Center
Harris, J.; Lynch, M.
2007-01-01
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
Baryon symmetric big bang cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1978-01-01
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Thermoelastic analysis of laminated plates. I - Symmetric specially orthotropic laminates
Wu, C.H.; Tauchert, T.R.
1980-04-01
Thermally induced deformations and stress resultants in symmetric laminated plates are analyzed. The method of M. Levy is used to study the transverse bending of a specially orthotropic laminate having two simply supported edges and subject to a temperature distribution that does not vary in a direction parallel to the simple supports. A solution is also obtained for the problem of in-plane stretching of the plate middle surface caused by a general three-dimensional temperature field. As an illustrative example, the thermoelastic response of a unidirectionally fiber-reinforced plate to a temperature variation that is linear in the thickness direction is computed.
Geometrodynamics in a spherically symmetric, static crossflow of null dust
Horvath, Zsolt; Kovacs, Zoltan; Gergely, Laszlo A.
2006-10-15
The spherically symmetric, static space-time generated by a crossflow of noninteracting radiation streams, treated in the geometrical optics limit (null dust), is equivalent to an anisotropic fluid forming a radiation atmosphere of a star. This reference fluid provides a preferred/internal time, which is employed as a canonical coordinate. Among the advantages we encounter a new Hamiltonian constraint, which becomes linear in the momentum conjugate to the internal time (therefore yielding a functional Schroedinger equation after quantization), and a strongly commuting algebra of the new constraints.
BDDC for nonsymmetric positive definite and symmetric indefinite problems
Tu, Xuemin; Li, Jing
2008-12-10
The balancing domain decomposition methods by constraints are extended to solving both nonsymmetric, positive definite and symmetric, indefinite linear systems. In both cases, certain nonstandard primal constraints are included in the coarse problems of BDDC algorithms to accelerate the convergence. Under the assumption that the subdomain size is small enough, a convergence rate estimate for the GMRES iteration is established that the rate is independent of the number of subdomains and depends only slightly on the subdomain problem size. Numerical experiments for several two-dimensional examples illustrate the fast convergence of the proposed algorithms.
Diagonalization of the symmetrized discrete i th right shift operator
NASA Astrophysics Data System (ADS)
Fuentes, Marc
2007-01-01
In this paper, we consider the symmetric part of the so-called ith right shift operator. We determine its eigenvalues as also the associated eigenvectors in a complete and closed form. The proposed proof is elementary, using only basical skills such as Trigonometry, Arithmetic and Linear algebra. The first section is devoted to the introduction of the tackled problem. Second and third parts contain almost all the ?technical? stuff of the proofE Afterwards, we continue with the end of the proof, provide a graphical illustration of the results, as well as an application on the polyhedral ?sandwiching? of a special compact of arising in Signal theory.
Using scaling to compute moments of inertia of symmetric objects
NASA Astrophysics Data System (ADS)
Ricardo, Bernard
2015-09-01
Moment of inertia is a very important property in the study of rotational mechanics. The concept of moment of inertia is analogous to mass in the linear motion, and its calculation is routinely done through integration. This paper provides an alternative way to compute moments of inertia of rigid bodies of regular shape using their symmetrical property. This approach will be very useful and preferred for teaching rotational mechanics at the undergraduate level, as it does not require the knowledge or the application of calculus. The seven examples provided in this paper will help readers to understand clearly how to use the method.
Recursive partitioned inversion of large (1500 x 1500) symmetric matrices
NASA Technical Reports Server (NTRS)
Putney, B. H.; Brownd, J. E.; Gomez, R. A.
1976-01-01
A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.
Linear-scaling Cholesky decomposition.
Schweizer, Sabine; Kussmann, Jörg; Doser, Bernd; Ochsenfeld, Christian
2008-04-30
We present linear-scaling routines for the calculation of the Cholesky decomposition of a symmetric positive-definite matrix and its inverse. As an example, we consider the inversion of the overlap matrix of DNA and amylose fragments as well as of linear alkanes, where the largest system corresponds to a 21,442 x 21,442 matrix. The efficiency and the scaling behavior are discussed and compared to standard LAPACK routines. Our Cholesky routines are publicly available on the web. PMID:17999386
Maximum-confidence discrimination among symmetric qudit states
Jimenez, O.; Solis-Prosser, M. A.; Delgado, A.; Neves, L.
2011-12-15
We study the maximum-confidence (MC) measurement strategy for discriminating among nonorthogonal symmetric qudit states. Restricting to linearly dependent and equally likely pure states, we find the optimal positive operator valued measure (POVM) that maximizes our confidence in identifying each state in the set and minimizes the probability of obtaining inconclusive results. The physical realization of this POVM is completely determined and it is shown that after an inconclusive outcome, the input states may be mapped into a new set of equiprobable symmetric states, restricted, however, to a subspace of the original qudit Hilbert space. By applying the MC measurement again onto this new set, we can still gain some information about the input states, although with less confidence than before. This leads us to introduce the concept of sequential maximum-confidence (SMC) measurements, where the optimized MC strategy is iterated in as many stages as allowed by the input set, until no further information can be extracted from an inconclusive result. Within each stage of this measurement our confidence in identifying the input states is the highest possible, although it decreases from one stage to the next. In addition, the more stages we accomplish within the maximum allowed, the higher will be the probability of correct identification. We will discuss an explicit example of the optimal SMC measurement applied in the discrimination among four symmetric qutrit states and propose an optical network to implement it.
Nontotally symmetric trifurcation of an SN 2 reaction pathway.
Harabuchi, Yu; Ono, Yuriko; Maeda, Satoshi; Taketsugu, Tetsuya; Keipert, Kristopher; Gordon, Mark S
2016-02-15
A new type of reaction pathway which involves a nontotally symmetric trifurcation was found and investigated for a typical SN 2-type reaction, NC(-) ?+?CH3 X ? NC?CH3 ?+?X(-) (X?=?F, Cl). A nontotally symmetric valley-ridge inflection (VRI) point was located along the C3 v reaction path. For X?=?F, the minimum energy path (MEP) starting from the transition state (TS) leads to a second-order saddle point with C3 v symmetry, which connects three product minima of Cs symmetry. For X?=?Cl, four product minima have been observed, of which three belong to Cs symmetry and one to C3 v symmetry. The branching path from the VRI point to the lower symmetry minima was determined by a linear interpolation technique. The branching mechanism is discussed based on the reaction path curvature and net atomic charges, and the possibility of a nonotally symmetric n-furcation is discussed. 2015 Wiley Periodicals, Inc. PMID:26511597
NASA Astrophysics Data System (ADS)
Laurent, Oscar; Zeh, Armin
2015-11-01
Combined U-Pb and Lu-Hf isotope data from zircon populations are widely used to constrain Hadean-Archean crustal evolution. Linear Hf isotope-age arrays are interpreted to reflect the protracted, internal reworking of crust derived from the (depleted) mantle during a short-lived magmatic event, and related 176Lu/177Hf ratios are used to constrain the composition of the reworked crustal reservoir. Results of this study, however, indicate that Hf isotope-age arrays can also result from complex geodynamic processes and crust-mantle interactions, as shown by U-Pb and Lu-Hf isotope analyses of zircons from well characterized granitoids of the Pietersburg Block (PB), northern Kaapvaal Craton (South Africa). Apart from scarce remnants of Paleoarchean crust, most granitoids of the PB with ages between 2.94 and 2.05 Ga (n = 32) define a straight Hf isotope-age array with low 176Lu/177Hf of 0.0022, although they show a wide compositional range, were derived from various sources and emplaced successively in different geodynamic settings. The crustal evolution occurred in five stages: (I) predominately mafic crust formation in an intra-oceanic environment (3.4-3.0 Ga); (II) voluminous TTG crust formation in an early accretionary orogen (3.0-2.92 Ga); (III) internal TTG crust reworking and subduction of TTG-derived sediments in an Andean-type setting (2.89-2.75 Ga); (IV) (post-)collisional high-K magmatism from both mantle and crustal sources (2.71-2.67 Ga); and (V) alkaline magmatism in an intra-cratonic environment (2.05-2.03 Ga). The inferred array results from voluminous TTG crust formation during stage II, and involvement of this crust during all subsequent stages by two different processes: (i) internal crust reworking through both partial melting and assimilation at 2.89-2.75 Ga, leading to the formation of biotite granites coeval with minor TTGs, and (ii) subduction of TTG-derived sediments underneath the PB, causing enrichment of the mantle that subsequently became source for high-K granitoids and mafic rocks at 2.68 and 2.05 Ga. Some scatter along the array might have resulted either from significant assimilation of ancient crust, intracrustal Lu/Hf fractionation or melting of heterogeneous mantle sources. Those results show that without any information about the nature and composition of zircon-hosting granitoids, Hf isotope-age data are of limited use to constrain Hadean-Archean magmatogenesis and geodynamics.
Observation of optical solitons in PT-symmetric lattices
NASA Astrophysics Data System (ADS)
Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf
2015-07-01
Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.
Observation of optical solitons in PT-symmetric lattices.
Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N; Peschel, Ulf
2015-01-01
Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated. PMID:26215165
Observation of optical solitons in PT-symmetric lattices
Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf
2015-01-01
Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated. PMID:26215165
Dirac-Lorentz Equation in Symmetrized Electrodynamics
NASA Astrophysics Data System (ADS)
van Meter, J. R.; Hartemann, F. V.; Chen, P.
1998-11-01
Motivated by considerations regarding high field electrodynamics and the classical limit of QED(M. Zolotorev, private communication, AAC 1998), the fundamental equations of classical electrodynamics are symmetrized to include magnetic charges. A double 4-potential formalism is introduced, in terms of which the field tensor and its dual are employed to symmetrize Maxwell's equations and the Lorentz force equation in covariant form. Within this framework, the symmetrized Dirac-Lorentz force equation is derived, giving the radiation reaction (self-force) for a particle possessing both electric and magnetic charge.
Nonlinearly PT-symmetric systems: Spontaneous symmetry breaking and transmission resonances
Miroshnichenko, Andrey E.; Kivshar, Yuri S.; Malomed, Boris A.
2011-07-15
We consider a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (in other words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates previously unexplored types of nonlinear Fano resonances, with completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically induced transparency. The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.
An application of eigenspace methods to symmetric flutter suppression
NASA Technical Reports Server (NTRS)
Fennell, Robert E.
1988-01-01
An eigenspace assignment approach to the design of parameter insensitive control laws for linear multivariable systems is presented. The control design scheme utilizes flexibility in eigenvector assignments to reduce control system sensitivity to changes in system parameters. The methods involve use of the singular value decomposition to provide an exact description of allowable eigenvectors in terms of a minimum number of design parameters. In a design example, the methods are applied to the problem of symmetric flutter suppression in an aeroelastic vehicle. In this example the flutter mode is sensitive to changes in dynamic pressure and eigenspace methods are used to enhance the performance of a stabilizing minimum energy/linear quadratic regulator controller and associated observer. Results indicate that the methods provide feedback control laws that make stability of the nominal closed loop systems insensitive to changes in dynamic pressure.
Stoncius, Sigitas; Butkus, Eugenius; Zilinskas, Albinas; Larsson, Krister; Ohrström, Lars; Berg, Ulf; Wärnmark, Kenneth
2004-08-01
The synthesis of a C2-symmetric cleft molecule 2 based on the fused framework between bicyclo[3.3.1]nonane and 4-oxo-5-azaindole, incorporating a self-complementary hydrogen-bonding motif, in both racemic and enantiomerically pure forms is reported. This cleft molecule is reminiscent of analogues of Tröger's base though with different cleft dimensions and tilt angles. The framework of 2 provides a building block for the construction of self-assembled hydrogen-bonded supramolecular structures. The solid-state structure of 2 is highly influenced by the limited solubility of (+/-)-2 and (-)-2. The solvents interact with the potential hydrogen-bonding motifs of (+/-)-2 and (-)-2, forming different three-dimensional structures as revealed by X-ray diffraction analysis. In the solid state (+/-)-(2)2 x 5DMF forms hydrogen-bonded pleated band structures that build up three-dimensional pens between adjacent bands in which two molecules of DMF are trapped. In contrast, the aggregate obtained from (-)-2, (-)-2 x 2AcOH, showed infinite bands of complex constitution. PMID:15287761
Martingale Rosenthal inequalities in symmetric spaces
Astashkin, S V
2014-12-31
We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.
Symmetric states: Their nonlocality and entanglement
Wang, Zizhu; Markham, Damian
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
Lax Operator for Macdonald Symmetric Functions
NASA Astrophysics Data System (ADS)
Nazarov, Maxim; Sklyanin, Evgeny
2015-07-01
Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the variables and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function.
The Stark Effect in Linear Potentials
ERIC Educational Resources Information Center
Robinett, R. W.
2010-01-01
We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…
Computational design of a self-assembling symmetrical β-propeller protein.
Voet, Arnout R D; Noguchi, Hiroki; Addy, Christine; Simoncini, David; Terada, Daiki; Unzai, Satoru; Park, Sam-Yong; Zhang, Kam Y J; Tame, Jeremy R H
2014-10-21
The modular structure of many protein families, such as β-propeller proteins, strongly implies that duplication played an important role in their evolution, leading to highly symmetrical intermediate forms. Previous attempts to create perfectly symmetrical propeller proteins have failed, however. We have therefore developed a new and rapid computational approach to design such proteins. As a test case, we have created a sixfold symmetrical β-propeller protein and experimentally validated the structure using X-ray crystallography. Each blade consists of 42 residues. Proteins carrying 2-10 identical blades were also expressed and purified. Two or three tandem blades assemble to recreate the highly stable sixfold symmetrical architecture, consistent with the duplication and fusion theory. The other proteins produce different monodisperse complexes, up to 42 blades (180 kDa) in size, which self-assemble according to simple symmetry rules. Our procedure is suitable for creating nano-building blocks from different protein templates of desired symmetry. PMID:25288768
Feijoo, David; Zezyulin, Dmitry A; Konotop, Vladimir V
2015-12-01
We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT-symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT-symmetric cases. Interactions and collisions between the conservative and PT-symmetric solitons are briefly investigated, as well. PMID:26764776
NASA Astrophysics Data System (ADS)
Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.
2015-12-01
We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
Level crossings in a PT-symmetric double well
NASA Astrophysics Data System (ADS)
Giachetti, Riccardo; Grecchi, Vincenzo
2016-03-01
We consider the eigenvalues (levels) and the eigenfunctions (states) of a one-parameter family of Hamiltonians {H}{{\\hslash }} with a PT-symmetric double well. We call nodes the zeros of the states that are stable in the free limit of an associated perturbation theory. For large positive parameter {{\\hslash }}, the m-nodes state {\\psi }m({{\\hslash }}) is PT-symmetric and the corresponding level {E}m({{\\hslash }}) is positive. For small {{\\hslash }} there are j-nodes states {\\psi }j+/- ({{\\hslash }}), localized about one of the two wells, namely one of the two stationary points of the potential which are real. The corresponding levels {E}j+/- ({{\\hslash }}) are non-real. We prove the existence of a crossing of each pair of levels ({E}2n+1({{\\hslash }}),{E}2n({{\\hslash }})) at a parameter {{{\\hslash }}}n\\gt 0, giving, for smaller parameters, the pair of complex levels ({E}n+({{\\hslash }}),{E}n-({{\\hslash }})). The connection between the states ({\\psi }2n+1({{\\hslash }}),{\\psi }2n({{\\hslash }})) is given by the instability of the imaginary node of {\\psi }2n+1({{\\hslash }}). We extend the analysis of the level crossings to the complex plane of the parameter and we propose a through understanding of the full process by considering the Stokes complex and the nodes.
The Topology of Three-Dimensional Symmetric Tensor Fields
NASA Technical Reports Server (NTRS)
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
1994-01-01
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
A Symmetrical Interpretation of the Klein-Gordon Equation
NASA Astrophysics Data System (ADS)
Heaney, Michael B.
2013-06-01
This paper presents a new Symmetrical Interpretation (SI) of relativistic quantum mechanics which postulates: quantum mechanics is a theory about complete experiments, not particles; a complete experiment is maximally described by a complex transition amplitude density; and this transition amplitude density never collapses. This SI is compared to the Copenhagen Interpretation (CI) for the analysis of Einstein's bubble experiment. This SI makes several experimentally testable predictions that differ from the CI, solves one part of the measurement problem, resolves some inconsistencies of the CI, and gives intuitive explanations of some previously mysterious quantum effects.
Architecture of the symmetric core of the nuclear pore.
Lin, Daniel H; Stuwe, Tobias; Schilbach, Sandra; Rundlet, Emily J; Perriches, Thibaud; Mobbs, George; Fan, Yanbin; Thierbach, Karsten; Huber, Ferdinand M; Collins, Leslie N; Davenport, Andrew M; Jeon, Young E; Hoelz, André
2016-04-15
The nuclear pore complex (NPC) controls the transport of macromolecules between the nucleus and cytoplasm, but its molecular architecture has thus far remained poorly defined. We biochemically reconstituted NPC core protomers and elucidated the underlying protein-protein interaction network. Flexible linker sequences, rather than interactions between the structured core scaffold nucleoporins, mediate the assembly of the inner ring complex and its attachment to the NPC coat. X-ray crystallographic analysis of these scaffold nucleoporins revealed the molecular details of their interactions with the flexible linker sequences and enabled construction of full-length atomic structures. By docking these structures into the cryoelectron tomographic reconstruction of the intact human NPC and validating their placement with our nucleoporin interactome, we built a composite structure of the NPC symmetric core that contains ~320,000 residues and accounts for ~56 megadaltons of the NPC's structured mass. Our approach provides a paradigm for the structure determination of similarly complex macromolecular assemblies. PMID:27081075
Symmetric Galerkin boundary formulations employing curved elements
NASA Technical Reports Server (NTRS)
Kane, J. H.; Balakrishna, C.
1993-01-01
Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.
Izzet, Guillaume; Akdas, Huriye; Hucher, Nicolas; Giorgi, Michel; Prangé, Thierry; Reinaud, Olivia
2006-02-01
Complexation of copper(II) by calix[6]arene-based ligands bearing either two or three N-benzylimidazole coordinating arms under basic conditions has been studied. Whereas the tris(imidazole) derivative stabilizes dicationic 5-coordinate aqua complexes in a mononuclear state with an intracavity bound guest, in the presence of hydroxide ions, the latter undergo dimerization. An X-ray structure revealed decoordination of one imidazole arm and formation of a bis(hydroxo) bridged Cu(II) core with a square-planar geometry for both metal centers sandwiched by two empty calixarene cavities. Upon methanolysis, the dinuclear complex underwent an unexpected rearrangement leading to the clean formation of a trinuclear complex. X-ray diffraction analyses of this novel species revealed a trinuclear core constructed around a central Cu(II) ion that is doubly bridged through either methoxide or hydroxide anions to two Cu(II) ions hold by two calixarene units. The same complex could be directly synthesized by reacting the ligand with copper(II) perchlorate in a 2:3 ratio in the presence of base. In solution, the tetrahydroxo Cu(3) complex was characterized by UV-vis and (1)H NMR spectroscopies and displayed an electron paramagnetic resonance (EPR) signal only below 100 K that accounts for a S = 1/2 fundamental state. Formation of the same di- and trinuclear species was observed with a calix[6]arene-based bis(imidazole) ligand, which demonstrates the generality of the reaction schemes. All these results emphasize the versatility of the calix[6]arene scaffold for the stabilization of metal complexes with various nuclearities. PMID:16441115
Technology Transfer Automated Retrieval System (TEKTRAN)
Both the amounts of and specific structures of the triacylglycerols (TAG) present in the oil phase of a margarine or spread are considered responsible for such properties as its spreadability, resistance to water/oil loss, and melting characteristics. A series of symmetrical and non-symmetrical TAG...
Symmetric and anti-symmetric LS hyperon potentials from lattice QCD
NASA Astrophysics Data System (ADS)
Ishii, Noriyoshi; Murano, Keiko; Nemura, Hidekatsu; Sasaki, Kenji; Inoue, Takashi; HAL QCD Collaboration
2014-09-01
We present recent results of odd-parity hyperon-hyperon potentials from lattice QCD. By using HAL QCD method, we generate hyperon-hyperon potentials from Nambu-Bethe-Salpeter (NBS) wave functions generated by lattice QCD simulation in the flavor SU(3) limit. Potentials in the irreducible flavor SU(3) representations are combined to make a Lambda-N potential which has a strong symmetric LS potential and a weak anti-symmetric LS potential. We discuss a possible cancellation between symmetric and anti-symmetric LS (Lambda-N) potentials after the coupled Sigma-N sector is integrated out. We present recent results of odd-parity hyperon-hyperon potentials from lattice QCD. By using HAL QCD method, we generate hyperon-hyperon potentials from Nambu-Bethe-Salpeter (NBS) wave functions generated by lattice QCD simulation in the flavor SU(3) limit. Potentials in the irreducible flavor SU(3) representations are combined to make a Lambda-N potential which has a strong symmetric LS potential and a weak anti-symmetric LS potential. We discuss a possible cancellation between symmetric and anti-symmetric LS (Lambda-N) potentials after the coupled Sigma-N sector is integrated out. This work is supported by JSPS KAKENHI Grant Number 25400244.
Dumur, Frédéric; Mayer, Cédric R; Hoang-Thi, Khuyen; Ledoux-Rak, Isabelle; Miomandre, Fabien; Clavier, Gilles; Dumas, Eddy; Méallet-Renault, Rachel; Frigoli, Michel; Zyss, Joseph; Sécheresse, Francis
2009-09-01
The synthesis, linear optical and nonlinear optical properties, as well as the electrochemical behavior of a series of pro-ligands containing the 4-(4-N,N-dimethylaminostyryl)-1-methyl pyridinium (DASP(+)) group as a push-pull moiety covalently linked to terpyridine or bipyridine as chelating ligands are reported in this full paper. The corresponding multifunctional Ru(II) and Zn(II) complexes were prepared and investigated. The structural, electronic, and optical properties of the pro-ligands and the ruthenium complexes were investigated using density functional theory (DFT) and time-dependent (TD) DFT calculations. A fairly good agreement was observed between the experimental and the calculated electronic spectra of the pro-ligands and their corresponding ruthenium complexes. A quenching of luminescence was evidenced in all ruthenium complexes compared with the free pro-ligands but even the terpyridine-functionalized metal complexes exhibited detectable luminescence at room temperature. Second order nonlinear optical (NLO) measurements were performed by Harmonic Light Scattering and the contribution of the DASP(+) moieties (and their relative ordering) and the metal-polypyridyl core need to be considered to explain the nonlinear optical properties of the metal complexes. PMID:19642646
Coe, Benjamin J; Jones, Lathe A; Harris, James A; Brunschwig, Bruce S; Asselberghs, Inge; Clays, Koen; Persoons, André
2003-01-29
We have used several techniques, including hyper-Rayleigh scattering and Stark spectroscopy, to investigate the effects of polyene chain length on the optical properties of complexes containing ruthenium(II) electron donor groups and pyridinium electron acceptors. In marked contrast with all other known donor-acceptor polyenes, conjugation extension beyond a single double bond in the dipolar complexes studied leads to blue-shifting of the intramolecular charge-transfer absorptions. Furthermore, the static first hyperpolarizabilities beta0 become maximized with trans-1,3-butadienyl linkages and then decrease in complexes with three CH=CH bonds. Our results clearly demonstrate that the molecular engineering criteria for metal-containing nonlinear optical chromophores can differ dramatically from those for purely organic compounds. PMID:12537472
Linear versus non-linear supersymmetry, in general
NASA Astrophysics Data System (ADS)
Ferrara, Sergio; Kallosh, Renata; Van Proeyen, Antoine; Wrase, Timm
2016-04-01
We study superconformal and supergravity models with constrained superfields. The underlying version of such models with all unconstrained superfields and linearly realized supersymmetry is presented here, in addition to the physical multiplets there are Lagrange multiplier (LM) superfields. Once the equations of motion for the LM superfields are solved, some of the physical superfields become constrained. The linear supersymmetry of the original models becomes non-linearly realized, its exact form can be deduced from the original linear supersymmetry. Known examples of constrained superfields are shown to require the following LM's: chiral superfields, linear superfields, general complex superfields, some of them are multiplets with a spin.
CAST: Contraction Algorithm for Symmetric Tensors
Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy
2014-09-22
Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.
Communication-avoiding symmetric-indefinite factorization
Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro
2014-11-13
We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result,more » the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.« less
Communication-avoiding symmetric-indefinite factorization
Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro
2014-11-13
We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTL^{T}P^{T} where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result, the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.
Self-bending symmetric cusp beams
Gong, Lei; Liu, Wei-Wei; Lu, Yao; Li, Yin-Mei; Ren, Yu-Xuan
2015-12-07
A type of self-bending symmetric cusp beams with four accelerating intensity maxima is theoretically and experimentally presented. Distinguished from the reported regular polygon beams, the symmetric cusp beams simultaneously exhibit peculiar features of natural autofocusing and self-acceleration during propagation. Further, such beams take the shape of a fine longitudinal needle-like structure at the focal region and possess the strong ability of self-healing over obstacles. All these intriguing properties were verified experimentally. Particularly, the spatial profile of the reconstructed beam exhibits spatially sculpted optical structure with four siamesed curved arms. Thus, we anticipate that the structured beam will benefit optical guiding and optofluidics in surprising ways.
Observational tests of Baryon symmetric cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1982-01-01
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiation from the decay of pi(0)-mesons produced in nucleon-antinucleon annihilations. Equations for the prediction of the amma ray background spectrum for the case of high redshifts are presented. The theoretical and observational plots of the background spectrum are shown to be in good agreement. Measurement of cosmic ray antiprotons and the use of high energy neutrino astronomy to look for antimatter elsewhere in the universe are also addressed.
Self-bending symmetric cusp beams
NASA Astrophysics Data System (ADS)
Gong, Lei; Liu, Wei-Wei; Ren, Yu-Xuan; Lu, Yao; Li, Yin-Mei
2015-12-01
A type of self-bending symmetric cusp beams with four accelerating intensity maxima is theoretically and experimentally presented. Distinguished from the reported regular polygon beams, the symmetric cusp beams simultaneously exhibit peculiar features of natural autofocusing and self-acceleration during propagation. Further, such beams take the shape of a fine longitudinal needle-like structure at the focal region and possess the strong ability of self-healing over obstacles. All these intriguing properties were verified experimentally. Particularly, the spatial profile of the reconstructed beam exhibits spatially sculpted optical structure with four siamesed curved arms. Thus, we anticipate that the structured beam will benefit optical guiding and optofluidics in surprising ways.
NASA Astrophysics Data System (ADS)
Chen, Xi; Xue, Long-Xin; Ju, Chun-Chuan; Wang, Ke-Zhi
2013-07-01
A novel Ru(II) complex of [Ru(bpy)2(Hbcpip)](ClO4)2 {where bpy = 2,2-bipyridine, Hbcpip = 2-(4-(9H-3,9'-bicarbazol-9-yl)phenyl)-1H-imidazo[4,5-f][1,10]phenanthroline} is synthesized and characterized. Calf-thymus DNA-binding properties of the complex were studied by UV-vis absorption and luminescence titrations, steady-state emission quenching by [Fe(CN)6]4-, DNA competitive binding with ethidium bromide, thermal denaturation and DNA viscosity measurements. The results indicate that the complex partially intercalated into the DNA with a binding constant of (5.5 ± 1.4) × 105 M-1 in buffered 50 mM NaCl. The acid-base properties of the complex were also studied by UV-visible and luminescence spectrophotometric pH titrations, and ground- and excited-state acidity ionization constant values were derived.
Integrability and vesture for harmonic maps into symmetric spaces
NASA Astrophysics Data System (ADS)
Beheshti, Shabnam; Tahvildar-Zadeh, Shadi
2016-05-01
After formulating the notion of integrability for axially symmetric harmonic maps from ℝ3 into symmetric spaces, we give a complete and rigorous proof that, subject to some mild restrictions on the target, all such maps are integrable. Furthermore, we prove that a variant of the inverse scattering method, called vesture (dressing) can always be used to generate new solutions for the harmonic map equations starting from any given solution. In particular, we show that the problem of finding N-solitonic harmonic maps into a non-compact Grassmann manifold SU(p,q)/S(U(p) × U(q)) is completely reducible via the vesture (dressing) method to a problem in linear algebra which we prove is solvable in general. We illustrate this method, and establish its agreement with previously known special cases, by explicitly computing a 1-solitonic harmonic map for the two cases (p = 1,q = 1) and (p = 2,q = 1) and showing that the family of solutions obtained in each case contains respectively the Kerr family of solutions to the Einstein vacuum equations, and the Kerr-Newman family of solutions to the Einstein-Maxwell equations in the hyperextreme sector of the corresponding parameters.
A modified direct preconditioner for indefinite symmetric Toeplitz systems
Concus, P. California Univ., Berkeley, CA . Dept. of Mathematics); Saylor, P. . Dept. of Computer Science)
1992-11-01
A modification is presented of the classical O(n[sup 2]) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
A modified direct preconditioner for indefinite symmetric Toeplitz systems
Concus, P. |; Saylor, P.
1992-11-01
A modification is presented of the classical O(n{sup 2}) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
An almost symmetric Strang splitting scheme for nonlinear evolution equations☆
Einkemmer, Lukas; Ostermann, Alexander
2014-01-01
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017
{P}{T}-Symmetric Dimer in a Generalized Model of Coupled Nonlinear Oscillators
NASA Astrophysics Data System (ADS)
Cuevas-Maraver, Jess; Khare, Avinash; Kevrekidis, Panayotis G.; Xu, Haitao; Saxena, Avadh
2015-11-01
In the present work, we explore the case of a general {P}{T}-symmetric dimer in the context of two both linearly and nonlinearly coupled cubic oscillators. To obtain an analytical handle on the system, we first explore the rotating wave approximation converting it into a discrete nonlinear Schrdinger type dimer. In the latter context, the stationary solutions and their stability are identified numerically but also wherever possible analytically. Solutions stemming from both symmetric and anti-symmetric special limits are identified. A number of special cases are explored regarding the ratio of coefficients of nonlinearity between oscillators over the intrinsic one of each oscillator. Finally, the considerations are extended to the original oscillator model, where periodic orbits and their stability are obtained. When the solutions are found to be unstable their dynamics is monitored by means of direct numerical simulations.
NASA Astrophysics Data System (ADS)
Clark, A.; Terpugov, V.; Medrano, F.; Cervantes, M.; Soto, D.
1999-12-01
A simplified method of synthesis and purification of Erbium-Tetraphenylporphyrin (ErTpp) complexes, and their incorporation within a silica gel by the sol-gel process, is presented. On the basis of optical spectroscopic measurements in the UV-VIS range it was found that in ErTpp complexes the tetraphenylporphyrin molecule served as a protective screen for erbium ions. The half-width of the erbium ion luminescence band for the 4S 3/2 → 4I 15/2 transition was narrower by a factor of 5-6 in the new material than the corresponding value in erbium doped glasses or glass ceramics. It was shown that the value of the nonlinear refraction coefficient in ErTpp gels could considerably exceed that of silica glasses.
NASA Astrophysics Data System (ADS)
Godtliebsen, Ian H.; Christiansen, Ove
2015-10-01
It is demonstrated how vibrational IR and Raman spectra can be calculated from damped response functions using anharmonic vibrational wave function calculations, without determining the potentially very many eigenstates of the system. We present an implementation for vibrational configuration interaction and vibrational coupled cluster, and describe how the complex equations can be solved using iterative techniques employing only real trial vectors and real matrix-vector transformations. Using this algorithm, arbitrary frequency intervals can be scanned independent of the number of excited states. Sample calculations are presented for the IR-spectrum of water, Raman spectra of pyridine and a pyridine-silver complex, as well as for the infra-red spectrum of oxazole, and vibrational corrections to the polarizability of formaldehyde.
Godtliebsen, Ian H; Christiansen, Ove
2015-10-01
It is demonstrated how vibrational IR and Raman spectra can be calculated from damped response functions using anharmonic vibrational wave function calculations, without determining the potentially very many eigenstates of the system. We present an implementation for vibrational configuration interaction and vibrational coupled cluster, and describe how the complex equations can be solved using iterative techniques employing only real trial vectors and real matrix-vector transformations. Using this algorithm, arbitrary frequency intervals can be scanned independent of the number of excited states. Sample calculations are presented for the IR-spectrum of water, Raman spectra of pyridine and a pyridine-silver complex, as well as for the infra-red spectrum of oxazole, and vibrational corrections to the polarizability of formaldehyde. PMID:26450293
On integrability of strings on symmetric spaces
NASA Astrophysics Data System (ADS)
Wulff, Linus
2015-09-01
In the absence of NSNS three-form flux the bosonic string on a symmetric space is described by a symmetric space coset sigma-model. Such models are known to be classically integrable. We show that the integrability extends also to cases with non-zero NSNS flux (respecting the isometries) provided that the flux satisfies a condition of the form H abc H cde ˜ R abde . We then turn our attention to the type II Green-Schwarz superstring on a symmetric space. We prove that if the space preserves some supersymmetry there exists a truncation of the full superspace to a supercoset space and derive the general form of the superisometry algebra. In the case of vanishing NSNS flux the corresponding supercoset sigma-model for the string is known to be integrable. We prove that the integrability extends to the full string by augmenting the supercoset Lax connection with terms involving the fermions which are not captured by the supercoset model. The construction is carried out to quadratic order in these fermions. This proves the integrability of strings on symmetric spaces supported by RR flux which preserve any non-zero amount of supersymmetry. Finally we also construct Lax connections for some supercoset models with non-zero NSNS flux describing strings in AdS 2,3 × S 2,3 × S 2,3 × T 2,3,4 backgrounds preserving eight supersymmetries.
Unidirectional nonlinear PT-symmetric optical structures
Ramezani, Hamidreza; Kottos, Tsampikos; El-Ganainy, Ramy; Christodoulides, Demetrios N.
2010-10-15
We show that nonlinear optical structures involving a balanced gain-loss profile can act as unidirectional optical valves. This is made possible by exploiting the interplay between the fundamental symmetries of parity (P) and time (T), with optical nonlinear effects. This unidirectional dynamics is specifically demonstrated for the case of an integrable PT-symmetric nonlinear system.
Symmetrical parametrizations of the lepton mixing matrix
Rodejohann, W.; Valle, J. W. F.
2011-10-01
Advantages of the original symmetrical form of the parametrization of the lepton mixing matrix are discussed. It provides a conceptually more transparent description of neutrino oscillations and lepton number violating processes like neutrinoless double beta decay, clarifying the significance of Dirac and Majorana phases. It is also ideal for parametrizing scenarios with light sterile neutrinos.
Dissociative recombination of highly symmetric polyatomic ions.
Douguet, Nicolas; Orel, Ann E; Greene, Chris H; Kokoouline, Viatcheslav
2012-01-13
A general first-principles theory of dissociative recombination is developed for highly symmetric molecular ions and applied to H(3)O(+) and CH(3)(+), which play an important role in astrophysical, combustion, and laboratory plasma environments. The theoretical cross sections obtained for the dissociative recombination of the two ions are in good agreement with existing experimental data from storage ring experiments. PMID:22324682
Conformal cylindrically symmetric spacetimes in modified gravity
NASA Astrophysics Data System (ADS)
Türkog˜lu, Murat Metehan; Dog˜ru, Melis Ulu
2015-11-01
We investigate cylindrically symmetric spacetimes in the context of f(R) gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle-Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special f(R) function convenient to Λ-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different f(R) models. Finally, geometrical and physical results of the solutions are discussed.
Amplituhedron Cells and Stanley Symmetric Functions
NASA Astrophysics Data System (ADS)
Lam, Thomas
2016-05-01
The amplituhedron was recently introduced in the study of scattering amplitudes in {N = 4} super Yang-Mills. We compute the cohomology class of a tree amplituhedron subvariety of the Grassmannian to be the truncation of an affine Stanley symmetric function.
Miniaturized symmetrization optics for junction laser
NASA Technical Reports Server (NTRS)
Hammer, Jacob M. (Inventor); Kaiser, Charlie J. (Inventor); Neil, Clyde C. (Inventor)
1982-01-01
Miniaturized optics comprising transverse and lateral cylindrical lenses composed of millimeter-sized rods with diameters, indices-of-refraction and spacing such that substantially all the light emitted as an asymmetrical beam from the emitting junction of the laser is collected and translated to a symmetrical beam.
Symmetric nonnegative matrix factorization: algorithms and applications to probabilistic clustering.
He, Zhaoshui; Xie, Shengli; Zdunek, Rafal; Zhou, Guoxu; Cichocki, Andrzej
2011-12-01
Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression. PMID:22042156
Alfvén modes in the Madison Symmetric Torus
NASA Astrophysics Data System (ADS)
Li, M.; Breizman, B. N.; Zheng, L. J.; Lin, L.; Ding, W. X.; Brower, D. L.
2014-08-01
This work presents a theoretical and computational analysis of core-localized energetic particle driven modes observed near the magnetic axis in the Madison Symmetric Torus [L. Lin, W. X. Ding, D. L. Brower et al., Phys. Plasmas 20, 030701 (2013)]. Using measured safety factor and plasma pressure profiles as input, the linear ideal MHD code Adaptive EiGenfunction Independent Solution (AEGIS) [L. J. Zheng and M. Kotschenreuther, J. Comput. Phys. 211, 748 (2006)] reveals Alfvénic modes close to the measured frequencies. The AEGIS results together with a reduced analytical model demonstrate that the modes are essentially "cylindrical" and dominated by a single poloidal component (m = 1). The modes are localized at the plasma core where the magnetic shear is weak and continuum damping is minimal. Detailed analysis establishes constraints on the safety factor and plasma pressure, under which two modes can exist simultaneously.
Propagation features of beams with axially symmetric polarization
NASA Astrophysics Data System (ADS)
Nesterov, A. V.; Niziev, V. G.
2001-04-01
The general solution of the wave equation for axially symmetric polarized (ASP) beams consists of two independent solutions: an azimuthally polarized beam and a beam with longitudinal and radial field components. The maximum of the longitudinal field is at the beam axis where the transverse component is equal to zero. While the longitudinal component is maximum in the waist it does not contribute to beam divergence here, and therefore the wavefront of ASP-beams is flat in the focal plane. The ASP-beams are free from polarization aberrations, which are inherent for linearly polarized beams passing through a lens with large annular apertures, and these beams are prospective for experiments on obtaining `diffraction-free' beams. The formulae and their electromagnetic field analysis in the case of sharp focusing of ASP-beams in the Debye approximation are presented.
Two loop QCD vertices at the symmetric point
Gracey, J. A.
2011-10-15
We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at the symmetric subtraction point at two loops in the MS scheme. In addition we renormalize each of the three vertices in their respective momentum subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the wave functions, coupling constant and gauge parameter renormalization constants of each of the schemes relative to MS are determined analytically. These are then used to derive the three loop anomalous dimensions of the gluon, quark, Faddeev-Popov ghost and gauge parameter as well as the {beta} function in an arbitrary linear covariant gauge for each MOM scheme. There is good agreement of the latter with earlier Landau gauge numerical estimates of Chetyrkin and Seidensticker.
Tight frame 6-band symmetric wavelets with limited redundancy
NASA Astrophysics Data System (ADS)
Abdelnour, Farras
2011-09-01
We consider the design of 6-channel tight frame symmetric wavelet with scaling factor M = 4. The lowpass filter is designed using either Grobner bases or truncated Taylor series methods. The bandpass and highpass filters are then designed using Grobner bases. The resulting filters have linear phase, smooth limit functions, and reduced redundancy. It was possible to obtain filterbanks with K0 (zeros at z = 1 and z = +/-j for the lowpass filter) up to 5 and Kmin (zeros at z = 1 for bandpass/highpass filters) of 1 or greater. The proposed filterbanks generate five wavelets and a scaling function with the underlying filters related as follows: H5-i(z) = Hi(-z), i = 0... 5.
Corelation between Complexity and Stability in Multicellular Organisms
NASA Astrophysics Data System (ADS)
Werman, Steven D.; Qaddour, Jihad; Deyoung, Gary; Misra, Prasanta K.
1997-03-01
We present a model to study the corelation between the complexity and stability of unicellular and multicellular organisms. We state the postulates made by us and define the thermodynamic functions and other parameters used to formulate the problem. We have also used several theorems based on reasonable assumptions to analyze the functional interactions which are non-symmetric, non-local and non-instantaneous. The mathematical model developed by using these hypotheses is explained in detail and a set of non-linear equations for each type of organism is presented. We present the results obtained by us by solving these equations.
Rings of continuous functions, symmetric products, and Frobenius algebras
NASA Astrophysics Data System (ADS)
Buchstaber, Viktor M.; Rees, E. G.
2004-02-01
A constructive proof is given for the classical theorem of Gel'fand and Kolmogorov (1939) characterising the image of the evaluation map from a compact Hausdorff space X into the linear space C(X)^* dual to the ring C(X) of continuous functions on X. Our approach to the proof enabled us to obtain a more general result characterising the image of the evaluation map from the symmetric products \\operatorname{Sym}^n(X) into C(X)^*. A similar result holds if X=\\mathbb C^m and leads to explicit equations for symmetric products of affine algebraic varieties as algebraic subvarieties in the linear space dual to the polynomial ring. This leads to a better understanding of the algebra of multisymmetric polynomials. The proof of all these results is based on a formula used by Frobenius in 1896 in defining higher characters of finite groups. This formula had no further applications for a long time; however, it has appeared in several independent contexts during the last fifteen years. It was used by A. Wiles and R.L. Taylor in studying representations and by H.-J. Hoehnke and K.W. Johnson and later by J. McKay in studying finite groups. It plays an important role in our work concerning multivalued groups. Several properties of this remarkable formula are described. It is also used to prove a theorem on the structure constants of Frobenius algebras, which have recently attracted attention due to constructions taken from topological field theory and singularity theory. This theorem develops a result of Hoehnke published in 1958. As a corollary, a direct self-contained proof is obtained for the fact that the 1-, 2-, and 3-characters of the regular representation determine a finite group up to isomorphism. This result was first published by Hoehnke and Johnson in 1992.
Symmetric Key Structural Residues in Symmetric Proteins with Beta-Trefoil Fold
Huang, Yanzhao; Xiao, Yi
2010-01-01
To understand how symmetric structures of many proteins are formed from asymmetric sequences, the proteins with two repeated beta-trefoil domains in Plant Cytotoxin B-chain family and all presently known beta-trefoil proteins are analyzed by structure-based multi-sequence alignments. The results show that all these proteins have similar key structural residues that are distributed symmetrically in their structures. These symmetric key structural residues are further analyzed in terms of inter-residues interaction numbers and B-factors. It is found that they can be distinguished from other residues and have significant propensities for structural framework. This indicates that these key structural residues may conduct the formation of symmetric structures although the sequences are asymmetric. PMID:21152439
NASA Astrophysics Data System (ADS)
Murillo Pulgarín, J. A.; Alañón Molina, A.; Boras, N.
2012-12-01
Synchronous fluorescence spectroscopy (SFS) is a rapid, sensitive and non-destructive method suitable for the analysis of multifluorophoric mixtures. In this study non linear variable angle synchronous spectrofluorimetry was applied to the determination of three fluoroquinololes in urine. Although this technique provides very good results, total resolution of multicomponent mixtures is not always achieved when the spectral profiles strongly overlap. Partial least-squares regression (PLS-1) was utilized to a develop calibration model that related synchronous fluorescence spectra to the analytical concentration of fluoroquinolones in the presence of urine. The same multicomponent mixture was determined using excitation emission matrix fluorescence (EEMF) along with N-way partial least squares regression (N-PLS and U-PLS). The determination was carried out in micellar medium 0.01 M with a pH of 4.8 provided by 0.2 M sodium acetate/acetic acid buffer. A central composite design was selected to obtain a calibration matrix of 25 standards plus a blank sample. The proposed methods were validated by application to a test set of synthetic samples. The results show that SFS with PLS-1 is a better method compared to EEMF with N-PLS or U-PLS because of the low RMSEP values of the former.
Meseguer, Carlos; Titos-Padilla, Silvia; Hänninen, Mikko M; Navarrete, R; Mota, A J; Evangelisti, Marco; Ruiz, José; Colacio, Enrique
2014-11-17
New types of linear tetranuclear Ln(III)-Ni(II)-Ni(II)-Ln(III) (Ln(III) = Dy (1), Gd (2)) complexes have been prepared using the multidentate ligand N,N'-bis(3-methoxysalicylidene)-1,3-diaminobenzene, which has two sets of NO and OO' coordination pockets that are able to selectively accommodate Ni(II) and Ln(III) ions, respectively. The X-ray structure analysis reveals that the Ni(II) ions are bridged by phenylenediimine groups forming a 12-membered metallacycle in the central body of the complex, whereas the Ln(III) ions are located at both sides of the metallacycle and linked to the Ni(II) ions by diphenoxo bridging groups. Phenylenediimine and diphenoxo bridging groups transmit ferromagnetic exchange interactions between the two Ni(II) ions and between the Ni(II) and the Ln(III) ions, respectively. Complex 1 shows slow relaxation of the magnetization at zero field and a thermal energy barrier Ueff = 7.4 K with HDC = 1000 Oe, whereas complex 2 exhibits an S = 9 ground state and significant magnetocaloric effect (-ΔSm = 18.5 J kg(-1) K(-1) at T = 3 K and ΔB = 5 T). PMID:25350578
MIC linearizer for satellite communications
NASA Astrophysics Data System (ADS)
Sato, G.
1985-05-01
MIC implementation of a predistortion-type nonlinearity compensating circuit or linearizer (LRZ) using FETAs in a distortion generator was studied and a compact, lightweight MIC-LRZ using tip devices was developed. The LRZ circuit has a symmetric construction which enables it to have a wideband characteristic, and its nonlinearities can be adjusted electrically. The LRZ can compensate nonlinearity up to saturation of the traveling wave tube amplifier (TWTA) and can provide large performance improvement using a TWTA with backoff operation. The TWTA with the soft-limiter LRZ (SL-LRZ) exhibits soft-limiter transfer characteristics in which the input-output amplitude response is linear up to saturation and phase nonlinearity is negligible. The MIC-LRZ and SL-LRZ are compact, lightweight, and effective for use with earth stations HPAs and satellite TWTAs.
Colgate, S.A.
1958-05-27
An improvement is presented in linear accelerators for charged particles with respect to the stable focusing of the particle beam. The improvement consists of providing a radial electric field transverse to the accelerating electric fields and angularly introducing the beam of particles in the field. The results of the foregoing is to achieve a beam which spirals about the axis of the acceleration path. The combination of the electric fields and angular motion of the particles cooperate to provide a stable and focused particle beam.
NASA Astrophysics Data System (ADS)
Dinh, Thanh-Chung; Renger, Thomas
2015-01-01
A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.
Dinh, Thanh-Chung; Renger, Thomas
2015-01-21
A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Q{sub y} transition dipole moments in Chl b homodimers is larger by about 9{sup ∘} than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.
Novoa, Néstor; Roisnel, Thierry; Hamon, Paul; Kahlal, Samia; Manzur, Carolina; Ngo, Hoang Minh; Ledoux-Rak, Isabelle; Saillard, Jean-Yves; Carrillo, David; Hamon, Jean-René
2015-11-01
We report the synthesis, characterization, crystal structures, nonlinear-optical (NLO) properties, and density functional theory (DFT) calculations of nickel(ii) and copper(ii) complex based ONO tridentate Schiff base ligands: two mononuclear compounds, [Ni(An-ONO)(NC5H5)] (5) and [Cu(An-ONO)(4-NC5H4C(CH3)3)] (6), and two heterobimetallic species, [M(Fc-ONO)(NC5H5)] (M = Ni, 7; Cu, 8), where An-ONOH2 (3) and Fc-ONOH2 (4) are the 1 : 1 condensation products of 2-aminophenol and p-anisoylacetone and ferrocenoylacetone, respectively. These compounds were characterised by microanalysis, FT-IR and X-ray crystallography in the solid state and in solution by UV-vis and (1)H and (13)C NMR spectroscopy. The crystal structures of 3-5, 7 and 8 have been determined and show for Schiff base complexes 5, 7 and 8 a four-coordinated square-planar environment for nickel and copper ions. The electrochemical behavior of all derivatives 3-8 was investigated by cyclic voltammetry in dichloromethane, and discussed on the basis of DFT-computed electronic structures of the neutral and oxidized forms of the compounds. The second-order NLO responses of 3-8 have been determined by harmonic light scattering measurements using a 10(-2) M solution of dichloromethane and working with a 1.91 μm incident wavelength, giving rather high β1.91 values of 350 and 290 × 10(-30) esu for the mononuclear species 5 and 6, respectively. The assignment and the nature of the electronic transitions observed in the UV-vis spectra were analyzed using time-dependent (TD) DFT calculations. They are dominated by LMCT, MLCT and π-π* transitions. PMID:26412689
Symmetric tensor decomposition description of fermionic many-body wave functions.
Uemura, Wataru; Sugino, Osamu
2012-12-21
The configuration interaction (CI) is a versatile wave function theory for interacting fermions, but it involves an extremely long CI series. Using a symmetric tensor decomposition method, we convert the CI series into a compact and numerically tractable form. The converted series encompasses the Hartree-Fock state in the first term and rapidly converges to the full-CI state, as numerically tested by using small molecules. Provided that the length of the symmetric tensor decomposition CI series grows only moderately with the increasing complexity of the system, the new method will serve as one of the alternative variational methods to achieve full CI with enhanced practicability. PMID:23368456
All-optical PT-symmetric conversion of amplitude (phase) modulation to phase (amplitude) modulation.
Gutiérrez, Oscar Ignacio Zaragoza; Mendoza, Luis Felipe Salinas; Rodríguez-Lara, B M
2016-02-22
We study electromagnetic field propagation through a planar three-waveguide coupler with linear gain or loss in a configuration that is the optical analog of a quantum PT-symmetric system. This model is experimentally feasible on at least four proven architectures: lossy waveguide couplers, pumped waveguides couplers, non-Hermitian electronics and coupled pumped whispering gallery mode resonators. We show that our device provides all-optical amplitude (phase) to phase (amplitude) conversion in the PT-symmetric regime at given propagation lenghts. The device has a π amplitude to phase conversion range if an extra binary phase is allowed in the reference signal, and a phase to amplitude conversion range that depends linearly on the gain-to-coupling ratio of the system. Our scheme may prove valuable in implementing phase shift keying formats, which have longer unrepeated transmission distance than intensity modulation schemes. PMID:26907051
Parity-time-symmetric plasmonic metamaterials
NASA Astrophysics Data System (ADS)
Alaeian, Hadiseh; Dionne, Jennifer A.
2014-03-01
We theoretically investigate the optical properties of parity-time (PT)-symmetric three-dimensional metamaterials composed of strongly coupled planar plasmonic waveguides. By tuning the loss-gain balance, we show how the initially isotropic material becomes both asymmetric and unidirectional. Investigation of the band structure near the material's exceptional point reveals several interesting optical properties, including double negative refraction, Bloch power oscillations, unidirectional invisibility, and reflection and transmission coefficients that are simultaneously equal to or greater than unity. The highly tunable optical dispersion of PT-symmetric metamaterials provides a foundation for designing an unconventional class of three-dimensional bulk synthetic media, with applications ranging from lossless subdiffraction-limited optical lenses to nonreciprocal nanophotonic devices.
Symmetrical Peripheral Gangrene Following Snake Bite
Shastri, Minal; Parikh, Mital; Patel, Dwijal; Chudasma, Ketan
2014-01-01
SPG (Symmetrical peripheral gangrene) is defined as symmetrical distal ischemic damage at two or more sites in the absence of large vessels obstruction. It has been ascribed to a number of infectious and non infectious conditions including connective tissue, cardiovascular, neoplastic and iatrogenic causes. We report a unique case of SPG in a 35-year-old Indian female who developed spontaneous gangrene of the distal phalanges of the right and left index, middle, ring and little fingers and the distal phalanges of all toes of the right and left foot following a snake bite. There have been very few cases of peripheral gangrene and acute renal failure associated with snake bite in literature. PMID:25386476
Spherically symmetric solutions in a FRW background
NASA Astrophysics Data System (ADS)
Moradpour, H.; Riazi, N.
2015-02-01
We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described.
Compensator configurations for load currents' symmetrization
NASA Astrophysics Data System (ADS)
Rusinaru, D.; Manescu, L. G.; Dinu, R. C.
2016-02-01
This paper approaches aspects regarding the mitigation effects of asymmetries in 3-phase 3-wire networks. The measure consisting in connecting of load current symmetrization devices at the load coupling point is presented. A time-variation of compensators parameters is determined as a function of the time-recorded electrical values. The general sizing principle of the load current symmetrization reactive components is based on a simple equivalent model of the unbalanced 3-phase loads. By using these compensators a certain control of the power components transits is ensured in the network. The control is based on the variations laws of the compensators parameters as functions of the recorded electrical values: [B] = [T]·[M]. The link between compensator parameters and measured values is ensured by a transformation matrix [T] for each operation conditions of the supply network. Additional conditions for improving of energy and efficiency performance of the compensator are considered: i.e. reactive power compensation. The compensator sizing algorithm was implemented into a MATLAB environment software, which generate the time-evolution of the parameters of load current symmetrization device. The input data of application takes into account time-recording of the electrical values. By using the compensator sizing software, some results were achieved for the case of a consumer connected at 20 kV busbar of a distribution substation, during 24 hours measurement session. Even the sizing of the compensators aimed some additional network operation aspects (power factor correction) correlated with the total or major load symmetrizations, the harmonics aspects of the network values were neglected.
Wave equation on spherically symmetric Lorentzian metrics
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.
2011-06-15
Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.
Symmetric space description of carbon nanotubes
NASA Astrophysics Data System (ADS)
Caselle, Michele; Magnea, Ulrika
2006-01-01
Using an innovative technique arising from the theory of symmetric spaces, we obtain an approximate analytic solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation in the insulating regime of a metallic carbon nanotube with symplectic symmetry and an odd number of conducting channels. This symmetry class is characterized by the presence of a perfectly conducting channel in the limit of infinite length of the nanotube. The derivation of the DMPK equation for this system has recently been performed by Takane, who also obtained the average conductance both analytically and numerically. Using the Jacobian corresponding to the transformation to radial coordinates and the parametrization of the transfer matrix given by Takane, we identify the ensemble of transfer matrices as the symmetric space of negative curvature SO*(4m + 2)/[SU(2m + 1) × U(1)] belonging to the DIII-odd Cartan class. We rederive the leading-order correction to the conductance of the perfectly conducting channel \\langle \\ln \\delta g \\rangle and its variance Var(ln δg). Our results are in complete agreement with Takane's. In addition, our approach based on the mapping to a symmetric space enables us to obtain new universal quantities: a universal group theoretical expression for the ratio \\mathrm {Var}(\\ln \\delta g)/\\langle \\ln \\delta g\\rangle , and as a by-product a novel expression for the localization length for the most general case of a symmetric space with BCm root system, in which all three types of roots are present.
Instability of hairy black holes in shift-symmetric Horndeski theories
NASA Astrophysics Data System (ADS)
Ogawa, Hiromu; Kobayashi, Tsutomu; Suyama, Teruaki
2016-03-01
Recently it was pointed out that in shift-symmetric scalar-tensor theories a black hole can have nontrivial scalar hair which depends linearly on time. We develop black hole perturbation theory for such solutions and compute the quadratic action of odd parity perturbations. We show that around all the solutions known so far with such time-dependent scalar hair the perturbations trigger instabilities or are presumably strongly coupled.
Spherically symmetric thick branes cosmological evolution
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Cavalcanti, R. T.; da Rocha, Roldão
2015-01-01
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed et al. (JHEP 1404:061. arXiv:1312.3576 [hep-th], 2014). The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, , which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in Ahmed et al. (2014), namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on . Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in Ahmed et al. (2014).
Oblique-incidence-induced phase transition in parity-time symmetric optical bilayers
NASA Astrophysics Data System (ADS)
Guo, Rui-Peng; Wu, Li-Ting; Cao, Xue-Wei; Chen, Jing
2016-02-01
We investigate the scattering of optical waves from one-dimensional parity-time ({ P }{ T }) symmetric structures of arbitrary complexity. We prove that it is feasible to observe the transition from an unbroken { P }{ T }-symmetric phase to a broken one when the angle of incidence increases. Analytical formulae are developed that emphasize the key roles played by the interference between the exponential increase and decayed fields in the gain and loss media, and the phase shifts when reflected/transmitted from the gain-loss boundary. A specific layer thickness is proposed. Distributions of field and energy flux under both phases are studied. This investigation shows that we can observe optical { P }{ T }-symmetric phase transition in a single structure that obeys the causality principle.
Gonzlez-Daz, Humberto; Arrasate, Sonia; Gmez-SanJuan, Asier; Sotomayor, Nuria; Lete, Esther; Besada-Porto, Lina; Ruso, Juan M
2013-01-01
In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature, temperature of addition, or time of reaction). The model also account for changes in chemical structure (connectivity structure and/or chirality paterns in substrate, product, electrophile agent, organolithium, and ligand of the asymmetric catalyst). The second model classifies more than 150,000 cases with 85-100% of Ac, Sn, and Sp. The data contains experimental shifts in up to 18 different pharmacological parameters determined in >3000 assays of ADMET (Absorption, Distribution, Metabolism, Elimination, and Toxicity) properties and/or interactions between 31723 drugs and 100 targets (metabolizing enzymes, drug transporters, or organisms). The third model classifies more than 260,000 cases of perturbations in the self-aggregation of drugs and surfactants to form micelles with Ac, Sn, and Sp of 94-95%. The model predicts changes in 8 physicochemical and/or thermodynamics output parameters (critic micelle concentration, aggregation number, degree of ionization, surface area, enthalpy, free energy, entropy, heat capacity) of self-aggregation due to perturbations. The perturbations refers to changes in initial temperature, solvent, salt, salt concentration, solvent, and/or structure of the anion or cation of more than 150 different drugs and surfactants. QSPR-Perturbation Theory models may be useful for multi-objective optimization of organic synthesis, physicochemical properties, biological activity, metabolism, and distribution profiles towards the design of new drugs, surfactants, asymmetric ligands for catalysts, and other materials. PMID:23889050
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 14 Aeronautics and Space 1 2013-01-01 2013-01-01 false Symmetrical flight conditions. 23.331... Flight Loads § 23.331 Symmetrical flight conditions. (a) The appropriate balancing horizontal tail load... inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through...
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Symmetrical flight conditions. 23.331... Flight Loads § 23.331 Symmetrical flight conditions. (a) The appropriate balancing horizontal tail load... inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through...
Reaction Cycle of Chaperonin GroEL via Symmetric "Football" Intermediate.
Taguchi, Hideki
2015-09-11
Chaperonin GroEL is an essential chaperone that assists in protein folding in the cell. Since one GroEL ring binds one GroES heptamer, the GroEL double ring permits the formation of two types of GroEL:GroES complexes: asymmetric 1:1 "bullet"-shaped and symmetric 1:2 "football"-shaped GroEL:GroES2 complexes. There have been continuing debates about the mechanism and which complex is critical to the chaperonin-assisted folding. In this review, I summarize the recent progress on the football complex. PMID:25900372
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
2012-04-02
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
Dissipative trapped-electron instability in quasihelically symmetric stellarators
Rafiq, T.; Hegna, C.C.
2006-05-15
The linear electrostatic dissipative trapped-electron mode is investigated in a quasihelically symmetric (QHS) stellarator and a configuration whose symmetry is spoiled by the addition of a mirror contribution to the magnetic spectrum. The effect of the trapped electrons is accounted for using the drift kinetic equation with an energy-dependent Krook collision operator and an effective collision frequency giving the rate of detrapping. The ballooning mode formalism and Wentzel-Kramers-Brillouin type boundary conditions are used to solve an eigenvalue problem for a drift wave equation with nearly adiabatic electrons in a fully three-dimensional magnetohydrodynamic equilibria. The trapped-electron growth rate is calculated using a perturbative approach. Multiple classes of helically localized and toroidally localized eigenfunctions in the ballooning space are calculated. The results of the QHS configuration is compared and contrasted with the results of the mirror configuration. The helically trapped modes are found to be most destabilizing. In both configurations the magnitude of the linear growth rates are comparable, crudely indicating the same level of anomalous flux as has also been observed in the edge region of experiments.
Spontaneous symmetry breaking in the S 3-symmetric scalar sector
NASA Astrophysics Data System (ADS)
Emmanuel-Costa, D.; Ogreid, O. M.; Osland, P.; Rebelo, M. N.
2016-02-01
We present a detailed study of the vacua of the S 3-symmetric three-Higgs-doublet potential, specifying the region of parameters where these minimisation solutions occur. We work with a CP conserving scalar potential and analyse the possible real and complex vacua with emphasis on the cases in which the CP symmetry can be spontaneously broken. Results are presented both in the reducible-representation framework of Derman, and in the irreducible-representation framework. Mappings between these are given. Some of these implementations can in principle accommodate dark matter and for that purpose it is important to identify the residual symmetries of the potential after spontaneous symmetry breakdown. We are also concerned with constraints from vacuum stability.
Invariant current approach to wave propagation in locally symmetric structures
NASA Astrophysics Data System (ADS)
Zampetakis, V. E.; Diakonou, M. K.; Morfonios, C. V.; Kalozoumis, P. A.; Diakonos, F. K.; Schmelcher, P.
2016-05-01
A theory for wave mechanical systems with local inversion and translation symmetries is developed employing the two-dimensional solution space of the stationary Schrödinger equation. The local symmetries of the potential are encoded into corresponding local basis vectors in terms of symmetry-induced two-point invariant currents which map the basis amplitudes between symmetry-related points. A universal wavefunction structure in locally symmetric potentials is revealed, independently of the physical boundary conditions, by using special local bases which are adapted to the existing local symmetries. The local symmetry bases enable efficient computation of spatially resolved wave amplitudes in systems with arbitrary combinations of local inversion and translation symmetries. The approach opens the perspective of a flexible analysis and control of wave localization in structurally complex systems.
Symmetric/asymmetric bifurcation behaviours of a bogie system
NASA Astrophysics Data System (ADS)
Xue-jun, Gao; Ying-hui, Li; Yuan, Yue; True, Hans
2013-02-01
Based on the bifurcation and stability theory of dynamical systems, the symmetric/asymmetric bifurcation behaviours and chaotic motions of a railway bogie system under a complex nonlinear wheel-rail contact relation are investigated in detail by the 'resultant bifurcation diagram' method with slowly increasing and decreasing speed. It is found that the stationary equilibrium solution and the periodic motions coexist due to the sub-critical Hopf bifurcation in the railway bogie system. It is also found that multiple solutions coexist in many speed ranges. The coexistence of multiple solutions may result in a jump and hysteresis of the oscillating amplitude for different kinds of disturbances. It should be avoided in the normal operation. Furthermore, it is found that symmetry-breaking of the system through a pitchfork bifurcation leads to asymmetric chaotic motions in the railway bogie system. The speed ranges of asymmetric chaotic motions are, however, small.
Waterbomb base: a symmetric single-vertex bistable origami mechanism
NASA Astrophysics Data System (ADS)
Hanna, Brandon H.; Lund, Jason M.; Lang, Robert J.; Magleby, Spencer P.; Howell, Larry L.
2014-09-01
The origami waterbomb base is a single-vertex bistable origami mechanism that has unique properties which may prove useful in a variety of applications. It also shows promise as a test bed for smart materials and actuation because of its straightforward geometry and multiple phases of motion, ranging from simple to more complex. This study develops a quantitative understanding of the symmetric waterbomb base's kinetic behavior. This is done by completing kinematic and potential energy analyses to understand and predict bistable behavior. A physical prototype is constructed and tested to validate the results of the analyses. Finite element and virtual work analyses based on the prototype are used to explore the locations of the stable equilibrium positions and the force-deflection response. The model results are verified through comparisons to measurements on a physical prototype. The resulting models describe waterbomb base behavior and provide an engineering tool for application development.
Lee, Myoung-Jae; Jung, Young-Dae
2015-02-15
The nonthermal and geometric effects on the propagation of the surface dust acoustic waves are investigated in a Lorentzian dusty plasma slab. The symmetric and anti-symmetric dispersion modes of the dust acoustic waves are obtained by the plasma dielectric function with the spectral reflection conditions the slab geometry. The variation of the nonthermal and geometric effects on the symmetric and the anti-symmetric modes of the surface plasma waves is also discussed.
Forced baroclinic ocean motions. III - The linear equatorial basin case
NASA Technical Reports Server (NTRS)
Cane, M. A.; Sarachik, E. S.
1979-01-01
The linear response to simple wind stress of an equatorial ocean described by baroclinic shallow water equations is studied. Three types of basin are considered in treating the linear spin-up of the equatorial ocean: a symmetric basin with zonal walls distant from the equator (compared to the equatorial radius of deformation); a symmetric basin with zonal walls near the equator; and an asymmetric basin with one wall near the equator and one distant. The approach to the steady (Sverdrup) solutions is analyzed, with special attention given to the fast planetary response. Numerical treatments of spin-up for various winds in each type of basin are also presented.
NASA Astrophysics Data System (ADS)
Hassan, Absar U.; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N.
2015-12-01
A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT -symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase-transition point. The conclusions of our analysis are in agreement with experimental data.
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis. PMID:26441450
Symmetry breaking of solitons in two-dimensional complex potentials
NASA Astrophysics Data System (ADS)
Yang, Jianke
2015-02-01
Symmetry breaking is reported for continuous families of solitons in the nonlinear Schrödinger equation with a two-dimensional complex potential. This symmetry breaking is forbidden in generic complex potentials. However, for a special class of partially parity-time-symmetric potentials, it is allowed. At the bifurcation point, two branches of asymmetric solitons bifurcate out from the base branch of symmetry-unbroken solitons. Stability of these solitons near the bifurcation point are also studied, and two novel properties for the bifurcated asymmetric solitons are revealed. One is that at the bifurcation point, zero and simple imaginary linear-stability eigenvalues of asymmetric solitons can move directly into the complex plane and create oscillatory instability. The other is that the two bifurcated asymmetric solitons, even though having identical powers and being related to each other by spatial mirror reflection, can possess different types of unstable eigenvalues and thus exhibit nonreciprocal nonlinear evolutions under random-noise perturbations.
Ushenko, Yu A; Gorskii, M P; Dubolazov, A V; Motrich, A V; Ushenko, V A; Sidor, M I
2012-08-31
Theory of polarisation-correlation analysis of laser images of histological sections of biopsy material from cervix tissue based on spatial frequency selection of linear and circular birefringence mechanisms is formulated. Comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy (CDMA), produced by fibrillar networks formed by myosin and collagen fibres of cervix tissue in different pathological conditions, namely, pre-cancer (dysplasia) and cancer (adenocarcinoma), are presented. The values and variation ranges of statistical (moments of the first - fourth order), correlation (excess-autocorrelation functions), and fractal (slopes of approximating curves and dispersion of extrema of logarithmic dependences of power spectra) parameters of the CDMA coordinate distributions are studied. Objective criteria for pathology diagnostics and differentiation of its severity degree are determined. (image processing)
NASA Astrophysics Data System (ADS)
Ushenko, Yu A.; Gorskii, M. P.; Dubolazov, A. V.; Motrich, A. V.; Ushenko, V. A.; Sidor, M. I.
2012-08-01
Theory of polarisation-correlation analysis of laser images of histological sections of biopsy material from cervix tissue based on spatial frequency selection of linear and circular birefringence mechanisms is formulated. Comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy (CDMA), produced by fibrillar networks formed by myosin and collagen fibres of cervix tissue in different pathological conditions, namely, pre-cancer (dysplasia) and cancer (adenocarcinoma), are presented. The values and variation ranges of statistical (moments of the first — fourth order), correlation (excess-autocorrelation functions), and fractal (slopes of approximating curves and dispersion of extrema of logarithmic dependences of power spectra) parameters of the CDMA coordinate distributions are studied. Objective criteria for pathology diagnostics and differentiation of its severity degree are determined.
Symmetrical and anti-symmetrical coherent perfect absorption for acoustic waves
Wei, Pengjiang; Croënne, Charles; Tak Chu, Sai; Li, Jensen
2014-03-24
We investigate tunable acoustic absorption enabled by the coherent control of input waves. It relies on coherent perfect absorption originally proposed in optics. By designing appropriate acoustic metamaterial structures with resonating effective bulk modulus or density, we show that complete absorption of incident waves impinging on the metamaterial can be achieved for either symmetrical or anti-symmetrical inputs in the forward and backward directions. By adjusting the relative phase between the two incident beams, absorption can be tuned effectively from unity to zero, making coherent control useful in applications like acoustic modulators, noise controllers, transducers, and switches.
Cruz, Alejandro; Padilla-Martínez, Itzia I; García-Báez, Efrén V
2012-01-01
Symmetric and non-symmetric 2-(N-H, N-methyl, N-ethylenyl and N-aryl)guanidinebenzothiazoles were synthesized from the reaction of ammonia, methylamine, pyrrolidine and aniline with dimethyl benzo[d]thiazol-2-yl-carbonodithioimidate as intermediate. The products were characterized by ¹H-, ¹³C-NMR spectroscopy and three of them by X-ray diffraction analysis. HN-phenyl protons formed intramolecular hydrogen bonds that assist the stereochemistry of the second substituent, whereas the HN-alkyl protons were involved in intermolecular hydrogen bonding. PMID:22922286
2 × 2 random matrix ensembles with reduced symmetry: from Hermitian to {PT} -symmetric matrices
NASA Astrophysics Data System (ADS)
Gong, Jiangbin; Wang, Qing-hai
2012-11-01
A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity-time ( {PT})-symmetric matrices. To illustrate the main idea, we first study 2 × 2 complex Hermitian matrix ensembles with O(2)-invariant constraints, yielding novel level-spacing statistics such as singular distributions, the half-Gaussian distribution, distributions interpolating between the GOE (Gaussian orthogonal ensemble) distribution and half-Gaussian distributions, as well as the gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2 × 2 {PT}-symmetric matrix ensembles with real eigenvalues. In particular, {PT}-symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of {PT}-symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian unitary ensemble) statistics or the ‘truncated-GUE’ statistics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Unidirectional flow over asymmetric and symmetric ripples
NASA Astrophysics Data System (ADS)
Wiberg, Patricia L.; Nelson, Jonathan M.
1992-08-01
An LDV-equipped flume has yielded detailed measurements of velocity and turbulence over fixed sets of two-dimensional symmetric and asymmetric ripples. The measured velocities over the ripples are compared with the Nelson and Smith (1989)results for flow over larger-scale dunes; the new results are larger in the outer region of the flow, and the velocity profiles exhibit no sharp inflection at the top of the lowest wake. A model for flow over bedforms which has yielded excellent agreement with dune measurements is presently modified to better represent the observed flow over ripples.
Dual frame symmetric wavelets with limited redundancy
NASA Astrophysics Data System (ADS)
Abdelnour, Farras
2009-08-01
In this paper we explore the design of 5-band dual frame (overcomplete) wavelets with a dilation factor M = 4. The resulting limit functions are significantly smoother than their orthogonal counterparts at the same dilation factor. An advantage of the proposed filters over the dyadic filterbanks (M = 2) is that the proposed filterbanks result in a reduced redundancy when compared with dyadic frames, while maintaining smoothness. The proposed filterbanks are symmetric and generate four wavelets and a scaling function for each the synthesis and analysis limit functions. All wavelets are equipped with at least one vanishing moment each.
Expanding symmetric multiprocessor capability through gang scheduling
Jette, M.A.
1998-03-01
Symmetric Multiprocessor (SMP) systems normally provide both space- sharing and time-sharing to insure high system utilization and good responsiveness. However the prevailing lack of concurrent scheduling for parallel programs precludes SMP use in addressing many large-scale problems. Tightly synchronized communications are impractical and normal time-sharing reduces the benefit of cache memory. Evidence gathered at Lawrence Livermore National Laboratory (LLNL) indicates that gang scheduling can increase the capability of SMP systems and parallel program performance without adverse impact upon system utilization or responsiveness.
Chaos in symmetric phase oscillator networks.
Bick, Christian; Timme, Marc; Paulikat, Danilo; Rathlev, Dirk; Ashwin, Peter
2011-12-01
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos; i.e., nonlinear interactions of phases give rise to the necessary instabilities. PMID:22243002
Hoop conjecture in spherically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Khuri, Marcus A.
2009-12-01
We give general sufficient conditions for the existence of trapped surfaces due to concentration of matter in spherically symmetric initial data sets satisfying the dominant energy condition. These results are novel in that they apply and are meaningful for arbitrary spacelike slices, that is, they do not require any auxiliary assumptions such as maximality, time symmetry, or special extrinsic foliations, and most importantly they can easily be generalized to the nonspherical case once an existence theory for a modified version of the Jang equation is developed. Moreover, our methods also yield positivity and monotonicity properties of the Misner-Sharp energy.
Electroweak Baryogenesis in R-symmetric Supersymmetry
Fok, R.; Kribs, Graham D.; Martin, Adam; Tsai, Yuhsin
2013-03-01
We demonstrate that electroweak baryogenesis can occur in a supersymmetric model with an exact R-symmetry. The minimal R-symmetric supersymmetric model contains chiral superfields in the adjoint representation, giving Dirac gaugino masses, and an additional set of "R-partner" Higgs superfields, giving R-symmetric \\mu-terms. New superpotential couplings between the adjoints and the Higgs fields can simultaneously increase the strength of the electroweak phase transition and provide additional tree-level contributions to the lightest Higgs mass. Notably, no light stop is present in this framework, and in fact, we require both stops to be above a few TeV to provide sufficient radiative corrections to the lightest Higgs mass to bring it up to 125 GeV. Large CP-violating phases in the gaugino/higgsino sector allow us to match the baryon asymmetry of the Universe with no constraints from electric dipole moments due to R-symmetry. We briefly discuss some of the more interesting phenomenology, particularly of the of the lightest CP-odd scalar.
Spherically Symmetric Solutions of Light Galileon
NASA Astrophysics Data System (ADS)
Momeni, D.; Houndjo, M. J. S.; Güdekli, E.; Rodrigues, M. E.; Alvarenga, F. G.; Myrzakulov, R.
2016-02-01
We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form {L}_{φ }= -η (partial φ )2+β G^{μ ν }partial _{μ }φ partial _{ν }φ . We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of f(R,R^{μ ν }T_{μ ν }m). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.
Fast numerical determination of symmetric sparsity patterns
Carter, R.G.
1994-08-01
The author considers a function g: {Re}{sup n} {yields} {Re}{sup n} for which the Jacobian is symmetric and sparse. Such functions often arise, for instance, in numerical optimization, where g is the gradient of some objective function f so that the Jacobian of g is the Hessian of f. In many such applications one can generate extremely efficient algorithms by taking advantage of the sparsity structure of the problem if this pattern is known a priori. Unfortunately, determining such sparsity structures by hand is often difficult and prone to error. If one suspects a mistake has been made, or if g is a {open_quotes}black box{close_quotes} so that the true structure is completely unknown, one often has no alternative but to compute the entire matrix by finite differences - a prohibitively expensive task for large problems. The author shows that it is possible to numerically determine symmetric sparsity patterns using a relatively small number of g evaluations. Numerical results are shown for n up to 100,000 in which all nonzeros in the Jacobian are correctly identified in about one-hundredth of the time required to estimate the sparsity structure by a full finite difference calculation. When a good initial guess for the sparsity structure is available, numerical results are presented for n up to 500,000, in which all missing nonzeros are correctly located almost five-thousand times faster than would be possible with a full finite difference calculation.
Parallel solution of the symmetric tridiagonal eigenproblem
Jessup, E.R.
1989-01-01
This thesis discusses methods for computing all eigenvalues and eigenvectors of a symmetric tridiagonal matrix on a distributed memory MIMD multiprocessor. Only those techniques having the potential for both high numerical accuracy and significant large-grained parallelism are investigated. These include the QL method or Cuppen's divide and conquer method based on rank-one updating to compute both eigenvalues and eigenvectors, bisection to determine eigenvalues, and inverse iteration to compute eigenvectors. To begin, the methods are compared with respect to computation time, communication time, parallel speedup, and accuracy. Experiments on an iPSC hyper-cube multiprocessor reveal that Cuppen's method is the most accurate approach, but bisection with inverse iteration is the fastest and most parallel. Because the accuracy of the latter combination is determined by the quality of the computed eigenvectors, the factors influencing the accuracy of inverse iteration are examined. This includes, in part, statistical analysis of the effects of a starting vector with random components. These results are used to develop an implementation of inverse iteration producing eigenvectors with lower residual error and better orthogonality than those generated by the EISPACK routine TINVIT. This thesis concludes with adaptations of methods for the symmetric tridiagonal eigenproblem to the related problem of computing the singular value decomposition (SVD) of a bidiagonal matrix.
Cyclicity of some symmetric nilpotent centers
NASA Astrophysics Data System (ADS)
García, Isaac A.
2016-03-01
In this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotent singularities of symmetric polynomial planar vector fields. The starting point is identifying a broad family of nilpotent symmetric fields for which existence of a center is equivalent to existence of a local analytic first integral, which, unlike the degenerate case, is not true in general for nilpotent singularities. We are able to relate so-called "focus quantities" to the "Poincaré-Lyapunov quantities" arising from the Poincaré first return map. When we apply the method to concrete examples, we show in some cases that the upper bound is sharp. Our approach is based on computational algebra methods for determining a minimal basis (constructed by focus quantities instead of by Poincaré-Lyapunov quantities because of the easier computability of the former) of the associated polynomial Bautin ideal in the parameter space of the family. The case in which the Bautin ideal is not radical is also treated.
The modelling of symmetric airfoil vortex generators
NASA Technical Reports Server (NTRS)
Reichert, B. A.; Wendt, B. J.
1996-01-01
An experimental study is conducted to determine the dependence of vortex generator geometry and impinging flow conditions on shed vortex circulation and crossplane peak vorticity for one type of vortex generator. The vortex generator is a symmetric airfoil having a NACA 0012 cross-sectional profile. The geometry and flow parameters varied include angle-of-attack alfa, chordlength c, span h, and Mach number M. The vortex generators are mounted either in isolation or in a symmetric counter-rotating array configuration on the inside surface of a straight pipe. The turbulent boundary layer thickness to pipe radius ratio is delta/R = 0. 17. Circulation and peak vorticity data are derived from crossplane velocity measurements conducted at or about 1 chord downstream of the vortex generator trailing edge. Shed vortex circulation is observed to be proportional to M, alfa, and h/delta. With these parameters held constant, circulation is observed to fall off in monotonic fashion with increasing airfoil aspect ratio AR. Shed vortex peak vorticity is also observed to be proportional to M, alfa, and h/delta. Unlike circulation, however, peak vorticity is observed to increase with increasing aspect ratio, reaching a peak value at AR approx. 2.0 before falling off.
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
2013-01-01
Nondimensional linear-bifurcation buckling equations for balanced, symmetrically laminated cylinders with negligible shell-wall anisotropies and subjected to uniform axial compression loads are presented. These equations are solved exactly for the practical case of simply supported ends. Nondimensional quantities are used to characterize the buckling behavior that consist of a stiffness-weighted length-to-radius parameter, a stiffness-weighted shell-thinness parameter, a shell-wall nonhomogeneity parameter, two orthotropy parameters, and a nondimensional buckling load. Ranges for the nondimensional parameters are established that encompass a wide range of laminated-wall constructions and numerous generic plots of nondimensional buckling load versus a stiffness-weighted length-to-radius ratio are presented for various combinations of the other parameters. These plots are expected to include many practical cases of interest to designers. Additionally, these plots show how the parameter values affect the distribution and size of the festoons forming each response curve and how they affect the attenuation of each response curve to the corresponding solution for an infinitely long cylinder. To aid in preliminary design studies, approximate formulas for the nondimensional buckling load are derived, and validated against the corresponding exact solution, that give the attenuated buckling response of an infinitely long cylinder in terms of the nondimensional parameters presented herein. A relatively small number of "master curves" are identified that give a nondimensional measure of the buckling load of an infinitely long cylinder as a function of the orthotropy and wall inhomogeneity parameters. These curves reduce greatly the complexity of the design-variable space as compared to representations that use dimensional quantities as design variables. As a result of their inherent simplicity, these master curves are anticipated to be useful in the ongoing development of buckling-design technology.
Multi-frequency EIT system with radially symmetric architecture: KHU Mark1.
Oh, Tong In; Woo, Eung Je; Holder, David
2007-07-01
We describe the development of a multi-frequency electrical impedance tomography (EIT) system (KHU Mark1) with a single balanced current source and multiple voltmeters. It was primarily designed for imaging brain function with a flexible strategy for addressing electrodes and a frequency range from 10 Hz-500 kHz. The maximal number of voltmeters is 64, and all of them can simultaneously acquire and demodulate voltage signals. Each voltmeter measures a differential voltage between a pair of electrodes. All voltmeters are configured in a radially symmetric architecture in order to optimize the routing of wires and minimize cross-talk. We adopted several techniques from existing EIT systems including digital waveform generation, a Howland current generator with a generalized impedance converter (GIC), digital phase-sensitive demodulation and tri-axial cables. New features of the KHU Mark1 system include multiple GIC circuits to maximize the output impedance of the current source at multiple frequencies. The voltmeter employs contact impedance measurements, data overflow detection, spike noise rejection, automatic gain control and programmable data averaging. The KHU Mark1 system measures both in-phase and quadrature components of trans-impedances. By using a script file describing an operating mode, the system setup can be easily changed. The performance of the developed multi-frequency EIT system was evaluated in terms of a common-mode rejection ratio, signal-to-noise ratio, linearity error and reciprocity error. Time-difference and frequency-difference images of a saline phantom with a banana object are presented showing a frequency-dependent complex conductivity of the banana. Future design of a more innovative system is suggested including miniaturization and wireless techniques. PMID:17664635
Solitary Waves of a $$\\mathcal {P}$$ $$\\mathcal {T}$$-Symmetric Nonlinear Dirac Equation
Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Saxena, Avadh; Cooper, Fred; Khare, Avinash; Comech, Andrew; Bender, Carl M.
2015-10-06
In our study we consider we consider a prototypical example of a mathcalP mathcalT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the mathcalP mathcalT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the mathcalP mathcalT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the mathcalP mathcalT-transition threshold. In the latter, they degenerate into linear waves. We also examine themore » dynamics of the model. Given the stability of the waveforms in the mathcalP mathcalT-exact phase, we consider them as initial conditions for parameters outside of that phase. We also find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding “quench”. The former can be characterized by an interesting form of bifrequency solutions that have been predicted on the basis of the SU symmetry. Finally, we explore some special, analytically tractable, but not mathcalP mathcalT-symmetric solutions in the massless limit of t- e model.« less
Symmetric instability in the Gulf Stream
NASA Astrophysics Data System (ADS)
Thomas, Leif N.; Taylor, John R.; Ferrari, Raffaele; Joyce, Terrence M.
2013-07-01
Analyses of wintertime surveys of the Gulf Stream (GS) conducted as part of the CLIvar MOde water Dynamic Experiment (CLIMODE) reveal that water with negative potential vorticity (PV) is commonly found within the surface boundary layer (SBL) of the current. The lowest values of PV are found within the North Wall of the GS on the isopycnal layer occupied by Eighteen Degree Water, suggesting that processes within the GS may contribute to the formation of this low-PV water mass. In spite of large heat loss, the generation of negative PV was primarily attributable to cross-front advection of dense water over light by Ekman flow driven by winds with a down-front component. Beneath a critical depth, the SBL was stably stratified yet the PV remained negative due to the strong baroclinicity of the current, suggesting that the flow was symmetrically unstable. A large eddy simulation configured with forcing and flow parameters based on the observations confirms that the observed structure of the SBL is consistent with the dynamics of symmetric instability (SI) forced by wind and surface cooling. The simulation shows that both strong turbulence and vertical gradients in density, momentum, and tracers coexist in the SBL of symmetrically unstable fronts. SI is a shear instability that draws its energy from geostrophic flows. A parameterization for the rate of kinetic energy (KE) extraction by SI applied to the observations suggests that SI could result in a net dissipation of 33 mW m-2 and 1 mW m-2 for surveys with strong and weak fronts, respectively. The surveys also showed signs of baroclinic instability (BCI) in the SBL, namely thermally direct vertical circulations that advect biomass and PV. The vertical circulation was inferred using the omega equation and used to estimate the rate of release of available potential energy (APE) by BCI. The rate of APE release was found to be comparable in magnitude to the net dissipation associated with SI. This result points to an energy pathway where the GS's reservoir of APE is drained by BCI, converted to KE, and then dissipated by SI and its secondary instabilities. Similar dynamics are likely to be found at other strong fronts forced by winds and/or cooling and could play an important role in the energy balance of the ocean circulation.
Chen, Jeffrey R; Numata, Kenji; Wu, Stewart T
2014-10-20
We report new methods for retrieving atmospheric constituents from symmetrically-measured lidar-sounding absorption spectra. The forward model accounts for laser line-center frequency noise and broadened line-shape, and is essentially linearized by linking estimated optical-depths to the mixing ratios. Errors from the spectral distortion and laser frequency drift are substantially reduced by averaging optical-depths at each pair of symmetric wavelength channels. Retrieval errors from measurement noise and model bias are analyzed parametrically and numerically for multiple atmospheric layers, to provide deeper insight. Errors from surface height and reflectance variations are reduced to tolerable levels by "averaging before log" with pulse-by-pulse ranging knowledge incorporated. PMID:25401639
Cutting Force Predication Based on Integration of Symmetric Fuzzy Number and Finite Element Method
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
2014-01-01
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force. PMID:24790556
Tunneling control using classical non-linear oscillator
Kar, Susmita; Bhattacharyya, S. P.
2014-04-24
A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.
Group Lifting Structures For Multirate Filter Banks, II: Linear Phase Filter Banks
Brislawn, Christopher M
2008-01-01
The theory of group lifting structures is applied to linear phase lifting factorizations for the two nontrivial classes of two-channel linear phase perfect reconstruction filter banks, the whole-and half-sample symmetric classes. Group lifting structures defined for the reversible and irreversible classes of whole-and half-sample symmetric filter banks are shown to satisfy the hypotheses of the uniqueness theorem for group lifting structures. It follows that linear phase lifting factorizations of whole-and half-sample symmetric filter banks are therefore independent of the factorization methods used to compute them. These results cover the specification of user-defined whole-sample symmetric filter banks in Part 2 of the ISO JPEG 2000 standard.
The synthesis of symmetrical bis-1,2,5-thiadiazole ligands.
Mullins, Michael J.; Abboud, Khalil A.; Philipp, Dean M.; Muller, Richard Partain; Goddard, William A., III; Athey, Phillip S.; Snelgrove, R. Vernon
2004-05-01
We have been engaged in a search for coordination catalysts for the copolymerization of polar monomers (such as vinyl chloride and vinyl acetate) with ethylene. We have been investigating complexes of late transition metals with heterocyclic ligands. In this report we describe the synthesis of a symmetrical bis-thiadiazole. We have characterized one of the intermediates using single crystal X-ray diffraction. Several unsuccessful approaches toward 1 are also described, which shed light on some of the unique chemistry of thiadiazoles.
Pearlstein, L.D.
1983-08-29
Equilibrium in quadrupole symmetric mirrors is fully three dimensional; however, because axial scale lengths are long compared with radial scale lengths (equivalently weak curvature) it is possible to reduce the complexity of the equations by expanding in the appropriate smallness parameter. Such a procedure leads to set of reduced MHD equations. The general theory will be presented, numerical results discussed, modifications due to finite Larmor radius will be added, and an analytic solution for sharp boundary pressure models will be developed.
A novel receptor based on a C3v-symmetrical PN3-calix[6]cryptand.
Zeng, Xianshun; Hucher, Nicolas; Reinaud, Olivia; Jabin, Ivan
2004-10-01
A C3v-symmetrical PN3-calix[6]cryptand was prepared in six steps from the known 1,3,5-tris-methylated calix[6]arene through a remarkably efficient [1 + 1] macrocyclization reaction. A 1H NMR study showed that the P,N-crypto cap rigidifies the whole edifice in a cone conformation ideal for molecular recognition applications. The ability of this new receptor to perform selective endo-complexation is illustrated with ammonium guests. PMID:15387616
Minimal Left-Right Symmetric Dark Matter
NASA Astrophysics Data System (ADS)
Heeck, Julian; Patra, Sudhanwa
2015-09-01
We show that left-right symmetric models can easily accommodate stable TeV-scale dark matter particles without the need for an ad hoc stabilizing symmetry. The stability of a newly introduced multiplet either arises accidentally as in the minimal dark matter framework or comes courtesy of the remaining unbroken Z2 subgroup of B -L . Only one new parameter is introduced: the mass of the new multiplet. As minimal examples, we study left-right fermion triplets and quintuplets and show that they can form viable two-component dark matter. This approach is, in particular, valid for S U (2 )×S U (2 )×U (1 ) models that explain the recent diboson excess at ATLAS in terms of a new charged gauge boson of mass 2 TeV.
Minimal Left-Right Symmetric Dark Matter.
Heeck, Julian; Patra, Sudhanwa
2015-09-18
We show that left-right symmetric models can easily accommodate stable TeV-scale dark matter particles without the need for an ad hoc stabilizing symmetry. The stability of a newly introduced multiplet either arises accidentally as in the minimal dark matter framework or comes courtesy of the remaining unbroken Z_{2} subgroup of B-L. Only one new parameter is introduced: the mass of the new multiplet. As minimal examples, we study left-right fermion triplets and quintuplets and show that they can form viable two-component dark matter. This approach is, in particular, valid for SU(2)SU(2)U(1) models that explain the recent diboson excess at ATLAS in terms of a new charged gauge boson of mass 2 TeV. PMID:26430988
Symmetric Satellite Swarms and Choreographic Crystals.
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
2016-01-01
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems. PMID:26799028
Radially symmetric transmon with long lifetime
NASA Astrophysics Data System (ADS)
Sandberg, Martin; Vissers, Michael; Gao, Jiansong; Pappas, David
2014-03-01
We present a radially symmetric design for a large pad transmon qubit. The symmetry reduces the dipole radiation by orders of magnitude relative to axial large pad qubits that are widely used for 3D-circuit QED experiments. The reduction in radiation allows for the use of large area structures that are needed to reduce the effects of interface losses. This enables long qubit lifetimes without the use of a high-Q cavity resonator. Energy relaxation and coherence times of up to 35 microseconds have been measured. The qubit can be implemented in a microstrip geometry. This gives the advantage of removing discontinuous ground planes that can cause stray resonances. In addition, this geometry is well suited for implementing and exploring circuits with direct qubit-qubit coupling.
Highly symmetric POVMs and their informational power
NASA Astrophysics Data System (ADS)
Słomczyński, Wojciech; Szymusiak, Anna
2016-01-01
We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension 2 (for qubits). In this case, we prove that the entropy is minimal, and hence, the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation, and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy, and the quantum dynamical entropy are described.
Cosmic ray antimatter and baryon symmetric cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.; Protheroe, R. J.; Kazanas, D.
1982-01-01
The relative merits and difficulties of the primary and secondary origin hypotheses for the observed cosmic-ray antiprotons, including the new low-energy measurement of Buffington, et al. We conclude that the cosmic-ray antiproton data may be evidence for antimatter galaxies and baryon symmetric cosmology. The present bar P data are consistent with a primary extragalactic component having /p=/equiv 1+/- 3.2/0.7x10 = to the -4 independent of energy. We propose that the primary extragalactic cosmic ray antiprotons are most likely from active galaxies and that expected disintegration of bar alpha/alpha ban alpha/alpha. We further predict a value for ban alpha/alpha =/equiv 10 to the -5, within range of future cosmic ray detectors.
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
1982-01-01
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
Symmetric Satellite Swarms and Choreographic Crystals
NASA Astrophysics Data System (ADS)
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
2016-01-01
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.
Plane-symmetric cosmology with relativistic hydrodynamics
NASA Astrophysics Data System (ADS)
Anninos, Peter
1998-09-01
A numerical code, developed for cosmology and to investigate fully nonlinear behavior in the plane-symmetric Einstein equations, is described in detail. The field equations are solved self-consistently with the general relativistic hydrodynamical conservation equations, using artificial viscosity methods for shock capturing and an ideal fluid stress-energy tensor with a cosmological constant. Several tests of the code are presented, including anisotropically expanding vacuum and isotropically expanding de Sitter, dust-filled and radiation-filled cosmologies, gravitational waves in flat and anisotropically expanding background models, sub- and super-horizon scale density perturbations in an expanding FLRW background, and both Newtonian and relativistic shock tube evolutions. Also discussed is a gauge drift instability that can appear in near-geodesic evolutions of density perturbations when the dynamical time scale of collapse becomes smaller than the cosmological expansion rate.
Symmetrical Taylor impact of glass bars
NASA Astrophysics Data System (ADS)
Murray, N. H.; Bourne, N. K.; Field, J. E.; Rosenberg, Z.
1998-07-01
Brar and Bless pioneered the use of plate impact upon bars as a technique for investigating the 1D stress loading of glass but limited their studies to relatively modest stresses (1). We wish to extend this technique by applying VISAR and embedded stress gauge measurements to a symmetrical version of the test in which two rods impact one upon the other. Previous work in the laboratory has characterised the glass types (soda-lime and borosilicate)(2). These experiments identify the failure mechanisms from high-speed photography and the stress and particle velocity histories are interpreted in the light of these results. The differences in response of the glasses and the relation of the fracture to the failure wave in uniaxial strain are discussed.
Implications of nonlinearity for spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Sen, Sourav; Ray, Arnab K.
2014-03-01
We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time dependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow toward a final and stable transonic state.
Torus quantization of symmetrically excited helium
Mueller, J. ); Burgdoerfer, J. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6377 ); Noid, D. )
1992-02-01
The recent discovery by Richter and Wintgen (J. Phys. B 23, L197 (1990)) that the classical helium atom is not globally ergodic has stimulated renewed interest in its semiclassical quantization. The Einstein-Brillouin-Keller quantization of Kolmogorov-Arnold-Moser tori around stable periodic orbits becomes locally possible in a selected region of phase space. Using a hyperspherical representation we have found a dynamically confining potential allowing for a stable motion near the Wannier ridge. The resulting semiclassical eigenenergies provide a test for full quantum calculations in the limit of very high quantum numbers. The relations to frequently used group-theoretical classifications for doubly excited states and to the periodic-orbit quantization of the chaotic portion of the phase space are discussed. The extrapolation of the semiclassical quantization to low-lying states give remarkably accurate estimates for the energies of all symmetric {ital L}=0 states of helium.
Consistency of PT-symmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2016-03-01
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric—the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.
Pseudo-Z symmetric space-times
Mantica, Carlo Alberto; Suh, Young Jin
2014-04-15
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A{sub k} is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS){sub 4} space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Optimal low symmetric dissipation Carnot engines and refrigerators.
de Tomás, C; Hernández, A Calvo; Roco, J M M
2012-01-01
A unified optimization criterion for Carnot engines and refrigerators is proposed. It consists of maximizing the product of the heat absorbed by the working system times the efficiency per unit time of the device, either the engine or the refrigerator. This criterion can be applied to both low symmetric dissipation Carnot engines and refrigerators. For engines the criterion coincides with the maximum power criterion and then the Curzon-Ahlborn efficiency η(CA)=1-√T(c)/T(h) is recovered, where T(h) and T(c) are the temperatures of the hot and cold reservoirs, respectively [Esposito, Kawai, Lindenberg, and Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. For refrigerators the criterion provides the counterpart of Curzon-Ahlborn efficiency for refrigerators ε(CA)=[1/(√1-(T(c)/T(h))]-1, first derived by Yan and Chen for the particular case of an endoreversible Carnot-type refrigerator with linear (Newtonian) finite heat transfer laws [Yan and Chen, J. Phys. D: Appl. Phys. 23, 136 (1990)]. PMID:22400500
Rectification in Symmetric Conjugated Molecules with Asymmetric Linkers
NASA Astrophysics Data System (ADS)
Batra, Arunabh; Meisner, Jeffrey S.; Widawsky, Jonathan R.; Huisman, Eek; Nuckolls, Colin; Venkataraman, Latha
2012-02-01
Demonstrating single-molecule rectification is an important step towards the realization of molecule-based electronic devices. Most molecules put forward as potential rectifiers employ asymmetric molecular backbones. In contrast, we show that we can create rectifying junctions by designing asymmetry only into the linker groups used to bond the molecule to metal electrodes. Our molecules consist of a conjugated backbone terminated with methylsulfide on one end and methyl-trimethyltin on the other. These molecules couple to Au electrodes through an Au-SMe donor acceptor bond, which serves as the electronically weak link, and a Au-C covalent bond, which is created in-situ after the SnMe3 cleaves off [1]. We create thousands of molecular junctions using a modified STM setup in a solution of molecules, measure their current-voltage (IV) characteristics and create averaged IV curves. We find that asymmetrically terminated molecules show non-linear IV curves with significant rectification, while molecules terminated symmetrically with either SMe or SnMe3 do not show substantial rectification. We also find that the rectification direction is dependent on molecular orientation in the junction. [1] Chen, W., et al., J. Am. Chem. Soc., 2011. 133(43): p. 17160-17163
Local Polynomial Regression for Symmetric Positive Definite Matrices
Yuan, Ying; Zhu, Hongtu; Lin, Weili; Marron, J. S.
2011-01-01
Summary Local polynomial regression has received extensive attention for the nonparametric estimation of regression functions when both the response and the covariate are in Euclidean space. However, little has been done when the response is in a Riemannian manifold. We develop an intrinsic local polynomial regression estimate for the analysis of symmetric positive definite (SPD) matrices as responses that lie in a Riemannian manifold with covariate in Euclidean space. The primary motivation and application of the proposed methodology is in computer vision and medical imaging. We examine two commonly used metrics, including the trace metric and the Log-Euclidean metric on the space of SPD matrices. For each metric, we develop a cross-validation bandwidth selection method, derive the asymptotic bias, variance, and normality of the intrinsic local constant and local linear estimators, and compare their asymptotic mean square errors. Simulation studies are further used to compare the estimators under the two metrics and to examine their finite sample performance. We use our method to detect diagnostic differences between diffusion tensors along fiber tracts in a study of human immunodeficiency virus. PMID:23008683
Gyrokinetic Studies of Microturbulence in the Madison Symmetric Torus
NASA Astrophysics Data System (ADS)
Williams, Zachary; Duff, James; Pueschel, M. J.; Terry, Paul
2015-11-01
Reversed-field pinches operating with Pulsed Poloidal Current Drive (PPCD) exhibit microturbulence that contributes to heat and particle transport. This work focuses on the analysis of high-frequency fluctuations in a recent 200 kA PPCD discharge in the Madison Symmetric Torus, for which strong experimental evidence of microturbulence exists. Local gyrokinetic simulations were performed at multiple radial positions outside the reversal surface using the
A permanent magnet tubular linear generator for wave energy conversion
NASA Astrophysics Data System (ADS)
Yu, Haitao; Liu, Chunyuan; Yuan, Bang; Hu, Minqiang; Huang, Lei; Zhou, Shigui
2012-04-01
A novel three-phase permanent magnet tubular linear generator (PMTLG) with Halbach array is proposed for the sea wave energy conversion. Non-linear axi-symmetrical finite element method (FEM) is implemented to calculate the magnetic fields along air-gap for different Halbach arrays of PMTLGs. The PMTLG characteristics are analyzed and the simulation results are validated by the experiment. An assistant tooth is implemented to greatly minimize the end and cogging effects which cause the oscillatory detent force.
NASA Astrophysics Data System (ADS)
Uhlmann, Armin
2016-03-01
This is an introduction to antilinear operators. In following Wigner the terminus antilinear is used as it is standard in Physics. Mathematicians prefer to say conjugate linear. By restricting to finite-dimensional complex-linear spaces, the exposition becomes elementary in the functional analytic sense. Nevertheless it shows the amazing differences to the linear case. Basics of antilinearity is explained in sects. 2, 3, 4, 7 and in sect. 1.2: Spectrum, canonical Hermitian form, antilinear rank one and two operators, the Hermitian adjoint, classification of antilinear normal operators, (skew) conjugations, involutions, and acq-lines, the antilinear counterparts of 1-parameter operator groups. Applications include the representation of the Lagrangian Grassmannian by conjugations, its covering by acq-lines. As well as results on equivalence relations. After remembering elementary Tomita-Takesaki theory, antilinear maps, associated to a vector of a two-partite quantum system, are defined. By allowing to write modular objects as twisted products of pairs of them, they open some new ways to express EPR and teleportation tasks. The appendix presents a look onto the rich structure of antilinear operator spaces.
Focal symmetrical encephalomalacia in a goat.
Oliveira, Diego M; Pimentel, Luciano A; Pessoa, André F; Dantas, Antônio F M; Uzal, Francisco; Riet-Correa, Franklin
2010-09-01
Focal symmetrical encephalomalacia (FSE) is the most prominent lesion seen in the chronic form of enterotoxemia caused by Clostridium perfringens type D in sheep. However, this lesion has not been reported in goats. The current paper reports a case of FSE in a goat from the state of Paraíba in the Brazilian semiarid region. As reported by the farmer, 30, 4-48-month-old animals from a flock of 150 goats died after showing nervous signs, including blindness and recumbence, for periods varying between 1 and 14 days. The flock was grazing native pasture supplemented with wheat and corn bran. Additionally, lactating goats were supplemented with soybeans. A 4-month-old goat with nervous signs was examined clinically and then necropsied 3 days after the onset of clinical signs. Bilateral, focal, and symmetrical areas of brown discoloration were observed in the internal capsule and thalamus. Histologic lesions in these areas consisted of multifocal, bilateral malacia with a few neutrophils; endothelial cell swelling; perivascular edema; and hemorrhages. The etiology of these lesions was not determined. However, FSE is considered pathognomonic for C. perfringens type D enterotoxemia in sheep, and it is speculated that this microorganism was the etiologic agent in the present case. The flock had been vaccinated against type D enterotoxemia only once, approximately 3 months before the beginning of the outbreak. Insufficient immunity due to the incorrect vaccination protocol, low efficacy of the vaccine used, and a diet including large amounts of highly fermentable carbohydrates were suspected to be predisposing factors for this outbreak. PMID:20807946
Resonance and antiresonance of symmetric and asymmetric cantilevered piezoelectric flexors.
Smits, J G; Choi, W S; Ballato, A
1997-01-01
The resonances of dynamically excited symmetric piezoelectric bimorphs have been determined from the equations of state. Under the effect of sinusoidal stimuli: a moment exerted at the tip M, a force exerted perpendicular to the plane of the bimorph also applied at the tip F, a uniformly applied pressure p, and an electrode voltage V, they respond with a sinusoidal tip rotation alpha, tip deflection delta, volume displacement nu, and electrode charge Q. All of the former are related to all of the latter through a dynamic admittance matrix B. The antiresonance frequency of the capacitance C have been found while also antiresonance in off-diagonal elements have been determined. The latter indicate that at these frequencies the bimorph does not work as an actuator or sensor in the particular domain of the off-diagonal. The mode shape at these antiresonance frequencies has been determined. The antiresonance of b(14) determines that for this frequency the tip has deflection but no rotation, while the antiresonance of b(24 ) indicates that the tip has rotation but no deflection. No antiresonance in the volume displacement is found, indicating that the bimorph is a pressure converter (microphone) at all frequencies. Micromachined piezoelectric heterogeneous bimorphs have been fabricated using the techniques of I.C. fabrication. Their deflections have been measured as a function of frequency and applied voltage, while these have been compared with the theoretical predictions. An anomalously large quadratic deflection has been found, superimposed on the linear piezoelectric behavior. The agreement between the linear part of the experimental deflection and the theory was quite good. PMID:18244123
Nonlinear dynamic analysis of quasi-symmetric anisotropic structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.
Entanglement equivalence of N-qubit symmetric states
Mathonet, P.; Krins, S.; Bastin, T.; Godefroid, M.; Solano, E.
2010-05-15
We study the interconversion of multipartite symmetric N-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or Greenberger-Horne-Zeilinger (GHZ) entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric N-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.
Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Jeon, G. J.
1983-01-01
Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.
Symmetric linear systems. [twin-lift helicopter control models for heavy construction use
NASA Technical Reports Server (NTRS)
Lewis, J.; Martin, C.
1983-01-01
Employment as a means of transportation in the civilian construction trades represents one of the many applications of the helicopter. However, a major limitation to its use in heavy construction has been that the mass which can be effectively and safely transported is severely restricted. The construction of the so-called 'heavy lift' helicopter provided one solution to this problem. But it has been found that there are physical and economic limitations to the payload which can be transported. The proposal has been made to overcome these limitations by making use of multiple helicopters to move a single mass. A study of the feasibility of this proposal showed that automatic control would be needed to make the concept successful. The present investigation is concerned with some initial models in regard to the twinlift problem, taking into account the control theoretic problems.
NASA Astrophysics Data System (ADS)
Jimenez, Carmen; Kurdyumov, Vadim
2015-11-01
Direct numerical simulations, including detailed chemistry and transport, are used to investigate the structure and stability of freely propagating lean hydrogen flames in planar narrow channels. Depending on the flame burning rate and the wall properties, the flame-wall heat exchange can result in flame extinction. For large heat losses only the fastest burning flames, corresponding to fast reactant flowing rates can propagate. We show that double flame solutions, symmetric and non-symmetric, can coexist for the same set of parameters. The symmetric solutions are calculated imposing symmetric boundary conditions in the channel mid-plane and when this restriction is relaxed non-symmetric solutions develop. This indicates that the symmetric flames are unstable to non-symmetric perturbations, as predicted before within the context of a constant density model. Moreover, the burning rates of the non-symmetric flames are found to be significantly larger than those of the corresponding symmetric solution and therefore the range of conditions for flame extinction and flashback also differ. This shows that assuming in CFD that the flame should reproduce the symmetry of the cold flow can have important safety implications in micro scale combustion devices burning lean hydrogen mixture.
Karsili, Tolga N V; Wenge, Andreas M; Marchetti, Barbara; Ashfold, Michael N R
2014-01-14
We report a combined experimental (H (Rydberg) atom photofragment translational spectroscopy) and theoretical (ab initio electronic structure and vibronic coupling calculations) study of the effects of symmetry on the photodissociation dynamics of phenols. Ultraviolet photoexcitation to the bound S1((1)ππ*) state of many phenols leads to some O-H bond fission by tunneling through the barrier under the conical intersection (CI) between the S1 and dissociative S2((1)πσ*) potential energy surfaces in the R(O-H) stretch coordinate. Careful analysis of the total kinetic energy release spectra of the resulting products shows that the radicals formed following S1 ← S0 excitation of phenol and symmetrically substituted phenols like 4-fluorophenol all carry an odd number of quanta in vibrational mode ν(16a), whereas those deriving from asymmetrically substituted systems like 3-fluorophenol or 4-methoxyphenol do not. This contrasting behavior can be traced back to symmetry. Symmetrically substituted phenols exist in two equivalent rotamers, which interconvert by tunneling through the barrier to OH torsional motion. Their states are thus best considered in the non-rigid G4 molecular symmetry group, wherein radiationless transfer from the S1 to S2 state requires a coupling mode of a2 symmetry. Of the three a2 symmetry parent modes, the out-of-plane ring puckering mode ν(16a) shows much the largest interstate coupling constant in the vicinity of the S1/S2 CI. The nuclear motions associated with ν(16a) are orthogonal to the dissociation coordinate, and are thus retained in the radical products. Introducing asymmetry (even a non-linear substituent in the 4-position) lifts the degeneracy of the rotamers, and lowers the molecular symmetry to Cs. Many more parent motions satisfy the reduced (a'') symmetry requirement to enable S1/S2 coupling, the most effective of which is OH torsion. This motion 'disappears' on O-H bond fission; symmetry thus imposes no restriction to forming radical products with vibrational quantum number v = 0. The present work yields values for the O-H bond strengths in 3-FPhOH and 4-MeOPhOH, and recommends modest revisions to the previously reported O-H bond strengths in other asymmetrically substituted phenols like 3- and 2-methylphenol and 4-hydroxyindole. PMID:24201655
Thermodynamic Analysis of Non-Linear Reissner-Nordström Black Holes
NASA Astrophysics Data System (ADS)
Cembranos, Jose; Cruz-Dombriz, Álvaro; Jarillo, Javier
2015-11-01
In the present article we study the Inverse Electrodynamics Model. This model is a gauge and parity invariant non-linear Electrodynamics theory, which respects the conformal invariance of standard Electrodynamics. This modified Electrodynamics model, when minimally coupled to General Relativity, is compatible with static and spherically symmetric Reissner-Nordstrom-like black-hole solutions. However, these black-hole solutions present more complex thermodynamic properties than their Reissner-Nordstrom black-hole solutions counterparts in standard Electrodynamics. In particular, in the Inverse Model a new stability region, with both the heat capacity and the free energy negative, arises. Moreover, unlike the scenario in standard Electrodynamics, a sole transition phase is possible for a suitable choice in the set of parameters of these solutions.
Xu, J. Raymond, K.N.
1999-01-25
A rational design of uranyl sequestering agents based on 3-hydroxy-2(1H)-pyridinone ligands has resulted in the first effective agents for mammalian uranyl decorporation. In this study crystal structures of uranyl complexes with four of these agents are compared and correlated with the chemical and biological properties. These hydroxypyridinone ligands bind the uranyl ion in the equator of a pentagonal prism; a solvent molecule fills the fifth coordination site. The tetradentate ligands are composed of two hydroxypyridonate groups connected by a diamine linker via amide coupling. The dihedral angles between two pyridinone ring planes in these complexes differ as the length of linear backbone changes, giving these molecules a ruffled shape. The physical parameters (such as NMR chemical shifts) of the uranyl complexes with tetradentate Me-3,2-HOPO ligands correlate with the length of the diamine linker, as does the in vivo activity. The ligands are amides of 3-hydroxy-N-methyl-2-(1H)-4-carboxypyridone. For L{sup 1} the amine is propane amine. For the tetradentate bis-amides the linker groups are (L{sup 3}) 1,3-diaminopropane, (L{sup 4}) 1,4-diaminobutane, (L{sup 5}) 1,5-diaminopentane. Crystal data: [UO{sub 2}(L{sup 1}){sub 2}{center_dot}DMF], space group, C2/c, cell constants: a = 37.430(8) {angstrom}, b = 7.0808(14) {angstrom}, c = 26.781(5) {angstrom}, {beta} = 130.17(3){degree}, V = 5424(2) {angstrom}{sup 3}, Z = 8. [UO{sub 2}L{sup 3}{center_dot}DMSO], Pnma, a = 8.4113(1) {angstrom}, b = 16.0140(3) {angstrom}, c = 16.7339(3) {angstrom}, V = 2254.03(5) {angstrom}{sup 3}, Z = 4. [UO{sub 2}L{sup 4}{center_dot}DMSO]{center_dot}DMSO{center_dot}H{sub 2}O{center_dot}0.5C{sub 6}H{sub 12}, P2{sub 1}/n, a = 26.7382(4) {angstrom}, b = 7.4472(1) {angstrom}, c = 31.4876(2) {angstrom}, V = 6209.05(13) {angstrom}{sup 3}, Z = 8. [UO{sub 2}L{sup 5}{center_dot}DMSO]{center_dot}DMSO, Pnma, a = 7.3808(1) {angstrom}, b = 14.7403(3) {angstrom}, c = 23.134(3) {angstrom}, V = 2516.88(8) {angstrom}{sup 3}, Z = 4.
A natural symmetrization for the plummer potential
NASA Astrophysics Data System (ADS)
Saitoh, Takayuki R.; Makino, Junichiro
2012-02-01
We propose a symmetrized form of the softened gravitational potential which is a natural extension of the Plummer potential. The gravitational potential at the position of particle i( xi, yi, zi), induced by particle j at ( xj, yj, zj), is given by: ϕij=-{Gmj}/{|rij2+ɛi2+ɛj2|}, where G is the gravitational constant, mj is the mass of particle j, rij = ∣( xi - xj) 2 + ( yi - yj) 2 + ( zi - zj) 2∣ 1/2 and ɛi and ɛj are the gravitational softening lengths of particles i and j, respectively. This form is formally an extension of the Newtonian potential to five dimensions. The derivative of this equation in the x, y, and z directions correspond to the gravitational accelerations in these directions and they are always symmetric between two particles. When one applies this potential to a group of particles with different softening lengths, as in the case with a tree code, an averaged gravitational softening length for the group can be used. We find that the most suitable averaged softening length for a group of particles is <ɛj2>=∑jNmjɛj2/M, where M=∑jNmj and N are the mass and number of all particles in the group, respectively. The leading error related to the softening length is O∑jδrjδ ɛj2/rij3, where δrj is the distance between particle j and the center of mass of the group and δɛj2=ɛj2-<ɛj2>. Using this averaged gravitational softening length with the tree method, one can use a single tree to evaluate the gravitational forces for a system of particles with a wide variety of gravitational softening lengths. Consequently, this will reduce the calculation cost of the gravitational force for such a system with different softenings without the need for complicated forms of softening. We present the result of simple numerical tests. We found that our modification of the Plummer potential works well.
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Symmetrical reciprocal compensation. 51.711... (CONTINUED) INTERCONNECTION Reciprocal Compensation for Transport and Termination of Telecommunications Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination...
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2011 CFR
2011-10-01
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Symmetrical reciprocal compensation. 51.711... (CONTINUED) INTERCONNECTION Reciprocal Compensation for Transport and Termination of Telecommunications Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination...
Reduction Formulae for Symmetric Products of Spin Matrices
NASA Astrophysics Data System (ADS)
Pal, Palash B.
2016-02-01
We show that, for SU(2) generators of arbitrary dimension D there exist identities that express the completely symmetric product of D matrices in terms of completely symmetric products of fewer number of matrices. We also indicate why such identities are important in characterizing electromagnetic interactions of particles.
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 3 2012-10-01 2012-10-01 false Symmetrical reciprocal compensation. 51.711 Section 51.711 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES... Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination of...
Spherically symmetric model atmospheres for late-type giant stars
NASA Astrophysics Data System (ADS)
Bennett, Philip Desmond
The ATHENA computer code was developed to model the extended atmospheres of late-type giant and supergiant stars. The atmospheres are assumed to be static, spherically symmetric and in radiative and hydrostatic equilibrium. Molecular line blanketing (for now) is handled using the simplifying assumption of mean opacity. The complete linearization method of Auer and Mihalas, adapted to spherical geometry, is used to solve the model system. The radiative transfer is solved by using variable Eddington factors to close the system of moment transfer equations, and the entire system of transfer equations plus constraints is solved efficiently by arrangement into the Rybicki block matrix form. The variable Eddington factors are calculated from the full angle-dependent formal solution of the radiative transfer problem using the impact parameter method of Hummer, Kunas. We were guided by the work of Mihalas and Hummer in their development of extended models of O stars, but our method differs in the choice of the independent variable. The radius depth scale used by Mihals and Hummer was found to fail because of the strongly temperature-dependent opacities of late-type atmospheres. Instead, we were able to achieve an exact linearization of the radius. This permitted the use of the numerically well-behaved column mass or optical depth scales. The resulting formulation is analogous to the plane-parallel complete linearization method and reduces to this method in the compact atmosphere limit. Models of M giants were calculated for Teff = 3000K and 3500K with opacities of the CN, TiO, and H2O molecules included, and the results were in general agreement with other published spherical models. These models were calculated assuming radiative equilibrium. The importance of convective energy transport was estimated by calculating the convective flux that would result from the temperature structure of the models. The standard local mixing length theory was used for this purpose. Convection was found to be important only at depths with tauRM greater than 15 for the low gravity models with log g = O, but significant out to tauRM is approximately 1 at the most transparent frequencies for the higher gravity models with log g = 2. Thus, the temperature structure of the surface layers and the emergent flux for the log g = O models should be accurately modelled but the emergent flux for the log g = 2 models may be in error by up to 5 percent at the most transparent frequencies.
Mühlenbeck, Cordelia; Liebal, Katja; Pritsch, Carla; Jacobsen, Thomas
2016-01-01
Symmetric structures are of importance in relation to aesthetic preference. To investigate whether the preference for symmetric patterns is unique to humans, independent of their cultural background, we compared two human populations with distinct cultural backgrounds (Namibian hunter-gatherers and German town dwellers) with one species of non-human great apes (Orangutans) in their viewing behavior regarding symmetric and asymmetric patterns in two levels of complexity. In addition, the human participants were asked to give their aesthetic evaluation of a subset of the presented patterns. The results showed that humans of both cultural groups fixated on symmetric patterns for a longer period of time, regardless of the pattern’s complexity. On the contrary, Orangutans did not clearly differentiate between symmetric and asymmetric patterns, but were much faster in processing the presented stimuli and scanned the complete screen, while both human groups rested on the symmetric pattern after a short scanning time. The aesthetic evaluation test revealed that the fixation preference for symmetric patterns did not match with the aesthetic evaluation in the Hai//om group, whereas in the German group aesthetic evaluation was in accordance with the fixation preference in 60 percent of the cases. It can be concluded that humans prefer well-ordered structures in visual processing tasks, most likely because of a positive processing bias for symmetry, which Orangutans did not show in this task, and that, in humans, an aesthetic preference does not necessarily accompany the fixation preference. PMID:27065184
5D non-symmetric gravity and geodesic confinement
NASA Astrophysics Data System (ADS)
Ghosh, Suman; Shankaranarayanan, S.
2013-09-01
This work focuses on an unexplored aspect of non-symmetric geometry where only the off-diagonal metric components along the extra dimension, in a 5-dimensional spacetime, are non-symmetric. We show that the energy densities of the stationary non-symmetric models are similar to that of brane models thereby mimicking the thick-brane scenario. We find that the massive test particles are confined near the location of the brane for both growing and decaying warp factors. This feature is unique to the non-symmetric nature of our model. We have also studied the dynamical models where standard 4D FLRW brane is embedded. Our analysis shows that the non-symmetric terms deconfine energy density at the early universe while automatically confine at late times.
Bicriterion seriation methods for skew-symmetric matrices.
Brusco, Michael J; Stahl, Stephanie
2005-11-01
The decomposition of an asymmetric proximity matrix into its symmetric and skew-symmetric components is a well-known principle in combinatorial data analysis. The seriation of the skew-symmetric component can emphasize information corresponding to the sign or absolute magnitude of the matrix elements, and the choice of objective criterion can have a profound impact on the ordering. In this research note, we propose a bicriterion approach for seriation of a skew-symmetric matrix incorporating both sign and magnitude information. Two numerical demonstrations reveal that the bicriterion procedure is an effective alternative to direct seriation of the skew-symmetric matrix, facilitating favourable trade-offs among sign and magnitude information. PMID:16293204
Phase Behavior of Symmetric Sulfonated Block Copolymers
Park, Moon Jeong; Balsara, Nitash P.
2008-08-21
Phase behavior of poly(styrenesulfonate-methylbutylene) (PSS-PMB) block copolymers was studied by varying molecular weight, sulfonation level, and temperature. Molecular weights of the copolymers range from 2.9 to 117 kg/mol. Ordered lamellar, gyroid, hexagonally perforated lamellae, and hexagonally packed cylinder phases were observed in spite of the fact that the copolymers are nearly symmetric with PSS volume fractions between 0.45 and 0.50. The wide variety of morphologies seen in our copolymers is inconsistent with current theories on block copolymer phase behavior such as self-consistent field theory. Low molecular weight PSS-PMB copolymers (<6.2 kg/mol) show order-order and order-disorder phase transitions as a function of temperature. In contrast, the phase behavior of high molecular weight PSS-PMB copolymers (>7.7 kg/mol) is independent of temperature. Due to the large value of Flory-Huggins interaction parameter, x, between the sulfonated and non-sulfonated blocks, PSS-PMB copolymers with PSS and PMB molecular weights of 1.8 and 1.4 kg/mol, respectively, show the presence of an ordered gyroid phase with a 2.5 nm diameter PSS network. A variety of methods are used to estimate x between PSS and PMB chains as a function of sulfonation level. Some aspects of the observed phase behavior of PSS-PMB copolymers can be rationalized using x.
Time-symmetric rolling tachyon profile
NASA Astrophysics Data System (ADS)
Longton, Matheson
2015-09-01
We investigate the tachyon profile of a time-symmetric rolling tachyon solution to open string field theory. We algebraically construct the solution of [1] at 6th order in the marginal parameter, and numerically evaluate the corresponding tachyon profile as well as the action and several correlation functions containing the equation of motion. We find that the marginal operator's singular self-OPE is properly regularized and all quantities we examine are finite. In contrast to the widely studied time-asymmetric case, the solution depends nontrivially on the strength of the deformation parameter. For example, we find that the number and period of oscillations of the tachyon field changes as the strength of the marginal deformation is increased. We use the recent renormalization scheme of [2], which contains two free parameters. At finite deformation parameter the tachyon profile depends on these parameters, while when the deformation parameter is small, the solution becomes insensitive to them and behaves like previously studied time-asymmetric rolling tachyon solutions. We also show that convergence of perturbation series is not as straightforward as in the time-asymmetric case with regular OPE, and find evidence that it may depend on the renormalization constants.
Symmetric weak ternary quantum homomorphic encryption schemes
NASA Astrophysics Data System (ADS)
Wang, Yuqi; She, Kun; Luo, Qingbin; Yang, Fan; Zhao, Chao
2016-03-01
Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general 3 × 3 unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled X (GCX(m,n)) gate was constructed and further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability pk = 1/33n, thus it can better protect the privacy of users’ data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.
The predation costs of symmetrical cryptic coloration.
Cuthill, Innes C; Hiby, Elly; Lloyd, Emily
2006-05-22
In psychological studies of visual perception, symmetry is accepted as a potent cue in visual search for cryptic objects, yet its importance for non-human animals has been assumed rather than tested. Furthermore, while the salience of bilateral symmetry has been established in laboratory-based search tasks using human subjects, its role in more natural settings, closer to those for which such perceptual mechanisms evolved, has not, to our knowledge, been investigated previously. That said, the salience of symmetry in visual search has a plausible adaptive rationale, because biologically important objects, such as prey, predators or conspecifics, usually have a plane of symmetry that is not present in their surroundings. We tested the conspicuousness to avian predators of cryptic artificial, moth-like targets, with or without bilateral symmetry in background-matching coloration, against oak trees in the field. In two independent experiments, symmetrical targets were predated at a higher rate than otherwise identical asymmetrical targets. There was a small, but significant, fitness cost to symmetry in camouflage patterns. Given that birds are the most commonly invoked predators shaping the evolution of defensive coloration in insects, this raises the question of why bilateral asymmetry is not more common in cryptic insects. PMID:16720401
On symplectic and symmetric ARKN methods
NASA Astrophysics Data System (ADS)
Shi, Wei; Wu, Xinyuan
2012-06-01
Symplecticness and symmetry are favorable properties for solving Hamiltonian systems. For the oscillatory second-order initial value problems of the form q+ωq=f(q,q), adapted Runge-Kutta-Nyström methods (ARKN methods, in short notation) were investigated by several authors. In a wide range of physical applications from molecular dynamics to nonlinear wave propagation, an important class of the problems is Hamiltonian systems for which symplectic methods should be preferred. Hence it is quite natural to raise a question of the symplecticness for ARKN methods. In this paper we investigate the symplecticness conditions of ARKN methods for separable Hamiltonian systems. We conclude that there exist only one-stage explicit symplectic ARKN (SARKN, in short notation) methods under the symplecticness conditions of ARKN methods. The SARKN methods have a special form and the algebraic order cannot exceed 2. We also point out that no ARKN method can be symmetric. An explicit SARKN method of order two is proposed with the analysis of phase and stability properties. The numerical results accompanied show good performance for the new explicit symplectic algorithm in comparison with the popular symplectic methods in the scientific literature.
Spherically symmetric conformal gravity and ``gravitational bubbles''
NASA Astrophysics Data System (ADS)
Berezin, V. A.; Dokuchaev, V. I.; Eroshenko, Yu. N.
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Mitotoxicity in distal symmetrical sensory peripheral neuropathies
Bennett, Gary J.; Doyle, Timothy; Salvemini, Daniela
2016-01-01
Chronic distal symmetrical sensory peripheral neuropathy is a common neurological complication of cancer chemotherapy, HIV treatment and diabetes. Although aetiology-specific differences in presentation are evident, the clinical signs and symptoms of these neuropathies are clearly similar. Data from animal models of neuropathic pain suggest that the similarities have a common cause: mitochondrial dysfunction in primary afferent sensory neurons. Mitochondrial dysfunction is caused by mitotoxic effects of cancer chemotherapeutic drugs of several chemical classes, HIV-associated viral proteins, and nucleoside reverse transcriptase inhibitor treatment, as well as the (possibly both direct and indirect) effects of excess glucose. The mitochondrial injury results in a chronic neuronal energy deficit, which gives rise to spontaneous nerve impulses and a compartmental neuronal degeneration that is first apparent in the terminal receptor arbor—that is, intraepidermal nerve fibres—of cutaneous afferent neurons. Preliminary data suggest that drugs that prevent mitochondrial injury or improve mitochondrial function could be useful in the treatment of these conditions. PMID:24840972
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Raju, P.; Sobhanbabu, K.
2016-04-01
Five dimensional spherically symmetric space-time filled with two minimally interacting fields; matter and holographic dark energy components is investigated in a scalar tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To obtain a determinate solution of the highly non-linear field equations we have used (i) a relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained represents a minimally interacting and radiating holographic dark energy model in five dimensional universe. Some physical and Kinematical properties of the model are, also, studied.
Particle-Hole Symmetric Luttinger Liquids in a Quantum Hall Circuit
NASA Astrophysics Data System (ADS)
Roddaro, Stefano; Pellegrini, Vittorio; Beltram, Fabio; Pfeiffer, Loren N.; West, Ken W.
2005-10-01
We report current transmission data through a split-gate constriction fabricated onto a two-dimensional electron system in the integer quantum Hall (QH) regime. Split-gate biasing drives interedge backscattering and is shown to lead to suppressed or enhanced transmission, in marked contrast to the expected linear Fermi-liquid behavior. This evolution is described in terms of particle-hole symmetry and allows us to conclude that an unexpected class of gate-controlled particle-hole-symmetric chiral Luttinger liquids (CLLs) can exist at the edges of our QH circuit. These results highlight the role of particle-hole symmetry on the properties of CLL edge states.
Fast axis servo for the fast and precise machining of non-rotational symmetric optics
NASA Astrophysics Data System (ADS)
Tian, Fujing; Yin, Ziqiang; Li, Shengyi
2014-08-01
A new long range tool servo-fast axis servo is developed, which is used for fabricating the non-rotational symmetric optics surface with millimeters' sag. The mechanism design, motion modeling and development of FAS device were studied. The FAS consists of a linear motor, aerostatic bearings, high-resolution encoder and a motion controller. A control strategy consists of a proportional, integral and derivative (PID) feedback controller and velocity/acceleration feedforward controller is implemented to accommodate the system control performance. Experimental tests have been carried out to verify the performance of the FAS system.
ERIC Educational Resources Information Center
Lancaster, Jeanette Elizabeth
2013-01-01
A central feature of complexity is that it is based on non-linear, recursive relations. However, in most current accounts of complexity such relations, while non-linear, are based on the reductive relations of a Newtonian onto-epistemological framework. This means that the systems that are emergent from the workings of such relations are a…
Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator
M.H. Redi; J. Canik; R.L. Dewar; J.L. Johnson; S. Klasky; W.A. Cooper; W. Kerbichler
2001-09-19
The magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), expected to achieve good stability and particle confinement is examined with a method that can lead to estimates of global stability. Making use of fully 3D, ideal-MHD stability codes, the QAS beta is predicted to be limited above 4% by ballooning and high-n kink modes. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space [s, alpha, theta(subscript ''k'')]; s is the edge normalized toroidal flux, alpha is the field line variable, and theta(subscript ''k'') is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, with new types of nonsymmetric, eigenvalue isosurfaces in both the stable and unstable spectrum. The isosurfaces around the most unstable points i n parameter space (well above marginal) are topologically spherical. In such cases, attempts to use ray tracing to construct global ballooning modes lead to a k-space runaway. Introduction of a reflecting cutoff in k(perpendicular) to model numerical truncation or finite Larmor radius (FLR) yields chaotic ray paths ergodically filling the allowed phase space, indicating that the global spectrum must be described using the language of quantum chaos theory. However, the isosurface for marginal stability in the cases studied are found to have a more complex topology, making estimation of FLR stabilization more difficult.
Symmetric interactions and interference between pitch and timbre.
Allen, Emily J; Oxenham, Andrew J
2014-03-01
Variations in the spectral shape of harmonic tone complexes are perceived as timbre changes and can lead to poorer fundamental frequency (F0) or pitch discrimination. Less is known about the effects of F0 variations on spectral shape discrimination. The aims of the study were to determine whether the interactions between pitch and timbre are symmetric, and to test whether musical training affects listeners' ability to ignore variations in irrelevant perceptual dimensions. Difference limens (DLs) for F0 were measured with and without random, concurrent, variations in spectral centroid, and vice versa. Additionally, sensitivity was measured as the target parameter and the interfering parameter varied by the same amount, in terms of individual DLs. Results showed significant and similar interference between pitch (F0) and timbre (spectral centroid) dimensions, with upward spectral motion often confused for upward F0 motion, and vice versa. Musicians had better F0DLs than non-musicians on average, but similar spectral centroid DLs. Both groups showed similar interference effects, in terms of decreased sensitivity, in both dimensions. Results reveal symmetry in the interference effects between pitch and timbre, once differences in sensitivity between dimensions and subjects are controlled. Musical training does not reliably help to overcome these effects. PMID:24606275
SL(2,R) duality-symmetric action for electromagnetic theory with electric and magnetic sources
Lee, Choonkyu; School of Physics, Korea Institute for Advanced Study, Seoul 130-722 ; Min, Hyunsoo
2013-12-15
For the SL(2,R) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials A{sup μ} and B{sup μ} in a judicious way. On the two potentials A{sup μ} and B{sup μ} the SL(2,R) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,Z)-invariant action. Also given is a Zwanziger-type action for SL(2,R) duality-invariant Born–Infeld electrodynamics which can be important for D-brane dynamics in string theory. -- Highlights: •We formulate a local, manifestly duality-symmetric, Zwanziger-type action. •Maxwell electrodynamics is generalized to include dilaton and axion fields. •SL(2,R) symmetry is manifest. •We formulate a local, manifestly duality-symmetric, nonlinear Born–Infeld action with SL(2,R) symmetry.
Microfabricated linear Paul-Straubel ion trap
Mangan, Michael A.; Blain, Matthew G.; Tigges, Chris P.; Linker, Kevin L.
2011-04-19
An array of microfabricated linear Paul-Straubel ion traps can be used for mass spectrometric applications. Each ion trap comprises two parallel inner RF electrodes and two parallel outer DC control electrodes symmetric about a central trap axis and suspended over an opening in a substrate. Neighboring ion traps in the array can share a common outer DC control electrode. The ions confined transversely by an RF quadrupole electric field potential well on the ion trap axis. The array can trap a wide array of ions.
Finite element Calculations of {P}{T}-Symmetric Bose-Einstein Condensates
NASA Astrophysics Data System (ADS)
Haag, Daniel; Dast, Dennis; Cartarius, Holger; Wunner, Günter
2015-11-01
{P}{T}-symmetric systems have been intensively studied in optical waveguides, where the {P}{T} symmetry is achieved by pumping and absorption processes. In such systems the {P}{T} symmetry leads to a wide range of effects promising technical and scientific applications. By analogy, balanced gain and loss of particles in Bose-Einstein condensates (BEC) can be described by introducing a {P}{T}-symmetric imaginary potential into the Gross-Pitaevskii equation (GPE). This equation can be solved numerically by various methods including the finite element approach. We apply this method to the GPE with arbitrary complex potentials and explicitly solve a double-well potential with shifted barriers.
Non-Vacuum Plane Symmetric Solutions and their Energy Contents in f ( R) Gravity
NASA Astrophysics Data System (ADS)
Amir, M. Jamil; Maqsood, Sidra
2016-02-01
The exact vacuum solutions of static plane symmetric spacetimes in four, five, six and n-dimensions in metric approach of f ( R) theory of gravity have already been found and are available in literature. In this paper, we extend the work done by Sharif and Farasat for the case of vacuum static plane symmetric solutions in f ( R) theory of gravity to non-vacuum case. Two non-vacuum solutions have been determined by using constant Ricci scalar assumption. Moreover, for some specific choices of f ( R) models, the energy distribution of these solutions has been explored by applying the generalized Landau-Lifshitz energy-momentum complex in the context of f ( R) theory of gravity. In addition, we discuss the stability conditions for these solutions.
NASA Astrophysics Data System (ADS)
Liang, Canbin; Tian, Guihua
1994-11-01
Electromagnetic fields yielding plane symmetric metrics in higher-dimensional spacetimes are exhausted and classified. It is shown that these EM fields must fall into one of the following two cases: (i)F it =F iz =0,i=1,...,n; (ii)Ftz=0. We give the general solution to the Einstein-Maxwell equations in higher dimensions corresponding to electromagnetic fields of case (ii) withF it =F iz , which covers all even-dimensional spacetimes as well as a subcase of odd-dimensional spacetimes.
Cotton-Type and Joint Invariants for Linear Elliptic Systems
Aslam, A.; Mahomed, F. M.
2013-01-01
Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results. PMID:24453871
Comparison of eigensolvers for symmetric band matrices
Moldaschl, Michael; Gansterer, Wilfried N.
2014-01-01
We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems. Of particular interest is a comparison of state-of-the-art tridiagonalization-based methods as implemented in Lapack or Plasma on the one hand, and the block divide-and-conquer (BD&C) algorithm as well as the block twisted factorization (BTF) method on the other hand. The BD&C algorithm does not require tridiagonalization of the original band matrix at all, and the current version of the BTF method tridiagonalizes the original band matrix only for computing the eigenvalues. Avoiding the tridiagonalization process sidesteps the cost of backtransformation of the eigenvectors. Beyond that, we discovered another disadvantage of the backtransformation process for band matrices: In several scenarios, a lot of gradual underflow is observed in the (optional) accumulation of the transformation matrix and in the (obligatory) backtransformation step. According to the IEEE 754 standard for floating-point arithmetic, this implies many operations with subnormal (denormalized) numbers, which causes severe slowdowns compared to the other algorithms without backtransformation of the eigenvectors. We illustrate that in these cases the performance of existing methods from Lapack and Plasma reaches a competitive level only if subnormal numbers are disabled (and thus the IEEE standard is violated). Overall, our performance studies illustrate that if the problem size is large enough relative to the bandwidth, BD&C tends to achieve the highest performance of all methods if the spectrum to be computed is clustered. For test problems with well separated eigenvalues, the BTF method tends to become the fastest algorithm with growing problem size. PMID:26594079
Recent advances in symmetric and network dynamics
NASA Astrophysics Data System (ADS)
Golubitsky, Martin; Stewart, Ian
2015-09-01
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network.
Symmetric coordinates in solids: magnetic Bloch oscillations
NASA Astrophysics Data System (ADS)
Zak, Joshua
2015-04-01
There has recently been a revival of the Bloch theory of energy bands in solids. This revival was caused, on one hand, by the discovery of topological insulators and the discovery of graphene, and, on the other end, by a very efficient new technique that was developed for creating artificial solids. These are the cold atoms in optical lattices. Last year geometric phases were measured in energy bands of cold atoms in a one-dimensional optical lattice by using Bloch oscillations. These phases are related to the Wyckoff positions, or the symmetry centers in the Bravais lattice. In this lecture a theoretical frame is developed for magnetic Bloch oscillations, meaning oscillations in the presence of a magnetic field. The theory is based on the kq-representation and the symmetric coordinates in solids. It is shown that for a Bloch electron in a magnetic field the orbit quasi-center is a conserved quantity. This is similar to the conservation of the quasi-momentum for an electron in a periodic potential. When an electric field is turned on, the orbit quasi-center oscillates in a similar way to the Bloch oscillations in the absence of a magnetic field. But there is a difference because the magnetic Brillouin zone is different. It depends on the strength of the magnetic field. An analogy is drawn between Bloch oscillations and magnetic Bloch oscillations. By using the magnetic translations it is indicated that a magnetic Wannier-Stark ladder appears in the spectrum of a Bloch electron in crossed magnetic and electric fields. The geometric phases for magnetic Bloch oscillations should be magnetic field dependent.
Recent advances in symmetric and network dynamics.
Golubitsky, Martin; Stewart, Ian
2015-09-01
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network. PMID:26428565
Communication complexity and information complexity
NASA Astrophysics Data System (ADS)
Pankratov, Denis
Information complexity enables the use of information-theoretic tools in communication complexity theory. Prior to the results presented in this thesis, information complexity was mainly used for proving lower bounds and direct-sum theorems in the setting of communication complexity. We present three results that demonstrate new connections between information complexity and communication complexity. In the first contribution we thoroughly study the information complexity of the smallest nontrivial two-party function: the AND function. While computing the communication complexity of AND is trivial, computing its exact information complexity presents a major technical challenge. In overcoming this challenge, we reveal that information complexity gives rise to rich geometrical structures. Our analysis of information complexity relies on new analytic techniques and new characterizations of communication protocols. We also uncover a connection of information complexity to the theory of elliptic partial differential equations. Once we compute the exact information complexity of AND, we can compute exact communication complexity of several related functions on n-bit inputs with some additional technical work. Previous combinatorial and algebraic techniques could only prove bounds of the form theta( n). Interestingly, this level of precision is typical in the area of information theory, so our result demonstrates that this meta-property of precise bounds carries over to information complexity and in certain cases even to communication complexity. Our result does not only strengthen the lower bound on communication complexity of disjointness by making it more exact, but it also shows that information complexity provides the exact upper bound on communication complexity. In fact, this result is more general and applies to a whole class of communication problems. In the second contribution, we use self-reduction methods to prove strong lower bounds on the information complexity of two of the most studied functions in the communication complexity literature: Gap Hamming Distance (GHD) and Inner Product mod 2 (IP). In our first result we affirm the conjecture that the information complexity of GHD is linear even under the uniform distribution. This strengthens the O(n) bound shown by Kerenidis et al. (2012) and answers an open problem by Chakrabarti et al. (2012). We also prove that the information complexity of IP is arbitrarily close to the trivial upper bound n as the permitted error tends to zero, again strengthening the O(n) lower bound proved by Braverman and Weinstein (2011). More importantly, our proofs demonstrate that self-reducibility makes the connection between information complexity and communication complexity lower bounds a two-way connection. Whereas numerous results in the past used information complexity techniques to derive new communication complexity lower bounds, we explore a generic way, in which communication complexity lower bounds imply information complexity lower bounds in a black-box manner. In the third contribution we consider the roles that private and public randomness play in the definition of information complexity. In communication complexity, private randomness can be trivially simulated by public randomness. Moreover, the communication cost of simulating public randomness with private randomness is well understood due to Newman's theorem (1991). In information complexity, the roles of public and private randomness are reversed: public randomness can be trivially simulated by private randomness. However, the information cost of simulating private randomness with public randomness is not understood. We show that protocols that use only public randomness admit a rather strong compression. In particular, efficient simulation of private randomness by public randomness would imply a version of a direct sum theorem in the setting of communication complexity. This establishes a yet another connection between the two areas. (Abstract shortened by UMI.).
Anisotropy of bituminous mixture in the linear viscoelastic domain
NASA Astrophysics Data System (ADS)
Di Benedetto, Hervé; Sauzéat, Cédric; Clec'h, Pauline
2016-03-01
Some anisotropic properties in the linear viscoelastic domain of bituminous mixtures compacted with a French LPC wheel compactor are highlighted in this paper. Bituminous mixture is generally considered as isotropic even if the compaction process on road or in laboratory induces anisotropic properties. Tension-compression complex modulus tests have been performed on parallelepipedic specimens in two directions: (i) direction of compactor wheel movement (direction I, which is horizontal) and (ii) direction of compaction (direction II, which is vertical). These tests consist in measuring sinusoidal axial and lateral strains as well as sinusoidal axial stress, when sinusoidal axial loading is applied on the specimen. Different loading frequencies and temperatures are applied. Two complex moduli, EI ^{*} and E_{II}^{*}, and four complex Poisson's ratios, ν_{II-I}^{*}, ν_{III-I}^{*}, ν_{I-II}^{*} and ν_{III-II}^{*}, were obtained. The vertical direction appears softer than the other ones for the highest frequencies. There are very few differences between the two directions I and II for parameters concerning viscous effects (phase angles \\varphi(EI) and \\varphi(E_{II}), and shift factors). The four Poisson's ratios reveal anisotropic properties but rheological tensor can be considered as symmetric when considering very similar values obtained for the two measured parameters (I-II and II-I) In addition, an anisotropic 3 dimensional version of the "2S2P1D" (2 springs, 2 parabolic creep elements and 1 dashpot) model, developed at the University of Lyon—ENTPE laboratory, is presented and used to simulate experimental results. The model simulation provides a good fit to the data. Stability of the material could also be investigated on the whole frequency-temperature range.
Painlevé transcendents and {P}{T}-symmetric Hamiltonians
NASA Astrophysics Data System (ADS)
Bender, Carl M.; Komijani, Javad
2015-11-01
Unstable separatrix solutions for the first and second Painlevé transcendents are studied both numerically and analytically. For a fixed initial condition, say y(0)=0, there is a discrete set of initial slopes y\\prime (0)={b}n that give rise to separatrix solutions. Similarly, for a fixed initial slope, say y’(0) = 0, there is a discrete set of initial values y(0)={c}n that give rise to separatrix solutions. For Painlevé I the large-n asymptotic behavior of b n is {b}n∼ {B}{{I}}{n}3/5 (n\\to ∞ ) and that of c n is {c}n∼ {C}{{I}}{n}2/5 (n\\to ∞ ), and for Painlevé II the large-n asymptotic behavior of b n is {b}n∼ {B}{{II}}{n}2/3 (n\\to ∞ ) and that of c n is {c}n∼ {C}{{II}}{n}1/3 (n\\to ∞ ). The constants {B}{{I}}, {C}{{I}}, {B}{{II}}, and {C}{{II}}, which are the coefficients in these asymptotic behaviors, are first determined numerically. Then, by using asymptotic methods, they are found analytically by reducing the nonlinear equations to the linear eigenvalue problems associated with the cubic and quartic {P}{T}-symmetric Hamiltonians H=\\frac{1}{2}{p}2+2{{i}}{x}3 and H=\\frac{1}{2}{p}2-\\frac{1}{2}{x}4.
Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-01-01
In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac-Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.
(Anti)symmetric multivariate trigonometric functions and corresponding Fourier transforms
NASA Astrophysics Data System (ADS)
Klimyk, A.; Patera, J.
2007-09-01
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix elements are sine or cosine functions of one variable each. These functions are eigenfunctions of the Laplace operator, satisfying specific conditions at the boundary of a certain domain F of the n-dimensional Euclidean space. Discrete and continuous orthogonality on F of the functions within each family allows one to introduce symmetrized and antisymmetrized multivariate Fourier-like transforms involving the symmetric and antisymmetric multivariate sine and cosine functions.
A Windows based graphical package for symmetrical components analysis
Yu, D.C.; Chen, D.; Ramasamy, S.; Flinn, D.G.
1995-11-01
A Microsoft{reg_sign} Windows{trademark} graphical package to facilitate the teaching and learning of symmetrical component is described in this paper. This package is written in Microsoft Visual Basic 3.0. This software calculates and displays graphically, the ABC sequence and the corresponding symmetrical component phasors. Students can manipulate the graphical displays by keyboard input or by mouse operation. The objective of this package is to help the students to better understand the various aspects of symmetrical components` analysis through a user-friendly Graphical User Interface (GUI).
(M-theory-)Killing spinors on symmetric spaces
NASA Astrophysics Data System (ADS)
Hustler, Noel; Lischewski, Andree
2015-08-01
We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form D = ∇ + Ω in a purely algebraic and algorithmic way, where Ω : TM → Λ∗(TM) is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e., (M, g, F) with (M, g) an eleven-dimensional Lorentzian (locally) symmetric space and F an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.
Linear or Nonlinear? Automatic Structure Discovery for Partially Linear Models
Zhang, Hao Helen; Cheng, Guang; Liu, Yufeng
2011-01-01
Partially linear models provide a useful class of tools for modeling complex data by naturally incorporating a combination of linear and nonlinear effects within one framework. One key question in partially linear models is the choice of model structure, that is, how to decide which covariates are linear and which are nonlinear. This is a fundamental, yet largely unsolved problem for partially linear models. In practice, one often assumes that the model structure is given or known and then makes estimation and inference based on that structure. Alternatively, there are two methods in common use for tackling the problem: hypotheses testing and visual screening based on the marginal fits. Both methods are quite useful in practice but have their drawbacks. First, it is difficult to construct a powerful procedure for testing multiple hypotheses of linear against nonlinear fits. Second, the screening procedure based on the scatterplots of individual covariate fits may provide an educated guess on the regression function form, but the procedure is ad hoc and lacks theoretical justifications. In this article, we propose a new approach to structure selection for partially linear models, called the LAND (Linear And Nonlinear Discoverer). The procedure is developed in an elegant mathematical framework and possesses desired theoretical and computational properties. Under certain regularity conditions, we show that the LAND estimator is able to identify the underlying true model structure correctly and at the same time estimate the multivariate regression function consistently. The convergence rate of the new estimator is established as well. We further propose an iterative algorithm to implement the procedure and illustrate its performance by simulated and real examples. Supplementary materials for this article are available online. PMID:22121305
NASA Astrophysics Data System (ADS)
Wang, Wei; Guo, Zhongyi; Ran, Lingling; Sun, Yongxuan; Shen, Fei; Li, Yan; Mao, Xiaoqin; Wang, Benyang; Fan, Guanghua; Qu, Shiliang
2016-03-01
A series of symmetrical nanoantennas with a symmetrical axis orientation angle of 45° or 135°, which are suitable for both X/Y linear and circular polarizations incidences simultaneously, have been designed and investigated in detail. We have deduced the transmitted matrix of the metasurface structure by rigorous mathematical theory, and found that the essential reason for the polarization-independence characteristics is that there are the same transmitted amplitudes and phases under the incidences of X/Y linear and circular polarization lights due to metasurface structure with the symmetrical axis’s orientation angles of 45° or 135°. Based on the V-shaped, C-shaped, U-shaped and elliptical slit nanoantennas, we have verified the proposed theory fully by numerical simulations. The independence of the incident polarizations is very important for the practical applications and developments of the metasurfaces.
Accommodation of a highly symmetric core within a symmetric protein superfold.
Brych, Stephen R; Kim, Jaewon; Logan, Timothy M; Blaber, Michael
2003-12-01
An alternative core packing group, involving a set of five positions, has been introduced into human acidic FGF-1. This alternative group was designed so as to constrain the primary structure within the core region to the same threefold symmetry present in the tertiary structure of the protein fold (the beta-trefoil superfold). The alternative core is essentially indistinguishable from the WT core with regard to structure, stability, and folding kinetics. The results show that the beta-trefoil superfold is compatible with a threefold symmetric constraint on the core region, as might be the case if the superfold arose as a result of gene duplication/fusion events. Furthermore, this new core arrangement can form the basis of a structural "building block" that can greatly simplify the de novo design of beta-trefoil proteins by using symmetric structural complementarity. Remaining asymmetry within the core appears to be related to asymmetry in the tertiary structure associated with receptor and heparin binding functionality of the growth factor. PMID:14627732
NASA Astrophysics Data System (ADS)
Polukhina, Oxana; Kurkin, Andrey; Vladykina, Ekaterina
2010-05-01
Three-layer stratification is proved to be a proper approximation of sea water density and background current profiles in some basins in the World Ocean with specific hydrological conditions. Such a medium is interesting from the point of view of internal gravity wave dynamics, because, in the symmetric about mid-depth case (equal thicknesses of the lower and the upper layers, equal small density jumps on the interfaces), it leads to disappearing of quadratic nonlinearity when described in the framework of weakly nonlinear evolutionary models, which are derived through the asymptotic expansion in small parameters of nonlinearity and dispersion. In this situation the nonlinear transformation of the internal wave disturbances, as is customary, is determined by the influence of the next-order - cubic - nonlinear term in asymptotic series, and for three-layer fluid model the cubic nonlinearity coefficient can have either sign depending on the layer depths (in contrast to traditional two-layer approximation, for which cubic nonlinearity is always negative). Appropriate nonlinear evolutionary equation is modified Korteweg - de Vries equation (mKdV). It is well-known integrable equation of KdV-type, providing solitary wave and breather solutions for positive cubic nonlinearity. The property of sign change for cubic nonlinear coefficient in the mKdV for internal gravity waves in symmetric three-layer fluid requires taking into account next-order nonlinear term (or terms), therefore higher-order extensions of mKdV equation are necessary to provide improved description of internal wave processes. In the present study we derive nonlinear evolution equations for both interfaces in symmetric three-layer fluid (under Boussinesq approximation) up to the fourth order in small parameters of nonlinearity (epsilon) and dispersion (?). Applying mKdV-scaling for ratio of these parameters (? = epsilon2) we obtain high-order mKdV equations for interfaces (they have different signs of even-power nonlinear and nonlinear dispersion terms). These equations include additional terms of nonlinearity (fourh and fifth power), nonlinear dispersion and linear dispersion (fifth derivative). Coefficients of these equations are found in the explicit form as functions of medium parameters (layer depths, densities), their signs are analyzed. But the equations derived are too complex for the analysis of the nonlinear wave dynamics, therefore a simplifying asymptotic nonlinear transformation of wavefield is suggested, which reduces these equations to a simpler equation having a form of mKdV equation with additional fourth and fifth power nonlinear terms. But for the particular case of three-layer symmetric fluid fourth power nonlinear correction has zero coefficient, and final equation has only one additional term: fifth power nonlinearity. Its coefficient after the transformation is negative for symmetric three-layer stratification. It is worth to notice that equations for both interfaces are reduced to the same equation, but the asymptotic transformations for the displacements of the interfaces differ by the sign of one term proportional to the square of the displacement amplitude. Thus, the asymptotic transformation introduces an asymmetry of the interfacial displacements in a clear, explicit form in contrast to complex high-order equations. Next, we considered the equation obtained after transformation (we call it 'extended mKdV'), and found its one-soliton solutions for positive cubic nonlinearity. These solitary waves can have either polarity, as well as solitons of mKdV equation, but they have amplitude limit, and while their amplitude grows up to this limit, solitons become wider in much the same manner as the solitons of Gardner equation (extended KdV equation with quadratic and cubic nonlinear terms) in a case of negative cubic nonlinearity (corresponding to internal waves in two-layer fluid). The solitary wave solutions of the improved weakly nonlinear theory are compared to the fully nonlinear solitary-like waves numerically simulated in the framework of Euler equations for slightly smoothed symmetric three-layer fluid with small density jumps. Qualitatively both solutions are in good agreement, but quantitative estimates show that improved weakly nonlinear theory underestimates limiting amplitude of solitary waves for about 30%.
Lee, Jihun; Blaber, Sachiko I; Dubey, Vikash K; Blaber, Michael
2011-04-15
Fibroblast growth factor-1, a member of the 3-fold symmetric β-trefoil fold, was subjected to a series of symmetric constraint mutations in a process termed "top-down symmetric deconstruction." The mutations enforced a cumulative exact 3-fold symmetry upon symmetrically equivalent positions within the protein and were combined with a stability screen. This process culminated in a β-trefoil protein with exact 3-fold primary-structure symmetry that exhibited excellent folding and stability properties. Subsequent fragmentation of the repeating primary-structure motif yielded a 42-residue polypeptide capable of spontaneous assembly as a homotrimer, producing a thermostable β-trefoil architecture. The results show that despite pronounced reduction in sequence complexity, pure symmetry in the design of a foldable, thermostable β-trefoil fold is possible. The top-down symmetric deconstruction approach provides a novel alternative means to successfully identify a useful polypeptide "building block" for subsequent "bottom-up" de novo design of target protein architecture. PMID:21315087
Bound states, scattering states, and resonant states in PT -symmetric open quantum systems
NASA Astrophysics Data System (ADS)
Garmon, Savannah; Gianfreda, Mariagiovanna; Hatano, Naomichi
2015-08-01
We study a simple open quantum system with a PT -symmetric defect potential as a prototype in order to illustrate a number of general features of PT -symmetric open quantum systems; however, the potential itself could be mimicked by a number of PT systems that have been experimentally studied quite recently. One key feature is the resonance in continuum (RIC), which appears in both the discrete spectrum and the scattering spectrum of such systems. The RIC wave function forms a standing wave extending throughout the spatial extent of the system and in this sense represents a resonance between the open environment associated with the leads of our model and the central PT -symmetric potential. We also illustrate that as one deforms the system parameters, the RIC may exit the continuum by splitting into a bound state and a virtual bound state at the band edge, a process which should be experimentally observable. We also study the exceptional points appearing in the discrete spectrum at which two eigenvalues coalesce; we categorize these as either EP2As, at which two real-valued solutions coalesce before becoming complex-valued, and EP2Bs, for which the two solutions are complex on either side of the exceptional point. The EP2As are associated with PT -symmetry breaking; we argue that these are more stable against parameter perturbation than the EP2Bs. We also study complex-valued solutions of the discrete spectrum for which the wave function is nevertheless spatially localized, something that is not allowed in traditional open quantum systems; we illustrate that these may form quasibound states in continuum under some circumstances. We also study the scattering properties of the system, including states that support invisible propagation and some general features of perfect transmission states. We finally use our model as a prototype for the construction of scattering states that satisfy PT -symmetric boundary conditions; while these states do not conserve the traditional probability current, we introduce the PT current which is preserved. The perfect transmission states appear as a special case of the PT -symmetric scattering states.
International Workshop on Linear Colliders 2010
None
2011-10-06
IWLC2010 International Workshop on Linear Colliders 2010ECFA-CLIC-ILC joint meeting: Monday 18 October - Friday 22 October 2010Venue: CERN and CICG (International Conference Centre Geneva, Switzerland)This year, the International Workshop on Linear Colliders organized by the European Committee for Future Accelerators (ECFA) will study the physics, detectors and accelerator complex of a linear collider covering both CLIC and ILC options.Contact Workshop SecretariatIWLC2010 is hostedby CERN
International Workshop on Linear Colliders 2010
None
2011-10-06
IWLC2010 International Workshop on Linear Colliders 2010ECFA-CLIC-ILC joint meeting: Monday 18 October - Friday 22 October 2010Venue: CERN and CICG (International Conference Centre Geneva, Switzerland) This year, the International Workshop on Linear Colliders organized by the European Committee for Future Accelerators (ECFA) will study the physics, detectors and accelerator complex of a linear collider covering both CLIC and ILC options.Contact Workshop Secretariat IWLC2010 is hosted by CERN
NASA Astrophysics Data System (ADS)
Butz, Tilman
2010-06-01
The conventional analysis of non-axially symmetric nuclear quadrupole interaction data requires two adjustable parameters, namely Vzz and the asymmetry parameter ?, and these two parameters are plotted separately versus an external parameter, e.g. temperature. Thus 2N parameters are fitted for N temperature points. In this way, possible interdependencies of electric field gradient tensor components are ignored. The correct strategy for the data analysis would be to analyze the data conventionally, plot the data in the Czjzek-plot, and for a linear trajectory perform a simultaneous fit of all data with N + 2 adjustable parameters (N values of a control parameter plus a scale factor plus the slope) in a second tier. The concept of trajectories can be extended to non-linear trajectories.
Flow-separation patterns on symmetric forebodies
NASA Technical Reports Server (NTRS)
Keener, Earl R.
1986-01-01
Flow-visualization studies of ogival, parabolic, and conical forebodies were made in a comprehensive investigation of the various types of flow patterns. Schlieren, vapor-screen, oil-flow, and sublimation flow-visualization tests were conducted over an angle-of-attack range from 0 deg. to 88 deg., over a Reynolds-number range from 0.3X10(6) to 2.0X10(6) (based on base diameter), and over a Mach number range from 0.1 to 2. The principal effects of angle of attack, Reynolds number, and Mach number on the occurrence of vortices, the position of vortex shedding, the principal surface-flow-separation patterns, the magnitude of surface-flow angles, and the extent of laminar and turbulent flow for symmetric, asymmetric, and wake-like flow-separation regimes are presented. It was found that the two-dimensional cylinder analogy was helpful in a qualitative sense in analyzing both the surface-flow patterns and the external flow field. The oil-flow studies showed three types of primary separation patterns at the higher Reynolds numbers owing to the influence of boundary-layer transition. The effect of angle of attack and Reynolds number is to change the axial location of the onset and extent of the primary transitional and turbulent separation regions. Crossflow inflectional-instability vortices were observed on the windward surface at angles of attack from 5 deg. to 55 deg. Their effect is to promote early transition. At low angles of attack, near 10 deg., an unexpected laminar-separation bubble occurs over the forward half of the forebody. At high angles of attack, at which vortex asymmetry occurs, the results support the proposition that the principal cause of vortex asymmetry is the hydrodynamic instability of the inviscid flow field. On the other hand, boundary-layer asymmetries also occur, especially at transitional Reynolds numbers. The position of asymmetric vortex shedding moves forward with increasing angle of attack and with increasing Reynolds number, and moves rearward with increasing Mach number.
Tu, Yi-Chen; Huang, Teng-Yi; Chiu, Nan-Fu
2014-01-01
We report a novel design wherein high-refractive-index zinc oxide (ZnO) intermediary layers are used in anti-symmetrically structured surface plasmon resonance (SPR) devices to enhance signal quality and improve the full width at half maximum (FWHM) of the SPR reflectivity curve. The surface plasmon (SP) modes of the ZnO intermediary layer were excited by irradiating both sides of the Au film, thus inducing a high electric field at the Au/ZnO interface. We demonstrated that an improvement in the ZnO (002) crystal orientation led to a decrease in the FWHM of the SPR reflectivity curves. We optimized the design of ZnO thin films using different parameters and performed analytical comparisons of the ZnO with conventional chromium (Cr) and indium tin oxide (ITO) intermediary layers. The present study is based on application of the Fresnel equation, which provides an explanation and verification for the observed narrow SPR reflectivity curve and optical transmittance spectra exhibited by (ZnO/Au), (Cr/Au), and (ITO/Au) devices. On exposure to ethanol, the anti-symmetrically structured showed a huge electric field at the Au/ZnO interface and a 2-fold decrease in the FWHM value and a 1.3-fold larger shift in angle interrogation and a 4.5-fold high-sensitivity shift in intensity interrogation. The anti-symmetrically structured of ZnO intermediate layers exhibited a wider linearity range and much higher sensitivity. It also exhibited a good linear relationship between the incident angle and ethanol concentration in the tested range. Thus, we demonstrated a novel and simple method for fabricating high-sensitivity, high-resolution SPR biosensors that provide high accuracy and precision over relevant ranges of analyte measurement. PMID:24361929
Noise Suppression Using Symmetric Exchange Gates in Spin Qubits.
Martins, Frederico; Malinowski, Filip K; Nissen, Peter D; Barnes, Edwin; Fallahi, Saeed; Gardner, Geoffrey C; Manfra, Michael J; Marcus, Charles M; Kuemmeth, Ferdinand
2016-03-18
We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise. PMID:27035316
Noise Suppression Using Symmetric Exchange Gates in Spin Qubits
NASA Astrophysics Data System (ADS)
Martins, Frederico; Malinowski, Filip K.; Nissen, Peter D.; Barnes, Edwin; Fallahi, Saeed; Gardner, Geoffrey C.; Manfra, Michael J.; Marcus, Charles M.; Kuemmeth, Ferdinand
2016-03-01
We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise.
Symmetrical ilial pseudofractures: A complication of chronic renal failure
Griffin, C.N. Jr.
1982-08-01
A patient with chronic renal failure and progressive symmetrical ilial pseudofractures (Looser zones, Milkman's syndrome) is presented. The literature is reviewed in light of the findings in this patient, and possible mechanisms of pseudofracture formation are discussed.
Topological States in Partially-PT-Symmetric Azimuthal Potentials.
Kartashov, Yaroslav V; Konotop, Vladimir V; Torner, Lluis
2015-11-01
We introduce partially-parity-time (pPT)-symmetric azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles. PMID:26588383
On the general properties of symmetric incomplete Airy beams.
Jáuregui, R; Quinto-Su, P A
2014-11-01
We study the general properties of a class of Airy beams symmetric under reflection of the transverse coordinates. Following a recent proposal, their angular spectra depend on the absolute value of the third power of the transverse components of the wave vector. The proposed beams are shown to be described by symmetric superpositions of incomplete Airy special functions. Their angular spectra do not correspond to any of those described by standard catastrophe optics. However, the morphologies of the symmetric beams are similar to some of those already classified within that scheme, differing mainly on the scaling exponents. Finally, the structural stability of three-dimensional symmetric incomplete Airy beams is experimentally probed. PMID:25401361
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2013 CFR
2013-10-01
... 47 Telecommunication 3 2013-10-01 2013-10-01 false Symmetrical reciprocal compensation. 51.711 Section 51.711 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES (CONTINUED) INTERCONNECTION Reciprocal Compensation for Transport and Termination of...
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
... inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through 23... angular inertia of the airplane in a rational or conservative manner. (c) Mutual influence of...
Symmetric polynomials in information theory: Entropy and subentropy
Jozsa, Richard; Mitchison, Graeme
2015-06-15
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.
A parallel algorithm for the non-symmetric eigenvalue problem
Dongarra, J.; Sidani, M. . Dept. of Computer Science Oak Ridge National Lab., TN )
1991-12-01
This paper describes a parallel algorithm for computing the eigenvalues and eigenvectors of a non-symmetric matrix. The algorithm is based on a divide-and-conquer procedure and uses an iterative refinement technique.
Symmetric Pin Diversion Detection using a Partial Defect Detector (PDET)
Sitaraman, S; Ham, Y S
2009-06-01
Since the signature from the Partial Defect Detector (PDET) is principally dependent on the geometric layout of the guide tube locations, the capability of the technique in detecting symmetric diversion of pins needs to be determined. The Monte Carlo simulation study consisted of cases where pins were removed in a symmetric manner and the resulting signatures were examined. In addition to the normalized gamma-to-neutron ratios, the neutron and gamma signatures normalized to their maximum values, were also examined. Examination of the shape of the three curves as well as of the peak-to-valley differences in excess of the maximum expected in intact assemblies, indicated pin diversion. A set of simulations with various symmetric patterns of diversion were examined. The results from these studies indicated that symmetric diversions as low as twelve percent could be detected by this methodology.
Topological States in Partially-PT -Symmetric Azimuthal Potentials
NASA Astrophysics Data System (ADS)
Kartashov, Yaroslav V.; Konotop, Vladimir V.; Torner, Lluis
2015-11-01
We introduce partially-parity-time (p PT ) -symmetric azimuthal potentials composed from individual PT -symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-P T -symmetric potentials. The vortex solitons in the p P T - and P T -symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles.
Tavara, Luis; Mantic, Vladislav; Salvadori, Alberto; Gray, Leonard J; Paris, Federico
2009-01-01
A symmetric boundary integral formulation for cohesive cracks growing in the interior of homogeneous linear elastic isotropic media and/or at interfaces between these media is developed and implemented in a numerical code. The solution of a problem that includes cohesive cracks depends on the cohesive law adopted. In the present work, models based on the concept of free energy density per unit undeformed area are considered. The corresponding constitutive cohesive equations present a softening branch which induces to the problem a potential instability. Thus, the development and implementation of a suitable solution algorithm capable of following the growth of the cohesive zone becomes an important issue. An arc-length control combined with a Newton-Raphson algorithm for iterative solution of nonlinear equations is used. The Boundary Element Method is very attractive for modeling cohesive crack problems as all nonlinearities are located on the boundaries (including the crack boundaries) of linear elastic domains. A Galerkin approximation scheme, applied to a suitable symmetric integral formulation, ensures an easy treatment of cracks in homogeneous media and excellent convergence behavior of the numerical solution. Numerical results for the wedge split test are presented and compared with experimental results available in the literature.
A Possible Method for Non-Hermitian and Non-PT-Symmetric Hamiltonian Systems
Li, Jun-Qing; Miao, Yan-Gang; Xue, Zhao
2014-01-01
A possible method to investigate non-Hermitian Hamiltonians is suggested through finding a Hermitian operator η+ and defining the annihilation and creation operators to be η+ -pseudo-Hermitian adjoint to each other. The operator η+ represents the η+ -pseudo-Hermiticity of Hamiltonians. As an example, a non-Hermitian and non-PT-symmetric Hamiltonian with imaginary linear coordinate and linear momentum terms is constructed and analyzed in detail. The operator η+ is found, based on which, a real spectrum and a positive-definite inner product, together with the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution, are obtained for the non-Hermitian and non-PT-symmetric Hamiltonian. Moreover, this Hamiltonian turns out to be coupled when it is extended to the canonical noncommutative space with noncommutative spatial coordinate operators and noncommutative momentum operators as well. Our method is applicable to the coupled Hamiltonian. Then the first and second order noncommutative corrections of energy levels are calculated, and in particular the reality of energy spectra, the positive-definiteness of inner products, and the related properties (the probability explanation of wave functions, the orthogonality of eigenstates, and the unitarity of time evolution) are found not to be altered by the noncommutativity. PMID:24896084
Parity-time symmetric cloak with isotropic modulation
NASA Astrophysics Data System (ADS)
Yang, Fan; Lei Mei, Zhong
2016-06-01
In this work, a different kind of parity-time (PT) symmetric one-way cloak is proposed. Different from conventional PT-cloak, it enjoys the property of isotropic modulation for refractive index profiles. By combining PT-symmetry with the concept of cloaking at a distance, the dilemma of realizing anisotropic modulation is removed. This combination facilitates the practical realization of PT-symmetric one-way cloak.
Rindler-like Horizon in Spherically Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Yang, Jinbo; He, Tangmei; Zhang, Jingyi
2016-02-01
In this paper, the Rindler-like horizon in a spherically symmetric spacetime is proposed. It is showed that just like the Rindler horizon in Minkowski spacetimes, there is also a Rindler-like horizon to a family of special observers in general spherically symmetric spacetimes. The entropy of this type of horizon is calculated with the thin film brick-wall model. The significance of entropy is discussed. Our results imply some connection between Bekeinstein-Hawking entropy and entanglement entropy.