Irreducibility and co-primeness as an integrability criterion for discrete equations
International Nuclear Information System (INIS)
Kanki, Masataka; Mada, Jun; Mase, Takafumi; Tokihiro, Tetsuji
2014-01-01
We study the Laurent property, the irreducibility and co-primeness of discrete integrable and non-integrable equations. First we study a discrete integrable equation related to the Somos-4 sequence, and also a non-integrable equation as a comparison. We prove that the conditions of irreducibility and co-primeness hold only in the integrable case. Next, we generalize our previous results on the singularities of the discrete Korteweg–de Vries (dKdV) equation. In our previous paper (Kanki et al 2014 J. Phys. A: Math. Theor. 47 065201) we described the singularity confinement test (one of the integrability criteria) using the Laurent property, and the irreducibility, and co-primeness of the terms in the bilinear dKdV equation, in which we only considered simplified boundary conditions. This restriction was needed to obtain simple (monomial) relations between the bilinear form and the nonlinear form of the dKdV equation. In this paper, we prove the co-primeness of the terms in the nonlinear dKdV equation for general initial conditions and boundary conditions, by using the localization of Laurent rings and the interchange of the axes. We assert that co-primeness of the terms can be used as a new integrability criterion, which is a mathematical re-interpretation of the confinement of singularities in the case of discrete equations. (paper)
Integrable peakon equations with cubic nonlinearity
International Nuclear Information System (INIS)
Hone, Andrew N W; Wang, J P
2008-01-01
We present a new integrable partial differential equation found by Vladimir Novikov. Like the Camassa-Holm and Degasperis-Procesi equations, this new equation admits peaked soliton (peakon) solutions, but it has nonlinear terms that are cubic, rather than quadratic. We give a matrix Lax pair for V Novikov's equation, and show how it is related by a reciprocal transformation to a negative flow in the Sawada-Kotera hierarchy. Infinitely many conserved quantities are found, as well as a bi-Hamiltonian structure. The latter is used to obtain the Hamiltonian form of the finite-dimensional system for the interaction of N peakons, and the two-body dynamics (N = 2) is explicitly integrated. Finally, all of this is compared with some analogous results for another cubic peakon equation derived by Zhijun Qiao. (fast track communication)
Tangent Lines without Derivatives for Quadratic and Cubic Equations
Carroll, William J.
2009-01-01
In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)
Exact solutions for the cubic-quintic nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Zhu Jiamin; Ma Zhengyi
2007-01-01
In this paper, the cubic-quintic nonlinear Schroedinger equation is solved through the extended elliptic sub-equation method. As a consequence, many types of exact travelling wave solutions are obtained which including bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions
A Unified Approach to Teaching Quadratic and Cubic Equations.
Ward, A. J. B.
2003-01-01
Presents a simple method for teaching the algebraic solution of cubic equations via completion of the cube. Shows that this method is readily accepted by students already familiar with completion of the square as a method for quadratic equations. (Author/KHR)
International Nuclear Information System (INIS)
Kutzelnigg, Werner; Mukherjee, Debashis
2004-01-01
The k-particle irreducible Brillouin conditions IBC k and the k-particle irreducible contracted Schroedinger equations ICSE k for a closed-shell state are analyzed in terms of a Moeller-Plesset-type perturbation expansion. The zeroth order is Hartree-Fock. From the IBC 2 (1) , i.e., from the two-particle IBC to first order in the perturbation parameter μ, one gets the leading correction λ 2 (1) to the two-particle cumulant λ 2 correctly. However, in order to construct the second-order energy E 2 , one also needs the second-order diagonal correction γ D (2) to the one-particle density matrix γ. This can be obtained: (i) from the idempotency of the n-particle density matrix, i.e., essentially from the requirement of n-representability; (ii) from the ICSE 1 (2) ; or (iii) by means of perturbation theory via a unitary transformation in Fock space. Method (ii) is very unsatisfactory, because one must first solve the ICSE 3 (2) to get λ 3 (2) , which is needed in the ICSE 2 (2) to get λ 2 (2) , which, in turn, is needed in the ICSE 1 (2) to get γ (2) . Generally the (k+1)-particle approximation is needed to obtain E k correctly. One gains something, if one replaces the standard hierarchy, in which one solves the ICSE k , ignoring λ k+1 and λ k+2 , by a renormalized hierarchy, in which only λ k+2 is ignored, and λ k+1 is expressed in terms of the λ p of lower particle rank via the partial trace relation for λ k+2 . Then the k-particle approximation is needed to obtain E k correctly. This is still poorer than coupled-cluster theory, where the k-particle approximation yields E k+1 . We also study the possibility to use some simple necessary n-representability conditions, based on the non-negativity of γ (2) and two related matrices, in order to get estimates for γ D (2) in terms of λ 2 (1) . In general these estimates are rather weak, but they can become close to the best possible bounds in special situations characterized by a very sparse structure of λ 2
Universal centers in the cubic trigonometric Abel equation
Directory of Open Access Journals (Sweden)
Jaume Giné
2014-02-01
Full Text Available We study the center problem for the trigonometric Abel equation $d \\rho/ d \\theta= a_1 (\\theta \\rho^2 + a_2(\\theta \\rho^3,$ where $a_1(\\theta$ and $a_2(\\theta$ are cubic trigonometric polynomials in $\\theta$. This problem is closely connected with the classical Poincaré center problem for planar polynomial vector fields. A particular class of centers, the so-called universal centers or composition centers, is taken into account. An example of non-universal center and a characterization of all the universal centers for such equation are provided.
Cubic Plus Association Equation of State for Flow Assurance Projects
DEFF Research Database (Denmark)
dos Santos, Leticia Cotia; Abunahman, Samir Silva; Tavares, Frederico Wanderley
2015-01-01
Thermodynamic hydrate inhibitors such as methanol, ethanol, (mono) ethylene glycol (MEG), and triethylene glycol (TEG) are widely used in the oil and gas industry. On modeling these compounds, we show here how the CPA equation of state was implemented in an in-house process simulator as an in......-built model: To validate the implementation, we show calulations for binary systems containing hydrate inhibitors and water or hydrocarbons using the Cubic Plus Association (CPA) and Soave-Redlich-Kwong (SRK) equation of states, also comparing against experimental data. For streams containing natural gas...
Scattering of quantized solitary waves in the cubic Schrodinger equation
International Nuclear Information System (INIS)
Dolan, L.
1976-01-01
The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states
Explosive attractor solutions to a universal cubic delay equation
Sanz-Orozco, D.; Berk, H. L.
2017-05-01
New explosive attractor solutions have been found in a universal cubic delay equation that has been studied in both the plasma and the fluid mechanics literature. Through computational simulations and analytic approximations, it is found that the oscillatory component of the explosive mode amplitude solutions are described through multi-frequency Fourier expansions with respect to a pseudo-time variable. The spectral dependence of these solutions as a function of a system parameter, ϕ , is studied. The mode amplitude that is described in the explosive regime has two main features: a well-known envelope ( t 0 - t ) - 5 / 2 , with t0 the blow-up time of the amplitude, and a spectrum of discrete oscillations with ever-increasing frequencies, which may give experimental information about the properties of a system's equilibrium.
Bistable dark solitons of a cubic-quintic Helmholtz equation
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2010-01-01
We provide a report on exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and nondegenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.
Study of nonlinear waves described by the cubic Schroedinger equation
International Nuclear Information System (INIS)
Walstead, A.E.
1980-01-01
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables
Study of nonlinear waves described by the cubic Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Walstead, A.E.
1980-03-12
The cubic Schroedinger equation (CSE) is ubiquitous as a model equation for the long-time evolution of finite-amplitude near-monochromatic dispersive waves. It incorporates the effects of the radiation field pressure on the constitutive properties of the supporting medium in a self-consistent manner. The properties of the uniformly transiating periodic wave solutions of the one-dimensional CSE are studied here. These (so-called cnoidal) waves are characterized by the values of four parameters. Whitham's averaged variational principle is used to derive a system of quasilinear evolution equations (the modulational equations) for the values of these parameters when they are slowly varying in space and time. Explicit expressions for the characteristic velocities of the modulational equations are obtained for the full set of cnoidal waves. Riemann invariants are obtained for several limits for the stable case, and growth rates are obtained for several limits, including the solitary wave chain, for the unstable case. The results for several nontrivial limiting cases agree with those obtained by independent methods by others. The dynamics of the CSE generalized to two spatial dimensions are studied for the unstable case. A large class of similarity solutions with cylindrical symmetry are obtained systematically using infinitesimal transformation group techniques. The methods are adapted to obtain the symmetries of the action functional of the CSE and to deduce nine integral invariants. A numerical study of the self-similar solutions reveals that they are modulationally unstable and that singularities dominate the dynamics of the CSE in two dimensions. The CSE is derived using perturbation theory for a specific problem in plasma physics: the evolution of the envelope of a near-monochromatic electromagnetic wave in a cold magnetized plasma. 13 figures, 2 tables.
International Nuclear Information System (INIS)
Xiao Yafeng; Xue Haili; Zhang Hongqing
2011-01-01
Based on Jacobi elliptic function and the Lame equation, the perturbation method is applied to get the multi-order envelope periodic solutions of the nonlinear Schrodinger equation and cubic nonlinear Schrodinger equation. These multi-order envelope periodic solutions can degenerate into the different envelope solitary solutions. (authors)
Solutions to the equations describing materials with competing quadratic and cubic nonlinearities
International Nuclear Information System (INIS)
Li-Na, Zhao; Ji, Lin; Zi-Shuang, Tong
2009-01-01
The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation
The phase space of the focused cubic Schroedinger equation: A numerical study
Energy Technology Data Exchange (ETDEWEB)
Burlakov, Yuri O. [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
1998-05-01
In a paper of 1988 [41] on statistical mechanics of the nonlinear Schroedinger equation, it was observed that a Gibbs canonical ensemble associated with the nonlinear Schroedinger equation exhibits behavior reminiscent of a phase transition in classical statistical mechanics. The existence of a phase transition in the canonical ensemble of the nonlinear Schroedinger equation would be very interesting and would have important implications for the role of this equation in modeling physical phenomena; it would also have an important bearing on the theory of weak solutions of nonlinear wave equations. The cubic Schroedinger equation, as will be shown later, is equivalent to the self-induction approximation for vortices, which is a widely used equation of motion for a thin vortex filament in classical and superfluid mechanics. The existence of a phase transition in such a system would be very interesting and actually very surprising for the following reasons: in classical fluid mechanics it is believed that the turbulent regime is dominated by strong vortex stretching, while the vortex system described by the cubic Schroedinger equation does not allow for stretching. In superfluid mechanics the self-induction approximation and its modifications have been used to describe the motion of thin superfluid vortices, which exhibit a phase transition; however, more recently some authors concluded that these equations do not adequately describe superfluid turbulence, and the absence of a phase transition in the cubic Schroedinger equation would strengthen their argument. The self-induction approximation for vortices takes into account only very localized interactions, and the existence of a phase transition in such a simplified system would be very unexpected. In this thesis the authors present a numerical study of the phase transition type phenomena observed in [41]; in particular, they find that these phenomena are strongly related to the splitting of the phase space into
Determination of asphaltene onset conditions using the cubic plus association equation of state
DEFF Research Database (Denmark)
Arya, Alay; von Solms, Nicolas; Kontogeorgis, Georgios M.
2015-01-01
The cubic-plus-association (CPA) equation of state (EoS) has already been proven to be a successful model for phase equilibrium calculations for systems containing associating components and has already been applied for asphaltene modeling by few researchers. In the present work, we apply the CPA...
Analytic smoothing effect for the cubic hyperbolic Schrodinger equation in two space dimensions
Directory of Open Access Journals (Sweden)
Gaku Hoshino
2016-01-01
Full Text Available We study the Cauchy problem for the cubic hyperbolic Schrodinger equation in two space dimensions. We prove existence of analytic global solutions for sufficiently small and exponential decaying data. The method of proof depends on the generalized Leibniz rule for the generator of pseudo-conformal transform acting on pseudo-conformally invariant nonlinearity.
DEFF Research Database (Denmark)
Arya, Alay; Liang, Xiaodong; von Solms, Nicolas
2017-01-01
In this study, different modeling approaches using the Cubic Plus Association (CPA) equation of state (EoS) are developed to calculate the asphaltene precipitation onset condition and asphaltene yield from degassed crude oil during the addition of n-paraffin. A single model parameter is fitted...
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros; Mitsotakis, Dimitrios
2016-01-01
In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank
Extension of the cubic-plus-association (CPA) equation of state to amines
DEFF Research Database (Denmark)
Kaarsholm, Mads Kristian; Derawi, Samer; Michelsen, Michael Locht
2005-01-01
The cubic-plus-association (CPA) equation of state has been extended to modeling mixtures containing amines. Special focus was given to primary and secondary amines, which are known to self-associate, thus forming hydrogen bonds in mixtures with alkanes. Pure-compound parameters have been determi...
Irreducibility conditions for extended superfields
International Nuclear Information System (INIS)
Sokatchev, E.
1981-05-01
The irreducible supermultiplets contained in an extended superfield are presented as sets of covariant derivatives of the superfield. Differential irreducibility constraints are easily obtained from this decomposition. (author)
Salmasi, Mahbod; Potter, Michael
2018-07-01
Maxwell's equations are discretized on a Face-Centered Cubic (FCC) lattice instead of a simple cubic as an alternative to the standard Yee method for improvements in numerical dispersion characteristics and grid isotropy of the method. Explicit update equations and numerical dispersion expressions, and the stability criteria are derived. Also, several tools available to the standard Yee method such as PEC/PMC boundary conditions, absorbing boundary conditions, and scattered field formulation are extended to this method as well. A comparison between the FCC and the Yee formulations is made, showing that the FCC method exhibits better dispersion compared to its Yee counterpart. Simulations are provided to demonstrate both the accuracy and grid isotropy improvement of the method.
Inelastic collision of two solitons for generalized BBM equation with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Jingdong Wei
2015-06-01
Full Text Available We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H^1(R energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution.
On the reflection of solitons of the cubic nonlinear Schrödinger equation
Katsaounis, Theodoros
2016-07-05
In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger equation as the underlying mathematical model, and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall.
International Nuclear Information System (INIS)
Carrington, M. E.; Kovalchuk, E.
2010-01-01
Transport coefficients can be obtained from two-point correlators using the Kubo formulas. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the resummed two-point function that is obtained from the three-loop three-particle irreducible resummed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the four-loop four-particle irreducible effective action for a scalar theory with cubic and quartic interactions, with a nonvanishing field expectation value. We obtain a set of integral equations that determine the resummed two-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.
Facão, M.; Carvalho, M. I.
2017-10-01
In this work, we present parameter regions for the existence of stable plain solitons of the cubic complex Ginzburg-Landau equation (CGLE) with higher-order terms associated with a fourth-order expansion. Using a perturbation approach around the nonlinear Schrödinger equation soliton and a full numerical analysis that solves an ordinary differential equation for the soliton profiles and using the Evans method in the search for unstable eigenvalues, we have found that the minimum equation allowing these stable solitons is the cubic CGLE plus a term known in optics as Raman-delayed response, which is responsible for the redshift of the spectrum. The other favorable term for the occurrence of stable solitons is a term that represents the increase of nonlinear gain with higher frequencies. At the stability boundary, a bifurcation occurs giving rise to stable oscillatory solitons for higher values of the nonlinear gain. These oscillations can have very high amplitudes, with the pulse energy changing more than two orders of magnitude in a period, and they can even exhibit more complex dynamics such as period-doubling.
Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1
Directory of Open Access Journals (Sweden)
Henri Schurz
2010-09-01
Full Text Available Semilinear stochastic heat equations perturbed by cubic-type nonlinearities and additive space-time noise with homogeneous boundary conditions are discussed in R^1. The space-time noise is supposed to be Gaussian in time and possesses a Fourier expansion in space along the eigenfunctions of underlying Lapace operators. We follow the concept of approximate strong (classical Fourier solutions. The existence of unique continuous L^2-bounded solutions is proved. Furthermore, we present a procedure for its numerical approximation based on nonstandard methods (linear-implicit and justify their stability and consistency. The behavior of related total energy functional turns out to be crucial in the presented analysis.
A reduction method for phase equilibrium calculations with cubic equations of state
Directory of Open Access Journals (Sweden)
D. V. Nichita
2006-09-01
Full Text Available In this work we propose a new reduction method for phase equilibrium calculations using a general form of cubic equations of state (CEOS. The energy term in the CEOS is a quadratic form, which is diagonalized by applying a linear transformation. The number of the reduction parameters is related to the rank of the matrix C with elements (1-Cij, where Cij denotes the binary interaction parameters (BIPs. The dimensionality of the problem depends only on the number of reduction parameters, and is independent of the number of components in the mixture.
Confalonieri, Sara
2015-01-01
Sara Confalonieri presents an overview of Cardano's mathematical treatises and, in particular, discusses the writings that deal with cubic equations. The author gives an insight into the latest of Cardano's algebraic works, the De Regula Aliza (1570), which displays the attempts to overcome the difficulties entailed by the casus irreducibilis. Notably some of Cardano's strategies in this treatise are thoroughly analyzed. Far from offering an ultimate account of De Regula Aliza, by one of the most outstanding scholars of the 16th century, the present work is a first step towards a better understanding.
A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation
Directory of Open Access Journals (Sweden)
S. Battal Gazi Karakoç
2016-02-01
Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.
Numerical solution of the Black-Scholes equation using cubic spline wavelets
Černá, Dana
2016-12-01
The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.
International Nuclear Information System (INIS)
Song, T.; Ma, Q.; Sun, X.W.; Liu, Z.J.; Fu, Z.J.; Wei, X.P.; Wang, T.; Tian, J.H.
2016-01-01
The phase transition, electronic band structure, and equation of state (EOS) of cubic TcN are investigated by first-principles pseudopotential method based on density-functional theory. The calculated enthalpies show that TcN has a transformation between zincblende and rocksalt phases and the pressure determined by the relative enthalpy is 32 GPa. The calculated band structure indicates the metallic feature and it might make cubic TcN a better candidate for hard materials. Particular attention is paid to the predictions of volume, bulk modulus and its pressure derivative which play a central role in the formulation of approximate EOSs using the quasi-harmonic Debye model. - Highlights: • The phase transition pressure and electronic band structure for cubic TcN are determined. • Particular attention is paid to investigate the equation of state parameters for cubic TcN. • The thermodynamic properties up to 80 GPa and 3000 K are successfully predicted.
Crosta, M.
2011-12-05
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Crosta, M.; Fratalocchi, Andrea; Trillo, S.
2011-01-01
We characterize the full family of soliton solutions sitting over a background plane wave and ruled by the cubic-quintic nonlinear Schrödinger equation in the regime where a quintic focusing term represents a saturation of the cubic defocusing nonlinearity. We discuss the existence and properties of solitons in terms of catastrophe theory and fully characterize bistability and instabilities of the dark-antidark pairs, revealing mechanisms of decay of antidark solitons into dispersive shock waves.
Numerical solution of the 1D kinetics equations using a cubic reduced nodal scheme
International Nuclear Information System (INIS)
Gomez T, A.M.; Valle G, E. del; Delfin L, A.; Alonso V, G.
2003-01-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as Θ scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
Hamano, Katsumi; Hirotsu, Shunsuke
1980-01-01
Phenomenological equations are derived which interrelate the anomalies in various thermodynamic quantities above the transition point of a cubic-to-tetragonal phase transition caused by an instability of a triply degenerate soft mode. The anomalous part of the Gibbs free energy is assumed to be a simple sum of the three parts which represent the contributions from the three fluctuation components. A cylindrical approximation is adopted to each of the three contributions by taking into account the symmetry of the fluctuations. The theory predicts that the adiabatic elastic compliances, s11s, s12s, and also s11s-s12s should exhibit anomalies proportional to the anomaly in the specific heat at constant pressure. This is in marked contrast with the result of the generalized Pippard equations derived by Garland, and by Janovec. The new equations are successfully tested for KMnF3, CsPbCl3, and CsPbBr3. The β-γ transition of NH4Br is also discussed.
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Michelsen, Michael Locht; Folas, Georgios
2006-01-01
In this second article of the review on the applications of the CPA (Cubic-Plus-Association) equation of state, the focus is placed on cross-associating systems. Various such mixtures are investigated, including (i) systems with two self-associating compounds ( e. g., water-alcohol systems...
Directory of Open Access Journals (Sweden)
Aleksandr Alekseev
2015-07-01
Full Text Available We establish necessary and sufficient conditions for existence of an integrating multiplier of a special form for systems of two cubic differential equations of the first order. We further study bifurcations of such systems with the change of parameters of their integrating multipliers.
International Nuclear Information System (INIS)
Wu Hongyu; Fei Jinxi; Zheng Chunlong
2010-01-01
An improved homogeneous balance principle and an F-expansion technique are used to construct exact self-similar solutions to the cubic-quintic nonlinear Schroedinger equation. Such solutions exist under certain conditions, and impose constraints on the functions describing dispersion, nonlinearity, and the external potential. Some simple self-similar waves are presented. (general)
DEFF Research Database (Denmark)
Arya, Alay; Maribo-Mogensen, Bjørn; Tsivintzelis, Ioannis
2014-01-01
The Cubic-Plus-Association (CPA) equation of state (EoS) has already been proven to be a successful model for phase equilibrium calculations for systems containing glycols. In the present work, we interface a thermodynamic property package (Thermo System), based on CPA, with Aspen HYSYS through...
Energy Technology Data Exchange (ETDEWEB)
Kato, M.; Tanaka, H. (Nihon Univ.,Fukushima, (Japan). Faculty of Enineering)
1990-03-01
As an equation of state of vapor-liquid equilibrium, an original pseudo-cubic equation of state was previously proposed by the authors of this report and its study is continued. In the present study, new effective critical values of hydrogen, helium and neon were determined empirically from vapor-liquid equilibrium data of literature values against their critical temperatures, critical pressures and critical volumes. The vapor-liquid equilibrium relations of binary system quantum gas mixtures were predicted combining the conventinal pseudo-cubic equation of state and the new effective critical values, and without using binary heteromolecular interaction parameter. The predicted values of hydrogen-ethylene, helium-propane and neon-oxygen systems were compared with literature values. As a result, it was indicated that the vapor-liquid relations of binary system mixtures containing hydrogen, helium and neon can be predicted with favorable accuracy combining the effective critical values and the three parameter pseudo-cubic equation of state. 37 refs., 3 figs., 4 tabs.
Andrews, David L.
2009-08-01
In recent years it has become evident that the primary concept of the photon has multiple interpretations, with widely differing secondary connotations. Despite the all-pervasive nature of this concept in science, some of the ancillary properties with which the photon is attributed in certain areas of application sit uneasily alongside those invoked in other areas. Certainly the range of applications extends far beyond what was envisaged in the original conception, now entering subjects extending from elementary particle physics and cosmology through to spectroscopy, statistical mechanics and photochemistry. Addressing this diverse context invites the question: What is there, that it is possible to assert as incontrovertibly true about the photon? Which properties are non-controversial, if others are the subject of debate? This paper describes an attempt to answer these questions, establishing as far as possible an irreducible core of what can rightly be asserted about the photon, and setting aside some of what often is, but should never be so asserted. Some of the more bewildering difficulties and differences of interpretation owe their origin to careless descriptions, highlighting a need to guard semantic precision; although simplifications are frequently and naturally expedient for didactic purposes, they carry the risk of becoming indelible. Focusing on such issues, the aim is to identify how much or how little about the photon can be regarded as truly non-controversial.
Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations
Energy Technology Data Exchange (ETDEWEB)
Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)
1996-12-31
In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).
Seadawy, Aly R.; Kumar, Dipankar; Chakrabarty, Anuz Kumar
2018-05-01
The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrödinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrödinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
DEFF Research Database (Denmark)
Coutinho, João A.P.; Kontogeorgis, Georgios M.; Stenby, Erling H.
1994-01-01
This work shows that, when suitable theoretically based combining rules are used for the cross energy and cross co-volume parameters, cubic equations of state (EoS) with the van der Waals one-fluid mixing rules can adequately represent phase equilibria for the asymmetric CO2/hydrocarbon mixtures...... for the prediction of phase behavior of petroleum fluids. A brief theoretical analysis on the temperature dependency of the Kij interaction parameter is also presented....
Directory of Open Access Journals (Sweden)
Hrubý Jan
2012-04-01
Full Text Available The study presents some preliminary results of the density gradient theory (GT combined with two different equations of state (EoS: the classical cubic equation by van der Waals and a recent approach based on the statistical associating fluid theory (SAFT, namely its perturbed-chain (PC modification. The results showed that the cubic EoS predicted for a given surface tension the density profile with a noticeable defect. Bulk densities predicted by the cubic EoS differed as much as by 100 % from the reference data. On the other hand, the PC-SAFT EoS provided accurate results for density profile and both bulk densities in the large range of temperatures. It has been shown that PC-SAFT is a promising tool for accurate modeling of nucleation using the GT. Besides the basic case of a planar phase interface, the spherical interface was analyzed to model a critical cluster occurring either for nucleation of droplets (condensation or bubbles (boiling, cavitation. However, the general solution for the spherical interface will require some more attention due to its numerical difficulty.
Kaulakys, B.; Alaburda, M.; Ruseckas, J.
2016-05-01
A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.
DEFF Research Database (Denmark)
Maia, Filipa Meireles; Tsivintzelis, Ioannis; Rodriguez, Oscar
2012-01-01
For the last decade ionic liquids have been regarded as compounds of interest by the academic and industrial communities. These compounds present several advantages when compared to other typical solvents. However, because of their novelty, a deep understanding of their phase behaviour and their ......For the last decade ionic liquids have been regarded as compounds of interest by the academic and industrial communities. These compounds present several advantages when compared to other typical solvents. However, because of their novelty, a deep understanding of their phase behaviour...... and their interactions with other components is still needed. In this work, we made a review of literature studies on modelling systems with ionic liquids using equation of state models. Furthermore, we applied the Cubic Plus Association (CPA) equation of state to describe the phase behaviour of two ionic liquids, 1...... is in progress for improving the modelling of LLE with the CPA equation of state....
DEFF Research Database (Denmark)
Fettouhi, André; Thomsen, Kaj
2010-01-01
In the creation of liquefied natural gas the formation of solids play a substantial role, hence detailed knowledge is needed about solid-liquid equilibria (SLE). In this abstract we shortly summarize the work we have carried out at CERE over the past year with SLE for many-component mixtures usin...... the Cubic-Plus-Association (CPA) equation of state. Components used in this work are highly relevant to the oil and gas industry and include light and heavy hydrocarbons, alcohols, water and carbon dioxide....
Global well-posedness for the radial defocusing cubic wave equation on $R^3$ and for rough data
Directory of Open Access Journals (Sweden)
Tristan Roy
2007-11-01
Full Text Available We prove global well-posedness for the radial defocusing cubic wave equation $$displaylines{ partial_{tt} u - Delta u = -u^{3} cr u(0,x = u_{0}(x cr partial_{t} u(0,x = u_{1}(x }$$ with data $(u_0, u_1 in H^{s} imes H^{s-1}$, $1 > s >7/10$. The proof relies upon a Morawetz-Strauss-type inequality that allows us to control the growth of an almost conserved quantity.
Dynamics of solitons and quasisolitons of the cubic third-order nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Karpman, V.I.; Juul Rasmussen, J.; Shagalov, A.G.
2001-01-01
The dynamics of soliton and quasisoliton solutions of the cubic third-order nonlinear Schrodinger equation is studied. Regular solitons exist due to a balance between the nonlinear terms and (linear) third-order dispersion; they are not important at small alpha (3) (alpha (3) is the coefficient...... in the third derivative term) and vanish at alpha3 -->0. The most essential, at small alpha (3), is a quasisoliton emitting resonant radiation (resonantly radiating soliton). Its relationship with the other (steady) quasisoliton, called embedded soliton, is studied analytically and also in numerical...
Explicit solutions of the cubic matrix nonlinear Schrödinger equation
International Nuclear Information System (INIS)
Demontis, Francesco; Mee, Cornelis van der
2008-01-01
In this paper, we derive a class of explicit solutions, global in (x, t) is an element of R 2 , of the focusing matrix nonlinear Schrödinger equation using straightforward linear algebra. We obtain both the usual and multiple pole multisoliton solutions as well as a new class of solutions exponentially decaying as x → ±∞
Moortgat, Joachim
2018-04-01
This work presents an efficient reservoir simulation framework for multicomponent, multiphase, compressible flow, based on the cubic-plus-association (CPA) equation of state (EOS). CPA is an accurate EOS for mixtures that contain non-polar hydrocarbons, self-associating polar water, and cross-associating molecules like methane, ethane, unsaturated hydrocarbons, CO2, and H2S. While CPA is accurate, its mathematical formulation is highly non-linear, resulting in excessive computational costs that have made the EOS unfeasible for large scale reservoir simulations. This work presents algorithms that overcome these bottlenecks and achieve an efficiency comparable to the much simpler cubic EOS approach. The main applications that require such accurate phase behavior modeling are 1) the study of methane leakage from high-pressure production wells and its potential impact on groundwater resources, 2) modeling of geological CO2 sequestration in brine aquifers when one is interested in more than the CO2 and H2O components, e.g. methane, other light hydrocarbons, and various tracers, and 3) enhanced oil recovery by CO2 injection in reservoirs that have previously been waterflooded or contain connate water. We present numerical examples of all those scenarios, extensive validation of the CPA EOS with experimental data, and analyses of the efficiency of our proposed numerical schemes. The accuracy, efficiency, and robustness of the presented phase split computations pave the way to more widespread adoption of CPA in reservoir simulators.
DEFF Research Database (Denmark)
Breil, Martin Peter; Kontogeorgis, Georgios; Behrens, Paul K.
2011-01-01
The cubic-plus-association (CPA) equation of state is applied in this work to mixtures containing acetic acid and water. A previously developed modification of the model, the so-called CPA-Huron−Vidal (CPA-HV), is used. New CPA parameters have been estimated based on the vapor pressure, liquid...... density, enthalpy of vaporization, and vapor-phase compressibility factor data. The CPA-HV parameters have been fitted to, among others, experimental vapor compressibility factor data and experimental relative volatility data at different temperature ranges. The purpose of the work was to investigate...... that satisfactory results are overall obtained, but if an excellent match is needed over the whole temperature range, then different interaction parameters need to be used at the various temperature ranges....
DEFF Research Database (Denmark)
Folas, Georgios; Kontogeorgis, Georgios; Michelsen, Michael Locht
2006-01-01
The cubic-plus-association (CPA) equation of state is applied to phase equilibria of mixtures containing alcohols, glycols, water, and aromatic or olefinic hydrocarbons. Previously, CPA has been successfully used for mixtures containing various associating compounds (alcohols, glycols, amines......, organic acids, and water) and aliphatic hydrocarbons. We show in this work that the model can be satisfactorily extended to complex vapor-liquid-liquid equilibria with aromatic or olefinic hydrocarbons. The solvation between aromatics/olefinics and polar compounds is accounted for. This is particularly...... important for mixtures containing water and glycols, but less so for mixtures with alcohols. For water/hydrocarbons, a single binary interaction parameter which accounts for the solvation is fitted to the experimental liquid-liquid equilibria (LLE) data. The interaction parameter of the physical term...
DEFF Research Database (Denmark)
Folas, Georgios; Kontogeorgis, Georgios; Michelsen, Michael Locht
2006-01-01
was given to low pressures and liquid-liquid equilibria. In this work, CPA is applied to two classes of mixtures containing polar chemicals for which high-pressure data are available: acetone-containing systems and dimethyl ether mixtures. They are of both scientific and industrial importance. Moreover, CPA......The cubic-plus-association (CPA) equation of state has been previously applied to vapor-liquid, liquid-liquid, and solid-liquid equilibria of mixtures containing associating compounds (water, alcohols, glycols, acids, amines). Although some high-pressure applications have been presented, emphasis...... to conventional models such as MHV2. Very good results are also obtained for multicomponent vapor-liquid-liquid equilibria for mixtures containing gases, water, and dimethyl ether. Finally, it is shown that high-pressure SLE can be predicted based on interaction parameters obtained from low-pressure SLE data....
Directory of Open Access Journals (Sweden)
Magdy A. El-Tawil
2009-01-01
Full Text Available A perturbing nonlinear Schrodinger equation is studied under general complex nonhomogeneities and complex initial conditions for zero boundary conditions. The perturbation method together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the symbolic solution algorithm is tested through computing the possible approximations under truncation procedures. The method of solution is illustrated through case studies and figures.
Phase equilibria of binary mixtures by molecular simulation and cubic equations of state
Directory of Open Access Journals (Sweden)
Cabral V.F.
2001-01-01
Full Text Available Molecular simulation data were used to study the performance of equations of state (EoS and combining rules usually employed in thermodynamic property calculations. The Monte Carlo method and the Gibbs ensemble technique were used for determining composition and densities of vapor and liquid phases in equilibrium for binary mixtures of Lennard-Jones fluids. Simulation results are compared to data in the literature and to those calculated by the t-PR-LJ EoS. The use of adequate combining rules has been shown to be very important for the satisfactory representation of molecular simulation data.
Solution of (3+1-Dimensional Nonlinear Cubic Schrodinger Equation by Differential Transform Method
Directory of Open Access Journals (Sweden)
Hassan A. Zedan
2012-01-01
Full Text Available Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Differential transform method can easily be applied to linear or nonlinear problems and reduces the size of computational work. With this method, exact solutions may be obtained without any need of cumbersome work, and it is a useful tool for analytical and numerical solutions.
Taraf, R.; Behbahani, R.; Moshfeghian, Mahmood
2008-12-01
A numerical algorithm is presented for direct calculation of the cricondenbar and cricondentherm coordinates of natural gas mixtures of known composition based on the Michelsen method. In the course of determination of these coordinates, the equilibrium mole fractions at these points are also calculated. In this algorithm, the property of the distance from the free energy surfaces to a tangent plane in equilibrium condition is added to saturation calculation as an additional criterion. An equation of state (EoS) was needed to calculate all required properties. Therefore, the algorithm was tested with Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), and modified Nasrifar-Moshfeghian (MNM) equations of state. For different EoSs, the impact of the binary interaction coefficient ( k ij) was studied. The impact of initial guesses for temperature and pressure was also studied. The convergence speed and the accuracy of the results of this new algorithm were compared with experimental data and the results obtained from other methods and simulation softwares such as Hysys, Aspen Plus, and EzThermo.
Parallel Construction of Irreducible Polynomials
DEFF Research Database (Denmark)
Frandsen, Gudmund Skovbjerg
Let arithmetic pseudo-NC^k denote the problems that can be solved by log space uniform arithmetic circuits over the finite prime field GF(p) of depth O(log^k (n + p)) and size polynomial in (n + p). We show that the problem of constructing an irreducible polynomial of specified degree over GF(p) ...... of polynomials is in arithmetic NC^3. Our algorithm works over any field and compared to other known algorithms it does not assume the ability to take p'th roots when the field has characteristic p....
Blow-up criteria for the 3D cubic nonlinear Schrödinger equation
International Nuclear Information System (INIS)
Holmer, Justin; Platte, Rodrigo; Roudenko, Svetlana
2010-01-01
We consider solutions u to the 3D nonlinear Schrödinger equation i∂ t u + Δu + |u| 2 u = 0. In particular, we are interested in finding criteria on the initial data u 0 that predict the asymptotic behaviour of u(t), e.g., whether u(t) blows up in finite time, exists globally in time but behaves like a linear solution for large times (scatters), or exists globally in time but does not scatter. This question has been resolved (at least for H 1 data) (Duyckaerts–Holmer–Roudenko) if M[u]E[u] ≤ M[Q]E[Q], where M[u] and E[u] denote the mass and energy of u and Q denotes the ground state solution to −Q + ΔQ + |Q| 2 Q = 0. Here we consider the complementary case M[u]E[u] > M[Q]E[Q]. In the first (analytical) part of the paper, we present a result due to Lushnikov, based on the virial identity and the generalized uncertainty principle, giving a sufficient condition for blow-up. By replacing the uncertainty principle in his argument with an interpolation-type inequality, we obtain a new blow-up condition that in some cases improves upon Lushnikov's condition. Our approach also allows for an adaptation to radial infinite-variance initial data that has a conceptual interpretation: for real-valued initial data, if a certain fraction of the mass is contained within the ball of radius M[u], then blow up occurs. We also show analytically (if one takes the numerically computed value of ||Q|| .H 1/2 ) that there exist Gaussian initial data u 0 with negative quadratic phase such that ||u 0 || .H 1/2 .H 1/2 but the solution u(t) blows up. In the second (numerical) part of the paper, we examine several different classes of initial data—Gaussian, super Gaussian, off-centred Gaussian, and oscillatory Gaussian—and for each class give the theoretical predictions for scattering or blow-up provided by the above theorems as well as the results of numerical simulation. We find that depending upon the form of the initial conditions, any of the three analytical criteria for blow
DEFF Research Database (Denmark)
Herslund, Peter Jørgensen; Thomsen, Kaj; Abildskov, Jens
2013-01-01
The complex fluid phase behaviour, of the binary system comprised of water and tetrahydrofuran (THF) is modelled by use of the cubic-plus-association (CPA) equation of state. A total of seven modelling approaches are analysed, differing only in their way of describing THF and its interactions...
DEFF Research Database (Denmark)
Afzal, Waheed; Breil, Martin Peter; Théveneau, Pascal
2009-01-01
previously reported in the literature, along with the data measured in this work have been modeled using the cubic-plus-association (CPA) equation of state (EoS). Satisfactory results have been obtained using temperature-independent interaction parameters. Useful remarks are presented about the application...
DEFF Research Database (Denmark)
Awan, Javeed; Tsivintzelis, Ioannis; Breil, Martin
2010-01-01
with the cubic-plus-association (CPA) equation of state. Useful remarks are presented about the application of Henry’s constant values to estimate binary interaction parameters of the CPA EoS for the description of whole vapor−liquid equilibria. The results using CPA EoS show that the cross association...
SU(N) Irreducible Schwinger Bosons
Mathur, Manu; Raychowdhury, Indrakshi; Anishetty, Ramesh
2010-01-01
We construct SU(N) irreducible Schwinger bosons satisfying certain U(N-1) constraints which implement the symmetries of SU(N) Young tableaues. As a result all SU(N) irreducible representations are simple monomials of $(N-1)$ types of SU(N) irreducible Schwinger bosons. Further, we show that these representations are free of multiplicity problems. Thus all SU(N) representations are made as simple as SU(2).
Irreducible Specht modules are signed Young modules
Hemmer, David J.
2005-01-01
Recently Donkin defined signed Young modules as a simultaneous generalization of Young and twisted Young modules for the symmetric group. We show that in odd characteristic, if a Specht module $S^\\lambda$ is irreducible, then $S^\\lambda$ is a signed Young module. Thus the set of irreducible Specht modules coincides with the set of irreducible signed Young modules. This provides evidence for our conjecture that the signed Young modules are precisely the class of indecomposable self-dual module...
International Nuclear Information System (INIS)
Roskosch, Dennis; Atakan, Burak
2015-01-01
Fluid selection for thermodynamic cycles like refrigeration cycles, heat pumps or organic Rankine cycles remains an actual topic. Generally the search for a working fluid is based on experimental approaches or on a not very systematic trial and error approach, far from being elegant. An alternative method may be a theory based reverse engineering approach, proposed and investigated here: The design process should start with an optimal process and with (abstract) properties of the fluid needed to fit into this optimal process, best described by some general equation of state and the corresponding fluid-describing parameters. These should be analyzed and optimized with respect to the defined model process, which also has to be optimized simultaneously. From this information real fluids can be selected or even synthesized which have fluid defining properties in the optimum regime like critical temperature or ideal gas capacities of heat, allowing to find new working fluids, not considered so far. The number and kind of the fluid-defining parameters is mainly based on the choice of the used EOS (equation of state). The property model used in the present work is based on the cubic Peng–Robinson equation, chosen due to its moderate numerical expense, sufficient accuracy as well as a general availability of the fluid-defining parameters for many compounds. The considered model-process works between the temperature levels of 273.15 and 333.15 K and can be used as heat pump for supplying buildings with heat, typically. The objective functions are the COP (coefficient of performance) and the VHC (volumetric heating capacity) as a function of critical pressure, critical temperature, acentric factor and two coefficients for the temperature-dependent isobaric ideal gas heat capacity. Also, the steam quality at the compressor entrance has to be regarded as a problem variable. The results give clear hints regarding optimal fluid parameters of the analyzed process and deepen
Ghanbari, Mehdi; Ahmadi, Mahdi; Lashanizadegan, Asghar
2017-06-01
The Cubic Equations of State (CEOSs) are the most important tools in PVT calculations due to their simplicity in use and their extrapolative abilities to condition well outside their correlation ranges. Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) are most successful in the CEOSs which have repeatedly been modified in order to improve their accuracy in wider ranges of temperature and pressure. Unfortunately, most of modifications carried out on these EOSs have no adequate justification for selecting either of these as the basic starting point for the modifications. In this paper, PR and SRK EOSs were critically compared with each other using some new features of their subcritical and supercritical results. For this purpose, the CEOSs were assessed using comprehensive tests of the PVT calculations in the vapor-liquid equilibrium (for pure hydrocarbons over a wide range of acentric factor values: Methane, Ethane Propane, Butane, Heptane and Nonane) and Joule-Thomson Inversion Curves' (JTICs) predictions (for compounds which have reliable JTICs data: Methane, Ethane, Ethylene, Nitrogen, Oxygen, Argon and Carbon dioxide) in subcritical and supercritical regions, respectively. The results indicated that the PR EOS by using any of realistic α-function forms will never be able to accurately predict the JTICs in full span. On the other hand, the subcritical results revealed that the great success of the PR CEOS in predicting liquid phase density is only due to its function in shifting the results of the SRK CEOS to the lower values with the same curve trend. In addition, the Patel and Teja's (PT) EOS, has been reevaluated and the results showed that most of the defects of PR EOS still remain. This article suggests that in order to develop CEOSs, the original SRK EOS is a better candidate than original and alternative forms of PR EOS.
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: smancas@mail.ucf.edu; Roy Choudhury, S. [Department of Mathematics, University of Central Florida, Orlando, FL 32816-1364 (United States)], E-mail: choudhur@longwood.cs.ucf.edu
2009-04-15
Comprehensive numerical simulations (reviewed in Dissipative Solitons, Akhmediev and Ankiewicz (Eds.), Springer, Berlin, 2005) of pulse solutions of the cubic-quintic Ginzburg-Landau Equation (CGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal various intriguing and entirely novel classes of solutions. In particular, there are five new classes of pulse or solitary waves solutions, viz. pulsating, creeping, snake, erupting, and chaotic solitons. In contrast to the regular solitary waves investigated in numerous integrable and non-integrable systems over the last three decades, these dissipative solitons are not stationary in time. Rather, they are spatially confined pulse-type structures whose envelopes exhibit complicated temporal dynamics. The numerical simulations also reveal very interesting bifurcations sequences of these pulses as the parameters of the CGLE are varied. In this paper, we address the issues of central interest in the area, i.e., the conditions for the occurrence of the five categories of dissipative solitons, as well the dependence of both their shape and their stability on the various parameters of the CGLE, viz. the nonlinearity, dispersion, linear and nonlinear gain, loss and spectral filtering parameters. Our predictions on the variation of the soliton amplitudes, widths and periods with the CGLE parameters agree with simulation results. First, we elucidate the Hopf bifurcation mechanism responsible for the various pulsating solitary waves, as well as its absence in Hamiltonian and integrable systems where such structures are absent. Next, we develop and discuss a variational formalism within which to explore the various classes of dissipative solitons. Given the complex dynamics of the various dissipative solutions, this formulation is, of necessity, significantly generalized over all earlier approaches in several crucial ways. Firstly, the starting formulation
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Ioannis, Smirlis; Iakovos, Yakoumis
1997-01-01
S. The proposed scheme employs a recent group-contribution method (Constantinou et al. Fluid Phase Equilib. 1995, 103 (1), 11) for estimating the acentric factor. The two critical properties are estimated via a generalized correlation for the ratio T-c/P-c (with the van der Waals surface area) and the cubic Eo...... pressures for several nonpolar and slightly polar heavy compounds with very satisfactory results, essentially independent of the experimental point used. Furthermore, the method yields critical properties for heavy alkanes (N-c > 20) and other compounds which are in very good agreement with recent available......Cubic equations of state (EoS) are often used for correlating and predicting phase equilibria. Before extending any EoS to mixtures, reliable vapor-pressure prediction is essential. This requires experimental, if possible, critical temperatures T-c, pressures P-c, and acentric factor omega...
Irreducible Traumatic Posterior Shoulder Dislocation
Directory of Open Access Journals (Sweden)
Blake Collier
2017-01-01
coracoid, marked limitation of abduction, and complete absence of external rotation with a fixed internal rotation deformity.2 Lesions commonly associated with traumatic posterior subluxation/dislocation are the reverse Hill-Sachs,3 a posterior labral detachment, glenohumeral ligament lesions,4 rotator cuff tears or posterior bony fractures.1 In order to make an accurate diagnosis it is important to obtain adequate x-ray imaging, including a “Y” view.2 Anteroposterior x-rays may show widening of the glenohumeral joint resembling a “light bulb” shape of the humeral head. However, definitive diagnosis is made by the “Y” view which shows the humeral head displaced posteriorly and no longer covering the glenoid fossa6. Irreducible acute posterior dislocation of the shoulder is extremely rare5 and only one other case has been reported in the literature.7
Directory of Open Access Journals (Sweden)
M.G. Hafez
2016-06-01
Full Text Available In this paper, the novel (G′/G-expansion method is applied to construct exact travelling wave solutions of the cubic nonlinear Schrodinger equation. This technique is straightforward and simple to use, and gives more new general solutions than the other existing methods. Various types of solitary and periodic wave solutions of this equation are derived. The obtained results may be helpful to describe the wave propagation in soliton physics, such as soliton propagation in optical fibers, modulus instability in plasma physics, etc. and provided us the firm mathematical foundation in soliton physics or any varied instances. Furthermore, three-dimensional modules plot of the solutions are also given to visualize the dynamics of the equation.
Three remarks on Powers' theorem about irreducible fields fulfilling CAR
International Nuclear Information System (INIS)
Baumann, K.
1986-01-01
First it is shown that within a relativistic Fermi field theory, a bound parallelPsi/sub k/( f,t)parallel 2 already implies canonical anticommutation relations (CAR). Then under Powers' assumptions a linear, first-order differential equation for the fields psi/sub k/(x,t) is derived. This shows that in the set of generalized free fields fulfilling CAR only the free fields are irreducible at time zero. Finally Fermi fields in two space-time dimensions are considered. It is shown that only four-fermion interaction might be compatible with CAR and a bound on the coupling strength is derived
Irreducible geometric subgroups of classical algebraic groups
Burness, Timothy C; Testerman, Donna M
2016-01-01
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p \\ge 0 with natural module W. Let H be a closed subgroup of G and let V be a non-trivial irreducible tensor-indecomposable p-restricted rational KG-module such that the restriction of V to H is irreducible. In this paper the authors classify the triples (G,H,V) of this form, where H is a disconnected maximal positive-dimensional closed subgroup of G preserving a natural geometric structure on W.
International Nuclear Information System (INIS)
Fewo, Serge I.; Kofane, Timoleon C.; Ngabireng, Claude M.
2008-01-01
With the help of the Maxwell equations, a basic equation modeling the propagation of ultrashort optical solitons in optical fiber is derived, namely the higher-order complex Ginzburg-Landau equation (HCGLE). Considering this one-dimensional HCGLE, we obtain a set of differential equations characterizing the variation of the pulse parameters called collective variables (CVs), of a pulse propagating in dispersion-managed (DM) fiber optic-links. Equations obtained are investigated numerically in order to observe the behaviour of pulse parameters along the optical fiber. A fully numerical simulation of the one-dimensional HCGLE finally tests the results of the CV theory. A good agreement between both methods is observed. Among various behaviours, chaotic pulses, attenuate pulses and stable pulses can be obtained under certain parameter values. (author)
Directory of Open Access Journals (Sweden)
Abdallah El Hadj. A.
2013-01-01
Full Text Available In this work, the solubilities of some anti-inflammatory (nabumetone, phenylbutazone and salicylamide and statin drugs (fluvastatin, atorvastatin, lovastatin, simvastatin and rosuvastatin were correlated using the Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT with one-parameter mixing rule and commonly used cubic equations of state Peng-Robinson (PR and Soave-Redlich-Kwong (SRK combining with van-der Waals-1 parameter (VDW1 and van-der Waals-2 parameters (VDW2 mixing rules. The experimental data for studied compounds were taken from literature at temperature and pressure in ranges (308-348 K and (100-360 bar respectively. The critical properties required for the correlation with PR and SRK were estimated using Gani and Noonalol contribution group methods whereas, PC-SAFT pure-component parameters; segment number (m, segment diameter (σ and energy parameter (ε/k have been estimated by tihic’s group contribution method for nabumetone. For phenylbutazone and salicylamide those parameters were determined using a linear correlation. For statin drugs, PC-SAFT parameters were fitted to solubility data, and binary interaction parameters (kij and lij have been obtained by fitting the experimental data. The result was found to be in good agreement with the experimental data and showed that PC-SAFT approach can be used to model solid-SCF equilibrium with better correlation accuracy than cubic equations of state.
Irreducible multivariate polynomials obtained from polynomials in ...
Indian Academy of Sciences (India)
Hall, 1409 W. Green Street, Urbana, IL 61801, USA. E-mail: Nicolae. ... Theorem A. If we write an irreducible polynomial f ∈ K[X] as a sum of polynomials a0,..., an ..... This shows us that deg ai = (n − i) deg f2 for each i = 0,..., n, so min k>0.
Some extensions and applications of Eisenstein Irreducibility ...
Indian Academy of Sciences (India)
Page 1. Some extensions and applications of Eisenstein Irreducibility. Criterion. Sudesh Kaur Khanduja ..... Beginning from the individual theorems, I grew ac- customed to delve more deeply into their relationships and to grasp whole theories as a single entity. That is how I conceived the idea of mathematical beauty .
Djoko, Martin; Kofane, T. C.
2018-06-01
We investigate the propagation characteristics and stabilization of generalized-Gaussian pulse in highly nonlinear homogeneous media with higher-order dispersion terms. The optical pulse propagation has been modeled by the higher-order (3+1)-dimensional cubic-quintic-septic complex Ginzburg-Landau [(3+1)D CQS-CGL] equation. We have used the variational method to find a set of differential equations characterizing the variation of the pulse parameters in fiber optic-links. The variational equations we obtained have been integrated numerically by the means of the fourth-order Runge-Kutta (RK4) method, which also allows us to investigate the evolution of the generalized-Gaussian beam and the pulse evolution along an optical doped fiber. Then, we have solved the original nonlinear (3+1)D CQS-CGL equation with the split-step Fourier method (SSFM), and compare the results with those obtained, using the variational approach. A good agreement between analytical and numerical methods is observed. The evolution of the generalized-Gaussian beam has shown oscillatory propagation, and bell-shaped dissipative optical bullets have been obtained under certain parameter values in both anomalous and normal chromatic dispersion regimes. Using the natural control parameter of the solution as it evolves, named the total energy Q, our numerical simulations reveal the existence of 3D stable vortex dissipative light bullets, 3D stable spatiotemporal optical soliton, stationary and pulsating optical bullets, depending on the used initial input condition (symmetric or elliptic).
The Slice Algorithm For Irreducible Decomposition of Monomial Ideals
DEFF Research Database (Denmark)
Roune, Bjarke Hammersholt
2009-01-01
Irreducible decomposition of monomial ideals has an increasing number of applications from biology to pure math. This paper presents the Slice Algorithm for computing irreducible decompositions, Alexander duals and socles of monomial ideals. The paper includes experiments showing good performance...
Irreducible Inguinal Hernias in the Paediatric Age Group | Ezomike ...
African Journals Online (AJOL)
BACKGROUND: An inguinal hernia is said to be irreducible when the content fails to return into the peritoneal cavity without surgical intervention. Irreducibility is an ever present risk in untreated inguinal hernias and its management remains an important part of pediatric surgery practice. When a hernia is irreducible ...
Quasiaverages, symmetry breaking and irreducible Green functions method
Directory of Open Access Journals (Sweden)
A.L.Kuzemsky
2010-01-01
Full Text Available The development and applications of the method of quasiaverages to quantum statistical physics and to quantum solid state theory and, in particular, to quantum theory of magnetism, were considered. It was shown that the role of symmetry (and the breaking of symmetries in combination with the degeneracy of the system was reanalyzed and essentially clarified within the framework of the method of quasiaverages. The problem of finding the ferromagnetic, antiferromagnetic and superconducting "symmetry broken" solutions of the correlated lattice fermion models was discussed within the irreducible Green functions method. A unified scheme for the construction of generalized mean fields (elastic scattering corrections and self-energy (inelastic scattering in terms of the equations of motion and Dyson equation was generalized in order to include the "source fields". This approach complements previous studies of microscopic theory of antiferromagnetism and clarifies the concepts of Neel sublattices for localized and itinerant antiferromagnetism and "spin-aligning fields" of correlated lattice fermions.
DEFF Research Database (Denmark)
Tsivintzelis, Ioannis; Ali, Shahid; Kontogeorgis, Georgios
2014-01-01
density data for both CO2 and CO2–water and for vapor–liquid equilibrium for mixtures of CO2 with various compounds present in transport systems. In all of these cases we consider various possibilities for modeling CO2 (inert, self-associating using two-, three-, and four sites) and the possibility......The CPA (cubic-plus-association) equation of state is applied in this work to a wide range of systems of relevance to CO2 transport. Both phase equilibria and densities over extensive temperature and pressure ranges are considered. More specifically in this study we first evaluate CPA against......” for applying CPA to acid gas mixtures. The overall conclusion is that CPA performs satisfactorily; the model in most cases correlates well binary data and predicts with good accuracy multicomponent vapor–liquid equilibria. Among the various approaches investigated, the best ones are when cross association...
Energy Technology Data Exchange (ETDEWEB)
Haruki, Masashi; Yahiro, Yukihito; Higashi, Hidenori; Iwai, Yoshio; Arai, Yasuhiko [Kyushu University, FUkuoka (Japan). Graduate School of Engineering
1999-08-01
A modified-Soave-Redlich-Kwong (MSRK) equation of state with an exponent-type mixing rule for the energy parameter and a conventional rule for the size parameter is applied to correlate the phase equilibria for four binary mixtures of water + hydrocarbon (benzene, hexane, decane, and dodecane) systems at high temperatures and pressures. It is noted that good correlation results are obtained by using the mixing rules with interaction parameters between unlike molecules. (author)
Irreducible projective representations and their physical applications
Yang, Jian; Liu, Zheng-Xin
2018-01-01
An eigenfunction method is applied to reduce the regular projective representations (Reps) of finite groups to obtain their irreducible projective Reps. Anti-unitary groups are treated specially, where the decoupled factor systems and modified Schur’s lemma are introduced. We discuss the applications of irreducible Reps in many-body physics. It is shown that in symmetry protected topological phases, geometric defects or symmetry defects may carry projective Rep of the symmetry group; while in symmetry enriched topological phases, intrinsic excitations (such as spinons or visons) may carry projective Rep of the symmetry group. We also discuss the applications of projective Reps in problems related to spectrum degeneracy, such as in search of models without sign problem in quantum Monte Carlo simulations.
Irreducible lateral dislocation of the elbow.
Directory of Open Access Journals (Sweden)
Chhaparwal M
1997-01-01
Full Text Available A rare case of an irreducible post-traumatic lateral dislocation of elbow is presented. The mechanism of injury was fall on a flexed elbow with trauma on its medial aspect resulting in pronation of the forearm. At open reduction, the brachialis muscle was in the form of a tight band which prevented reduction. The ulnar nerve was entrapped in the joint.
International Nuclear Information System (INIS)
Yang, Jyisy; Griffiths, Peter R.; Goodwin, Anthony R.H.
2003-01-01
The (ρ,T,p) and (vapor + liquid) equilibria for fluid mixtures containing either CO 2 or H 2 S have been determined from 13 equations of state. The estimated values have been compared with published experimental results. CO 2 and H 2 S were used to represent non-polar and polar fluids, respectively. The equations of state investigated were as follows: (a) the Lee-Kesler equation; (b) two equations that included new reference fluids for the Lee-Kesler method; (c) three so-called extended equations of state; and (d) seven cubic equations of state. After adjustment of the binary interaction parameters the predicted values differed from the experimental data by about 0.8% for CO 2 mixtures while for H 2 S mixtures the uncertainty was about ±2.8%. Somewhat larger errors, although still lower than ±5%, were obtained for co-existing phase densities; the Lee-Kesler method provided results of the highest accuracy. The cubic equations proposed by Schmidt and Wenzel and Valderrama provide the most reliable predictions of both single and co-existing phase densities. Comparison of the predicted (vapor + liquid) equilibrium with experiment shows that each of the seven cubic equations provides results of similar accuracy and all within ±6%
Directory of Open Access Journals (Sweden)
A. C. D. Freitas
2013-03-01
Full Text Available Ionic liquids (IL have been described as novel environmentally benign solvents because of their remarkable characteristics. Numerous applications of these solvents continue to grow at an exponential rate. In this work, high pressure vapor liquid equilibria for 17 different IL + gas binary systems were modeled at different temperatures with Peng-Robinson (PR and Soave-Redlich-Kwong (SRK equations of state, combined with the van der Waals mixing rule with two binary interaction parameters (vdW-2. The experimental data were taken from the literature. The optimum binary interaction parameters were estimated by minimization of an objective function based on the average absolute relative deviation of liquid and vapor phases, using the modified Simplex algorithm. The solubilities of all gases studied in this work decrease as the temperature increases and increase with increasing pressure. The correlated results were highly satisfactory, with average absolute relative deviations of 2.10% and 2.25% for PR-vdW-2 and SRK-vdW-2, respectively.
On relativistic irreducible quantum fields fulfilling CCR
International Nuclear Information System (INIS)
Baumann, K.
1987-01-01
Let phi be a relativistic scalar field fulfilling canonical commutation relations (CCR). Furthermore it is assumed that the time zero fields and momenta form an irreducible set. Based on estimates given by Herbst [I. W. Herbst, J. Math. Phys. 17, 1210 (1976)], and by methods developed by Powers [R. T. Powers, Commun. Math. Phys. 4, 145 (1967)], it is shown that phi has to be a free field in n>3 space dimensions. For n = 3 (resp. n = 2) restrictions that look similar to the restriction in a formal :phi 4 : 3 /sub +/ 1 (resp. :phi 6 : 2 /sub +/ 1 ) theory are obtained
Products of Irreducible Characters Having Complex-Valued Constituents
Directory of Open Access Journals (Sweden)
Lisa R. Hendrixson
2017-06-01
Full Text Available First, we prove that when a finite solvable group $G$ has a faithful irreducible character $\\chi$ such that $\\chi\\overline{\\chi}$ has two irreducible constituents, both must be real-valued. Then, we study the situation where $\\chi\\overline{\\chi}$ has exactly three distinct nonprincipal irreducible constituents, two of which are complex conjugates. In this case, we prove that $G$ has derived length bounded above by $6$.
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Philippos, Coutsikos; Vassilis, Harismiadis
1998-01-01
A novel method for investigating the performance of the repulsive and attractive terms of a cubic equation of state (EoS) along with different combining rules for the cross covolume (b(12)) and cross-energy (a(12)) parameters used with the van der Waals one-fluid theory is presented. The method...... utilizes the EoS-derived liquid-phase activity coefficient which is separated into a combinatorial-free volume part (gamma(c-fv)), obtained from the repulsive term of the EoS, and a residual one (gamma(res)) obtained from the attractive term. Athermal systems (alkane solutions) are used where we can......(c-fv) values with the experimental ones suggest that the van der Waals (vdW) repulsive term is applicable not only to mixtures with spherical molecules, as originally suggested by van der Waals, but also to very asymmetric ones. On the other hand, the attractive term leads to gamma(res) values that can...
An irreducible ankle fracture dislocation: the Bosworth injury
Schepers, Tim; Hagenaars, Tjebbe; den Hartog, Dennis
2012-01-01
Irreducible fracture dislocations of the ankle are rare and represent true orthopedic emergencies. We present a case of a fracture dislocation that was irreducible owing to a fixed dislocation of the proximal fibular fragment posterior to the lateral ridge of the tibia. This particular type of
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.
1993-01-01
The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs
Cubication of conservative nonlinear oscillators
International Nuclear Information System (INIS)
Belendez, Augusto; Alvarez, Mariela L; Fernandez, Elena; Pascual, Inmaculada
2009-01-01
A cubication procedure of the nonlinear differential equation for conservative nonlinear oscillators is analysed and discussed. This scheme is based on the Chebyshev series expansion of the restoring force, and this allows us to approximate the original nonlinear differential equation by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A, while in a Taylor expansion of the restoring force these coefficients are independent of A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain an approximate frequency-amplitude relation as a function of the complete elliptic integral of the first kind. Some conservative nonlinear oscillators are analysed to illustrate the usefulness and effectiveness of this scheme.
Irreducible multiqutrit correlations in Greenberger-Horne-Zeilinger-type states
Energy Technology Data Exchange (ETDEWEB)
Zhang, Fu-Lin [Physics Department, School of Science, Tianjin University, Tianjin 300072 (China); Chen, Jing-Ling [Theoretical Physics Division, Chern Institute of Mathematics, Nankai University, Tianjin, 300071 (China); Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore)
2011-12-15
Following the idea of the continuity approach by D. L. Zhou [Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multiparty correlations in two families of n-qutrit Greenberger-Horne-Zeilinger-type states. For the pure states in one of the families, the irreducible 2-party, n-party, and (n-m)-party (0
Irreducible multiqutrit correlations in Greenberger-Horne-Zeilinger-type states
International Nuclear Information System (INIS)
Zhang, Fu-Lin; Chen, Jing-Ling
2011-01-01
Following the idea of the continuity approach by D. L. Zhou [Phys. Rev. Lett. 101, 180505 (2008)], we obtain the degrees of irreducible multiparty correlations in two families of n-qutrit Greenberger-Horne-Zeilinger-type states. For the pure states in one of the families, the irreducible 2-party, n-party, and (n-m)-party (0< m< n-2) correlations are nonzero, which is different from the n-qubit case. We also derive the correlation distributions in the n-qutrit maximal slice state, which can be uniquely determined by its (n-1)-qutrit-reduced density matrices among pure states. It is proved that there is no irreducible n-qutrit correlation in the maximal slice state. This enlightens us to give a discussion about how to characterize the pure states with irreducible n-party correlation in arbitrarily high-dimensional systems by the way of the continuity approach.
Irreducible Tests for Space Mission Sequencing Software
Ferguson, Lisa
2012-01-01
As missions extend further into space, the modeling and simulation of their every action and instruction becomes critical. The greater the distance between Earth and the spacecraft, the smaller the window for communication becomes. Therefore, through modeling and simulating the planned operations, the most efficient sequence of commands can be sent to the spacecraft. The Space Mission Sequencing Software is being developed as the next generation of sequencing software to ensure the most efficient communication to interplanetary and deep space mission spacecraft. Aside from efficiency, the software also checks to make sure that communication during a specified time is even possible, meaning that there is not a planet or moon preventing reception of a signal from Earth or that two opposing commands are being given simultaneously. In this way, the software not only models the proposed instructions to the spacecraft, but also validates the commands as well.To ensure that all spacecraft communications are sequenced properly, a timeline is used to structure the data. The created timelines are immutable and once data is as-signed to a timeline, it shall never be deleted nor renamed. This is to prevent the need for storing and filing the timelines for use by other programs. Several types of timelines can be created to accommodate different types of communications (activities, measurements, commands, states, events). Each of these timeline types requires specific parameters and all have options for additional parameters if needed. With so many combinations of parameters available, the robustness and stability of the software is a necessity. Therefore a baseline must be established to ensure the full functionality of the software and it is here where the irreducible tests come into use.
Irreducible almost simple subgroups of classical algebraic groups
Burness, Timothy C; Marion, Claude; Testerman, Donna M
2015-01-01
Let G be a simple classical algebraic group over an algebraically closed field K of characteristic p\\geq 0 with natural module W. Let H be a closed subgroup of G and let V be a nontrivial p-restricted irreducible tensor indecomposable rational KG-module such that the restriction of V to H is irreducible. In this paper the authors classify the triples (G,H,V) of this form, where V \
International Nuclear Information System (INIS)
Schek, I.; Wyatt, R.E.
1986-01-01
Molecular multiphoton processes are treated in the Recursive Residue Generation Method (A. Nauts and R.E. Wyatt, Phys. Rev. Lett 51, 2238 (1983)) by converting the molecular-field Hamiltonian matrix into tridiagonal form, using the Lanczos equations. In this study, the self-energies (diagonal) and linking (off-diagaonal) terms in the tridiagonal matrix are obtained by comparing linked moment diagrams in both representations. The dynamics of the source state is introduced and computed in terms of the linked and the irreducible moments
Irreducible descriptive sets of attributes for information systems
Moshkov, Mikhail
2010-01-01
The maximal consistent extension Ext(S) of a given information system S consists of all objects corresponding to attribute values from S which are consistent with all true and realizable rules extracted from the original information system S. An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B. We show that there exists only one irreducible descriptive set of attributes. We present a polynomial algorithm for this set construction. We also study relationships between the cardinality of irreducible descriptive set of attributes and the number of attributes in S. The obtained results will be useful for the design of concurrent data models from experimental data. © 2010 Springer-Verlag.
Cubic Pencils and Painlev\\'e Hamiltonians
Kajiwara, Kenji; Masuda, Tetsu; Noumi, Masatoshi; Ohta, Yasuhiro; Yamada, Yasuhiko
2004-01-01
We present a simple heuristic method to derive the Painlev\\'e differential equations from the corresponding geometry of rational surafces. We also give a direct relationship between the cubic pencils and Seiberg-Witten curves.
DEFF Research Database (Denmark)
Arya, Alay; Liang, Xiaodong; von Solms, Nicolas
2016-01-01
using various equations of state and empirical models. In the past few years, association models based on CPA and SAFT equations of state have been found to be promising models for studies of asphaltene precipitation. In this work, we compare asphaltene precipitation results obtained from different...
Alexander-equivalent Zariski pairs of irreducible sextics
DEFF Research Database (Denmark)
Eyral, Christophe; Oka, Mutsuo
2009-01-01
The existence of Alexander-equivalent Zariski pairs dealing with irreducible curves of degree 6 was proved by Degtyarev. However, no explicit example of such a pair is available (only the existence is known) in the literature. In this paper, we construct the first concrete example.......The existence of Alexander-equivalent Zariski pairs dealing with irreducible curves of degree 6 was proved by Degtyarev. However, no explicit example of such a pair is available (only the existence is known) in the literature. In this paper, we construct the first concrete example....
International Nuclear Information System (INIS)
Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F
2009-01-01
A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations
Irreducible Fifth Metatarsophalangeal Joint after Car Crush Injury
Turkmensoy, Fatih; Erinc, Samet; Ergin, Omer Naci; Ozkan, Korhan; Kemah, Bahattin
2015-01-01
Metatarsophalangeal joint dislocations are uncommon injuries. Herein, an irreducible dislocation of fifth metatarsophalangeal joint with fractures on the second, third, and fourth metatarsal head was reported. Joint reduction could not be achieved which necessitated open reduction. Six months after surgery the patient was walking and doing his daily activities without any complaints. He had returned to his pretrauma functional level. PMID:25861501
Irreducible descriptive sets of attributes for information systems
Moshkov, Mikhail; Skowron, Andrzej; Suraj, Zbigniew
2010-01-01
. An irreducible descriptive set for the considered information system S is a minimal (relative to the inclusion) set B of attributes which defines exactly the set Ext(S) by means of true and realizable rules constructed over attributes from the considered set B
Irreducible Fifth Metatarsophalangeal Joint after Car Crush Injury
Directory of Open Access Journals (Sweden)
Fatih Turkmensoy
2015-01-01
Full Text Available Metatarsophalangeal joint dislocations are uncommon injuries. Herein, an irreducible dislocation of fifth metatarsophalangeal joint with fractures on the second, third, and fourth metatarsal head was reported. Joint reduction could not be achieved which necessitated open reduction. Six months after surgery the patient was walking and doing his daily activities without any complaints. He had returned to his pretrauma functional level.
Nonlinear dynamics of quadratically cubic systems
International Nuclear Information System (INIS)
Rudenko, O V
2013-01-01
We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg–de Vries, and nonlinear Schrödinger partial differential equations. Some problems are solved exactly in the space–time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed. (methodological notes)
DEFF Research Database (Denmark)
Tzirakis, Fragkiskos; Karakatsani, Eirini; Kontogeorgis, Georgios
2016-01-01
Dew point specifications are of high interest in the natural gas industry. The CPA equation of state (EoS) was previously validated against both water content and phase equilibrium data. Moreover, solid model parameters were estimated for four natural gas main components (methane, ethane, propane...
Moortgat, J.
2017-12-01
We present novel simulation tools to model multiphase multicomponent flow and transport in porous media for mixtures that contain non-polar hydrocarbons, self-associating polar water, and cross-associating molecules like methane, ethane, unsaturated hydrocarbons, CO2 and H2S. Such mixtures often occur when CO2 is injected and stored in saline aquifers, or when methane is leaking into groundwater. To accurately predict the species transfer between aqueous, gaseous and oleic phases, and the subsequent change in phase properties, the self- and cross-associating behavior of molecules needs to be taken into account, particularly at the typical temperatures and pressures in deep formations. The Cubic-Plus-Association equation-of-state (EOS) has been demonstrated to be highly accurate for such problems but its excessive computational cost has prevented widespread use in reservoir simulators. We discuss the thermodynamical framework and develop sophisticated numerical algorithms that allow reservoir simulations with efficiencies comparable to a simple cubic EOS. This approach improves our predictive powers for highly nonlinear fluid behavior related to geological carbon sequestration, such as density driven flow and natural convection (solubility trapping), evaporation of water into the CO2-rich gas phase, and competitive dissolution-evaporation when CO2 is injected in, e.g., methane saturated aquifers. Several examples demonstrate the accuracy and robustness of this EOS framework for complex applications.
Energy Technology Data Exchange (ETDEWEB)
Gomez T, A.M.; Valle G, E. del [IPN-ESFM, 07738 Mexico D.F. (Mexico); Delfin L, A.; Alonso V, G. [ININ, 52045 Ocoyoacac, Estado de Mexico (Mexico)] e-mail: armagotorres@aol.com
2003-07-01
In this work a finite differences technique centered in mesh based on a cubic reduced nodal scheme type finite element to solve the equations of the kinetics 1 D that include the equations corresponding to the concentrations of precursors of delayed neutrons is described. The technique of finite elements used is that of Galerkin where so much the neutron flux as the concentrations of precursors its are spatially approached by means of a three grade polynomial. The matrices of rigidity and of mass that arise during this discretization process are numerically evaluated using the open quadrature non standard of Newton-Cotes and that of Radau respectively. The purpose of the application of these quadratures is the one of to eliminate in the global matrices the couplings among the values of the flow in points of the discretization with the consequent advantages as for the reduction of the order of the matrix associated to the discreet problem that is to solve. As for the time dependent part the classical integration scheme known as {theta} scheme is applied. After carrying out the one reordering of unknown and equations it arrives to a reduced system that it can be solved but quickly. With the McKin compute program developed its were solved three benchmark problems and those results are shown for the relative powers. (Author)
DEFF Research Database (Denmark)
Cismondi, Martin; Mollerup, Jørgen M.; Zabaloy, Marcelo S.
2010-01-01
for a great diversity of mixtures. Nevertheless, the models for representing phase equilibria and physico-chemical properties of asymmetric systems may require more flexible mixing rules than the classical quadratic van der Waals (vdW) mixing rules or their equivalent (with regard to the number of available...... interaction parameters) in modern equations of state.In particular, the phase equilibria of binary mixtures containing CO2 and heavy n-alkanes have been studied by an important number of authors and using different types of models, achieving only partially accurate results and realizing the difficulties...
On the Directly and Subdirectly Irreducible Many-Sorted Algebras
Directory of Open Access Journals (Sweden)
Climent Vidal J.
2015-03-01
Full Text Available A theorem of single-sorted universal algebra asserts that every finite algebra can be represented as a product of a finite family of finite directly irreducible algebras. In this article, we show that the many-sorted counterpart of the above theorem is also true, but under the condition of requiring, in the definition of directly reducible many-sorted algebra, that the supports of the factors should be included in the support of the many-sorted algebra. Moreover, we show that the theorem of Birkhoff, according to which every single-sorted algebra is isomorphic to a subdirect product of subdirectly irreducible algebras, is also true in the field of many-sorted algebras.
Irreducible diagrams in Landau-Ginzburg field theory
Energy Technology Data Exchange (ETDEWEB)
Witten, Jr, T A [Michigan Univ., Ann Arbor (USA). Dept. of Psychology
1981-10-19
It is shown that the free energy W of a Landau-Ginzburg-Wilson field theory with O(n) symmetry may be written in terms of the generating function V of diagrams irreducible in both propagator and interaction lines. This generalizes and simplifies a recent result of Des Cloizeaux. The functions W and V are related by a type of Legendre transformation on the bare mass variable.
General quantum polynomials: irreducible modules and Morita equivalence
International Nuclear Information System (INIS)
Artamonov, V A
1999-01-01
In this paper we continue the investigation of the structure of finitely generated modules over rings of general quantum (Laurent) polynomials. We obtain a description of the lattice of submodules of periodic finitely generated modules and describe the irreducible modules. We investigate the problem of Morita equivalence of rings of general quantum polynomials, consider properties of division rings of fractions, and solve Zariski's problem for quantum polynomials
Irreducible integrable theories form tensor products of conformal models
International Nuclear Information System (INIS)
Mathur, S.D.; Warner, N.P.
1991-01-01
By using Toda field theories we show that there are perturbations of direct products of conformal theories that lead to irreducible integrable field theories. The same affine Toda theory can be truncated to different quantum integrable models for different choices of the charge at infinity and the coupling. The classification of integrable models that can be obtained in this fashion follows the classification of symmetric spaces of type G/H with rank H = rank G. (orig.)
Irreducible mass for the Tomimatsu-Sato space-time
Energy Technology Data Exchange (ETDEWEB)
Calvani, M [Padua Univ. (Italy). Ist. di Astronomia; Salmistraro, F; Catenacci, R
1979-01-01
A global definition of irreducible mass for the odd delta T-S metrics is investigated. It is found that its expression in terms of the source parameters is the same for all the members of the family and reduces to the formula that holds in the Kerr case (delta = 1). As a consequence, it is shown that processes with msub(ir) = const no longer imply zero variations of the horizon's area for delta > 1.
Generalized Vaidya spacetime for cubic gravity
Ruan, Shan-Ming
2016-03-01
We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.
Directory of Open Access Journals (Sweden)
Gary R. Nicklason
2015-07-01
Full Text Available We consider center conditions for plane polynomial systems of Abel type consisting of a linear center perturbed by the sum of 2 homogeneous polynomials of degrees n and 2n-1 where $n \\ge 2$. Using properties of Abel equations we obtain two general systems valid for arbitrary values on n. For the cubic n=2 systems we find several sets of new center conditions, some of which show that the results in a paper by Hill, Lloyd and Pearson which were conjectured to be complete are in fact not complete. We also present a particular system which appears to be a counterexample to a conjecture by Zoladek et al. regarding rational reversibility in cubic polynomial systems.
On irreducible representations of the ultrahyperbolic BMS group
International Nuclear Information System (INIS)
McCarthy, Patrick J.; Melas, Evangelos
2003-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all asymptotically flat Lorentzian space-times. As such, B is the best candidate for the universal symmetry group of General Relativity. However, in studying quantum gravity, space-times with signatures other than the usual Lorentzian one, and complex space-times, are frequently considered. Generalisations of B appropriate to these other signatures have been defined earlier. Here, the generalisation B(2,2) appropriate to the ultrahyperbolic signature (+,+,-,-) is described in detail, and the irreducible unitary representations (IRs) of B(2,2) are analysed. It is proved that all induced IRs of B(2,2) arise from IRs of compact 'little groups'. These little groups, which are closed subgroups of K=SO(2)xSO(2), are classified here in detail, with particular attention paid to those of infinite order
Construction of the irreducibles of B(2, 2)
International Nuclear Information System (INIS)
Melas, Evangelos
2006-01-01
The ordinary Bondi-Metzner-Sachs (BMS) group B is the common asymptotic symmetry group of all radiating, asymptotically flat, Lorentzian spacetimes. As such, B is the best candidate for the universal symmetry group of general relativity. However, in studying quantum gravity, spacetimes with signatures other than the usual Lorentzian one and complex spacetimes are frequently considered. Generalizations of B appropriate to these other signatures have been defined earlier. In particular, the generalization B(2, 2) appropriate to the ultrahyperbolic signature (+, +, -, -) has been described in detail, and the study of its irreducible unitary representations (IRs) of B(2, 2) has been initiated. The infinite little groups have been given explicitly, but the finite little groups have only been partially described. This study is completed by describing in detail the finite little groups and by giving all the necessary information in order to construct the IRs of B(2, 2) in all cases
A practical criterion of irreducibility of multi-loop Feynman integrals
International Nuclear Information System (INIS)
Baikov, P.A.
2006-01-01
A practical criterion for the irreducibility (with respect to integration by part identities) of a particular Feynman integral to a given set of integrals is presented. The irreducibility is shown to be related to the existence of stable (with zero gradient) points of a specially constructed polynomial
Kinks in systems with cubic and quartic anharmonicity
International Nuclear Information System (INIS)
Kashcheev, V.N.
1988-01-01
For a classical system of interacting particles with on-site cubic or quartic anharmonicity explicit analytic solutions of the d'Alembert equation are obtained in the form of kinks in the presence of dissipation (viscous or Rayleigh) and a constant force. These kinks will be asymptotically stable in the case of quartic anharmonicity and unstable in the case cubic anharmonicity
Purely cubic action for string field theory
Horowitz, G. T.; Lykken, J.; Rohm, R.; Strominger, A.
1986-01-01
It is shown that Witten's (1986) open-bosonic-string field-theory action and a closed-string analog can be written as a purely cubic interaction term. The conventional form of the action arises by expansion around particular solutions of the classical equations of motion. The explicit background dependence of the conventional action via the Becchi-Rouet-Stora-Tyutin operator is eliminated in the cubic formulation. A closed-form expression is found for the full nonlinear gauge-transformation law.
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type-checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, is conjectured to have decidable type checking, and has an implemented type-checker. Our new type theory, called guarded cubical type theory, provides a computational interpretation of extensionality for guarded recursive...
DEFF Research Database (Denmark)
Birkedal, Lars; Bizjak, Aleš; Clouston, Ranald
2016-01-01
This paper improves the treatment of equality in guarded dependent type theory (GDTT), by combining it with cubical type theory (CTT). GDTT is an extensional type theory with guarded recursive types, which are useful for building models of program logics, and for programming and reasoning...... with coinductive types. We wish to implement GDTT with decidable type checking, while still supporting non-trivial equality proofs that reason about the extensions of guarded recursive constructions. CTT is a variation of Martin-L\\"of type theory in which the identity type is replaced by abstract paths between...... terms. CTT provides a computational interpretation of functional extensionality, enjoys canonicity for the natural numbers type, and is conjectured to support decidable type-checking. Our new type theory, guarded cubical type theory (GCTT), provides a computational interpretation of extensionality...
Siudzińska, Katarzyna; Chruściński, Dariusz
2018-03-01
In matrix algebras, we introduce a class of linear maps that are irreducibly covariant with respect to the finite group generated by the Weyl operators. In particular, we analyze the irreducibly covariant quantum channels, that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.
The finite - dimensional star and grade star irreducible representation of SU(n/1)
International Nuclear Information System (INIS)
Han Qi-zhi.
1981-01-01
We derive the conditions of star and grade star representations of SU(n/1) and give some examples of them. We also give a brief review of the finite - dimensional irreducible representations of SU(n/1). (author)
Quotients of irreducible N=2 superconformal coset theories by discrete symmetries
International Nuclear Information System (INIS)
Bailin, D.; Love, A.
1990-01-01
The spectrum of massless states is studied for the irreducible N=2 superconformal coset theories when these theories are quotiented by discrete symmetries, including the effect of embedding the discrete symmetries in the gauge group. (orig.)
Neural Mechanisms of Updating under Reducible and Irreducible Uncertainty.
Kobayashi, Kenji; Hsu, Ming
2017-07-19
Adaptive decision making depends on an agent's ability to use environmental signals to reduce uncertainty. However, because of multiple types of uncertainty, agents must take into account not only the extent to which signals violate prior expectations but also whether uncertainty can be reduced in the first place. Here we studied how human brains of both sexes respond to signals under conditions of reducible and irreducible uncertainty. We show behaviorally that subjects' value updating was sensitive to the reducibility of uncertainty, and could be quantitatively characterized by a Bayesian model where agents ignore expectancy violations that do not update beliefs or values. Using fMRI, we found that neural processes underlying belief and value updating were separable from responses to expectancy violation, and that reducibility of uncertainty in value modulated connections from belief-updating regions to value-updating regions. Together, these results provide insights into how agents use knowledge about uncertainty to make better decisions while ignoring mere expectancy violation. SIGNIFICANCE STATEMENT To make good decisions, a person must observe the environment carefully, and use these observations to reduce uncertainty about consequences of actions. Importantly, uncertainty should not be reduced purely based on how surprising the observations are, particularly because in some cases uncertainty is not reducible. Here we show that the human brain indeed reduces uncertainty adaptively by taking into account the nature of uncertainty and ignoring mere surprise. Behaviorally, we show that human subjects reduce uncertainty in a quasioptimal Bayesian manner. Using fMRI, we characterize brain regions that may be involved in uncertainty reduction, as well as the network they constitute, and dissociate them from brain regions that respond to mere surprise. Copyright © 2017 the authors 0270-6474/17/376972-11$15.00/0.
Higher-Order Approximation of Cubic-Quintic Duffing Model
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Babazadeh, H.
2011-01-01
We apply an Artificial Parameter Lindstedt-Poincaré Method (APL-PM) to find improved approximate solutions for strongly nonlinear Duffing oscillations with cubic-quintic nonlinear restoring force. This approach yields simple linear algebraic equations instead of nonlinear algebraic equations...
Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme
Energy Technology Data Exchange (ETDEWEB)
Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)
Interpolation of natural cubic spline
Directory of Open Access Journals (Sweden)
Arun Kumar
1992-01-01
Full Text Available From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.
The irreducible needs of children for development: a frame of reference to health care
Directory of Open Access Journals (Sweden)
Maria De La Ó Ramallo Veríssimo
2018-03-01
Full Text Available ABSTRACT A comprehensive health care to children implies in caring for their development, by perceiving the needs based on a suitable reference to children’s specificities. This theoretical study aimed to analyze the “irreducible needs of children” frame of reference, based on a child development theory. We performed a comparative analysis between the contents of children’s irreducible needs and the components of the Bioecological Theory of Human Development. An extensive correspondence was verified among the components of the Bioecological Theory and the following essential needs: ongoing nurturing relationships; experiences tailored to individual differences; developmentally appropriate experiences; limit setting, structure and expectations; stable, supportive communities and cultural continuity. The need for physical protection, safety, and regulation is not explicit in the elements of the theory, although it is also verified in their definitions. We concluded that the irreducible needs’ reference can support nurses in health care and in child development promotion.
Closed-form irreducible differential formulations of the Wilson renormalization group
International Nuclear Information System (INIS)
Vvedensky, D.D.; Chang, T.S.; Nicoll, J.F.
1983-01-01
We present a detailed derivation of the one-particle--irreducible (1PI) differential renormalization-group generators originally developed by Nicoll and Chang and by Chang, Nicoll, and Young. We illustrate the machinery of the irreducible formulation by calculating to order epsilon 2 the characteristic time exponent z for the time-dependent Ginsburg-Landau model in the cases of conserved and nonconserved order parameter. We then calculate both z and eta to order epsilon 2 by applying to the 1PI generator an extension of the operator expansion technique developed by Wegner for the Wilson smooth-cutoff renormalization-group generator
Regularizing cubic open Neveu-Schwarz string field theory
International Nuclear Information System (INIS)
Berkovits, Nathan; Siegel, Warren
2009-01-01
After introducing non-minimal variables, the midpoint insertion of Y Y-bar in cubic open Neveu-Schwarz string field theory can be replaced with an operator N ρ depending on a constant parameter ρ. As in cubic open superstring field theory using the pure spinor formalism, the operator N ρ is invertible and is equal to 1 up to a BRST-trivial quantity. So unlike the linearized equation of motion Y Y-bar QV = 0 which requires truncation of the Hilbert space in order to imply QV = 0, the linearized equation N ρ QV = 0 directly implies QV = 0.
Shape Preserving Interpolation Using C2 Rational Cubic Spline
Directory of Open Access Journals (Sweden)
Samsul Ariffin Abdul Karim
2016-01-01
Full Text Available This paper discusses the construction of new C2 rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters αi, βi, and γi. The sufficient conditions for the positivity are derived on one parameter γi while the other two parameters αi and βi are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with C2 continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and C2 continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives di, i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the new C2 rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is ft∈C3t0,tn is also investigated in detail.
Description of the higher massless irreducible integer spins in the BRST approach
International Nuclear Information System (INIS)
Pashnev, A.; Tsulaya, M.
1998-01-01
The BRST approach is applied to the description of irreducible massless higher spins representations of the Poincare group in arbitrary dimensions. The total system of constraints in such theory includes both the first and the second class constraints. The corresponding nilpotent BRST charge contains terms up to the seventh degree in ghosts
An algorithm to compute the canonical basis of an irreducible Uq(g)-module
de Graaf, W. A.
2002-01-01
An algorithm is described to compute the canonical basis of an irreducible module over a quantized enveloping algebra of a finite-dimensional semisimple Lie algebra. The algorithm works for modules that are constructed as a submodule of a tensor product of modules with known canonical bases.
Fourier-Laplace transform of irreducible regular differential systems on the Riemann sphere
International Nuclear Information System (INIS)
Sabbah, C
2004-01-01
It is shown that the Fourier-Laplace transform of an irreducible regular differential system on the Riemann sphere underlies a polarizable regular twistor D-module if one considers only the part at finite distance. The associated holomorphic bundle defined away from the origin of the complex plane is therefore equipped with a natural harmonic metric having a tame behaviour near the origin
Global Well-Posedness for Cubic NLS with Nonlinear Damping
Antonelli, Paolo
2010-11-04
We study the Cauchy problem for the cubic nonlinear Schrödinger equation, perturbed by (higher order) dissipative nonlinearities. We prove global in-time existence of solutions for general initial data in the energy space. In particular we treat the energy-critical case of a quintic dissipation in three space dimensions. © Taylor & Francis Group, LLC.
Bifurcation of rupture path by linear and cubic damping force
Dennis L. C., C.; Chew X., Y.; Lee Y., C.
2014-06-01
Bifurcation of rupture path is studied for the effect of linear and cubic damping. Momentum equation with Rayleigh factor was transformed into ordinary differential form. Bernoulli differential equation was obtained and solved by the separation of variables. Analytical or exact solutions yielded the bifurcation was visible at imaginary part when the wave was non dispersive. For the dispersive wave, bifurcation of rupture path was invisible.
Galois action on solutions of a differential equation
Hendriks, Peter A.; Put, Marius van der
Consider a second-order differential equation of the form y '' + ay' + by = O with a,b is an element of Q(x). Kovacic's algorithm tries to compute a solution of the associated Riccati equation that is algebraic and of minimal degree over (Q) over bar(x). The coefficients of the monic irreducible
Directory of Open Access Journals (Sweden)
J. Buitrago
Full Text Available A new classical 2-spinor approach to U(1 gauge theory is presented in which the usual four-potential vector field is replaced by a symmetric second rank spinor. Following a lagrangian formulation, it is shown that the four-rank spinor representing the Maxwell field tensor has a U(1 local gauge invariance in terms of the electric and magnetic field strengths. When applied to the magnetic field of a monopole, this formulation, via the irreducible representation condition for the gauge group, leads to a quantization condition differing by a factor 2 of the one predicted by Dirac without relying on any kind of singular vector potentials. Finally, the U(1 invariant spinor equations, are applied to electron magnetic resonance which has many applications in the study of materials. Keywords: Weyl 2-spinor lenguage, Dirac equation, Gauge theories, Charge quantization
Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures
Brakman, C.M.
1986-01-01
Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a
The planar cubic Cayley graphs
Georgakopoulos, Agelos
2018-01-01
The author obtains a complete description of the planar cubic Cayley graphs, providing an explicit presentation and embedding for each of them. This turns out to be a rich class, comprising several infinite families. He obtains counterexamples to conjectures of Mohar, Bonnington and Watkins. The author's analysis makes the involved graphs accessible to computation, corroborating a conjecture of Droms.
On the intersection of irreducible components of the space of finite-dimensional Lie algebras
International Nuclear Information System (INIS)
Gorbatsevich, Vladimir V
2012-01-01
The irreducible components of the space of n-dimensional Lie algebras are investigated. The properties of Lie algebras belonging to the intersection of all the irreducible components of this kind are studied (these Lie algebras are said to be basic or founding Lie algebras). It is proved that all Lie algebras of this kind are nilpotent and each of these Lie algebras has an Abelian ideal of codimension one. Specific examples of founding Lie algebras of arbitrary dimension are described and, to describe the Lie algebras in general, we state a conjecture. The concept of spectrum of a Lie algebra is considered and some of the most elementary properties of the spectrum are studied. Bibliography: 6 titles.
Irreducible Representations of Oscillatory and Swirling Flows in Active Soft Matter
Ghose, Somdeb; Adhikari, R.
2014-03-01
Recent experiments imaging fluid flow around swimming microorganisms have revealed complex time-dependent velocity fields that differ qualitatively from the stresslet flow commonly employed in theoretical descriptions of active matter. Here we obtain the most general flow around a finite sized active particle by expanding the surface stress in irreducible Cartesian tensors. This expansion, whose first term is the stresslet, must include, respectively, third-rank polar and axial tensors to minimally capture crucial features of the active oscillatory flow around translating Chlamydomonas and the active swirling flow around rotating Volvox. The representation provides explicit expressions for the irreducible symmetric, antisymmetric, and isotropic parts of the continuum active stress. Antisymmetric active stresses do not conserve orbital angular momentum and our work thus shows that spin angular momentum is necessary to restore angular momentum conservation in continuum hydrodynamic descriptions of active soft matter.
Baryonic sources using irreducible representations of the double-covered octahedral group
International Nuclear Information System (INIS)
Basak, S.; Edwards, R.; Fiebig, R.; Fleming, G.T.; Heller, U.M.; Morningstar, C.; Richards, D.; Sato, I.; Wallace, S.
2005-01-01
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation
On the mixed symmetry irreducible representations of the Poincare group in the BRST approach
International Nuclear Information System (INIS)
Burdik, C.; Pashnev, A.; Tsulaya, M.
2001-01-01
The Lagrangian description of irreducible massless representations of the Poincare group with the corresponding Young tableaux having two rows along with some explicit examples including the notoph and Weyl tensor is given. For this purpose the method of the BRST constructions is used adopted to the systems of the second class constraints by the construction of auxiliary representations of the algebras of constraints in terms of Verma modules
A bound for the Schur index of irreducible representations of finite groups
Energy Technology Data Exchange (ETDEWEB)
Kiselev, D D [M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow (Russian Federation)
2013-08-31
We construct an optimal bound for the Schur index of irreducible complex representations of finite groups over the field of rational numbers, when only the prime divisors of the order of the group are known. We study relationships with compatible and universally compatible extensions of number fields. We give a simpler proof of the well-known Berman-Yamada bound for the Schur index over the field Q{sub p}. Bibliography: 7 titles.
Baryonic sources using irreducible representations of the double-covered octahedral group
International Nuclear Information System (INIS)
Basak, S.; Edwards, R.; Fiebig, R.; Fleming, G. T.; Heller, U. M.; Morningstar, C.; Richards, D.; Sato, I.; Wallace, S.
2004-01-01
Irreducible representations (IRs) of the double-covered octahedral group are used to construct lattice source and sink operators for three-quark baryons. The goal is to achieve a good coupling to higher spin states as well as ground states. Complete sets of local and nonlocal straight-link operators are explicitly shown for isospin 1/2 and 3/2 baryons. The orthogonality relations of the IR operators are confirmed in a quenched lattice simulation
Analytic vectors and irreducible representations of nilpotent Lie groups and algebras
International Nuclear Information System (INIS)
Arnal, D.
1978-01-01
Let U be a unitary irreducible locally faithful representation of a nilpotent Lie group G, V the universal enveloping algebra of G, M a simple module on V with kernel ker dU, then there exists an automorphism of V keeping ker dU invariant such that, after transport of structure, M is isomorphic to a submodule of the space of analytic vectors for U. (Auth.)
Directory of Open Access Journals (Sweden)
Morteza Nakhaei Amroodi
2015-11-01
Full Text Available Background: Although anterior shoulder dislocation is the most prevalent type of body dislocation, irreducible anterior shoulder dislocation is seldom reported in the literature, which is usually due to physical obstacles. Objectives: This study presents our findings regarding the causes of irreducibility of anterior shoulder dislocation associated with displaced fracture of the greater tuberosity. Patients and Methods: CT scans, open reduction of the joint, and internal fixation of the tuberosity was performed in seven patients with irreducible anterior shoulder dislocation associated with displaced fracture of the greater tuberosity. Results: As confirmed by intraoperative findings, the CT scans showed the cause of irreducible shoulder dislocation in six cases was the interposition of the long head of biceps (LHB in the anterior of the head that was displaced from the fracture line between the greater and lesser tuberosities. In another case, the greater and lesser tuberosities were attached to each other and were separated from the head. This fractured part was trapped. Conclusions: We suggest that performing CT scans in all cases of anterior shoulder dislocations with displaced fracture of the greater tuberosity can help surgeons to diagnose the accompanying fractures and possible complications, such as irreducibility. If the fracture line passes through the bicipital groove or in the case of a shield fracture, possible irreducibility should be borne in mind.
Numbers for reducible cubic scrolls
Directory of Open Access Journals (Sweden)
Israel Vainsencher
2004-12-01
Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.
Randomized Block Cubic Newton Method
Doikov, Nikita; Richtarik, Peter
2018-01-01
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\cal O}(1/\\epsilon)$, ${\\cal O}(1/\\sqrt{\\epsilon})$ and ${\\cal O}(\\log (1/\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.
Randomized Block Cubic Newton Method
Doikov, Nikita
2018-02-12
We study the problem of minimizing the sum of three convex functions: a differentiable, twice-differentiable and a non-smooth term in a high dimensional setting. To this effect we propose and analyze a randomized block cubic Newton (RBCN) method, which in each iteration builds a model of the objective function formed as the sum of the natural models of its three components: a linear model with a quadratic regularizer for the differentiable term, a quadratic model with a cubic regularizer for the twice differentiable term, and perfect (proximal) model for the nonsmooth term. Our method in each iteration minimizes the model over a random subset of blocks of the search variable. RBCN is the first algorithm with these properties, generalizing several existing methods, matching the best known bounds in all special cases. We establish ${\\\\cal O}(1/\\\\epsilon)$, ${\\\\cal O}(1/\\\\sqrt{\\\\epsilon})$ and ${\\\\cal O}(\\\\log (1/\\\\epsilon))$ rates under different assumptions on the component functions. Lastly, we show numerically that our method outperforms the state-of-the-art on a variety of machine learning problems, including cubically regularized least-squares, logistic regression with constraints, and Poisson regression.
INVESTIGATION OF CURVES SET BY CUBIC DISTRIBUTION OF CURVATURE
Directory of Open Access Journals (Sweden)
S. A. Ustenko
2014-03-01
Full Text Available Purpose. Further development of the geometric modeling of curvelinear contours of different objects based on the specified cubic curvature distribution and setpoints of curvature in the boundary points. Methodology. We investigate the flat section of the curvilinear contour generating under condition that cubic curvature distribution is set. Curve begins and ends at the given points, where angles of tangent slope and curvature are also determined. It was obtained the curvature equation of this curve, depending on the section length and coefficient c of cubic curvature distribution. The analysis of obtained equation was carried out. As well as, it was investigated the conditions, in which the inflection points of the curve are appearing. One should find such an interval of parameter change (depending on the input data and the section length, in order to place the inflection point of the curvature graph outside the curve section borders. It was determined the dependence of tangent slope of angle to the curve at its arbitrary point, as well as it was given the recommendations to solve a system of integral equations that allow finding the length of the curve section and the coefficient c of curvature cubic distribution. Findings. As the result of curves research, it is found that the criterion for their selection one can consider the absence of inflection points of the curvature on the observed section. Influence analysis of the parameter c on the graph of tangent slope angle to the curve showed that regardless of its value, it is provided the same rate of angle increase of tangent slope to the curve. Originality. It is improved the approach to geometric modeling of curves based on cubic curvature distribution with its given values at the boundary points by eliminating the inflection points from the observed section of curvilinear contours. Practical value. Curves obtained using the proposed method can be used for geometric modeling of curvilinear
Cubic colloids : Synthesis, functionalization and applications
Castillo, S.I.R.
2015-01-01
This thesis is a study on cubic colloids: micron-sized cubic particles with rounded corners (cubic superballs). Owing to their shape, particle packing for cubes is more efficient than for spheres and results in fascinating phase and packing behavior. For our cubes, the particle volume fraction when
Algebraic limit cycles in polynomial systems of differential equations
International Nuclear Information System (INIS)
Llibre, Jaume; Zhao Yulin
2007-01-01
Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4
International Nuclear Information System (INIS)
Bros, J.
1984-01-01
An account is given of the present status of many-particle structure analysis in the general framework of massive quantum field theory. Two main questions are discussed, namely: i) the equivalence between the asymptotic completeness of a field and the r-particle irreducibility of associated Bether-Salpeter type kernels; ii) the derivation of extended analyticity properties of the Green functions and multiparticle collision amplitudes around the corresponding physical regions. Substantial results concerning the 3→3 particle processes are described. An analogous multiparticle version of these results yields a partial understanding of the general case
On the geometry of certain irreducible non-torus plane sextics
DEFF Research Database (Denmark)
Eyral, Christophe; Oka, Mutsuo
2009-01-01
An irreducible non-torus plane sextic with simple singularities is said to be special if its fundamental group factors to a dihedral group. There exist (exactly) ten configurations of simple singularities that are realizable by such curves. Among them, six are realizable by non-special sextics...... as well. We conjecture that for each of these six configurations there always exists a non-special curve whose fundamental group is abelian, and we prove this conjecture for three configurations (another one has already been treated in one of our previous papers). As a corollary, we obtain new explicit...
Cubic metaplectic forms and theta functions
Proskurin, Nikolai
1998-01-01
The book is an introduction to the theory of cubic metaplectic forms on the 3-dimensional hyperbolic space and the author's research on cubic metaplectic forms on special linear and symplectic groups of rank 2. The topics include: Kubota and Bass-Milnor-Serre homomorphisms, cubic metaplectic Eisenstein series, cubic theta functions, Whittaker functions. A special method is developed and applied to find Fourier coefficients of the Eisenstein series and cubic theta functions. The book is intended for readers, with beginning graduate-level background, interested in further research in the theory of metaplectic forms and in possible applications.
Cathodoluminescence of cubic boron nitride
International Nuclear Information System (INIS)
Tkachev, V.D.; Shipilo, V.B.; Zajtsev, A.M.
1985-01-01
Three optically active defects are detected in mono- and polycrystal cubic boron nitride (β-BN). Analysis of intensity of temperature dependences, halfwidth and energy shift of 1.76 eV narrow phononless line (center GC-1) makes it possible to interprete the observed cathodoluminescence spectra an optical analog of the Moessbaner effect. Comparison of the obtained results with the known data for diamond monocrystals makes it possible to suggest that the detected center GC-1 is a nitrogen vacancy . The conclusion, concerning the Moessbauer optical spectra application, is made to analyze structural perfection of β-BN crystal lattice
Simplifying Differential Equations for Multiscale Feynman Integrals beyond Multiple Polylogarithms.
Adams, Luise; Chaubey, Ekta; Weinzierl, Stefan
2017-04-07
In this Letter we exploit factorization properties of Picard-Fuchs operators to decouple differential equations for multiscale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the irreducible factors of the Picard-Fuchs operator. As a side product, our method can be used to easily convert the differential equations for Feynman integrals which evaluate to multiple polylogarithms to an ϵ form.
Multi-dimensional cubic interpolation for ICF hydrodynamics simulation
International Nuclear Information System (INIS)
Aoki, Takayuki; Yabe, Takashi.
1991-04-01
A new interpolation method is proposed to solve the multi-dimensional hyperbolic equations which appear in describing the hydrodynamics of inertial confinement fusion (ICF) implosion. The advection phase of the cubic-interpolated pseudo-particle (CIP) is greatly improved, by assuming the continuities of the second and the third spatial derivatives in addition to the physical value and the first derivative. These derivatives are derived from the given physical equation. In order to evaluate the new method, Zalesak's example is tested, and we obtain successfully good results. (author)
A new look at the free electromagnetic field. The Gauss law as a hamiltonian equation of motion
International Nuclear Information System (INIS)
Aldaya, V.; Navarro-Salas, J.
1992-01-01
A new canonical formalism for the free electromagnetic field is proposed in terms of an infinite-dimensional Lie group. The Gauss law is derived as a hamiltonian equation of motion and the quantum theory is obtained by constructing the irreducible representation of the group. The quantum Gauss law thus appears as an additional polarization equation and not as a constraint equation. (orig.)
Cathodoluminescence of cubic boron nitride
International Nuclear Information System (INIS)
Tkachev, V.D.; Shipilo, V.B.; Zaitsev, A.M.
1985-01-01
Three types of optically active defect were observed in single-crystal and polycrystalline cubic boron nitride (β-BN). An analysis of the temperature dependences of the intensity, half-width, and energy shift of a narrow zero-phonon line at 1.76 eV (GC-1 center) made it possible to interpret the observed cathodoluminescence spectra as an optical analog of the Moessbauer effect. A comparison of the results obtained in the present study with the available data on diamond single crystals made it possible to identify the observed GC-1 center as a nitrogen vacancy. It was concluded that optical Moessbauer-type spectra can be used to analyze structure defects in the crystal lattice of β-BN
Martensitic cubic → tetragonal transition
International Nuclear Information System (INIS)
Schumann, H.
1983-01-01
Indium-thallium alloys containing 14 to 30% At. Tl have a cubic face-centred beta phase wich changes into a tetragonal face-centred alpha martensite during solidification. The martensite contains twin crystals that are large enough to be seen by means of a light microscope. The phenomenological crystallographic martensite theory was used to calculate Miller's index of the habit plane, the formation of the surface relief, the orientation relations and the critical thickness ratio of the twins. In a beta monocrystal frequently only one of the 24 crystallographic possible habit planes are formed at one end of the sample and migrate through the whole crystal when the temperature drops. Externally applied tension and compression influence in different ways the direction in which the habit plane moves and can even destroy the twinned structure, i.e. they can modify the substructure of the martensite crystal. This induces superelasticity, an effect that has also been described quantitatively. (author)
Searching dependency between algebraic equations: An algorithm applied to automated reasoning
International Nuclear Information System (INIS)
Yang Lu; Zhang Jingzhong
1990-01-01
An efficient computer algorithm is given to decide how many branches of the solution to a system of algebraic also solve another equation. As one of the applications, this can be used in practice to verify a conjecture with hypotheses and conclusion expressed by algebraic equations, despite the variety of reducible or irreducible. (author). 10 refs
Eliminating cubic terms in the pseudopotential lattice Boltzmann model for multiphase flow
Huang, Rongzong; Wu, Huiying; Adams, Nikolaus A.
2018-05-01
It is well recognized that there exist additional cubic terms of velocity in the lattice Boltzmann (LB) model based on the standard lattice. In this work, elimination of these cubic terms in the pseudopotential LB model for multiphase flow is investigated, where the force term and density gradient are considered. By retaining high-order (≥3 ) Hermite terms in the equilibrium distribution function and the discrete force term, as well as introducing correction terms in the LB equation, the additional cubic terms of velocity are entirely eliminated. With this technique, the computational simplicity of the pseudopotential LB model is well maintained. Numerical tests, including stationary and moving flat and circular interface problems, are carried out to show the effects of such cubic terms on the simulation of multiphase flow. It is found that the elimination of additional cubic terms is beneficial to reduce the numerical error, especially when the velocity is relatively large. Numerical results also suggest that these cubic terms mainly take effect in the interfacial region and that the density-gradient-related cubic terms are more important than the other cubic terms for multiphase flow.
Irreducibility and Computational Equivalence 10 Years After Wolfram's A New Kind of Science
2013-01-01
It is clear that computation is playing an increasingly prominent role in the development of mathematics, as well as in the natural and social sciences. The work of Stephen Wolfram over the last several decades has been a salient part in this phenomenon helping founding the field of Complex Systems, with many of his constructs and ideas incorporated in his book A New Kind of Science (ANKS) becoming part of the scientific discourse and general academic knowledge--from the now established Elementary Cellular Automata to the unconventional concept of mining the Computational Universe, from today's widespread Wolfram's Behavioural Classification to his principles of Irreducibility and Computational Equivalence. This volume, with a Foreword by Gregory Chaitin and an Afterword by Cris Calude, covers these and other topics related to or motivated by Wolfram's seminal ideas, reporting on research undertaken in the decade following the publication of Wolfram's NKS book. Featuring 39 authors, its 23 contributions are o...
International Nuclear Information System (INIS)
Wang Fan; Chen Zhida
2006-01-01
A new strategy to search for the good quantum numbers for the corner-sharing spin systems, as archetypal plaquettes of the lattices, was suggested for the first time in order to study on geometric spin frustration. The calculations on energy spectra by using the irreducible tensor operator method with the new strategy can be much reduced. As representative examples the energy spectra for the spin pentamer of the tetrahedron with a centered spin site and the spin heptamer of three corner-sharing equilateral-triangle were examined in order to confirm efficiency of the new strategy. Through our code, with automatically searching for the good quantum numbers, the projection operators S iz , S ix and S iy matrices in the ground state space for the spin heptamer were reliably constructed
Pryadko, Leonid P.; Dumer, Ilya; Kovalev, Alexey A.
2015-03-01
We construct a lower (existence) bound for the threshold of scalable quantum computation which is applicable to all stabilizer codes, including degenerate quantum codes with sublinear distance scaling. The threshold is based on enumerating irreducible operators in the normalizer of the code, i.e., those that cannot be decomposed into a product of two such operators with non-overlapping support. For quantum LDPC codes with logarithmic or power-law distances, we get threshold values which are parametrically better than the existing analytical bound based on percolation. The new bound also gives a finite threshold when applied to other families of degenerate quantum codes, e.g., the concatenated codes. This research was supported in part by the NSF Grant PHY-1416578 and by the ARO Grant W911NF-11-1-0027.
Radial head button holing: a cause of irreducible anterior radial head dislocation
Energy Technology Data Exchange (ETDEWEB)
Shin, Su-Mi; Chai, Jee Won; You, Ja Yeon; Park, Jina [Seoul National University Seoul Metropolitan Government Boramae Medical Center, Department of Radiology, Seoul (Korea, Republic of); Bae, Kee Jeong [Seoul National University Seoul Metropolitan Government Boramae Medical Center, Department of Orthopedic Surgery, Seoul (Korea, Republic of)
2016-10-15
''Buttonholing'' of the radial head through the anterior joint capsule is a known cause of irreducible anterior radial head dislocation associated with Monteggia injuries in pediatric patients. To the best of our knowledge, no report has described an injury consisting of buttonholing of the radial head through the annular ligament and a simultaneous radial head fracture in an adolescent. In the present case, the radiographic findings were a radial head fracture with anterior dislocation and lack of the anterior fat pad sign. Magnetic resonance imaging (MRI) clearly demonstrated anterior dislocation of the fractured radial head through the torn annular ligament. The anterior joint capsule and proximal portion of the annular ligament were interposed between the radial head and capitellum, preventing closed reduction of the radial head. Familiarity with this condition and imaging findings will aid clinicians to make a proper diagnosis and fast decision to perform an open reduction. (orig.)
Wu, Bofeng; Huang, Chao-Guang
2018-04-01
The 1 /r expansion in the distance to the source is applied to the linearized f (R ) gravity, and its multipole expansion in the radiation field with irreducible Cartesian tensors is presented. Then, the energy, momentum, and angular momentum in the gravitational waves are provided for linearized f (R ) gravity. All of these results have two parts, which are associated with the tensor part and the scalar part in the multipole expansion of linearized f (R ) gravity, respectively. The former is the same as that in General Relativity, and the latter, as the correction to the result in General Relativity, is caused by the massive scalar degree of freedom and plays an important role in distinguishing General Relativity and f (R ) gravity.
Experimental test of the irreducible four-qubit Greenberger-Horne-Zeilinger paradox
Su, Zu-En; Tang, Wei-Dong; Wu, Dian; Cai, Xin-Dong; Yang, Tao; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Żukowski, Marek; Pan, Jian-Wei
2017-03-01
The paradox of Greenberger-Horne-Zeilinger (GHZ) disproves directly the concept of EPR elements of reality, based on the EPR correlations, in an all-versus-nothing way. A three-qubit experimental demonstration of the GHZ paradox was achieved nearly 20 years ago, followed by demonstrations for more qubits. Still, the GHZ contradictions underlying the tests can be reduced to a three-qubit one. We show an irreducible four-qubit GHZ paradox, and report its experimental demonstration. The bound of a three-setting-per-party Bell-GHZ inequality is violated by 7 σ . The fidelity of the GHZ state was around 81 % , and an entanglement witness reveals a violation of the separability threshold by 19 σ .
Topics in Cubic Special Geometry
Bellucci, Stefano; Roychowdhury, Raju
2011-01-01
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one) can be introduced or removed through suitable, lower unitriangular symplectic transformations, dubbed Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to the d=4 U-duality group G4, in symmetric cases they generally have a non-trivial action on the unique quartic invariant polynomial I4 of the charge representation R of G4. This leads to interesting phenomena in relation to theory of extremal black hole attractors; namely, the possibility to make transitions between different charge orbits of R, with corresponding change of the supersymmetry properties of the supported attractor solutions. Furthermore, a suitable action of PQ transformations can also set I4 to zero, or vice versa it can generate a non-vanishing I4: this corresponds to transitions between "large" and "small" charge orbit...
Cubical local partial orders on cubically subdivided spaces - existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
The geometric models of Higher Dimensional Automata and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes, such ...... that the underlying geometry of an HDA may be quite complicated....
Cubical local partial orders on cubically subdivided spaces - Existence and construction
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
2006-01-01
The geometric models of higher dimensional automata (HDA) and Dijkstra's PV-model are cubically subdivided topological spaces with a local partial order. If a cubicalization of a topological space is free of immersed cubic Möbius bands, then there are consistent choices of direction in all cubes...... that the underlying geometry of an HDA may be quite complicated....
Analysis of moderately thin-walled beam cross-sections by cubic isoparametric elements
DEFF Research Database (Denmark)
Høgsberg, Jan Becker; Krenk, Steen
2014-01-01
In technical beam theory the six equilibrium states associated with homogeneous tension, bending, shear and torsion are treated as individual load cases. This enables the formulation of weak form equations governing the warping from shear and torsion. These weak form equations are solved...... numerically by introducing a cubic-linear two-dimensional isoparametric element. The cubic interpolation of this element accurately represents quadratic shear stress variations along cross-section walls, and thus moderately thin-walled cross-sections are effectively discretized by these elements. The ability...
The cyclicity of a cubic system with nonradical Bautin ideal
Levandovskyy, Viktor; Romanovski, Valery G.; Shafer, Douglas S.
We present a method for investigating the cyclicity of an elementary focus or center of a polynomial system of differential equations by means of complexification of the system and application of algorithms of computational algebra, showing an approach to treating the case that the Bautin ideal B of focus quantities is not a radical ideal (more precisely, when the ideal B is not radical, where B is the ideal generated by the shortest initial string of focus quantities that, like the Bautin ideal, determines the center variety). We illustrate the method with a family of cubic systems.
Bistable Helmholtz solitons in cubic-quintic materials
International Nuclear Information System (INIS)
Christian, J. M.; McDonald, G. S.; Chamorro-Posada, P.
2007-01-01
We propose a nonlinear Helmholtz equation for modeling the evolution of broad optical beams in media with a cubic-quintic intensity-dependent refractive index. This type of nonlinearity is appropriate for some semiconductor materials, glasses, and polymers. Exact analytical soliton solutions are presented that describe self-trapped nonparaxial beams propagating at any angle with respect to the reference direction. These spatially symmetric solutions are, to the best of our knowledge, the first bistable Helmholtz solitons to be derived. Accompanying conservation laws (both integral and particular forms) are also reported. Numerical simulations investigate the stability of the solitons, which appear to be remarkably robust against perturbations
Cubical sets as a classifying topos
DEFF Research Database (Denmark)
Spitters, Bas
Coquand’s cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. We show that the underlying cube category is the opposite of the Lawvere theory of De...... Morgan algebras. The topos of cubical sets itself classifies the theory of ‘free De Morgan algebras’. This provides us with a topos with an internal ‘interval’. Using this interval we construct a model of type theory following van den Berg and Garner. We are currently investigating the precise relation...
Efimova, Olga Yu.
2010-01-01
The modification of simplest equation method to look for exact solutions of nonlinear partial differential equations is presented. Using this method we obtain exact solutions of generalized Korteweg-de Vries equation with cubic source and exact solutions of third-order Kudryashov-Sinelshchikov equation describing nonlinear waves in liquids with gas bubbles.
Modeling the dispersion of atmospheric pollution using cubic splines and chapeau functions
Energy Technology Data Exchange (ETDEWEB)
Pepper, D W; Kern, C D; Long, P E
1979-01-01
Two methods that can be used to solve complex, three-dimensional, advection-diffusion transport equations are investigated. A quasi-Lagrangian cubic spline method and a chapeau function method are compared in advecting a passive scalar. The methods are simple to use, computationally fast, and reasonably accurate. Little numerical dissipation is manifested by the schemes. In simple advection tests with equal mesh spacing, the chapeau function method maintains slightly more accurate peak values than the cubic spline method. In tests with unequal mesh spacing, the cubic spline method has less noise, but slightly more damping than the standard chapeau method has. Both cubic splines and chapeau functions can be used to solve the three-dimensional problem of gaseous emissions dispersion without excessive programing complexity or storage requirements. (10 diagrams, 39 references, 2 tables)
Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier
DEFF Research Database (Denmark)
Neumeyer, Stefan; Sorokin, Vladislav; Thomsen, Jon Juel
2016-01-01
We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing–Mathieu equation with appended quadratic nonlinearity is considered as the model system......, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic...... nonlinearities may generate additional amplitude–frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi...
A Note on Cubic Convolution Interpolation
Meijering, E.; Unser, M.
2003-01-01
We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.
Cubical version of combinatorial differential forms
DEFF Research Database (Denmark)
Kock, Anders
2010-01-01
The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry.......The theory of combinatorial differential forms is usually presented in simplicial terms. We present here a cubical version; it depends on the possibility of forming affine combinations of mutual neighbour points in a manifold, in the context of synthetic differential geometry....
Ober, Ciprian-Andrei; Peștean, Cosmin Petru; Bel, Lucia Victoria; Taulescu, Marian; Cătoi, Cornel; Bogdan, Sidonia; Milgram, Joshua; Schwarz, Guenter; Oana, Liviu Ioan
2016-09-22
True vaginal prolapse is a rare condition in dogs and it is occasionally observed in animals with constipation, dystocia, or forced separation during breeding. If a true prolapse occurs, the bladder, the uterine body and/or distal part of the colon, may be present in the prolapse. A 2-year-old intact non pregnant Central Asian Shepherd dog in moderate condition, was presented for a true vaginal and rectal prolapse. The prolapses were confirmed by physical examination and ultrasonography. Herniation of the urinary bladder was identified within the vaginal prolapse. The necrotic vaginal wall was resected, the urinary bladder was reduced surgically and fixed to the right abdominal wall to prevent recurrence. Rectal resection and anastomosis was necessary to correct the rectal prolapse. Recurrence of the prolapses was not observed and the dog recovered completely after the surgical treatment. In our opinion, extreme tenesmus arising from constipation may have predisposed to the vaginal prolapse with bladder incarceration and secondarily to rectal prolapse. In the young female dog, true vaginal prolapse with secondary involvement of the urinary bladder and irreducible rectal prolapse is an exceptionally rare condition.
Directory of Open Access Journals (Sweden)
Michael Brown
2015-11-01
Full Text Available Approximations based on two-particle irreducible (2PI effective actions (also known as Φ-derivable, Cornwall–Jackiw–Tomboulis or Luttinger–Ward functionals depending on context have been widely used in condensed matter and non-equilibrium quantum/statistical field theory because this formalism gives a robust, self-consistent, non-perturbative and systematically improvable approach which avoids problems with secular time evolution. The strengths of 2PI approximations are often described in terms of a selective resummation of Feynman diagrams to infinite order. However, the Feynman diagram series is asymptotic and summation is at best a dangerous procedure. Here we show that, at least in the context of a toy model where exact results are available, the true strength of 2PI approximations derives from their self-consistency rather than any resummation. This self-consistency allows truncated 2PI approximations to capture the branch points of physical amplitudes where adjustments of coupling constants can trigger an instability of the vacuum. This, in effect, turns Dyson's argument for the failure of perturbation theory on its head. As a result we find that 2PI approximations perform better than Padé approximation and are competitive with Borel–Padé resummation. Finally, we introduce a hybrid 2PI–Padé method.
Irreducible Greens' Functions method in the theory of highly correlated systems
International Nuclear Information System (INIS)
Kuzemsky, A.L.
1994-09-01
The self-consistent theory of the correlation effects in Highly Correlated Systems (HCS) is presented. The novel Irreducible Green's Function (IGF) method is discussed in detail for the Hubbard model and random Hubbard model. The interpolation solution for the quasiparticle spectrum, which is valid for both the atomic and band limit is obtained. The (IGF) method permits to calculate the quasiparticle spectra of many-particle systems with the complicated spectra and strong interaction in a very natural and compact way. The essence of the method deeply related to the notion of the Generalized Mean Fields (GMF), which determine the elastic scattering corrections. The inelastic scattering corrections leads to the damping of the quasiparticles and are the main topic of the present consideration. The calculation of the damping has been done in a self-consistent way for both limits. For the random Hubbard model the weak coupling case has been considered and the self-energy operator has been calculated using the combination of the IGF method and Coherent Potential Approximation (CPA). The other applications of the method to the s-f model, Anderson model, Heisenberg antiferromagnet, electron-phonon interaction models and quasiparticle tunneling are discussed briefly. (author). 79 refs
Undecidability and Irreducibility Conditions for Open-Ended Evolution and Emergence.
Hernández-Orozco, Santiago; Hernández-Quiroz, Francisco; Zenil, Hector
2018-01-01
Is undecidability a requirement for open-ended evolution (OEE)? Using methods derived from algorithmic complexity theory, we propose robust computational definitions of open-ended evolution and the adaptability of computable dynamical systems. Within this framework, we show that decidability imposes absolute limits on the stable growth of complexity in computable dynamical systems. Conversely, systems that exhibit (strong) open-ended evolution must be undecidable, establishing undecidability as a requirement for such systems. Complexity is assessed in terms of three measures: sophistication, coarse sophistication, and busy beaver logical depth. These three complexity measures assign low complexity values to random (incompressible) objects. As time grows, the stated complexity measures allow for the existence of complex states during the evolution of a computable dynamical system. We show, however, that finding these states involves undecidable computations. We conjecture that for similar complexity measures that assign low complexity values, decidability imposes comparable limits on the stable growth of complexity, and that such behavior is necessary for nontrivial evolutionary systems. We show that the undecidability of adapted states imposes novel and unpredictable behavior on the individuals or populations being modeled. Such behavior is irreducible. Finally, we offer an example of a system, first proposed by Chaitin, that exhibits strong OEE.
Irreducible kernels and nonperturbative expansions in a theory with pure m -> m interaction
International Nuclear Information System (INIS)
Iagolnitzer, D.
1983-01-01
Recent results on the structure of the S matrix at the m-particle threshold (m>=2) in a simplified m->m scattering theory with no subchannel interaction are extended to the Green function F on the basis of off-shell unitarity, through an adequate mathematical extension of some results of Fredholm theory: local two-sheeted or infinite-sheeted structure of F around s=(mμ) 2 depending on the parity of (m-1) (ν-1) (where μ>0 is the mass and ν is the dimension of space-time), off-shell definition of the irreducible kernel U [which is the analogue of the K matrix in the two different parity cases (m-1)(ν-1) odd or even] and related local expansion of F, for (m-1)(ν-1) even, in powers of sigmasup(β)lnsigma(sigma=(mμ) 2 -s). It is shown that each term in this expansion is the dominant contribution to a Feynman-type integral in which each vertex is a kernel U. The links between kernel U and Bethe-Salpeter type kernels G of the theory are exhibited in both parity cases, as also the links between the above expansion of F and local expansions, in the Bethe-Salpeter type framework, of Fsub(lambda) in terms of Feynman-type integrals in which each vertex is a kernel G and which include both dominant and subdominant contributions. (orig.)
A reliable treatment for nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Khani, F.; Hamedi-Nezhad, S.; Molabahrami, A.
2007-01-01
Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schroedinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation
A modified linear algebraic approach to electron scattering using cubic splines
International Nuclear Information System (INIS)
Kinney, R.A.
1986-01-01
A modified linear algebraic approach to the solution of the Schrodiner equation for low-energy electron scattering is presented. The method uses a piecewise cubic-spline approximation of the wavefunction. Results in the static-potential and the static-exchange approximations for e - +H s-wave scattering are compared with unmodified linear algebraic and variational linear algebraic methods. (author)
DEFF Research Database (Denmark)
Kruger, Francois; Kontogeorgis, Georgios M.; von Solms, Nicolas
2018-01-01
Accurate thermodynamic predictions for systems containing glycols are essential for the design and commissioning of novel subsea natural gas dehydration units. Previously it has been shown that the Cubic-Plus-Association (CPA) equation of state can be used to model VLE, SLE and LLE for mixtures...
Directory of Open Access Journals (Sweden)
Álvaro Duque S.J.
2002-06-01
Full Text Available Las matrices de las representaciones irreducibles de un grupo G se usan para el cómputo de la Transformada Generalizada de Fourier de una función definida en G. Existen muchas otras aplicaciones para las representaciones irreducibles de un grupo. Nosotros elaborarnos un software que calcula las matrices de las representacionesirreducibles del grupo simétrico en la forma serninormal de Young. Este programa corre en el Sistema Algebraico Computacional CoCoA.
On Application of Non-cubic EoS to Compositional Reservoir Simulation
DEFF Research Database (Denmark)
Yan, Wei; Michelsen, Michael Locht; Stenby, Erling Halfdan
Compositional reservoir simulation uses almost exclusively cubic equations of state (EoS) such as the SRK EoS and the PR EoS. This is in contrast with process simulation in the downstream industry where more recent and advanced thermodynamic models are quickly adopted. Many of these models are non-cubic...... EoS, such as the PC-SAFT EoS. A major reason for the use of the conventional cubic EoS in reservoir simulation is the concern over computation time. Flash computation is the most time consuming part in compositional reservoir simulation, and the extra complexity of the non-cubic EoS may significantly...... increase the time consumption. In addition to this, the non-cubic EoS also needs a C7+ characterization. The main advantage of the non-cubic EoS is that it provides for a more accurate descrition of fluid properties, and it is therefore of interest to investigate the computational aspects of using...
Poincare group and relativistic wave equations in 2+1 dimensions
Energy Technology Data Exchange (ETDEWEB)
Gitman, Dmitri M. [Instituto de Fisica, Universidade de Sao Paulo, Sao Paulo, SP (Brazil); Shelepin, A.L. [Moscow Institute of Radio Engenering, Electronics and Automation, Moscow (Russian Federation)
1997-09-07
Using the generalized regular representation, an explicit construction of the unitary irreducible representations of the (2+1)-Poincare group is presented. A detailed description of the angular momentum and spin in 2+1 dimensions is given. On this base the relativistic wave equations for all spins (including fractional) are constructed. (author)
An explicit approximate solution to the Duffing-harmonic oscillator by a cubication method
International Nuclear Information System (INIS)
Belendez, A.; Mendez, D.I.; Fernandez, E.; Marini, S.; Pascual, I.
2009-01-01
The nonlinear oscillations of a Duffing-harmonic oscillator are investigated by an approximated method based on the 'cubication' of the initial nonlinear differential equation. In this cubication method the restoring force is expanded in Chebyshev polynomials and the original nonlinear differential equation is approximated by a Duffing equation in which the coefficients for the linear and cubic terms depend on the initial amplitude, A. The replacement of the original nonlinear equation by an approximate Duffing equation allows us to obtain explicit approximate formulas for the frequency and the solution as a function of the complete elliptic integral of the first kind and the Jacobi elliptic function, respectively. These explicit formulas are valid for all values of the initial amplitude and we conclude this cubication method works very well for the whole range of initial amplitudes. Excellent agreement of the approximate frequencies and periodic solutions with the exact ones is demonstrated and discussed and the relative error for the approximate frequency is as low as 0.071%. Unlike other approximate methods applied to this oscillator, which are not capable to reproduce exactly the behaviour of the approximate frequency when A tends to zero, the cubication method used in this Letter predicts exactly the behaviour of the approximate frequency not only when A tends to infinity, but also when A tends to zero. Finally, a closed-form expression for the approximate frequency is obtained in terms of elementary functions. To do this, the relationship between the complete elliptic integral of the first kind and the arithmetic-geometric mean as well as Legendre's formula to approximately obtain this mean are used.
International Nuclear Information System (INIS)
McGavin, Dennis G; Tennant, W Craighead
2009-01-01
In setting up a spin Hamiltonian (SH) to study high-spin Zeeman and high-spin nuclear and/or electronic interactions in electron paramagnetic resonance (EPR) experiments, it is argued that a maximally reduced SH (MRSH) framed in tesseral combinations of spherical tensor operators is necessary. Then, the SH contains only those terms that are necessary and sufficient to describe the particular spin system. The paper proceeds then to obtain interrelationships between the parameters of the MRSH and those of alternative SHs expressed in Cartesian tensor and Stevens operator-equivalent forms. The examples taken, initially, are those of Cartesian and Stevens' expressions for high-spin Zeeman terms of dimension BS 3 and BS 5 . Starting from the well-known decomposition of the general Cartesian tensor of second rank to three irreducible tensors of ranks 0, 1 and 2, the decomposition of Cartesian tensors of ranks 4 and 6 are treated similarly. Next, following a generalization of the tesseral spherical tensor equations, the interrelationships amongst the parameters of the three kinds of expressions, as derived from equivalent SHs, are determined and detailed tables, including all redundancy equations, set out. In each of these cases the lowest symmetry, 1-bar Laue class, is assumed and then examples of relationships for specific higher symmetries derived therefrom. The validity of a spin Hamiltonian containing mixtures of terms from the three expressions is considered in some detail for several specific symmetries, including again the lowest symmetry. Finally, we address the application of some of the relationships derived here to seldom-observed low-symmetry effects in EPR spectra, when high-spin electronic and nuclear interactions are present.
The Weyl approach to the representation theory of reflection equation algebra
International Nuclear Information System (INIS)
Saponov, P A
2004-01-01
The present paper deals with the representation theory of reflection equation algebra, connected to a Hecke type R-matrix. Up to some reasonable additional conditions, the R-matrix is arbitrary (not necessary originating from quantum groups). We suggest a universal method for constructing finite dimensional irreducible representations in the framework of the Weyl approach well known in the representation theory of classical Lie groups and algebras. With this method a series of irreducible modules is constructed. The modules are parametrized by Young diagrams. The spectrum of central elements s k Tr q L k is calculated in the single-row and single-column representations. A rule for the decomposition of the tensor product of modules into a direct sum of irreducible components is also suggested
Exact optical solitons in (n + 1)-dimensions with anti-cubic nonlinearity
Younis, Muhammad; Shahid, Iram; Anbreen, Sumaira; Rizvi, Syed Tahir Raza
2018-02-01
The paper studies the propagation of optical solitons in (n + 1)-dimensions under anti-cubic law of nonlinearity. The bright, dark and singular optical solitons are extracted using the extended trial equation method. The constraint conditions, for the existence of these solitons, are also listed. Additionally, a couple of other solutions known as singular periodic and Jacobi elliptic solutions, fall out as a by-product of this scheme. The obtained results are new and reported first time in (n + 1)-dimensions with anti-cubic law of nonlinearity.
On the structure of critical energy levels for the cubic focusing NLS on star graphs
International Nuclear Information System (INIS)
Adami, Riccardo; Noja, Diego; Cacciapuoti, Claudio; Finco, Domenico
2012-01-01
We provide information on a non-trivial structure of phase space of the cubic nonlinear Schrödinger (NLS) on a three-edge star graph. We prove that, in contrast to the case of the standard NLS on the line, the energy associated with the cubic focusing Schrödinger equation on the three-edge star graph with a free (Kirchhoff) vertex does not attain a minimum value on any sphere of constant L 2 -norm. We moreover show that the only stationary state with prescribed L 2 -norm is indeed a saddle point. (fast track communication)
Dipaths and dihomotopies in a cubical complex
DEFF Research Database (Denmark)
Fajstrup, Lisbeth
2005-01-01
In the geometric realization of a cubical complex without degeneracies, a $\\Box$-set, dipaths and dihomotopies may not be combinatorial, i.e., not geometric realizations of combinatorial dipaths and equivalences. When we want to use geometric/topological tools to classify dipaths on the 1-skeleton...
Some elements go cubic under pressure
Czech Academy of Sciences Publication Activity Database
Legut, Dominik
2007-01-01
Roč. 60, č. 10 (2007), s. 17-17 ISSN 0031-9228 Institutional research plan: CEZ:AV0Z20410507 Keywords : ab initio * polonium * cubic structure Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 5.133, year: 2007
The Exact Limit of Some Cubic Towers
DEFF Research Database (Denmark)
Anbar Meidl, Nurdagül; Beelen, Peter; Nguyen, Nhut
2017-01-01
Recently, a new explicit tower of function fields was introduced by Bassa, Beelen, Garcia and Stichtenoth (BBGS). This resulted in currently the best known lower bound for Ihara’s constant in the case of non-prime finite fields. In particular over cubic fields, the tower’s limit is at least as go...
Nonrelativistic equations of motion for particles with arbitrary spin
International Nuclear Information System (INIS)
Fushchich, V.I.; Nikitin, A.G.
1981-01-01
First- and second-order Galileo-invariant systems of differential equations which describe the motion of nonrelativistic particles of arbitrary spin are derived. The equations can be derived from a Lagrangian and describe the dipole, quadrupole, and spin-orbit interaction of the particles with an external field; these interactions have traditionally been regarded as purely relativistic effects. The problem of the motion of a nonrelativistic particle of arbitrary spin in a homogeneous magnetic field is solved exactly on the basis of the obtained equations. The generators of all classes of irreducible representations of the Galileo group are found
Neutronics equations: Positiveness; compactness; spectral theory; time asymptotic behavior
International Nuclear Information System (INIS)
Mokhtar-Kharroubi, M.
1987-12-01
Neutronics equations are studied: the continuous model (with and without delayed neutrons) and the multigroup model. Asymptotic descriptions of these equations (t→+∞) are obtained, either by the Dunford method or by using semigroup perturbation techniques, after deriving the spectral theory for the equations. Compactness problems are reviewed, and a general theory of compact injection in neutronic functional space is derived. The effects of positiveness in neutronics are analyzed: the irreducibility of the transport semigroup, and the properties of the main eigenvalue (existence, nonexistence, frame, strict dominance, strict monotony in relation to all the parameters). A class of transport operators whose real spectrum can be completely described is shown [fr
Directory of Open Access Journals (Sweden)
Ioseph L. Buchbinder
2018-01-01
Full Text Available We investigate cubic interactions between a chiral superfield and higher spin superfields corresponding to irreducible representations of the 4 D , N = 1 super-Poincaré algebra. We do this by demanding an invariance under the most general transformation, linear in the chiral superfield. Following Noether’s method we construct an infinite tower of higher spin supercurrent multiplets which are quadratic in the chiral superfield and include higher derivatives. The results are that a single, massless, chiral superfield can couple only to the half-integer spin supermultiplets ( s + 1 , s + 1 / 2 and for every value of spin there is an appropriate improvement term that reduces the supercurrent multiplet to a minimal multiplet which matches that of superconformal higher spins. On the other hand a single, massive, chiral superfield can couple only to higher spin supermultiplets of type ( 2 l + 2 , 2 l + 3 / 2 (only odd values of s, s = 2 l + 1 and there is no minimal multiplet. Furthermore, for the massless case we discuss the component level higher spin currents and provide explicit expressions for the integer and half-integer spin conserved currents together with a R-symmetry current.
International Nuclear Information System (INIS)
Fernandez Nunez, J.; Garcia Fuertes, W.; Perelomov, A.M.
2005-01-01
We reexpress the quantum Calogero-Sutherland model for the Lie algebra E 7 and the particular value of the coupling constant κ=1 by using the fundamental irreducible characters of the algebra as dynamical variables. For that, we need to develop a systematic procedure to obtain all the Clebsch-Gordan series required to perform the change of variables. We describe how the resulting quantum Hamiltonian operator can be used to compute more characters and Clebsch-Gordan series for this exceptional algebra
Electron–soliton dynamics in chains with cubic nonlinearity
International Nuclear Information System (INIS)
Sales, M O; Moura, F A B F de
2014-01-01
In our work, we consider the problem of electronic transport mediated by coupling with solitonic elastic waves. We study the electronic transport in a 1D unharmonic lattice with a cubic interaction between nearest neighboring sites. The electron-lattice interaction was considered as a linear function of the distance between neighboring atoms in our study. We numerically solve the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet. Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the chain. Moreover, we demonstrate that the existence of a mobile electron–soliton pair exhibits a counter-intuitive dependence with the value of the electron-lattice coupling. (paper)
Numerical Simulation of Sloshing Phenomena in Cubic Tank with Multiple Baffles
Directory of Open Access Journals (Sweden)
Mi-An Xue
2012-01-01
Full Text Available A two-phase fluid flow model solving Navier-Stokes equations was employed in this paper to investigate liquid sloshing phenomena in cubic tank with horizontal baffle, perforated vertical baffle, and their combinatorial configurations under the harmonic motion excitation. Laboratory experiment of liquid sloshing in cubic tank with perforated vertical baffle was carried out to validate the present numerical model. Fairly good agreements were obtained from the comparisons between the present numerical results and the present experimental data, available numerical data. Liquid sloshing in cubic tank with multiple baffles was investigated numerically in detail under different external excitation frequencies. Power spectrum of the time series of free surface elevation was presented with the aid of fast Fourier transform technique. The dynamic impact pressures acting on the normal and parallel sidewalls were discussed in detail.
Quasiparticle Interference on Cubic Perovskite Oxide Surfaces.
Okada, Yoshinori; Shiau, Shiue-Yuan; Chang, Tay-Rong; Chang, Guoqing; Kobayashi, Masaki; Shimizu, Ryota; Jeng, Horng-Tay; Shiraki, Susumu; Kumigashira, Hiroshi; Bansil, Arun; Lin, Hsin; Hitosugi, Taro
2017-08-25
We report the observation of coherent surface states on cubic perovskite oxide SrVO_{3}(001) thin films through spectroscopic-imaging scanning tunneling microscopy. A direct link between the observed quasiparticle interference patterns and the formation of a d_{xy}-derived surface state is supported by first-principles calculations. We show that the apical oxygens on the topmost VO_{2} plane play a critical role in controlling the coherent surface state via modulating orbital state.
HRTEM studies of dislocations in cubic BN
International Nuclear Information System (INIS)
Nistor, L.C.; Tendeloo, G. van; Dinca, G.
2004-01-01
The atomic structure of dislocations in cubic boron nitride has been investigated by high resolution transmission electron microscopy. Most of the perfect dislocations, screw and 60 edge, are dissociated. A 60 dislocation which was undissociated has been analysed. Computer simulation is performed in an attempt to characterise the core structure. Twinning dislocations and dislocations resulting from the intersection of stacking faults are also revealed. (copyright 2004 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
HRTEM studies of dislocations in cubic BN
Energy Technology Data Exchange (ETDEWEB)
Nistor, L.C. [National Institute for Materials Physics, P.O. Box MG-7 Magurele, 077125 Bucharest (Romania); Tendeloo, G. van [University of Antwerp, EMAT, Groenenborgerlaan 171, 2020 Antwerp (Belgium); Dinca, G. [Dacia Synthetic Diamond Factory, Timisoara av. 5, P.O. Box 58-52, 077350 Bucharest (Romania)
2004-09-01
The atomic structure of dislocations in cubic boron nitride has been investigated by high resolution transmission electron microscopy. Most of the perfect dislocations, screw and 60 edge, are dissociated. A 60 dislocation which was undissociated has been analysed. Computer simulation is performed in an attempt to characterise the core structure. Twinning dislocations and dislocations resulting from the intersection of stacking faults are also revealed. (copyright 2004 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)
A discussion of the relativistic equal-time equation
International Nuclear Information System (INIS)
Chengrui, Q.; Danhua, Q.
1981-03-01
Ruan Tu-nan et al have proposed an equal-time equation for composite particles which is derived from Bethe-Salpeter (B-S) equation. Its advantage is that the kernel of this equation is a completely definite single rearrangement of the B-S irreducible kernel without any artificial assumptions. In this paper we shall give a further discussion of the properties of this equation. We discuss the behaviour of this equation as the mass of one of the two particles approaches the limit M 2 → infinite in the ladder approximation of single photon exchange. We show that up to order O(α 4 ) this equation is consistent with the Dirac equation. If the crossed two photon exchange diagrams are taken into account the difference between them is of order O(α 6 ). (author)
International Nuclear Information System (INIS)
Horiai, Koui; Uehara, Hiromichi
2011-01-01
Graphical abstract: Available rotational and vibrational-rotational spectral lines of DF and HF are analyzed simultaneously using a non-Born-Oppenheimer effective Hamiltonian. Research highlights: → Simultaneous analysis of DF and HF spectral data. → Application of a non-Born-Oppenheimer effective Hamiltonian. → Twenty irreducible molecular constants for HF have been determined. - Abstract: Analytic expressions of corrections for the breakdown of the Born-Oppenheimer approximation to Dunham's Y ij with optimal parameters, i.e., determinable clusters of expansion coefficients, are applied to a data analysis of the rotational and vibrational-rotational transitions of HF reported in the literature. All the available spectral lines of the two isotopologues, DF and HF, are simultaneously fitted to a single set of molecular parameters of HF within experimental errors. Fitting of a data set of 595 spectral transitions for DF and HF has generated only 20 minimal independent parameter values, i.e., 'irreducible' molecular constants of HF, that are sufficient to precisely generate 82 Y ij coefficients and 144 band constants in total: 41 Y ij and 72 band constants each for DF and HF.
Minimal knotted polygons in cubic lattices
International Nuclear Information System (INIS)
Van Rensburg, E J Janse; Rechnitzer, A
2011-01-01
In this paper we examine numerically the properties of minimal length knotted lattice polygons in the simple cubic, face-centered cubic, and body-centered cubic lattices by sieving minimal length polygons from a data stream of a Monte Carlo algorithm, implemented as described in Aragão de Carvalho and Caracciolo (1983 Phys. Rev. B 27 1635), Aragão de Carvalho et al (1983 Nucl. Phys. B 215 209) and Berg and Foester (1981 Phys. Lett. B 106 323). The entropy, mean writhe, and mean curvature of minimal length polygons are computed (in some cases exactly). While the minimal length and mean curvature are found to be lattice dependent, the mean writhe is found to be only weakly dependent on the lattice type. Comparison of our results to numerical results for the writhe obtained elsewhere (see Janse van Rensburg et al 1999 Contributed to Ideal Knots (Series on Knots and Everything vol 19) ed Stasiak, Katritch and Kauffman (Singapore: World Scientific), Portillo et al 2011 J. Phys. A: Math. Theor. 44 275004) shows that the mean writhe is also insensitive to the length of a knotted polygon. Thus, while these results for the mean writhe and mean absolute writhe at minimal length are not universal, our results demonstrate that these values are quite close the those of long polygons regardless of the underlying lattice and length
A Local Net Volume Equation for Iowa
Jerold T. Hahn
1976-01-01
As a part of the 1974 Forest Survey of Iowa, the Station''s Forst Resources Evaluatioin Research Staff developed a merchantable tree volume equation and tables of coefficients for Iowa. They were developed for both board-foot (International ?-inch rule) and cubic foot volumes, for several species and species groups of growing-stock trees. The equation and...
Neutrosophic Cubic MCGDM Method Based on Similarity Measure
Directory of Open Access Journals (Sweden)
Surapati Pramanik
2017-06-01
Full Text Available The notion of neutrosophic cubic set is originated from the hybridization of the concept of neutrosophic set and interval valued neutrosophic set. We define similarity measure for neutrosophic cubic sets and prove some of its basic properties.
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
Spinning solitons in cubic-quintic nonlinear media ... features of families of bright vortex solitons (doughnuts, or 'spinning' solitons) in both conservative and dissipative cubic-quintic nonlinear media. ... Pramana – Journal of Physics | News.
DEFF Research Database (Denmark)
Arya, Alay; Liang, Xiaodong; von Solms, Nicolas
2017-01-01
Gas injection is a proven enhanced oil recovery technique. The gas injection changes the reservoir oil composition, temperature, and pressure conditions, which may result in asphaltene precipitation. In this work, we have used a modeling approach from the literature in order to predict asphaltene...
A splitting algorithm for the wavelet transform of cubic splines on a nonuniform grid
Sulaimanov, Z. M.; Shumilov, B. M.
2017-10-01
For cubic splines with nonuniform nodes, splitting with respect to the even and odd nodes is used to obtain a wavelet expansion algorithm in the form of the solution to a three-diagonal system of linear algebraic equations for the coefficients. Computations by hand are used to investigate the application of this algorithm for numerical differentiation. The results are illustrated by solving a prediction problem.
Dubbers, Dirk
2013-01-01
This concise tutorial provides the bachelor student and the practitioner with a short text on quantum physics that allows them to understand a wealth of quantum phenomena based on a compact, well readable, yet still concise and accurate description of nonrelativistic quantum theory. This “quadrature of the circle” is achieved by concentrating first on the simplest quantum system that still displays all basic features of quantum theory, namely, a system with only two quantized energy levels. For most readers it is very helpful to understand such simple systems before slowly proceeding to more demanding topics like particle entanglement, quantum chaos, or the use of irreducible tensors. This tutorial does not intend to replace the standard textbooks on quantum mechanics, but will help the average student to understand them, often for the first time.
Correlation and prediction equations for eight-week bodyweight in ...
African Journals Online (AJOL)
Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives ... Cubic; Compound; Power; Sigmoidal; Growth; and Exponential equation. ... logarithmic, inverse, compound, growth and exponential) have significant ...
Application of the CPA equation of state to glycol/hydrocarbons liquid-liquid equilibria
DEFF Research Database (Denmark)
Derawi, Samer; Michelsen, Michael Locht; Kontogeorgis, Georgios
2003-01-01
The Cubic Plus Association (CPA) equation of state is a thermodynamic model, which combines the well-known cubic SRK (Soave-Redlich-Kwong) equation of state and the association term proposed by Wertheim, typically employed in models like SAFT (statistical associating fluid theory). CPA has been...
Directory of Open Access Journals (Sweden)
S.H. Chen
1996-01-01
Full Text Available A modified Lindstedt–Poincaré method is presented for extending the range of the validity of perturbation expansion to strongly nonlinear oscillations of a system with quadratic and cubic nonlinearities. Different parameter transformations are introduced to deal with equations with different nonlinear characteristics. All examples show that the efficiency and accuracy of the present method are very good.
Dlouhy, Brian J; Policeni, Bruno A; Menezes, Arnold H
2017-07-01
OBJECTIVE Os odontoideum (OO) is a craniovertebral junction (CVJ) abnormality in which an ossicle (small bone) is cranial to a hypoplastic dens by a variable gap. This abnormality can result in instability, which may be reducible or irreducible. What leads to irreducibility in OO is unclear. Therefore, the authors sought to better understand the causes of irreducibility in OO. METHODS A retrospective review was conducted, which identified more than 200 patients who had undergone surgical treatment for OO between 1978 and 2015 at the University of Iowa Hospitals and Clinics. Only the 41 patients who had irreducible OO were included in this study. All inpatient and outpatient records were retrospectively reviewed, and patient demographics, clinical presentation, radiographic findings, surgical treatment, and operative findings were recorded and analyzed. RESULTS The cohort of 41 patients who were found to have irreducible OO included both children and adults. A majority of patients were adults (61% were 18 years or older). Clinical presentation included neck pain and headache in the majority of patients (93%). Weakness, sensory disturbances, and myelopathy were invariably present in all 41 patients (100%). Down syndrome was much more common in the pediatric cohort than in the adult cohort; of the 16 pediatric patients, 6 had Down syndrome (38%), and none of the adults did. Of the 16 pediatric patients, 5 had segmentation failure (31%) in the subaxial spine, and none of the adults did. A form of atlantoaxial dislocation was seen in all cases. On CT imaging, atlantoaxial facets were dislocated in all 41 cases but did not have osseous changes that would have prevented reduction. On MRI, the transverse ligament was identified anterior and inferior to the ossicle and superior to the hypoplastic odontoid process in all cases in which these studies were available (i.e., post-MRI era; 36 of 36 cases). The ligament was hypointense on T2-weighted images but also had an
Black holes in a cubic Galileon universe
Energy Technology Data Exchange (ETDEWEB)
Babichev, E.; Charmousis, C.; Lehébel, A.; Moskalets, T., E-mail: eugeny.babichev@th.u-psud.fr, E-mail: christos.charmousis@th.u-psud.fr, E-mail: antoine.lehebel@th.u-psud.fr, E-mail: tetiana.moskalets@th.u-psud.fr [Laboratoire de Physique Théorique, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay (France)
2016-09-01
We find and study the properties of black hole solutions for a subclass of Horndeski theory including the cubic Galileon term. The theory under study has shift symmetry but not reflection symmetry for the scalar field. The Galileon is assumed to have linear time dependence characterized by a velocity parameter. We give analytic 3-dimensional solutions that are akin to the BTZ solutions but with a non-trivial scalar field that modifies the effective cosmological constant. We then study the 4-dimensional asymptotically flat and de Sitter solutions. The latter present three different branches according to their effective cosmological constant. For two of these branches, we find families of black hole solutions, parametrized by the velocity of the scalar field. These spherically symmetric solutions, obtained numerically, are different from GR solutions close to the black hole event horizon, while they have the same de-Sitter asymptotic behavior. The velocity parameter represents black hole primary hair.
Cubic phase control of ultrashort laser pulses
International Nuclear Information System (INIS)
Mecseki, K.; Erdelyi, M.; Kovacs, A.P.; Szabo, G.
2006-01-01
Complete test of publication follows. The temporal shape of an ultrashort laser pulse may change upon propagating through a linear dispersive medium having a phase shift ψω. The change can be characterized by the Taylor-coefficients of the phase shift which are calculated around the central frequency ω 0 of the pulse. Measurements and independent control of the group delay dispersion (GDD, ψ'(ω 0 )) and the third order dispersion (TOD, ψ'(ω 0 )) are important in several research fields, particularly in the generation of ultrashort laser pulses by chirped pulse amplification (CPA) and pulse shaping for molecular control. The GDD and the TOD of an ideal pulse compressor are equal to the negative of the corresponding dispersion coefficients of the medium. However, in the case of prism-pair and grating-pair compressor is different from the ratio of the coefficients of the medium to be compensated for. Therefore it is necessary to develop so-called cubic compressors that are able to control the TOD of the pulse, yet, do not affect the GDD. In this paper a new cubic compressor setup is investigated theoretically and experimentally, which resembles the set-up proposed by White, however, we control the GDD and the TOD by the position of a birefringent, semi-cylinder crystal place around the focal point of an achromatic lens. For the evaluation of the phase shift introduced by the proposed cubic compressor, a ray tracing program was written. The program allows optimizing the compressor parameters, such as the radius of the crystal, magnification of the lens etc. Calcite was applied because it is a strong birefringent material. Calculations showed that there is a trajectory, along which shifting the crystal the TOD can be tuned independently of the GDD. The value of the TOD changed in a relatively wide range between -3.15 x 10 5 fs 3 and -1.67 x 10 5 fs 3 . Although the defocus also affects the angular dispersion of the pulse leaving the compressor, if does not exceed
Cubic martensite in high carbon steel
Chen, Yulin; Xiao, Wenlong; Jiao, Kun; Ping, Dehai; Xu, Huibin; Zhao, Xinqing; Wang, Yunzhi
2018-05-01
A distinguished structural characteristic of martensite in Fe-C steels is its tetragonality originating from carbon atoms occupying only one set of the three available octahedral interstitial sites in the body-centered-cubic (bcc) Fe lattice. Such a body-centered-tetragonal (bct) structure is believed to be thermodynamically stable because of elastic interactions between the interstitial carbon atoms. For such phase stability, however, there has been a lack of direct experimental evidence despite extensive studies of phase transformations in steels over one century. In this Rapid Communication, we report that the martensite formed in a high carbon Fe-8Ni-1.26C (wt%) steel at room temperature induced by applied stress/strain has actually a bcc rather than a bct crystal structure. This finding not only challenges the existing theories on the stability of bcc vs bct martensite in high carbon steels, but also provides insights into the mechanism for martensitic transformation in ferrous alloys.
Expansion into lattice harmonics in cubic symmetries
Kontrym-Sznajd, G.
2018-05-01
On the example of a few sets of sampling directions in the Brillouin zone, this work shows how important the choice of the cubic harmonics is on the quality of approximation of some quantities by a series of such harmonics. These studies led to the following questions: (1) In the case that for a given l there are several independent harmonics, can one use in the expansion only one harmonic with a given l?; (2) How should harmonics be ordered: according to l or, after writing them in terms of (x4 + y4 + z4)n (x2y2z2)m, according to their degree q = n + m? To enable practical applications of such harmonics, they are constructed in terms of the associated Legendre polynomials up to l = 26. It is shown that electron momentum densities, reconstructed from experimental data for ErGa3 and InGa3, are described much better by harmonics ordered with q.
International Nuclear Information System (INIS)
Mittal, R.C.; Rohila, Rajni
2016-01-01
In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.
Mesostructured germanium with cubic pore symmetry
Energy Technology Data Exchange (ETDEWEB)
Armatas, G S; Kanatzidis, M G [Michigan State Univ., Michigan (United States), Dept. of Chemistry
2006-11-15
Regular mesoporous oxide materials have been widely studied and have a range of potential applications, such as catalysis, absorption and separation. They are not generally considered for their optical and electronic properties. Elemental semiconductors with nanopores running through them represent a different form of framework material with physical characteristics contrasting with those of the more conventional bulk, thin film and nanocrystalline forms. Here we describe cubic meso structured germanium, MSU-Ge-l, with gyroidal channels containing surfactant molecules, separated by amorphous walls that lie on the gyroid (G) minimal surface as in the mesoporous silica MCM-48. Although Ge is a high-meltin covalent semiconductor that is difficult to prepare from solution polymerization, we succeeded in assembling a continuous Ge network using a suitable precursor for Ge{sup 4-} atoms. Our results indicate that elemental semiconductors from group 14 of the periodic table can be made to adopt meso structured forms such as MSU-Ge-1, which features two three-dimensional labyrinthine tunnels obeying la3d space group symmetry and separated by a continuous germanium minimal surface that is otherwise amorphous. A consequence of this new structure for germanium, which has walls only one nanometre thick, is a wider electronic energy bandgap (1.4 eV versus 0.66 eV) than has crystalline or amorphous Ge. Controlled oxidation of MSU-Ge-1 creates a range of germanium suboxides with continuously varying Ge:O ratio and a smoothly increasing energy gap. (author)
Topological Oxide Insulator in Cubic Perovskite Structure
Jin, Hosub; Rhim, Sonny H.; Im, Jino; Freeman, Arthur J.
2013-01-01
The emergence of topologically protected conducting states with the chiral spin texture is the most prominent feature at the surface of topological insulators. On the application side, large band gap and high resistivity to distinguish surface from bulk degrees of freedom should be guaranteed for the full usage of the surface states. Here, we suggest that the oxide cubic perovskite YBiO3, more than just an oxide, defines itself as a new three-dimensional topological insulator exhibiting both a large bulk band gap and a high resistivity. Based on first-principles calculations varying the spin-orbit coupling strength, the non-trivial band topology of YBiO3 is investigated, where the spin-orbit coupling of the Bi 6p orbital plays a crucial role. Taking the exquisite synthesis techniques in oxide electronics into account, YBiO3 can also be used to provide various interface configurations hosting exotic topological phenomena combined with other quantum phases. PMID:23575973
International Nuclear Information System (INIS)
Dubbers, Dirk; Stoeckmann, Hans-Juergen
2013-01-01
Helps in a compact form to reach good understanding of quantum physics. Shows important analogies between problems across different disciplines. Concise and accurate, written in a readable and lively style. Concentrates on the simplest quantum system which still displays the basic features of quantum theory. Chapters end with a general outlook on multi-level systems. Results are applied to a multitude of topics in modern science, from particle physics and quantum optics to time standards and magnetic resonance imaging. This concise tutorial provides the bachelor student and the practitioner with a short text on quantum physics that allows them to understand a wealth of quantum phenomena based on a compact, well readable, yet still concise and accurate description of nonrelativistic quantum theory. This ''quadrature of the circle'' is achieved by concentrating first on the simplest quantum system that still displays all basic features of quantum theory, namely, a system with only two quantized energy levels. For most readers it is very helpful to understand such simple systems before slowly proceeding to more demanding topics like particle entanglement, quantum chaos, or the use of irreducible tensors. This tutorial does not intend to replace the standard textbooks on quantum mechanics, but will help the average student to understand them, often for the first time.
Bifurcation of limit cycles for cubic reversible systems
Directory of Open Access Journals (Sweden)
Yi Shao
2014-04-01
Full Text Available This article is concerned with the bifurcation of limit cycles of a class of cubic reversible system having a center at the origin. We prove that this system has at least four limit cycles produced by the period annulus around the center under cubic perturbations
General Reducibility and Solvability of Polynomial Equations ...
African Journals Online (AJOL)
General Reducibility and Solvability of Polynomial Equations. ... Unlike quadratic, cubic, and quartic polynomials, the general quintic and higher degree polynomials cannot be solved algebraically in terms of finite number of additions, ... Galois Theory, Solving Polynomial Systems, Polynomial factorization, Polynomial Ring ...
Energy Technology Data Exchange (ETDEWEB)
Mancas, Stefan C. [Department of Mathematics, Embry–Riddle Aeronautical University, Daytona Beach, FL 32114-3900 (United States); Rosu, Haret C., E-mail: hcr@ipicyt.edu.mx [IPICYT, Instituto Potosino de Investigacion Cientifica y Tecnologica, Apdo Postal 3-74 Tangamanga, 78231 San Luis Potosí, SLP (Mexico)
2013-09-02
We emphasize two connections, one well known and another less known, between the dissipative nonlinear second order differential equations and the Abel equations which in their first-kind form have only cubic and quadratic terms. Then, employing an old integrability criterion due to Chiellini, we introduce the corresponding integrable dissipative equations. For illustration, we present the cases of some integrable dissipative Fisher, nonlinear pendulum, and Burgers–Huxley type equations which are obtained in this way and can be of interest in applications. We also show how to obtain Abel solutions directly from the factorization of second order nonlinear equations.
Kraiem, Hazar; Manon, Yannick; Anne-Archard, Dominique; Fillaudeau, Luc
2012-01-01
During cell cultures in bioreactor, micro-organism physiology closely interacts with physico-chemical parameters (gas and feed flow rates, mixing, temperature, pH, pressure). The specificity of microbial bioreactions in relation with irreducible couplings between heat and mass transfers and fluid mechanics, led into complex (three phases medium) and dynamic (auto-biocatalytic reaction) systems. Our scientific approach aims to investigate, understand and control dynamic interactions between ph...
Vaibhav, V.
2011-04-01
The paper addresses the problem of constructing non-reflecting boundary conditions for two types of one dimensional evolution equations, namely, the cubic nonlinear Schrödinger (NLS) equation, ∂tu+Lu-iχ|u|2u=0 with L≡-i∂x2, and the equation obtained by letting L≡∂x3. The usual restriction of compact support of the initial data is relaxed by allowing it to have a constant amplitude along with a linear phase variation outside a compact domain. We adapt the pseudo-differential approach developed by Antoine et al. (2006) [5] for the NLS equation to the second type of evolution equation, and further, extend the scheme to the aforementioned class of initial data for both of the equations. In addition, we discuss efficient numerical implementation of our scheme and produce the results of several numerical experiments demonstrating its effectiveness.
The matrix nonlinear Schrodinger equation in dimension 2
DEFF Research Database (Denmark)
Zuhan, L; Pedersen, Michael
2001-01-01
In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence is obtained for this equation. This condition is in terms of an exact stationary solution...... of a semilinear elliptic equation. In the scalar case, the MNLS reduces to the well-known cubic nonlinear Schrodinger equation for which existence of solutions has been studied by many authors. (C) 2001 Academic Press....
Optical characterisation of cubic silicon carbide
International Nuclear Information System (INIS)
Jackson, S.M.
1998-09-01
The varied properties of Silicon Carbide (SiC) are helping to launch the material into many new applications, particularly in the field of novel semiconductor devices. In this work, the cubic form of SiC is of interest as a basis for developing integrated optical components. Here, the formation of a suitable SiO 2 buried cladding layer has been achieved by high dose oxygen ion implantation. This layer is necessary for the optical confinement of propagating light, and hence optical waveguide fabrication. Results have shown that optical propagation losses of the order of 20 dB/cm are obtainable. Much of this loss can be attributed to mode leakage and volume scattering. Mode leakage is a function of the effective oxide thickness, and volume scattering related to the surface layer damage. These parameters have been shown to be controllable and so suggests that further reduction in the waveguide loss is feasible. Analysis of the layer growth mechanism by RBS, XTEM and XPS proves that SiO 2 is formed, and that the extent, of formation depends on implant dose and temperature. The excess carbon generated is believed to exit the oxide layer by a number of varying mechanisms. The result of this appears to be a number of stable Si-C-O intermediaries that, form regions to either depth extreme of the SiO 2 layer. Early furnace tests suggest a need to anneal at, temperatures approaching the melting point of the silicon substrate, and that the quality of the virgin material is crucial in controlling the resulting oxide growth. (author)
Neutron Dose Measurement Using a Cubic Moderator
International Nuclear Information System (INIS)
Sheinfeld, M.; Mazor, T.; Cohen, Y.; Kadmon, Y.; Orion, I.
2014-01-01
The Bonner Sphere Spectrometer (BSS), introduced In July 1960 by a research group from Rice University, Texas, is a major approach to neutron spectrum estimation. The BSS, also known as multi-sphere spectrometer, consists of a set of a different diameters polyethylene spheres, carrying a small LiI(Eu) scintillator in their center. What makes this spectrometry method such widely used, is its almost isotropic response, covering an extraordinary wide range of energies, from thermal up to even hundreds of MeVs. One of the most interesting and useful consequences of the above study is the 12'' sphere characteristics, as it turned out that the response curve of its energy dependence, have a similar shape compared with the neutron's dose equivalent as a function of energy. This inexplicable and happy circumstance makes it virtually the only monitoring device capable providing realistic neutron dose estimates over such a wide energy range. However, since the detection mechanism is not strictly related to radiation dose, one can expect substantial errors when applied to widely different source conditions. Although the original design of the BSS included a small 4mmx4mmO 6LiI(Eu) scintillator, other thermal neutron detectors has been used over the years: track detectors, activation foils, BF3 filled proportional counters, etc. In this study we chose a Boron loaded scintillator, EJ-254, as the thermal neutron detector. The neutron capture reaction on the boron has a Q value of 2.78 MeV of which 2.34 MeV is shared by the alpha and lithium particles. The high manufacturing costs, the encasement issue, the installation efficiency and the fabrication complexity, led us to the idea of replacing the sphere with a cubic moderator. This article describes the considerations, as well as the Monte-Carlo simulations done in order to examine the applicability of this idea
DEFF Research Database (Denmark)
Jonasson, Ari Jonas; Persson, Ole Hilding; Rasmussen, Peter
1998-01-01
Isothermal pressure-composition VLE data have been measured for four systems containing acetic acid and a gaseous component. The gaseous components are carbon monoxide, carbon dioxide, hydrogen and methane. The measurements were made in a static cell and the compositions of the gas and the liquid...... phases were measured by a gas chromatograph.A new model (ACE, Association + Cubic Equation of state) was developed. It is based on a cubic equation of state and a model for the dimerization of acetic acid. It was applied to correlate the experimental VLE data with good results....
Gevrey multiscale expansions of singular solutions of PDEs with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Alberto Lastra
2018-02-01
Full Text Available We study a singularly perturbed PDE with cubic nonlinearity depending on a complex perturbation parameter $\\epsilon$. This is a continuation of the precedent work [22] by the first author. We construct two families of sectorial meromorphic solutions obtained as a small perturbation in $\\epsilon$ of two branches of an algebraic slow curve of the equation in time scale. We show that the nonsingular part of the solutions of each family shares a common formal power series in $\\epsilon$ as Gevrey asymptotic expansion which might be different one to each other, in general.
Bounds on Cubic Lorentz-Violating Terms in the Fermionic Dispersion Relation
Bertolami, O.; Rosa, J. G.
2004-01-01
We study the recently proposed Lorentz-violating dispersion relation for fermions and show that it leads to two distinct cubic operators in the momentum. We compute the leading order terms that modify the non-relativistic equations of motion and use experimental results for the hyperfine transition in the ground state of the ${}^9\\textrm Be^+$ ion to bound the values of the Lorentz-violating parameters $\\eta_1$ and $\\eta_2$ for neutrons. The resulting bounds depend on the value of the Lorenz-...
Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes
Energy Technology Data Exchange (ETDEWEB)
Ghodsi, Ahmad; Najafi, Farzaneh [Ferdowsi University of Mashhad, Department of Physics, Mashhad (Iran, Islamic Republic of)
2017-08-15
A special class of higher curvature theories of gravity, Ricci cubic gravity (RCG), in general d dimensional space-time has been investigated in this paper. We have used two different approaches, the linearized equations of motion and the auxiliary field formalism to study the massive and massless graviton propagating modes of the AdS background. Using the auxiliary field formalism, we have found the renormalized boundary stress tensor to compute the mass of the Schwarzschild-AdS and Lifshitz black holes in RCG theory. (orig.)
Motion of a Rigid Rod Rocking Back and Forth Cubic-Quintic Duffing Oscillators
DEFF Research Database (Denmark)
Ganji, S. S.; Barari, Amin; Karimpour, S.
2012-01-01
In this work, we implemented the first-order approximation of the Iteration Perturbation Method (IPM) for approximating the behavior of a rigid rod rocking back and forth on a circular surface without slipping as well as Cubic-Quintic Duffing Oscillators. Comparing the results with the exact...... solution, has led us to significant consequences. The results reveal that the IPM is very effective, simple and convenient to systems of nonlinear equations. It is predicted that IPM can be utilized as a widely applicable approach in engineering....
Etching of semiconductor cubic crystals: Determination of the dissolution slowness surfaces
Tellier, C. R.
1990-03-01
Equations of the representative surface of dissolution slowness for cubic crystals are determined in the framework of a tensorial approach of the orientation-dependent etching process. The independent dissolution constants are deduced from symmetry considerations. Using previous data on the chemical etching of germanium and gallium arsenide crystals, some possible polar diagrams of the dissolution slowness are proposed. A numerical and graphical simulation method is used to obtain the derived dissolution shapes. The influence of extrema in the dissolution slowness on the successive dissolution shapes is also examined. A graphical construction of limiting shapes of etched crystals appears possible using the tensorial representation of the dissolution slowness.
Self-similar optical pulses in competing cubic-quintic nonlinear media with distributed coefficients
International Nuclear Information System (INIS)
Zhang Jiefang; Tian Qing; Wang Yueyue; Dai Chaoqing; Wu Lei
2010-01-01
We present a systematic analysis of the self-similar propagation of optical pulses within the framework of the generalized cubic-quintic nonlinear Schroedinger equation with distributed coefficients. By appropriately choosing the relations between the distributed coefficients, we not only retrieve the exact self-similar solitonic solutions, but also find both the approximate self-similar Gaussian-Hermite solutions and compact solutions. Our analytical and numerical considerations reveal that proper choices of the distributed coefficients could make the unstable solitons stable and could restrict the nonlinear interaction between the neighboring solitons.
On q-power cycles in cubic graphs
DEFF Research Database (Denmark)
Bensmail, Julien
2017-01-01
In the context of a conjecture of Erdos and Gyárfás, we consider, for any q ≥ 2, the existence of q-power cycles (i.e. with length a power of q) in cubic graphs. We exhibit constructions showing that, for every q ≥ 3, there exist arbitrarily large cubic graphs with no q-power cycles. Concerning...... the remaining case q = 2 (which corresponds to the conjecture of Erdos and Gyárfás), we show that there exist arbitrarily large cubic graphs whose only 2-power cycles have length 4 only, or 8 only....
Curvelet-domain multiple matching method combined with cubic B-spline function
Wang, Tong; Wang, Deli; Tian, Mi; Hu, Bin; Liu, Chengming
2018-05-01
Since the large amount of surface-related multiple existed in the marine data would influence the results of data processing and interpretation seriously, many researchers had attempted to develop effective methods to remove them. The most successful surface-related multiple elimination method was proposed based on data-driven theory. However, the elimination effect was unsatisfactory due to the existence of amplitude and phase errors. Although the subsequent curvelet-domain multiple-primary separation method achieved better results, poor computational efficiency prevented its application. In this paper, we adopt the cubic B-spline function to improve the traditional curvelet multiple matching method. First, select a little number of unknowns as the basis points of the matching coefficient; second, apply the cubic B-spline function on these basis points to reconstruct the matching array; third, build constraint solving equation based on the relationships of predicted multiple, matching coefficients, and actual data; finally, use the BFGS algorithm to iterate and realize the fast-solving sparse constraint of multiple matching algorithm. Moreover, the soft-threshold method is used to make the method perform better. With the cubic B-spline function, the differences between predicted multiple and original data diminish, which results in less processing time to obtain optimal solutions and fewer iterative loops in the solving procedure based on the L1 norm constraint. The applications to synthetic and field-derived data both validate the practicability and validity of the method.
Mechanical and Thermophysical Properties of Cubic Rock-Salt AlN Under High Pressure
Lebga, Noudjoud; Daoud, Salah; Sun, Xiao-Wei; Bioud, Nadhira; Latreche, Abdelhakim
2018-03-01
Density functional theory, density functional perturbation theory, and the Debye model have been used to investigate the structural, elastic, sound velocity, and thermodynamic properties of AlN with cubic rock-salt structure under high pressure, yielding the equilibrium structural parameters, equation of state, and elastic constants of this interesting material. The isotropic shear modulus, Pugh ratio, and Poisson's ratio were also investigated carefully. In addition, the longitudinal, transverse, and average elastic wave velocities, phonon contribution to the thermal conductivity, and interesting thermodynamic properties were predicted and analyzed in detail. The results demonstrate that the behavior of the elastic wave velocities under increasing hydrostatic pressure explains the hardening of the corresponding phonons. Based on the elastic stability criteria under pressure, it is found that AlN with cubic rock-salt structure is mechanically stable, even at pressures up to 100 GPa. Analysis of the Pugh ratio and Poisson's ratio revealed that AlN with cubic rock-salt structure behaves in brittle manner.
Singularly perturbed Burger-Huxley equation: Analytical solution ...
African Journals Online (AJOL)
The work presented considers the initial boundary value problem for nonlinear singularly perturbed time dependent Burger- Huxley equation. The equation contains two terms with nonlinearities, the cubic term and the advection term. Generally, the severe difficulties of two types encounter in solving this problem. The first ...
The numerical simulation of convection delayed dominated diffusion equation
Directory of Open Access Journals (Sweden)
Mohan Kumar P. Murali
2016-01-01
Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.
Predicting logging residues: an interim equation for Appalachian oak sawtimber
A. Jeff Martin
1975-01-01
An equation, using dbh, dbh², bole length, and sawlog height to predict the cubic-foot volume of logging residue per tree, was developed from data collected on 36 mixed oaks in southwestern Virginia. The equation produced reliable results for small sawtimber trees, but additional research is needed for other species, sites, and utilization practices.
Creation and annihilation of solitons in the string nonlinear equation
International Nuclear Information System (INIS)
Aguero G, M.A.; Espinosa G, A.A.; Martinez O, J.
1997-01-01
Starting from the cubic-quintic Schroedinger equation it is obtained the nonlinear string equation. This system supports regular and singular solitons. It is shown that two singular solitons could be generated after the interaction of two regular solitons and viceversa. (Author)
Analysis of RIA standard curve by log-logistic and cubic log-logit models
International Nuclear Information System (INIS)
Yamada, Hideo; Kuroda, Akira; Yatabe, Tami; Inaba, Taeko; Chiba, Kazuo
1981-01-01
In order to improve goodness-of-fit in RIA standard analysis, programs for computing log-logistic and cubic log-logit were written in BASIC using personal computer P-6060 (Olivetti). Iterative least square method of Taylor series was applied for non-linear estimation of logistic and log-logistic. Hear ''log-logistic'' represents Y = (a - d)/(1 + (log(X)/c)sup(b)) + d As weights either 1, 1/var(Y) or 1/σ 2 were used in logistic or log-logistic and either Y 2 (1 - Y) 2 , Y 2 (1 - Y) 2 /var(Y), or Y 2 (1 - Y) 2 /σ 2 were used in quadratic or cubic log-logit. The term var(Y) represents squares of pure error and σ 2 represents estimated variance calculated using a following equation log(σ 2 + 1) = log(A) + J log(y). As indicators for goodness-of-fit, MSL/S sub(e)sup(2), CMD% and WRV (see text) were used. Better regression was obtained in case of alpha-fetoprotein by log-logistic than by logistic. Cortisol standard curve was much better fitted with cubic log-logit than quadratic log-logit. Predicted precision of AFP standard curve was below 5% in log-logistic in stead of 8% in logistic analysis. Predicted precision obtained using cubic log-logit was about five times lower than that with quadratic log-logit. Importance of selecting good models in RIA data processing was stressed in conjunction with intrinsic precision of radioimmunoassay system indicated by predicted precision. (author)
Plastic fluctuations in empty crystals formed by cubic wireframe particles
McBride, John M.; Avendaño, Carlos
2018-05-01
We present a computer simulation study of the phase behavior of colloidal hard cubic frames, i.e., particles with nonconvex cubic wireframe geometry interacting purely by excluded volume. Despite the propensity of cubic wireframe particles to form cubic phases akin to their convex counterparts, these particles exhibit unusual plastic fluctuations in which a random and dynamic fraction of particles rotate around their lattice positions in the crystal lattice while the remainder of the particles remains fully ordered. We argue that this unexpected effect stems from the nonconvex geometry of the particles in which the faces of a particle can be penetrated by the vertices of the nearest neighbors even at high number densities.
Bicontinuous cubic liquid crystalline nanoparticles for oral delivery of Doxorubicin
DEFF Research Database (Denmark)
Swarnakar, Nitin K; Thanki, Kaushik; Jain, Sanyog
2014-01-01
PURPOSE: The present study explores the potential of bicontinous cubic liquid crystalline nanoparticles (LCNPs) for improving therapeutic potential of doxorubicin. METHODS: Phytantriol based Dox-LCNPs were prepared using hydrotrope method, optimized for various formulation components, process...
DEFF Research Database (Denmark)
Ekman, Ulrik
2009-01-01
This article argues that Blur Building, Diller & Scofidio's architectural project for the Swiss Expo 2002, demonstrated performatively and interactively how contemporary worldmaking involves cultural and technological invention and construction both, implying our cultural co-evolution with ubiqui......This article argues that Blur Building, Diller & Scofidio's architectural project for the Swiss Expo 2002, demonstrated performatively and interactively how contemporary worldmaking involves cultural and technological invention and construction both, implying our cultural co......-evolution with ubiquitous computing and media such that "worlding" must today be approached and approximated as a question of realities that mix virtuality and actuality. This article not only touches upon the actual inventions produced in this project--with its atmospheric architecture of tensegrity structures, its vast...
Spinor bose gases in cubic optical lattice
International Nuclear Information System (INIS)
Mobarak, Mohamed Saidan Sayed Mohamed
2014-01-01
In recent years the quantum simulation of condensed-matter physics problems has resulted from exciting experimental progress in the realm of ultracold atoms and molecules in optical lattices. In this thesis we analyze theoretically a spinor Bose gas loaded into a three-dimensional cubic optical lattice. In order to account for different superfluid phases of spin-1 bosons with a linear Zeeman effect, we work out a Ginzburg-Landau theory for the underlying spin-1 Bose-Hubbard model. To this end we add artificial symmetry-breaking currents to the spin-1 Bose-Hubbard Hamiltonian in order to break the global U (1) symmetry. With this we determine a diagrammatic expansion of the grand-canonical free energy up to fourth order in the symmetry-breaking currents and up to the leading non-trivial order in the hopping strength which is of first order. As a cross-check we demonstrate that the resulting grand-canonical free energy allows to recover the mean-field theory. Applying a Legendre transformation to the grand-canonical free energy, where the symmetry-breaking currents are transformed to order parameters, we obtain the effective Ginzburg-Landau action. With this we calculate in detail at zero temperature the Mott insulator-superfluid quantum phase boundary as well as condensate and particle number density in the superfluid phase. We find that both mean-field and Ginzburg-Landau theory yield the same quantum phase transition between the Mott insulator and superfluid phases, but the range of validity of the mean-field theory turns out to be smaller than that of the Ginzburg-Landau theory. Due to this finding we expect that the Ginzburg-Landau theory gives better results for the superfluid phase and, thus, we restrict ourselves to extremize only the effective Ginzburg-Landau action with respect to the order parameters. Without external magnetic field the superfluid phase is a polar (ferromagnetic) state for anti-ferromagnetic (ferromagnetic) interactions, i.e. only the
Nanodefects in ultrahard crystalline cubic boron nitride
International Nuclear Information System (INIS)
Nistor, S. V.; Stefan, M.; Goovaerts, E.; Schoemaker, D.
2002-01-01
Cubic boron nitride (cBN), the second hardest known material after diamond, exhibits high thermal conductivity and an excellent ability to be n or p doped, which makes it a strong candidate for the next generation of high-temperature micro optical and micro electronic devices. According to recent studies, cBN exhibits a better resistance to radiation damage than diamond, which suggests potential applications in extreme radiation environments. Crystalline cBN powders of up to 0.5 mm linear size is obtained in a similar way as diamond, by catalytic conversion of hexagonal BN (hBN) to cBN at even higher pressures (> 5GPa) and temperatures (∼ 1900 K). Considering the essential role played by the nanodefects (point defects and impurities) in determining its physical properties, it is surprising how limited is the amount of published data concerning the properties of nanodefects in this material, especially by Electron Paramagnetic Resonance (EPR) spectroscopy, the most powerful method for identification and characterization of nanodefects in both insulators and semiconductors. This seems to be due mainly to the absence of natural cBN gems and the extreme difficulties in producing even mm 3 sized synthetic crystals. We shall present our recent EPR studies on cBN crystalline powders, performed in a broad temperature range from room temperature (RT) down to 1.2 K on several sorts of large size cBN powder grits of yellow and amber color for industrial applications. Previous multifrequency (9.3 GHz and 95 GHz) EPR studies of brown to black cBN crystallites prepared with excess of boron, resulted in the discovery of two new types of paramagnetic point defects with different spectral properties, called the D1 and D2 centers. Our X(9.3 GHz)-band EPR investigations resulted in the observation in amber cBN crystalline powders of a spectrum with a strong temperature dependence of the lineshape. It was found that for high and low temperatures, respectively, the numerical
The Combinatorial Rigidity Conjecture is False for Cubic Polynomials
DEFF Research Database (Denmark)
Henriksen, Christian
2003-01-01
We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995.......We show that there exist two cubic polynomials with connected Julia sets which are combinatorially equivalent but not topologically conjugate on their Julia sets. This disproves a conjecture by McMullen from 1995....
Interaction of dispersed cubic phases with blood components
DEFF Research Database (Denmark)
Bode, J C; Kuntsche, Judith; Funari, S S
2013-01-01
The interaction of aqueous nanoparticle dispersions, e.g. based on monoolein/poloxamer 407, with blood components is an important topic concerning especially the parenteral way of administration. Therefore, the influence of human and porcine plasma on dispersed cubic phases was investigated. Part...... activity of cubic phases based on monoolein and poloxamer 188, on soy phosphatidylcholine, glycerol dioleate and polysorbate 80 or the parenteral fat emulsion Lipofundin MCT 20%....
Solving Linear Differential Equations
Nguyen, K.A.; Put, M. van der
2010-01-01
The theme of this paper is to 'solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field K. Representations of semi-simple Lie algebras and differential Galo is theory are the main tools. The results extend
Transdermal delivery of paeonol using cubic gel and microemulsion gel
Luo, Maofu; Shen, Qi; Chen, Jinjin
2011-01-01
Background The aim of this study was to develop new systems for transdermal delivery of paeonol, in particular microemulsion gel and cubic gel formulations. Methods Various microemulsion vehicles were prepared using isopropyl myristate as an oil phase, polyoxyethylated castor oil (Cremophor® EL) as a surfactant, and polyethylene glycol 400 as a cosurfactant. In the optimum microemulsion gel formulation, carbomer 940 was selected as the gel matrix, and consisted of 1% paeonol, 4% isopropyl myristate, 28% Cremophor EL/polyethylene glycol 400 (1:1), and 67% water. The cubic gel was prepared containing 3% paeonol, 30% water, and 67% glyceryl monooleate. Results A skin permeability test using excised rat skins indicated that both the cubic gel and microemulsion gel formulations had higher permeability than did the paeonol solution. An in vivo pharmacokinetic study done in rats showed that the relative bioavailability of the cubic gel and microemulsion gel was enhanced by about 1.51-fold and 1.28-fold, respectively, compared with orally administered paeonol suspension. Conclusion Both the cubic gel and microemulsion gel formulations are promising delivery systems to enhance the skin permeability of paeonol, in particular the cubic gel. PMID:21904450
International Nuclear Information System (INIS)
Palacios, Sergio L.
2004-01-01
We propose two simple ansaetze that allow us to obtain different analytical solutions of the high dispersive cubic and cubic-quintic nonlinear Schroedinger equations. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media
Partial regularity of weak solutions to a PDE system with cubic nonlinearity
Liu, Jian-Guo; Xu, Xiangsheng
2018-04-01
In this paper we investigate regularity properties of weak solutions to a PDE system that arises in the study of biological transport networks. The system consists of a possibly singular elliptic equation for the scalar pressure of the underlying biological network coupled to a diffusion equation for the conductance vector of the network. There are several different types of nonlinearities in the system. Of particular mathematical interest is a term that is a polynomial function of solutions and their partial derivatives and this polynomial function has degree three. That is, the system contains a cubic nonlinearity. Only weak solutions to the system have been shown to exist. The regularity theory for the system remains fundamentally incomplete. In particular, it is not known whether or not weak solutions develop singularities. In this paper we obtain a partial regularity theorem, which gives an estimate for the parabolic Hausdorff dimension of the set of possible singular points.
Bifurcation of cubic nonlinear parallel plate-type structure in axial flow
International Nuclear Information System (INIS)
Lu Li; Yang Yiren
2005-01-01
The Hopf bifurcation of plate-type beams with cubic nonlinear stiffness in axial flow was studied. By assuming that all the plates have the same deflections at any instant, the nonlinear model of plate-type beam in axial flow was established. The partial differential equation was turned into an ordinary differential equation by using Galerkin method. A new algebraic criterion of Hopf bifurcation was utilized to in our analysis. The results show that there's no Hopf bifurcation for simply supported plate-type beams while the cantilevered plate-type beams has. At last, the analytic expression of critical flow velocity of cantilevered plate-type beams in axial flow and the purely imaginary eigenvalues of the corresponding linear system were gotten. (authors)
Effective evolution equations from quantum mechanics
Leopold, Nikolai
2018-01-01
The goal of this thesis is to provide a mathematical rigorous derivation of the Schrödinger-Klein-Gordon equations, the Maxwell-Schrödinger equations and the defocusing cubic nonlinear Schrödinger equation in two dimensions. We study the time evolution of the Nelson model (with ultraviolet cutoff) in a limit where the number N of charged particles gets large while the coupling of each particle to the radiation field is of order N^{−1/2}. At time zero it is assumed that almost all charges a...
Moiseiwitsch, B L
2005-01-01
Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco
Directory of Open Access Journals (Sweden)
Akira Abe
2010-01-01
and are the driving and natural frequencies, respectively. The application of Galerkin's procedure to the equation of motion yields nonlinear ordinary differential equations with quadratic and cubic nonlinear terms. The steady-state responses are obtained by using the discretization approach of the MMS in which the definition of the detuning parameter, expressing the relationship between the natural frequency and the driving frequency, is changed in an attempt to improve the accuracy of the solutions. The validity of the solutions is discussed by comparing them with solutions of the direct approach of the MMS and the finite difference method.
Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William
2016-01-01
Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19
Oscillating particle-like solutions of nonlinear Klein-Gordon equation
International Nuclear Information System (INIS)
Bogolubsky, I.L.
1976-01-01
A denumerable set of oscillating spherically-symmetric particle-like solutions of the Klein-Gordon equation with cubic nonlinearity is found. Extended particles modelled by them turn out to be slightly radiating and long-lived
Large-Eddy Simulation on Plume Dispersion within Regular Arrays of Cubic Buildings
Nakayama, H.; Jurcakova, K.; Nagai, H.
2010-09-01
There is a potential problem that hazardous and flammable materials are accidentally or intentionally released into the atmosphere, either within or close to populated urban areas. For the assessment of human health hazard from toxic substances, the existence of high concentration peaks in a plume should be considered. For the safety analysis of flammable gas, certain critical threshold levels should be evaluated. Therefore, in such a situation, not only average levels but also instantaneous magnitudes of concentration should be accurately predicted. However, plume dispersion is an extremely complicated process strongly influenced by the existence of buildings. In complex turbulent flows, such as impinging, separated and circulation flows around buildings, plume behaviors can be no longer accurately predicted using empirical Gaussian-type plume model. Therefore, we perform Large-Eddy Simulations (LES) on turbulent flows and plume dispersions within and over regular arrays of cubic buildings with various roughness densities and investigate the influence of the building arrangement pattern on the characteristics of mean and fluctuation concentrations. The basic equations for the LES model are composed of the spatially filtered continuity equation, Navier-Stokes equation and transport equation of concentration. The standard Smagorinsky model (Smagorinsky, 1963) that has enough potential for environment flows is used and its constant is set to 0.12 for estimating the eddy viscosity. The turbulent Schmidt number is 0.5. In our LES model, two computational regions are set up. One is a driver region for generation of inflow turbulence and the other is a main region for LES of plume dispersion within a regular array of cubic buildings. First, inflow turbulence is generated by using Kataoka's method (2002) in the driver region and then, its data are imposed at the inlet of the main computational region at each time step. In this study, the cubic building arrays with λf=0
Analysis and prediction of the alpha-function parameters used in cubic equations of state
DEFF Research Database (Denmark)
Privata, Romain; Viscontea, Maxime; Zazoua-Khames, Anis
2015-01-01
and compared regarding their ability to reproduce vapor pressure, heat of vaporization, liquid heat capacity, liquid density and second virial coefficient data. To reach this objective, extensive databanks of alpha function parameters were created. In particular, pitfalls of Twu-type alpha functions were...
Application of the cubic-plus-association (CPA) equation of state to cross-associating systems
DEFF Research Database (Denmark)
Folas, Georgios; Gabrielsen, Jostein; Michelsen, Michael Locht
2005-01-01
-independent interaction parameter provides very adequate VLE correlations over extended temperature and pressure ranges, yielding also a very satisfactory description of the azeotropic behavior. LLE of heavy alcohol-water systems is best described with the CR-1 combining rule and a single interaction parameter....... Satisfactory predictions of multicomponent, multiphase equilibria of water-alcohol-alkane systems at various conditions are achieved using solely one interaction parameter per binary. A study of the dominant binary systems for the prediction of the multicomponent systems demonstrates that both the binary...
DEFF Research Database (Denmark)
Folas, Georgios; Derawi, Samer; Michelsen, Michael Locht
2005-01-01
. Very satisfactory VLE and SLE prediction is achieved for alcohol-hydrocarbon systems, while the sensitivity of the LLE to the interaction parameter is demonstrated. It has been shown that CPA can perform VLE/LLE/SLE calculations in the case of alcohol-hydrocarbon binary systems with a single...... interaction parameter. Satisfactory SLE correlation of alcohol/glycol-water systems is achieved using a single interaction parameter over an extended temperature range. Moreover, satisfactory prediction was achieved for the multiphase equilibria of the mixture acetic acid-water-hexane based solely on binary...
Stability analysis of cavity solitons governed by the cubic-quintic Ginzburg-Landau equation
International Nuclear Information System (INIS)
Ding, Edwin; Kutz, J Nathan; Luh, Kyle
2011-01-01
A theoretical model is proposed to describe the formation of two-dimensional solitons in a laser cavity, extending the concept of the mode locking of temporal solitons in fibre lasers to spatial mode locking in nonlinear crystals. A linear stability analysis of the governing model based upon radial symmetry is performed to characterize the multi-pulsing instability of the laser as a function of gain. It is found that a stable n-pulse solution of the system bifurcates into a (n + 1)-pulse solution through the development of a periodic solution (Hopf bifurcation), and the results are consistent with simulations of the full model.
[Multimodal medical image registration using cubic spline interpolation method].
He, Yuanlie; Tian, Lianfang; Chen, Ping; Wang, Lifei; Ye, Guangchun; Mao, Zongyuan
2007-12-01
Based on the characteristic of the PET-CT multimodal image series, a novel image registration and fusion method is proposed, in which the cubic spline interpolation method is applied to realize the interpolation of PET-CT image series, then registration is carried out by using mutual information algorithm and finally the improved principal component analysis method is used for the fusion of PET-CT multimodal images to enhance the visual effect of PET image, thus satisfied registration and fusion results are obtained. The cubic spline interpolation method is used for reconstruction to restore the missed information between image slices, which can compensate for the shortage of previous registration methods, improve the accuracy of the registration, and make the fused multimodal images more similar to the real image. Finally, the cubic spline interpolation method has been successfully applied in developing 3D-CRT (3D Conformal Radiation Therapy) system.
Deformation of the cubic open string field theory
Energy Technology Data Exchange (ETDEWEB)
Lee, Taejin, E-mail: taejin@kangwon.ac.kr
2017-05-10
We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.
Deformation of the cubic open string field theory
Directory of Open Access Journals (Sweden)
Taejin Lee
2017-05-01
Full Text Available We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.
Cubic interactions of Maxwell-like higher spins
Energy Technology Data Exchange (ETDEWEB)
Francia, Dario [Scuola Normale Superiore and INFN,Piazza dei Cavalieri, 7 I-56126 Pisa (Italy); Monaco, Gabriele Lo [Dipartimento di Fisica, Università di Pisa,Piazza Fibonacci, 3, I-56126, Pisa (Italy); Dipartimento di Fisica, Università di Milano-Bicocca,Piazza della Scienza 3, I-20126 Milano (Italy); Mkrtchyan, Karapet [Max Planck Institut für Gravitationsphysik,Am Mühlenberg 1, Potsdam 14476 (Germany)
2017-04-12
We study the cubic vertices for Maxwell-like higher-spins in flat and (A)dS background spaces of any dimension. Reducibility of their free spectra implies that a single cubic vertex involving any three fields subsumes a number of couplings among different particles of various spins. The resulting vertices do not involve traces of the fields and in this sense are simpler than their Fronsdal counterparts. We propose an extension of both the free theory and of its cubic deformation to a more general class of partially reducible systems, that one can obtain from the original theory upon imposing trace constraints of various orders. The key to our results is a version of the Noether procedure allowing to systematically account for the deformations of the transversality conditions to be imposed on the gauge parameters at the free level.
Deformation of the cubic open string field theory
International Nuclear Information System (INIS)
Lee, Taejin
2017-01-01
We study a consistent deformation of the cubic open bosonic string theory in such a way that the non-planar world sheet diagrams of the perturbative string theory are mapped onto their equivalent planar diagrams of the light-cone string field theory with some length parameters fixed. An explicit evaluation of the cubic string vertex in the zero-slope limit yields the correct relationship between the string coupling constant and the Yang–Mills coupling constant. The deformed cubic open string field theory is shown to produce the non-Abelian Yang–Mills action in the zero-slope limit if it is defined on multiple D-branes. Applying the consistent deformation systematically to multi-string world sheet diagrams, we may be able to calculate scattering amplitudes with an arbitrary number of external open strings.
Pinch technique for Schwinger-Dyson equations
International Nuclear Information System (INIS)
Binosi, Daniele; Papavassiliou, Joannis
2007-01-01
In the context of scalar QED we derive the pinch technique self-energies and vertices directly from the Schwinger-Dyson equations. After reviewing the perturbative construction, we discuss in detail the general methodology and the basic field-theoretic ingredients necessary for the completion of this task. The construction requires the simultaneous treatment of the equations governing the scalar self-energy and the fundamental interaction vertices. The resulting non-trivial rearrangement of terms generates dynamically the Schwinger-Dyson equations for the corresponding Green's functions of the background field method. The proof relies on the extensive use of the all-order Ward-identities satisfied by the full vertices of the theory and by the one-particle-irreducible kernels appearing in the usual skeleton expansion. The Ward identities for these latter quantities are derived formally, and several subtleties related to the structure of the multiparticle kernels are addressed. The general strategy for the generalization of the method in a non-Abelian context is briefly outlined, and some of the technical difficulties are discussed
Generalized Born-Infeld actions and projective cubic curves
Energy Technology Data Exchange (ETDEWEB)
Ferrara, S. [Department of Physics, CERN Theory Division, CH - 1211 Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044, Frascati (Italy); Porrati, M. [CCPP, Department of Physics, NYU, 4 Washington Pl., New York, NY, 10003 (United States); Sagnotti, A. [Department of Physics, CERN Theory Division, CH - 1211 Geneva 23 (Switzerland); Stora, R. [Department of Physics, CERN Theory Division, CH - 1211 Geneva 23 (Switzerland); Laboratoire d' Annecy-le-Vieux de Physique Theorique (LAPTH), F-74941, Annecy-le-Vieux, Cedex (France); Yeranyan, A. [INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, I-00044, Frascati (Italy); Centro Studi e Ricerche Enrico Fermi, Via Panisperna 89A, 00184, Roma (Italy)
2015-04-01
We investigate U(1){sup n} supersymmetric Born-Infeld Lagrangians with a second non-linearly realized supersymmetry. The resulting non-linear structure is more complex than the square root present in the standard Born-Infeld action, and nonetheless the quadratic constraints determining these models can be solved exactly in all cases containing three vector multiplets. The corresponding models are classified by cubic holomorphic prepotentials. Their symmetry structures are associated to projective cubic varieties. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
3D confocal imaging in CUBIC-cleared mouse heart
Energy Technology Data Exchange (ETDEWEB)
Nehrhoff, I.; Bocancea, D.; Vaquero, J.; Vaquero, J.J.; Lorrio, M.T.; Ripoll, J.; Desco, M.; Gomez-Gaviro, M.V.
2016-07-01
Acquiring high resolution 3D images of the heart enables the ability to study heart diseases more in detail. Here, the CUBIC (clear, unobstructed brain imaging cocktails and computational analysis) clearing protocol was adapted for thick mouse heart sections to increase the penetration depth of the confocal microscope lasers into the tissue. The adapted CUBIC clearing of the heart lets the antibody penetrate deeper into the tissue by a factor of five. The here shown protocol enables deep 3D highresolution image acquisition in the heart. This allows a much more accurate assessment of the cellular and structural changes that underlie heart diseases. (Author)
Eisenstein Series Identities Involving the Borweins' Cubic Theta Functions
Directory of Open Access Journals (Sweden)
Ernest X. W. Xia
2012-01-01
Full Text Available Based on the theories of Ramanujan's elliptic functions and the (p, k-parametrization of theta functions due to Alaca et al. (2006, 2007, 2006 we derive certain Eisenstein series identities involving the Borweins' cubic theta functions with the help of the computer. Some of these identities were proved by Liu based on the fundamental theory of elliptic functions and some of them may be new. One side of each identity involves Eisenstein series, the other products of the Borweins' cubic theta functions. As applications, we evaluate some convolution sums. These evaluations are different from the formulas given by Alaca et al.
3D confocal imaging in CUBIC-cleared mouse heart
International Nuclear Information System (INIS)
Nehrhoff, I.; Bocancea, D.; Vaquero, J.; Vaquero, J.J.; Lorrio, M.T.; Ripoll, J.; Desco, M.; Gomez-Gaviro, M.V.
2016-01-01
Acquiring high resolution 3D images of the heart enables the ability to study heart diseases more in detail. Here, the CUBIC (clear, unobstructed brain imaging cocktails and computational analysis) clearing protocol was adapted for thick mouse heart sections to increase the penetration depth of the confocal microscope lasers into the tissue. The adapted CUBIC clearing of the heart lets the antibody penetrate deeper into the tissue by a factor of five. The here shown protocol enables deep 3D highresolution image acquisition in the heart. This allows a much more accurate assessment of the cellular and structural changes that underlie heart diseases. (Author)
Total Positivity of the Cubic Trigonometric Bézier Basis
Directory of Open Access Journals (Sweden)
Xuli Han
2014-01-01
Full Text Available Within the general framework of Quasi Extended Chebyshev space, we prove that the cubic trigonometric Bézier basis with two shape parameters λ and μ given in Han et al. (2009 forms an optimal normalized totally positive basis for λ,μ∈(-2,1]. Moreover, we show that for λ=-2 or μ=-2 the basis is not suited for curve design from the blossom point of view. In order to compute the corresponding cubic trigonometric Bézier curves stably and efficiently, we also develop a new corner cutting algorithm.
Peng, L.; Pan, H.; Ma, H.; Zhao, P.; Qin, R.; Deng, C.
2017-12-01
The irreducible water saturation (Swir) is a vital parameter for permeability prediction and original oil and gas estimation. However, the complex pore structure of the rocks makes the parameter difficult to be calculated from both laboratory and conventional well logging methods. In this study, an effective statistical method to predict Swir is derived directly from nuclear magnetic resonance (NMR) data based on fractal theory. The spectrum of transversal relaxation time (T2) is normally considered as an indicator of pore size distribution, and the micro- and meso-pore's fractal dimension in two specific range of T2 spectrum distribution are calculated. Based on the analysis of the fractal characteristics of 22 core samples, which were drilled from four boreholes of tight lithologic oil reservoirs of Ordos Basin in China, the positive correlation between Swir and porosity is derived. Afterwards a predicting model for Swir based on linear regressions of fractal dimensions is proposed. It reveals that the Swir is controlled by the pore size and the roughness of the pore. The reliability of this model is tested and an ideal consistency between predicted results and experimental data is found. This model is a reliable supplementary to predict the irreducible water saturation in the case that T2 cutoff value cannot be accurately determined.
How additive noise generates a phantom attractor in a model with cubic nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Bashkirtseva, Irina; Ryashko, Lev, E-mail: lev.ryashko@urfu.ru
2016-10-07
Two-dimensional nonlinear system forced by the additive noise is studied. We show that an increasing noise shifts random states and localizes them in a zone far from deterministic attractors. This phenomenon of the generation of the new “phantom” attractor is investigated on the base of probability density functions, mean values and variances of random states. We show that increasing noise results in the qualitative changes of the form of pdf, sharp shifts of mean values, and spikes of the variance. To clarify this phenomenon mathematically, we use the fast–slow decomposition and averaging over the fast variable. For the dynamics of the mean value of the slow variable, a deterministic equation is derived. It is shown that equilibria and the saddle-node bifurcation point of this deterministic equation well describe the stochastic phenomenon of “phantom” attractor in the initial two-dimensional stochastic system. - Highlights: • Two-dimensional nonlinear system with cubic nonlinearity is studied. • Additive noise generates a new phantom attractor. • By averaging over the fast variable one-dimensional equation is derived. • Phantom attractor appearance is analyzed by bifurcation analysis of this equation.
Tricomi, FG
2013-01-01
Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff
A New Theory of Non-Linear Thermo-Elastic Constitutive Equation of Isotropic Hyperelastic Materials
Li, Chen; Liao, Yufei
2018-03-01
Considering the influence of temperature and strain variables on materials. According to the relationship of conjugate stress-strain, a complete and irreducible non-linear constitutive equation of isotropic hyperelastic materials is derived and the constitutive equations of 16 types of isotropic hyperelastic materials are given we study the transformation methods and routes of 16 kinds of constitutive equations and the study proves that transformation of two forms of constitutive equation. As an example of application, the non-linear thermo-elastic constitutive equation of isotropic hyperelastic materials is combined with the natural vulcanized rubber experimental data in the existing literature base on MATLAB, The results show that the fitting accuracy is satisfactory.
Barbu, Viorel
2016-01-01
This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.
Systems of Inhomogeneous Linear Equations
Scherer, Philipp O. J.
Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.
Symbolic dynamics of the Lorenz equations
International Nuclear Information System (INIS)
Fang Hai-ping; Hao Bailin.
1994-07-01
The Lorenz equations are investigated in a wide range of parameters by using the method of symbolic dynamics. First, the systematics of stable periodic orbits in the Lorenz equations is compared with that of the one-dimensional cubic map, which shares the same discrete symmetry with the Lorenz model. The systematics is then ''corrected'' in such a way as to encompass all the known periodic windows of the Lorenz equations with only one exception. Second, in order to justify the above approach and to understand the exceptions, another 1D map with a discontinuity is extracted from an extension of the geometric Lorenz attractor and its symbolic dynamics is constructed. All this has to be done in light of symbolic dynamics of two-dimensional maps. Finally, symbolic dynamics for the actual Poincare return map of the Lorenz equations is constructed in a heuristic way. New periodic windows of the Lorenz equations and their parameters can be predicted from this symbolic dynamics in combination with the 1D cubic map. The extended geometric 2D Lorenz map and the 1D antisymmetric map with a discontinuity describe the topological aspects of the Lorenz equations to high accuracy. (author). 44 refs, 17 figs, 8 tabs
Numerical investigation of sixth order Boussinesq equation
Kolkovska, N.; Vucheva, V.
2017-10-01
We propose a family of conservative finite difference schemes for the Boussinesq equation with sixth order dispersion terms. The schemes are of second order of approximation. The method is conditionally stable with a mild restriction τ = O(h) on the step sizes. Numerical tests are performed for quadratic and cubic nonlinearities. The numerical experiments show second order of convergence of the discrete solution to the exact one.
Specific heat of the simple-cubic Ising model
Feng, X.; Blöte, H.W.J.
2010-01-01
We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions
C2-rational cubic spline involving tension parameters
Indian Academy of Sciences (India)
preferred which preserves some of the characteristics of the function to be interpolated. In order to tackle such ... Shape preserving properties of the rational (cubic/quadratic) spline interpolant have been studied ... tension parameters which is used to interpolate the given monotonic data is described in. [6]. Shape preserving ...
Initial post dynamic buckling of a quadratic-cubic column ...
African Journals Online (AJOL)
In this investigation, we determine the dynamic buckling load of an imperfect finite column resting on a mixed quadratic-cubic nonlinear elastic foundation trapped by an explicitly time dependent sinusoidally slowly varying dynamic load .The resultant coefficients are dynamically slowly varying and the formulation contains ...
Phonons in face-centred cubic calcium and strontium
International Nuclear Information System (INIS)
Singh, S.P.; Rathore, R.P.S.
1984-01-01
The axially symmetric and unpaired forces are employed to analyse the phonon dispersion and elastic behaviour of face centred cubic calcium and strontium which have so far not been studied adequately. The model with three parameters predicts the results which agree marvellously with the recently measured data. (author)
One billion cubic meters of gas produced in Kikinda area
Energy Technology Data Exchange (ETDEWEB)
Vicicevic, M; Duric, N
1969-10-01
The Kikinda gas reservoir has just passed a milestone in producing one billion cubic meters of natural gas. The reservoir was discovered in 1962, and its present production amounts to 26 million cu m. One of the biggest problems was formation of hydrates, which has successfully been solved by using methanol. Four tables show production statistics by years and productive formations.
Physical vapor deposition of cubic boron nitride thin films
International Nuclear Information System (INIS)
Kester, D.J.
1991-01-01
Cubic boron nitride was successfully deposited using physical vapor-deposition methods. RF-sputtering, magnetron sputtering, dual-ion-beam deposition, and ion-beam-assisted evaporation were all used. The ion-assisted evaporation, using boron evaporation and bombardment by nitrogen and argon ions, led to successful cubic boron nitride growth over the widest and most controllable range of conditions. It was found that two factors were important for c-BN growth: bombardment of the growing film and the presence of argon. A systematic study of the deposition conditions was carried out. It was found that the value of momentum transferred into the growing from by the bombarding ions was critical. There was a very narrow transition range in which mixed cubic and hexagonal phase films were prepared. Momentum-per-atom value took into account all the variables involved in ion-assisted deposition: deposition rate, ion energy, ion flux, and ion species. No other factor led to the same control of the process. The role of temperature was also studied; it was found that at low temperatures only mixed cubic and hexagonal material are deposited
Particle Creation in Oscillating Cavities with Cubic and Cylindrical Geometry
Setare, M. R.; Dinani, H. T.
2008-04-01
In the present paper we study the creation of massless scalar particles from the quantum vacuum due to the dynamical Casimir effect by oscillating cavities with cubic and cylindrical geometry. To the first order of the amplitude we derive the expressions for the number of the created particles.
Influence of strontium on the cubic to ordered hexagonal phase
Indian Academy of Sciences (India)
... Refresher Courses · Symposia · Live Streaming. Home; Journals; Bulletin of Materials Science; Volume 23; Issue 6. Influence of strontium on the cubic to ordered hexagonal phase transformation in barium magnesium niobate. M Thirumal A K Ganguli. Phase Transitions Volume 23 Issue 6 December 2000 pp 495-498 ...
Estimating the board foot to cubic foot ratio
Steve P. Verrill; Victoria L. Herian; Henry N. Spelter
2004-01-01
Certain issues in recent softwood lumber trade negotiations have centered on the method for converting estimates of timber volumes reported in cubic meters to board feet. Such conversions depend on many factors; three of the most important of these are log length, diameter, and taper. Average log diameters vary by region and have declined in the western United States...
Temperature dependence of critical resolved shear stress for cubic metals
International Nuclear Information System (INIS)
Rashid, H.; Fazal-e-Aleem; Ali, M.
1996-01-01
The experimental measurements for critical resolved shear stress of various BCC and FCC metals have been explained by using Radiation Model. The temperature dependence of CRSS for different cubic metals is found to the first approximation, to upon the type of the crystal. A good agreement between experimental observations and predictions of the Radiation Model is found. (author)
Hardness and thermal stability of cubic silicon nitride
DEFF Research Database (Denmark)
Jiang, Jianzhong; Kragh, Flemming; Frost, D. J.
2001-01-01
The hardness and thermal stability of cubic spinel silicon nitride (c-Si3N4), synthesized under high-pressure and high-temperature conditions, have been studied by microindentation measurements, and x-ray powder diffraction and scanning electron microscopy, respectively The phase at ambient...
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael
2015-10-24
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines
Barton, Michael; Calo, Victor M.
2015-01-01
We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.
Cationic Phospholipids Forming Cubic Phases: Lipoplex Structure and Transfection Efficiency
Energy Technology Data Exchange (ETDEWEB)
Koynova, Rumiana; Wang, Li; MacDonald, Robert C. (NWU)
2008-10-29
The transfection activity and the phase behavior of two novel cationic O-alkyl-phosphatidylcholines, 1,2-dioleoyl-sn-glycero-3-hexylphosphocholine (C6-DOPC) and 1,2-dierucoyl-sn-glycero-3-ethylphosphocholine (di22:1-EPC), have been examined with the aim of more completely understanding the mechanism of lipid-mediated DNA delivery. Both lipids form cubic phases: C6-DOPC in the entire temperature range from -10 to 90 C, while di22:1-EPC exhibits an irreversible lamellar-cubic transition between 50 and 70 C on heating. The lipoplexes formed by C6-DOPC arrange into hexagonal phase, while the lipoplexes of di22:1-EPC are lamellar. Both lipids exhibit lower transfection activity than the lamellar-forming 1,2-dioleoyl-sn-glycero-3-ethylphosphocholine (EDOPC). Thus, for the studied cationic phospholipid-DNA systems, the lipoplex phase state is a factor that does not seem to correlate with transfection activity. The parameter that exhibits better correlation with the transfection activity within the present data set is the phase state of the lipid dispersion prior to the addition of DNA. Thus, the lamellar lipid dispersion (EDOPC) produces more efficient lipoplexes than the dispersion with coexisting lamellar and cubic aggregates (diC22:1-EPC), which is even more efficient than the purely cubic dispersions (C6-DOPC; diC22:1-EPC after heating). It could be inferred from these data and from previous research that cubic phase lipid aggregates are unlikely to be beneficial to transfection. The lack of correlation between the phase state of lipoplexes and their transfection activity observed within the present data set does not mean that lipid phase state is generally unimportant for lipofection: a viewpoint now emerging from our previous studies is that the critical factor in lipid-mediated transfection is the structural evolution of lipoplexes within the cell, upon interacting and mixing with cellular lipids.
Cationic phospholipids forming cubic phases: lipoplex structure and transfection efficiency.
Koynova, Rumiana; Wang, Li; Macdonald, Robert C
2008-01-01
The transfection activity and the phase behavior of two novel cationic O-alkyl-phosphatidylcholines, 1,2-dioleoyl- sn-glycero-3-hexylphosphocholine (C6-DOPC) and 1,2-dierucoyl- sn-glycero-3-ethylphosphocholine (di22:1-EPC), have been examined with the aim of more completely understanding the mechanism of lipid-mediated DNA delivery. Both lipids form cubic phases: C6-DOPC in the entire temperature range from -10 to 90 degrees C, while di22:1-EPC exhibits an irreversible lamellar-cubic transition between 50 and 70 degrees C on heating. The lipoplexes formed by C6-DOPC arrange into hexagonal phase, while the lipoplexes of di22:1-EPC are lamellar. Both lipids exhibit lower transfection activity than the lamellar-forming 1,2-dioleoyl- sn-glycero-3-ethylphosphocholine (EDOPC). Thus, for the studied cationic phospholipid-DNA systems, the lipoplex phase state is a factor that does not seem to correlate with transfection activity. The parameter that exhibits better correlation with the transfection activity within the present data set is the phase state of the lipid dispersion prior to the addition of DNA. Thus, the lamellar lipid dispersion (EDOPC) produces more efficient lipoplexes than the dispersion with coexisting lamellar and cubic aggregates (diC22:1-EPC), which is even more efficient than the purely cubic dispersions (C6-DOPC; diC22:1-EPC after heating). It could be inferred from these data and from previous research that cubic phase lipid aggregates are unlikely to be beneficial to transfection. The lack of correlation between the phase state of lipoplexes and their transfection activity observed within the present data set does not mean that lipid phase state is generally unimportant for lipofection: a viewpoint now emerging from our previous studies is that the critical factor in lipid-mediated transfection is the structural evolution of lipoplexes within the cell, upon interacting and mixing with cellular lipids.
B-splines and Faddeev equations
International Nuclear Information System (INIS)
Huizing, A.J.
1990-01-01
Two numerical methods for solving the three-body equations describing relativistic pion deuteron scattering have been investigated. For separable two body interactions these equations form a set of coupled one-dimensional integral equations. They are plagued by singularities which occur in the kernel of the integral equations as well as in the solution. The methods to solve these equations differ in the way they treat the singularities. First the Fuda-Stuivenberg method is discussed. The basic idea of this method is an one time iteration of the set of integral equations to treat the logarithmic singularities. In the second method, the spline method, the unknown solution is approximated by splines. Cubic splines have been used with cubic B-splines as basis. If the solution is approximated by a linear combination of basis functions, an integral equation can be transformed into a set of linear equations for the expansion coefficients. This set of linear equations is solved by standard means. Splines are determined by points called knots. A proper choice of splines to approach the solution stands for a proper choice of the knots. The solution of the three-body scattering equations has a square root behaviour at a certain point. Hence it was investigated how the knots should be chosen to approximate the square root function by cubic B-splines in an optimal way. Before applying this method to solve numerically the three-body equations describing pion-deuteron scattering, an analytically solvable example has been constructed with a singularity structure of both kernel and solution comparable to those of the three-body equations. The accuracy of the numerical solution was determined to a large extent by the accuracy of the approximation of the square root part. The results for a pion laboratory energy of 47.4 MeV agree very well with those from literature. In a complete calculation for 47.7 MeV the spline method turned out to be a factor thousand faster than the Fuda
From the Dyson-Schwinger to the Transport Equation in the Background Field Gauge of QCD
Wang, Q; Stöcker, H; Greiner, W
2003-01-01
The non-equilibrium quantum field dynamics is usually described in the closed-time-path formalism. The initial state correlations are introduced into the generating functional by non-local source terms. We propose a functional approach to the Dyson-Schwinger equation, which treats the non-local and local source terms in the same way. In this approach, the generating functional is formulated for the connected Green functions and one-particle-irreducible vertices. The great advantages of our approach over the widely used two-particle-irreducible method are that it is much simpler and that it is easy to implement the procedure in a computer program to automatically generate the Feynman diagrams for a given process. The method is then applied to a pure gluon plasma to derive the gauge-covariant transport equation from the Dyson-Schwinger equation in the background covariant gauge. We discuss the structure of the kinetic equation and show its relationship with the classical one. We derive the gauge-covariant colli...
On current contribution to Fronsdal equations
Misuna, N. G.
2018-03-01
We explore a local form of second-order Vasiliev equations proposed in [arxiv:arXiv:1706.03718] and obtain an explicit expression for quadratic corrections to bosonic Fronsdal equations, generated by gauge-invariant higher-spin currents. Our analysis is performed for general phase factor, and for the case of parity-invariant theory we find the agreement with expressions for cubic vertices available in the literature. This provides an additional indication that local frame proposed in [arxiv:arXiv:1706.03718] is the proper one.
Ab initio study of cubic complex Bi2CrCuO6 perovskite
International Nuclear Information System (INIS)
Fajardo, F.; Cardona, R.; Landinez Tellez, D.A.; Arbey Rodriguez M, J.; Roa-Rojas, J.
2008-01-01
We report a detailed calculation of the structural and electronic properties for the cubic complex Bi 2 CrCuO 6 perovskite material by density functional theory. The exchange-correlation potential was included through the generalized gradient approximation. From the adjusting of Murnaghan state equation to the energy as a function of volume data, we obtain an ideal lattice parameter of 7.763 A. The density of states study was carried out considering the two spin polarizations. Results reveal that this material behaves as a conductor to the spin-down polarization and evidence a semiconductor tendency to the spin-up configuration. This tendency to the half-metallicity character is corroborated by the integer number of magnetic moment (3.0 μ B ), which is attributed to the Cr-spin-up orbital contribution
Development and application of a three-parameter RK-PR equation of state
DEFF Research Database (Denmark)
Cismondi, Martin; Mollerup, Jørgen
2005-01-01
In this work, we confirm the somehow previously expressed but not widespread idea that the limitations of cubic equations of state like Soave-Redlich-Kwong equation (SRK) or Peng-Robinson equation (PR) are a consequence of their two-parameter density dependence rather than of their empiric......-PR) equation offers the best performance among cubic three-parameter density functionalities. A simple temperature dependence was developed and a straightforward parameterization procedure established. This simple - and optimized from pure compound data - three-parameter equation of state (3P-EoS) will allow...... in a later stage, by systematic study and comparison to other types of 3P-EoS, to find out what the actual possibilities and limitations of cubic EoS are in the modelling of phase equilibria for asymmetric systems. (c) 2005 Elsevier B.V. All rights reserved....
Hajabdollahi, Farzaneh; Premnath, Kannan N.
2018-05-01
Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the relaxation times or the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that can be used to tune the effective sound speed, and thereby alleviating the numerical stiffness. In the present paper, we present a GI formulation of the preconditioned cascaded central-moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice, for steady flows. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Such parameter dependent corrections eliminate the remaining truncation errors arising from the degeneracy of the diagonal third-order moments and fully restore Galilean invariance without cubic defects for the preconditioned LB scheme on a standard lattice. Several
Indian Academy of Sciences (India)
regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.
International Nuclear Information System (INIS)
Gross, F.
1986-01-01
Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs
Highly Aminated Mesoporous Silica Nanoparticles with Cubic Pore Structure
Suteewong, Teeraporn
2011-01-19
Mesoporous silica with cubic symmetry has attracted interest from researchers for some time. Here, we present the room temperature synthesis of mesoporous silica nanoparticles possessing cubic Pm3n symmetry with very high molar ratios (>50%) of 3-aminopropyl triethoxysilane. The synthesis is robust allowing, for example, co-condensation of organic dyes without loss of structure. By means of pore expander molecules, the pore size can be enlarged from 2.7 to 5 nm, while particle size decreases. Adding pore expander and co-condensing fluorescent dyes in the same synthesis reduces average particle size further down to 100 nm. After PEGylation, such fluorescent aminated mesoporous silica nanoparticles are spontaneously taken up by cells as demonstrated by fluorescence microscopy.
Polarization Change in Face-Centered Cubic Opal Films
Wolff, Christian; Romanov, Sergei; Küchenmeister, Jens; Peschel, Ulf; Busch, Kurt
2011-10-01
Artificial opals are a popular platform for investigating fundamental properties of Photonic Crystals (PhC). In this work, we provide a theoretical analysis of polarization-resolved transmission experiments through thin opal films. Despite the full cubic symmetry of the PhC, this system provides a very efficient mechanism for manipulating the polarization state of light. Based on band structure calculations and Bloch mode analysis, we find that this effect closely resembles classical birefringence. Due to the cubic symmetry, however, a description using tensorial quantities is not possible. This indicates fundamental limitations of effective material models for Photonic Crystals and demonstrates the importance of accurately modelling the microscopic geometry of such systems.
Highly Aminated Mesoporous Silica Nanoparticles with Cubic Pore Structure
Suteewong, Teeraporn; Sai, Hiroaki; Cohen, Roy; Wang, Suntao; Bradbury, Michelle; Baird, Barbara; Gruner, Sol M.; Wiesner, Ulrich
2011-01-01
Mesoporous silica with cubic symmetry has attracted interest from researchers for some time. Here, we present the room temperature synthesis of mesoporous silica nanoparticles possessing cubic Pm3n symmetry with very high molar ratios (>50%) of 3-aminopropyl triethoxysilane. The synthesis is robust allowing, for example, co-condensation of organic dyes without loss of structure. By means of pore expander molecules, the pore size can be enlarged from 2.7 to 5 nm, while particle size decreases. Adding pore expander and co-condensing fluorescent dyes in the same synthesis reduces average particle size further down to 100 nm. After PEGylation, such fluorescent aminated mesoporous silica nanoparticles are spontaneously taken up by cells as demonstrated by fluorescence microscopy.
Trace spaces in a pre-cubical complex
DEFF Research Database (Denmark)
Raussen, Martin
2009-01-01
In directed algebraic topology, directed irreversible (d)-paths and spaces consisting of d-paths are studied from a topological and from a categorical point of view. Motivated by models for concurrent computation, we study in this paper spaces of d-paths in a pre-cubical complex. Such paths...... are equipped with a natural arc length which moreover is shown to be invariant under directed homotopies. D-paths up to reparametrization (called traces) can thus be represented by arc length parametrized d-paths. Under weak additional conditions, it is shown that trace spaces in a pre-cubical complex...... are separable metric spaces which are locally contractible and locally compact. Moreover, they have the homotopy type of a CW-complex....
A local cubic smoothing in an adaptation mode
International Nuclear Information System (INIS)
Dikoussar, N.D.
2001-01-01
A new approach to a local curve approximation and the smoothing is proposed. The relation between curve points is defined using a special cross-ratio weight functions. The coordinates of three curve points are used as parameters for both the weight functions and the tree-point cubic model (TPS). A very simple in computing and stable to random errors cubic smoother in an adaptation mode (LOCUS) is constructed. The free parameter of TPS is estimated independently of the fixed parameters by recursion with the effective error suppression and can be controlled by the cross-ratio parameters. Efficiency and the noise stability of the algorithm are confirmed by examples and by comparison with other known non-parametric smoothers
3D Medical Image Interpolation Based on Parametric Cubic Convolution
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.
Perfect 3-colorings of the cubic graphs of order 10
Directory of Open Access Journals (Sweden)
Mehdi Alaeiyan
2017-10-01
Full Text Available Perfect coloring is a generalization of the notion of completely regular codes, given by Delsarte. A perfect m-coloring of a graph G with m colors is a partition of the vertex set of G into m parts A_1, A_2, ..., A_m such that, for all $ i,j \\in \\lbrace 1, ... , m \\rbrace $, every vertex of A_i is adjacent to the same number of vertices, namely, a_{ij} vertices, of A_j. The matrix $A=(a_{ij}_{i,j\\in \\lbrace 1,... ,m\\rbrace }$, is called the parameter matrix. We study the perfect 3-colorings (also known as the equitable partitions into three parts of the cubic graphs of order 10. In particular, we classify all the realizable parameter matrices of perfect 3-colorings for the cubic graphs of order 10.
Global Sufficient Optimality Conditions for a Special Cubic Minimization Problem
Directory of Open Access Journals (Sweden)
Xiaomei Zhang
2012-01-01
Full Text Available We present some sufficient global optimality conditions for a special cubic minimization problem with box constraints or binary constraints by extending the global subdifferential approach proposed by V. Jeyakumar et al. (2006. The present conditions generalize the results developed in the work of V. Jeyakumar et al. where a quadratic minimization problem with box constraints or binary constraints was considered. In addition, a special diagonal matrix is constructed, which is used to provide a convenient method for justifying the proposed sufficient conditions. Then, the reformulation of the sufficient conditions follows. It is worth noting that this reformulation is also applicable to the quadratic minimization problem with box or binary constraints considered in the works of V. Jeyakumar et al. (2006 and Y. Wang et al. (2010. Finally some examples demonstrate that our optimality conditions can effectively be used for identifying global minimizers of the certain nonconvex cubic minimization problem.
Taper and volume equations for selected Appalachian hardwood species
A. Jeff Martin
1981-01-01
Coefficients for five taper/volume models are developed for 18 Appalachian hardwood species. Each model can be used to estimate diameter at any point on the bole, height to any preselected diameter, and cubic-foot volume between any two points on the bole. The resulting equations were tested on six sets of independent data and an evaluation of these tests is included,...
Perturbation method for periodic solutions of nonlinear jerk equations
International Nuclear Information System (INIS)
Hu, H.
2008-01-01
A Lindstedt-Poincare type perturbation method with bookkeeping parameters is presented for determining accurate analytical approximate periodic solutions of some third-order (jerk) differential equations with cubic nonlinearities. In the process of the solution, higher-order approximate angular frequencies are obtained by Newton's method. A typical example is given to illustrate the effectiveness and simplicity of the proposed method
Magnetic ground states in nanocuboids of cubic magnetocrystalline anisotropy
Energy Technology Data Exchange (ETDEWEB)
Bonilla, F.J., E-mail: fbonilla@cicenergigune.com; Lacroix, L.-M.; Blon, T., E-mail: thomas.blon@insa-toulouse.fr
2017-04-15
Flower and easy-axis vortex states are well-known magnetic configurations that can be stabilized in small particles. However, <111> vortex (V<111>), i.e. a vortex state with its core axis along the hard-axis direction, has been recently evidenced as a stable configuration in Fe nanocubes of intermediate sizes in the flower/vortex transition. In this context, we present here extensive micromagnetic simulations to determine the different magnetic ground states in ferromagnetic nanocuboids exhibiting cubic magnetocrystalline anisotropy (MCA). Focusing our study in the single-domain/multidomain size range (10–50 nm), we showed that V<111> is only stable in nanocuboids exhibiting peculiar features, such as a specific size, shape and magnetic environment, contrarily to the classical flower and easy-axis vortex states. Thus, to track experimentally these V<111> states, one should focused on (i) nanocuboids exhibiting a nearly perfect cubic shape (size distorsion <12%) made of (ii) a material which combines a zero or positive MCA and a high saturation magnetization, such as Fe or FeCo; and (iii) a low magnetic field environment, V<111> being only observed in virgin or remanent states. - Highlights: • The <111> vortex is numerically determined in nanocubes of cubic anisotropy. • It constitutes an intermediate state in the single-domain limit. • Such a vortex can only be stabilized in perfect or slightly deformed nanocuboids. • It exists in nanocuboids made of materials with zero or positive cubic anisotropy. • The associated magnetization reversal is described by a rotation of the vortex axis.
Synthesis and Optical Properties of Cubic Gold Nanoframes
Au, Leslie; Chen, Yeechi; Zhou, Fei; Camargo, Pedro H. C.; Lim, Byungkwon; Li, Zhi-Yuan; Ginger, David S.; Xia, Younan
2008-01-01
This paper describes a facile method of preparing cubic Au nanoframes with open structures via the galvanic replacement reaction between Ag nanocubes and AuCl2−. A mechanistic study of the reaction revealed that the formation of Au nanoframes relies on the diffusion of both Au and Ag atoms. The effect of the edge length and ridge thickness of the nanoframes on the localized surface plasmon resonance peak was explored by a combination of discrete dipole approximation calculations and single na...
Orientational anharmonicity of interatomic interaction in cubic monocrystals
International Nuclear Information System (INIS)
Belomestnykh, Vladimir N.; Tesleva, Elena P.
2010-01-01
Anharmonicity of interatomic interaction from a position of physical acoustics under the standard conditions is investigated. It is shown that the measure of anharmonicity of interatomic interaction (Grilneisen parameter) is explicitly expressed through velocities of sound. Calculation results of orientation anharmonicity are shown on the example of 116 cubic monocrystals with different lattice structural type and type of chemical bond. Two types of anharmonicity interatomic interaction anisotropy are determined. Keywords: acoustics, orientational anharmonicity, Gruneisen parameter, velocity of sound
Light scattering by cubical particle in the WKB approximation
Directory of Open Access Journals (Sweden)
redouane lamsoudi
2017-11-01
Full Text Available In this work, we determined the analytical expressions of the form factor of a cubical particle in the WKB approximation. We adapted some variables (size parameter, refractive index, the scattering angle and found the form factor in the approximation of Rayleigh-Gans-Debye (RGD, Anomalous Diffraction (AD, and determined the efficiency factor of the extinction. Finally, to illustrate our formalism, we analyzed some numerical examples
Legendre-tau approximations for functional differential equations
Ito, K.; Teglas, R.
1986-01-01
The numerical approximation of solutions to linear retarded functional differential equations are considered using the so-called Legendre-tau method. The functional differential equation is first reformulated as a partial differential equation with a nonlocal boundary condition involving time-differentiation. The approximate solution is then represented as a truncated Legendre series with time-varying coefficients which satisfy a certain system of ordinary differential equations. The method is very easy to code and yields very accurate approximations. Convergence is established, various numerical examples are presented, and comparison between the latter and cubic spline approximation is made.
Polishuk, Ilya
2013-03-14
This study is the first comparative investigation of predicting the isochoric and the isobaric heat capacities, the isothermal and the isentropic compressibilities, the isobaric thermal expansibilities, the thermal pressure coefficients, and the sound velocities of ionic liquids by statistical associating fluid theory (SAFT) equation of state (EoS) models and cubic-plus-association (CPA). It is demonstrated that, taking into account the high uncertainty of the literature data (excluding sound velocities), the generalized for heavy compounds version of SAFT+Cubic (GSAFT+Cubic) appears as a robust estimator of the auxiliary thermodynamic properties under consideration. In the case of the ionic liquids the performance of PC-SAFT seems to be less accurate in comparison to ordinary compounds. In particular, PC-SAFT substantially overestimates heat capacities and underestimates the temperature and pressure dependencies of sound velocities and compressibilities. An undesired phenomenon of predicting high fictitious critical temperatures of ionic liquids by PC-SAFT should be noticed as well. CPA is the less accurate estimator of the liquid phase properties, but it is advantageous in modeling vapor pressures and vaporization enthalpies of ionic liquids. At the same time, the preliminary results indicate that the inaccuracies in predicting the deep vacuum vapor pressures of ionic liquids do not influence modeling of phase equilibria in their mixtures at much higher pressures.
Dry Powder Precursors of Cubic Liquid Crystalline Nanoparticles (cubosomes)
International Nuclear Information System (INIS)
Spicer, Patrick T.; Small, William B.; Small, William B.; Lynch, Matthew L.; Burns, Janet L.
2002-01-01
Cubosomes are dispersed nanostructured particles of cubic phase liquid crystal that have stimulated significant research interest because of their potential for application in controlled-release and drug delivery. Despite the interest, cubosomes can be difficult to fabricate and stabilize with current methods. Most of the current work is limited to liquid phase processes involving high shear dispersion of bulk cubic liquid crystalline material into sub-micron particles, limiting application flexibility. In this work, two types of dry powder cubosome precursors are produced by spray-drying: (1) starch-encapsulated monoolein is produced by spray-drying a dispersion of cubic liquid crystalline particles in an aqueous starch solution and (2) dextran-encapsulated monoolein is produced by spray-drying an emulsion formed by the ethanol-dextran-monoolein-water system. The encapsulants are used to decrease powder cohesion during drying and to act as a soluble colloidal stabilizer upon hydration of the powders. Both powders are shown to form (on average) 0.6 μm colloidally-stable cubosomes upon addition to water. However, the starch powders have a broader particle size distribution than the dextran powders because of the relative ease of spraying emulsions versus dispersions. The developed processes enable the production of nanostructured cubosomes by end-users rather than just specialized researchers and allow tailoring of the surface state of the cubosomes for broader application
On a new series of integrable nonlinear evolution equations
International Nuclear Information System (INIS)
Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.
1980-10-01
Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)
International Nuclear Information System (INIS)
Dumitrescu, T.S.
1977-01-01
A new method is applied in order to obtain the irreducible single row representations of the groups under study. For the case U(3) contained in SO(3) also an explicit realization is constructed. The method has the advantage of being simpler than the previously used ones. (author)
International Nuclear Information System (INIS)
Iagolnitzer, D.
1983-11-01
Recent axiomatic results on the (non holonomic) analytic structure of the multiparticle S matrix and Green functions are reviewed and related general conjectures are described: (i) formal expansions of Green functions in terms of (holonomic) Feynman-type integrals in which each vertex represents an irreducible kernel, and (ii) ''graph by graph unitarity'' and other discontinuity formulae of the latter. These conjectures are closely linked with unitarity or asymptotic completeness equations, which they yield in a formal sense. In constructive field theory, a direct proof of the first conjecture (together with an independent proof of the second) would thus imply, as a first step, asymptotic completeness in that sense
International Nuclear Information System (INIS)
Melde, T.; Canton, L.; Svenne, J.P.
2002-01-01
We formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As an application, we develop a spinless, one-dimensional (1-D) model that mimics three-nucleon dynamics in one dimension. Using simple two-body potentials that reproduce the deuteron binding, we obtain that the three-body system binds at about 7.5 MeV. We then consider two types of residual pionic corrections in the dynamical equation; one related to the 2π-exchange three-body diagram, the other to the 1π-exchange three-body diagram. We find that the first contribution can produce an additional binding effect of about 0.9 MeV. The second term produces smaller binding effects, which are, however, dependent on the uncertainty in the off-shell extrapolation of the two-body t-matrix. This presents interesting analogies with what occurs in three dimensions. The paper also discusses the general three-particle quantum scattering problem, for motion restricted to the fall line. (author)
Kuriakose, Maju; Raetz, Samuel; Hu, Qing Miao; Nikitin, Sergey M.; Chigarev, Nikolay; Tournat, Vincent; Bulou, Alain; Lomonosov, Alexey; Djemia, Philippe; Gusev, Vitalyi E.; Zerr, Andreas
2017-10-01
Water ice is a molecular solid whose behavior under compression reveals the interplay of covalent bonding in molecules and forces acting between them. This interplay determines high-pressure phase transitions, the elastic and plastic behavior of H2O ice, which are the properties needed for modeling the convection and internal structure of the giant planets and moons of the solar system as well as H2O -rich exoplanets. We investigated experimentally and theoretically elastic properties and phase transitions of cubic H2O ice at room temperature and high pressures between 10 and 82 GPa. The time-domain Brillouin scattering (TDBS) technique was used to measure longitudinal sound velocities (VL) in polycrystalline ice samples compressed in a diamond anvil cell. The high spatial resolution of the TDBS technique revealed variations of VL caused by elastic anisotropy, allowing us to reliably determine the fastest and the slowest sound velocity in a single crystal of cubic H2O ice and thus to evaluate existing equations of state. Pressure dependencies of the single-crystal elastic moduli Ci j(P ) of cubic H2O ice to 82 GPa have been obtained which indicate its hardness and brittleness. These results were compared with ab initio calculations. It is suggested that the transition from molecular ice VII to ionic ice X occurs at much higher pressures than proposed earlier, probably above 80 GPa.
CMB spectral distortions as solutions to the Boltzmann equations
Energy Technology Data Exchange (ETDEWEB)
Ota, Atsuhisa, E-mail: a.ota@th.phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
2017-01-01
We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of μ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.
Differential Equations Compatible with KZ Equations
International Nuclear Information System (INIS)
Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.
2000-01-01
We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions
X-Ray Elastic Constants for Cubic Materials
Energy Technology Data Exchange (ETDEWEB)
Malen, K
1974-10-15
The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account
Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices
International Nuclear Information System (INIS)
Cramer, M.; Eisert, J.; Illuminati, F.
2004-01-01
We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices
Inhomogeneous atomic Bose-Fermi mixtures in cubic lattices.
Cramer, M; Eisert, J; Illuminati, F
2004-11-05
We determine the ground state properties of inhomogeneous mixtures of bosons and fermions in cubic lattices and parabolic confining potentials. For finite hopping we determine the domain boundaries between Mott-insulator plateaux and hopping-dominated regions for lattices of arbitrary dimension within mean-field and perturbation theory. The results are compared with a new numerical method that is based on a Gutzwiller variational approach for the bosons and an exact treatment for the fermions. The findings can be applied as a guideline for future experiments with trapped atomic Bose-Fermi mixtures in optical lattices.
X-Ray Elastic Constants for Cubic Materials
Energy Technology Data Exchange (ETDEWEB)
Malen, K.
1974-10-15
The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account
X-Ray Elastic Constants for Cubic Materials
International Nuclear Information System (INIS)
Malen, K.
1974-10-01
The stress-strain relation to be used in X-ray stress measurements in anisotropic texture-free media is studied. The method for evaluation of appropriate elastic constants for a cubic medium is described. Some illustrative numerical examples have been worked out including line broadening due to elastic anisotropy. The elastic stress and strain compatibility at grain boundaries is taken into account using Kroner's method. These elastic constants obviously only apply when no internal stresses due to plastic deformation are present. The case of reorientation of free interstitials in the stress field can be taken into account
Trapping of cubic ZnO nanocrystallites at ambient conditions
DEFF Research Database (Denmark)
Decremps, F.; Pellicer-Porres, J.; Datchi, F.
2002-01-01
Dense powder of nanocrystalline ZnO has been recovered at ambient conditions in the metastable cubic structure after a heat treatment at high pressure (15 GPa and 550 K). Combined x-ray diffraction (XRD) and x-ray absorption spectroscopy (XAS) experiments have been performed to probe both long......-range order and local crystallographic structure of the recovered sample. Within uncertainty of these techniques (about 5%), all the crystallites are found to adopt the NaCl structure. From the analysis of XRD and XAS spectra, the cell volume per chemical formula unit is found to be 19.57(1) and 19...
Synthesis and Optical Properties of Cubic Gold Nanoframes.
Au, Leslie; Chen, Yeechi; Zhou, Fei; Camargo, Pedro H C; Lim, Byungkwon; Li, Zhi-Yuan; Ginger, David S; Xia, Younan
2008-12-01
This paper describes a facile method of preparing cubic Au nanoframes with open structures via the galvanic replacement reaction between Ag nanocubes and AuCl(2) (-). A mechanistic study of the reaction revealed that the formation of Au nanoframes relies on the diffusion of both Au and Ag atoms. The effect of the edge length and ridge thickness of the nanoframes on the localized surface plasmon resonance peak was explored by a combination of discrete dipole approximation calculations and single nanoparticle spectroscopy. With their hollow and open structures, the Au nanoframes represent a novel class of substrates for applications including surface plasmonics and surface-enhanced Raman scattering.
Topological Characterization of Carbon Graphite and Crystal Cubic Carbon Structures.
Siddiqui, Wei Gao Muhammad Kamran; Naeem, Muhammad; Rehman, Najma Abdul
2017-09-07
Graph theory is used for modeling, designing, analysis and understanding chemical structures or chemical networks and their properties. The molecular graph is a graph consisting of atoms called vertices and the chemical bond between atoms called edges. In this article, we study the chemical graphs of carbon graphite and crystal structure of cubic carbon. Moreover, we compute and give closed formulas of degree based additive topological indices, namely hyper-Zagreb index, first multiple and second multiple Zagreb indices, and first and second Zagreb polynomials.
Method of forming an abrasive compact of cubic boron nitride
International Nuclear Information System (INIS)
Bell, F.R.
1976-01-01
This patent concerns an abrasive compact comprising diamond or cubic boron nitride or mixtures thereof held in a matrix of a refractory substance and a substance which dissolves the abrasive particle to at least a limited extent. The compact may be made by subjecting a powdered mixture of the ingredients to conditions of temperature and pressure at which the abrasive particle is crystallographically stable and the solvent substance acts to dissolve the abrasive particle. The refractory substance and solvent substance are preferably so chosen that during compact manufacture there is interaction resulting in the formation of a hard material
Rotary Ultrasonic Machining of Poly-Crystalline Cubic Boron Nitride
Directory of Open Access Journals (Sweden)
Kuruc Marcel
2014-12-01
Full Text Available Poly-crystalline cubic boron nitride (PCBN is one of the hardest material. Generally, so hard materials could not be machined by conventional machining methods. Therefore, for this purpose, advanced machining methods have been designed. Rotary ultrasonic machining (RUM is included among them. RUM is based on abrasive removing mechanism of ultrasonic vibrating diamond particles, which are bonded on active part of rotating tool. It is suitable especially for machining hard and brittle materials (such as glass and ceramics. This contribution investigates this advanced machining method during machining of PCBN.
Soliton interaction in quadratic and cubic bulk media
DEFF Research Database (Denmark)
Johansen, Steffen Kjær; Bang, Ole
2000-01-01
Summary form only given. The understanding of how and to what extend the cubic nonlinearity affects beam propagation and spatial soliton formation in quadratic media is of vital importance in fundamental and applied nonlinear physics. We consider beam propagation under type-I SHG conditions...... in lossless bulk second order nonlinear optical materials with a nonvanishing third order nonlinearity. It is known that in pure second order systems a single soliton can never collapse whereas in systems with both nonlinearities and that stable single soliton propagation can only in some circumstances...
Compressibility and thermal expansion of cubic silicon nitride
DEFF Research Database (Denmark)
Jiang, Jianzhong; Lindelov, H.; Gerward, Leif
2002-01-01
The compressibility and thermal expansion of the cubic silicon nitride (c-Si3N4) phase have been investigated by performing in situ x-ray powder-diffraction measurements using synchrotron radiation, complemented with computer simulations by means of first-principles calculations. The bulk...... compressibility of the c-Si3N4 phase originates from the average of both Si-N tetrahedral and octahedral compressibilities where the octahedral polyhedra are less compressible than the tetrahedral ones. The origin of the unit cell expansion is revealed to be due to the increase of the octahedral Si-N and N-N bond...
A new cubic theory of gravity in five dimensions: black hole, Birkhoff's theorem and C-function
Energy Technology Data Exchange (ETDEWEB)
Oliva, Julio [Instituto de Fisica, Facultad de Ciencias, Universidad Austral de Chile, Valdivia (Chile); Ray, Sourya, E-mail: julio.oliva@docentes.uach.c, E-mail: ray@cecs.c [Centro de Estudios CientIficos (CECS), Casilla 1469, Valdivia (Chile)
2010-11-21
We present a new cubic theory of gravity in five dimensions which has second-order traced field equations, analogous to BHT new massive gravity in three dimensions. Moreover, for static spherically symmetric spacetimes all the field equations are of second order, and the theory admits a new asymptotically locally flat black hole. Furthermore, we prove the uniqueness of this solution, study its thermodynamical properties and show the existence of a C-function for the theory following the arguments of Anber and Kastor (2008 J. High Energy Phys. JHEP05(2008)061 (arXiv:0802.1290 [hep-th])) in pure Lovelock theories. Finally, we include the Einstein-Gauss-Bonnet and cosmological terms and find new asymptotically AdS black holes at the point where the three maximally symmetric solutions of the theory coincide. These black holes may also possess a Cauchy horizon.
Andrei Andreevich Bolibrukh's works on the analytic theory of differential equations
Anosov, Dmitry V.; Leksin, Vladimir P.
2011-02-01
This paper contains an account of A.A. Bolibrukh's results obtained in the new directions of research that arose in the analytic theory of differential equations as a consequence of his sensational counterexample to the Riemann-Hilbert problem. A survey of results of his students in developing topics first considered by Bolibrukh is also presented. The main focus is on the role of the reducibility/irreducibility of systems of linear differential equations and their monodromy representations. A brief synopsis of results on the multidimensional Riemann-Hilbert problem and on isomonodromic deformations of Fuchsian systems is presented, and the main methods in the modern analytic theory of differential equations are sketched. Bibliography: 69 titles.
A numerical scheme for the generalized Burgers–Huxley equation
Directory of Open Access Journals (Sweden)
Brajesh K. Singh
2016-10-01
Full Text Available In this article, a numerical solution of generalized Burgers–Huxley (gBH equation is approximated by using a new scheme: modified cubic B-spline differential quadrature method (MCB-DQM. The scheme is based on differential quadrature method in which the weighting coefficients are obtained by using modified cubic B-splines as a set of basis functions. This scheme reduces the equation into a system of first-order ordinary differential equation (ODE which is solved by adopting SSP-RK43 scheme. Further, it is shown that the proposed scheme is stable. The efficiency of the proposed method is illustrated by four numerical experiments, which confirm that obtained results are in good agreement with earlier studies. This scheme is an easy, economical and efficient technique for finding numerical solutions for various kinds of (nonlinear physical models as compared to the earlier schemes.
Plastic deformation of cubic zirconia single crystals at 1400 C
International Nuclear Information System (INIS)
Baufeld, B.; Baither, D.; Bartsch, M.; Messerschmidt, U.
1998-01-01
Cubic zirconia single crystals stabilized with 11 mol% yttria were deformed in air at 1400 C and around 1200 C at different strain rates along [1 anti 12] and [100] compression directions. The strain rate sensitivity of the flow stress was determined by strain rate cycling and stress relaxation tests. The microstructure of the deformed specimens was investigated by transmission high-voltage electron microscopy, including contrast extinction analysis for determining the Burgers vectors as well as stereo pairs and wide-angle tilting experiments to find the active slip planes. At deformation along [1 anti 12], the primary and secondary slip planes are of {100} type. Previous experiments had shown that the dislocations move easily on these planes in an athermal way. During deformation along [100], mainly dislocations on {100} planes are activated, which move in a viscous way by the aid of thermal activation. The discussion of the different deformation behaviours during deformation along [1 anti 12] and [100] is based on the different dynamic properties of dislocations and the fact that recovery is an essential feature of the deformation of cubic zirconia at 1400 C. The results on the shape of the deformation curve and the strain rate sensitivity of the flow stress are partly at variance with those of previous authors. (orig.)
Efficient LBM visual simulation on face-centered cubic lattices.
Petkov, Kaloian; Qiu, Feng; Fan, Zhe; Kaufman, Arie E; Mueller, Klaus
2009-01-01
The Lattice Boltzmann method (LBM) for visual simulation of fluid flow generally employs cubic Cartesian (CC) lattices such as the D3Q13 and D3Q19 lattices for the particle transport. However, the CC lattices lead to suboptimal representation of the simulation space. We introduce the face-centered cubic (FCC) lattice, fD3Q13, for LBM simulations. Compared to the CC lattices, the fD3Q13 lattice creates a more isotropic sampling of the simulation domain and its single lattice speed (i.e., link length) simplifies the computations and data storage. Furthermore, the fD3Q13 lattice can be decomposed into two independent interleaved lattices, one of which can be discarded, which doubles the simulation speed. The resulting LBM simulation can be efficiently mapped to the GPU, further increasing the computational performance. We show the numerical advantages of the FCC lattice on channeled flow in 2D and the flow-past-a-sphere benchmark in 3D. In both cases, the comparison is against the corresponding CC lattices using the analytical solutions for the systems as well as velocity field visualizations. We also demonstrate the performance advantages of the fD3Q13 lattice for interactive simulation and rendering of hot smoke in an urban environment using thermal LBM.
Defect ordering in aliovalently doped cubic zirconia from first principles
International Nuclear Information System (INIS)
Bogicevic, A.; Wolverton, C.; Crosbie, G.M.; Stechel, E.B.
2001-01-01
Defect ordering in aliovalently doped cubic-stabilized zirconia is studied using gradient corrected density-functional calculations. Intra- and intersublattice ordering interactions are investigated for both cation (Zr and dopant ions) and anion (oxygen ions and vacancies) species. For yttria-stabilized zirconia, the crystal structure of the experimentally identified, ordered compound δ-Zr 3 Y 4 O 12 is established, and we predict metastable zirconia-rich ordered phases. Anion vacancies repel each other at short separations, but show an energetic tendency to align as third-nearest neighbors along directions. Calculations with divalent (Be, Mg, Ca, Sr, Ba) and trivalent (Y, Sc, B, Al, Ga, In) oxides show that anion vacancies prefer to be close to the smaller of the cations (Zr or dopant ion). When the dopant cation is close in size to Zr, the vacancies show no particular preference, and are thus less prone to be bound preferentially to any particular cation type when the vacancies traverse such oxides. This ordering tendency offers insight into the observed high conductivity of Y 2 O 3 - and Sc 2 O 3 -stabilized zirconia, as well as recent results using, e.g., lanthanide oxides. The calculations point to In 2 O 3 as a particularly promising stabilizer for high ionic conductivity. Thus we are able to directly link (thermodynamic) defect ordering to (kinetic) ionic conductivity in cubic-stabilized zirconia using first-principles atomistic calculations
Relativistic wave equations without the Velo-Zwanziger pathology
International Nuclear Information System (INIS)
Khalil, M.A.K.
1976-06-01
For particles described by relativistic wave equations of the form: (-iGAMMA x delta + m) psi(x) = 0 interacting with an external field B(x) it is known that the ''noncausal'' propagation characteristics are not present when (1) GAMMA 0 is diagonalizable and (2) B(x) = -eGAMMA/sub mu/A/sup mu/(x) (Amar--Dozzio). The ''noncausality''difficulties arise for the Rarita--Schwinger spin 3 / 2 equation, with nondiagonalizable GAMMA 0 , in minimal coupling (i.e., B(x) = -eGAMMA x A(x)) and the PDK spin 1 equation, with diagonalizable GAMMA 0 , in a quadrupole coupling (Velo--Zwanziger) where either (1) or (2) of the Amar--Dozzio (sufficient) conditions are violated. Some sufficient conditions are derived and explored where the Velo--Zwanziger ''noncausality'' pathology can be avoided, even though one, or the other, or both of the conditions (1) and (2) are violated. Examples with both reducible and irreducible wave equations are included
Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun
2018-01-01
In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.
Directory of Open Access Journals (Sweden)
Sudha Ellison Mathe
2017-08-01
Full Text Available Multiplication in finite fields is used in many applications, especially in cryptography. It is a basic and the most computationally intensive operation from among all such operations. Several systolic multipliers are proposed in the literature that offer low hardware complexity or high speed. In this paper, a bit‐parallel polynomial basis systolic multiplier for generic irreducible polynomials is proposed based on a modified interleaved multiplication method. The hardware complexity and delay of the proposed multiplier are estimated, and a comparison with the corresponding multipliers available in the literature is presented. Of the corresponding multipliers, the proposed multiplier achieves a reduction in the hardware complexity of up to 20% when compared to the best multiplier for m = 163. The synthesis results of application‐specific integrated circuit and field‐programmable gate array implementations of the proposed multiplier are also presented. From the synthesis results, it is inferred that the proposed multiplier achieves low power consumption and low area complexitywhen compared to the best of the corresponding multipliers.
Convergence of method of lines approximations to partial differential equations
International Nuclear Information System (INIS)
Verwer, J.G.; Sanz-Serna, J.M.
1984-01-01
Many existing numerical schemes for evolutionary problems in partial differential equations (PDEs) can be viewed as method of lines (MOL) schemes. This paper treats the convergence of one-step MOL schemes. The main purpose is to set up a general framework for a convergence analysis applicable to nonlinear problems. The stability materials for this framework are taken from the field of nonlinear stiff ODEs. In this connection, important concepts are the logarithmic matrix norm and C-stability. A nonlinear parabolic equation and the cubic Schroedinger equation are used for illustrating the ideas. (Auth.)
Hairy black holes in cubic quasi-topological gravity
Energy Technology Data Exchange (ETDEWEB)
Dykaar, Hannah [Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada); Department of Physics, McGill University,3600 rue University, Montreal, QC, H3A 2T8 (Canada); Hennigar, Robie A.; Mann, Robert B. [Department of Physics and Astronomy, University of Waterloo,200 University Avenue West, Waterloo, ON, N2L 3G1 (Canada)
2017-05-09
We construct a class of five dimensional black hole solutions to cubic quasi-topological gravity with conformal scalar hair and study their thermodynamics. We find these black holes provide the second example of black hole λ-lines: a line of second order (continuous) phase transitions, akin to the fluid/superfluid transition of {sup 4}He. Examples of isolated critical points are found for spherical black holes, marking the first in the literature to date. We also find various novel and interesting phase structures, including an isolated critical point occurring in conjunction with a double reentrant phase transition. The AdS vacua of the theory are studied, finding ghost-free configurations where the scalar field takes on a non-zero constant value, in notable contrast to the five dimensional Lovelock case.
Bifurcation diagram of a cubic three-parameter autonomous system
Directory of Open Access Journals (Sweden)
Lenka Barakova
2005-07-01
Full Text Available In this paper, we study the cubic three-parameter autonomous planar system $$displaylines{ dot x_1 = k_1 + k_2x_1 - x_1^3 - x_2,cr dot x_2 = k_3 x_1 - x_2, }$$ where $k_2, k_3$ are greater than 0. Our goal is to obtain a bifurcation diagram; i.e., to divide the parameter space into regions within which the system has topologically equivalent phase portraits and to describe how these portraits are transformed at the bifurcation boundaries. Results may be applied to the macroeconomical model IS-LM with Kaldor's assumptions. In this model existence of a stable limit cycles has already been studied (Andronov-Hopf bifurcation. We present the whole bifurcation diagram and among others, we prove existence of more difficult bifurcations and existence of unstable cycles.
Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion
Sannomiya, Noriaki; Katsura, Hosho; Nakayama, Yu
2017-03-01
We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges Q and Q†. Each supercharge is built solely from spinless fermion operators and depends on a parameter g . The system is strongly interacting for small g , and in the extreme limit g =0 , the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-g limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of g and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.
Lipidic cubic phase serial millisecond crystallography using synchrotron radiation
Directory of Open Access Journals (Sweden)
Przemyslaw Nogly
2015-03-01
Full Text Available Lipidic cubic phases (LCPs have emerged as successful matrixes for the crystallization of membrane proteins. Moreover, the viscous LCP also provides a highly effective delivery medium for serial femtosecond crystallography (SFX at X-ray free-electron lasers (XFELs. Here, the adaptation of this technology to perform serial millisecond crystallography (SMX at more widely available synchrotron microfocus beamlines is described. Compared with conventional microcrystallography, LCP-SMX eliminates the need for difficult handling of individual crystals and allows for data collection at room temperature. The technology is demonstrated by solving a structure of the light-driven proton-pump bacteriorhodopsin (bR at a resolution of 2.4 Å. The room-temperature structure of bR is very similar to previous cryogenic structures but shows small yet distinct differences in the retinal ligand and proton-transfer pathway.
A cubic autocatalytic reaction in a continuous stirred tank reactor
Energy Technology Data Exchange (ETDEWEB)
Yakubu, Aisha Aliyu; Yatim, Yazariah Mohd [School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM, Penang Malaysia (Malaysia)
2015-10-22
In the present study, the dynamics of the cubic autocatalytic reaction model in a continuous stirred tank reactor with linear autocatalyst decay is studied. This model describes the behavior of two chemicals (reactant and autocatalyst) flowing into the tank reactor. The behavior of the model is studied analytically and numerically. The steady state solutions are obtained for two cases, i.e. with the presence of an autocatalyst and its absence in the inflow. In the case with an autocatalyst, the model has a stable steady state. While in the case without an autocatalyst, the model exhibits three steady states, where one of the steady state is stable, the second is a saddle point while the last is spiral node. The last steady state losses stability through Hopf bifurcation and the location is determined. The physical interpretations of the results are also presented.
The electric field of a uniformly charged cubic shell
McCreery, Kaitlin; Greenside, Henry
2018-01-01
As an integrative and insightful example for undergraduates learning about electrostatics, we discuss how to use symmetry, Coulomb's law, superposition, Gauss's law, and visualization to understand the electric field E (x ,y ,z ) produced by a uniformly charged cubic shell. We first discuss how to deduce qualitatively, using freshman-level physics, the perhaps surprising fact that the interior electric field is nonzero and has a complex structure, pointing inwards from the middle of each face of the shell and pointing outwards towards each edge and corner. We then discuss how to understand the quantitative features of the electric field by plotting an analytical expression for E along symmetry lines and on symmetry surfaces of the shell.
Quantum-Carnot engine for particle confined to cubic potential
Energy Technology Data Exchange (ETDEWEB)
Sutantyo, Trengginas Eka P., E-mail: trengginas.eka@gmail.com; Belfaqih, Idrus H., E-mail: idrushusin21@gmail.com; Prayitno, T. B., E-mail: teguh-budi@unj.ac.id [Department of Physics, State University of Jakarta, Jl. Pemuda No.10, Rawamangun, Jakarta Timur 13220 (Indonesia)
2015-09-30
Carnot cycle consists of isothermal and adiabatic processes which are reversible. Using analogy in quantum mechanics, these processes can be well explained by replacing variables in classical process with a quantum system. Quantum system which is shown in this paper is a particle that moves under the influence of a cubic potential which is restricted only to the state of the two energy levels. At the end, the efficiency of the system is shown as a function of the width ratio between the initial conditions and the farthest wall while expanding. Furthermore, the system efficiency will be considered 1D and 2D cases. The providing efficiencies are different due to the influence of the degeneration of energy and the degrees of freedom of the system.
Quantum-Carnot engine for particle confined to cubic potential
International Nuclear Information System (INIS)
Sutantyo, Trengginas Eka P.; Belfaqih, Idrus H.; Prayitno, T. B.
2015-01-01
Carnot cycle consists of isothermal and adiabatic processes which are reversible. Using analogy in quantum mechanics, these processes can be well explained by replacing variables in classical process with a quantum system. Quantum system which is shown in this paper is a particle that moves under the influence of a cubic potential which is restricted only to the state of the two energy levels. At the end, the efficiency of the system is shown as a function of the width ratio between the initial conditions and the farthest wall while expanding. Furthermore, the system efficiency will be considered 1D and 2D cases. The providing efficiencies are different due to the influence of the degeneration of energy and the degrees of freedom of the system
Quantum corrections for the cubic Galileon in the covariant language
Energy Technology Data Exchange (ETDEWEB)
Saltas, Ippocratis D. [Institute of Astrophysics and Space Sciences, Faculty of Sciences, Campo Grande, PT1749-016 Lisboa (Portugal); Vitagliano, Vincenzo, E-mail: isaltas@fc.ul.pt, E-mail: vincenzo.vitagliano@ist.utl.pt [Multidisciplinary Center for Astrophysics and Department of Physics, Instituto Superior Técnico, University of Lisbon, Av. Rovisco Pais 1, 1049-001 Lisboa (Portugal)
2017-05-01
We present for the first time an explicit exposition of quantum corrections within the cubic Galileon theory including the effect of quantum gravity, in a background- and gauge-invariant manner, employing the field-reparametrisation approach of the covariant effective action at 1-loop. We show that the consideration of gravitational effects in combination with the non-linear derivative structure of the theory reveals new interactions at the perturbative level, which manifest themselves as higher-operators in the associated effective action, which' relevance is controlled by appropriate ratios of the cosmological vacuum and the Galileon mass scale. The significance and concept of the covariant approach in this context is discussed, while all calculations are explicitly presented.
THERMODYNAMIC PARAMETERS OF LEAD SULFIDE CRYSTALS IN THE CUBIC PHASE
Directory of Open Access Journals (Sweden)
T. O. Parashchuk
2016-07-01
Full Text Available Geometric and thermodynamic parameters of cubic PbS crystals were obtained using the computer calculations of the thermodynamic parameters within density functional theory method DFT. Cluster models for the calculation based on the analysis of the crystal and electronic structure. Temperature dependence of energy ΔE and enthalpy ΔH, Gibbs free energy ΔG, heat capacity at constant pressure CP and constant volume CV, entropy ΔS were determined on the basis of ab initio calculations of the crystal structure of molecular clusters. Analytical expressions of temperature dependences of thermodynamic parameters which were approximated with quantum-chemical calculation points have been presented. Experimental results compared with theoretically calculated data.
Perbaikan Metode Penghitungan Debit Sungai Menggunakan Cubic Spline Interpolation
Directory of Open Access Journals (Sweden)
Budi I. Setiawan
2007-09-01
Full Text Available Makalah ini menyajikan perbaikan metode pengukuran debit sungai menggunakan fungsi cubic spline interpolation. Fungi ini digunakan untuk menggambarkan profil sungai secara kontinyu yang terbentuk atas hasil pengukuran jarak dan kedalaman sungai. Dengan metoda baru ini, luas dan perimeter sungai lebih mudah, cepat dan tepat dihitung. Demikian pula, fungsi kebalikannnya (inverse function tersedia menggunakan metode. Newton-Raphson sehingga memudahkan dalam perhitungan luas dan perimeter bila tinggi air sungai diketahui. Metode baru ini dapat langsung menghitung debit sungaimenggunakan formula Manning, dan menghasilkan kurva debit (rating curve. Dalam makalah ini dikemukaan satu canton pengukuran debit sungai Rudeng Aceh. Sungai ini mempunyai lebar sekitar 120 m dan kedalaman 7 m, dan pada saat pengukuran mempunyai debit 41 .3 m3/s, serta kurva debitnya mengikuti formula: Q= 0.1649 x H 2.884 , dimana Q debit (m3/s dan H tinggi air dari dasar sungai (m.
Experimental core electron density of cubic boron nitride
DEFF Research Database (Denmark)
Wahlberg, Nanna; Bindzus, Niels; Bjerg, Lasse
as well as experimental result. The redistribution of electron density will, if not accounted for, result in increased thermal parameters. It is estimated that 1.7-2 electrons is transferred from boron to nitrogen. [1]: N. Bindzus, T. Straasø, N. Wahlberg, J. Becker, L. Bjerg, N. Lock, A.-C. Dippel, and B......Experimental core electron density of cubic boron nitride Nanna Wahlberg*, Niels Bindzus*, Lasse Bjerg*, Jacob Becker*, and Bo B. Iversen* *Aarhus University, Department of Chemistry, CMC, Langelandsgade 140, 8000 Århus, Denmark The resent progress in powder diffraction provides data of quality...... obtained. The displacement parameters reported here are significantly lower than those previously reported, stressing the importance of an adequate description of the core density. The charge transfer from boron to nitrogen clearly affects the inner electron density, which is evident from theoretical...
Linear electro-optic effect in cubic silicon carbide
Tang, Xiao; Irvine, Kenneth G.; Zhang, Dongping; Spencer, Michael G.
1991-01-01
The first observation is reported of the electrooptic effect of cubic silicon carbide (beta-SiC) grown by a low-pressure chemical vapor deposition reactor using the hydrogen, silane, and propane gas system. At a wavelength of 633 nm, the value of the electrooptic coefficient r41 in beta-SiC is determined to be 2.7 +/- 0.5 x 10 (exp-12) m/V, which is 1.7 times larger than that in gallium arsenide measured at 10.6 microns. Also, a half-wave voltage of 6.4 kV for beta-SiC is obtained. Because of this favorable value of electrooptic coefficient, it is believed that silicon carbide may be a promising candidate in electrooptic applications for high optical intensity in the visible region.
Point defects in cubic boron nitride after neutron irradiation
International Nuclear Information System (INIS)
Atobe, Kozo; Honda, Makoto; Ide, Munetoshi; Yamaji, Hiromichi; Matsukawa, Tokuo; Fukuoka, Noboru; Okada, Moritami; Nakagawa, Masuo.
1993-01-01
The production of point defects induced by reactor neutrons and the thermal behavior of defects in sintered cubic boron nitride are investigated using the optical absorption and electron spin resonance (ESR) methods. A strong structureless absorption over the visible region was observed after fast neutron irradiation to a dose of 5.3 x 10 16 n/cm 2 (E > 0.1 MeV) at 25 K. This specimen also shows an ESR signal with g-value 2.006 ± 0.001, which can be tentatively identified as an electron trapped in a nitrogen vacancy. On examination of the thermal decay of the signal, the activation energy for recovery of the defects was determined to be about 1.79 eV. (author)
Spatial 't Hooft loop to cubic order in hot QCD
Giovannangeli, P.
2002-01-01
Spatial 't Hooft loops of strength k measure the qualitative change in the behaviour of electric colour flux in confined and deconfined phase of SU (N) gauge theory. They show an area law in the deconfined phase, known analytica lly to two loop order with a ``k-scaling'' law k(N-k). In this paper we comput e the O(g^3) correction to the tension. It is due to neutral gluon fields that get their mass through interaction with the wall. The simple k-scaling is lost in cubic order. The generic problem of non-convexity shows up in this order an d the cure is provided. The result for large N is explicitely given. We show tha t nonperturbative effects appear at O(g^5).
G2 cubic transition between two circles with shape control
Habib, Zulfiqar; Sakai, Manabu
2009-01-01
This paper describes a method for joining two circles with an S-shaped or with a broken back C-shaped transition curve, composed of at most two spiral segments. In highway and railway route design or car-like robot path planning, it is often desirable to have such a transition. It is shown that a single cubic curve can be used for blending or for a transition curve preserving G2 continuity with local shape control parameter and more flexible constraints. Provision of the shape parameter and flexibility provide freedom to modify the shape in a stable manner which is an advantage over previous work by Meek, Walton, Sakai and Habib.
Dynamic Displacement Disorder of Cubic BaTiO3
Paściak, M.; Welberry, T. R.; Kulda, J.; Leoni, S.; Hlinka, J.
2018-04-01
The three-dimensional distribution of the x-ray diffuse scattering intensity of BaTiO3 has been recorded in a synchrotron experiment and simultaneously computed using molecular dynamics simulations of a shell model. Together, these have allowed the details of the disorder in paraelectric BaTiO3 to be clarified. The narrow sheets of diffuse scattering, related to the famous anisotropic longitudinal correlations of Ti ions, are shown to be caused by the overdamped anharmonic soft phonon branch. This finding demonstrates that the occurrence of narrow sheets of diffuse scattering agrees with a displacive picture of the cubic phase of this textbook ferroelectric material. The presented methodology allows one to go beyond the harmonic approximation in the analysis of phonons and phonon-related scattering.
Principal spectra describing magnetooptic permittivity tensor in cubic crystals
Energy Technology Data Exchange (ETDEWEB)
Hamrlová, Jana [Nanotechnology Centre, VSB – Technical University of Ostrava, listopadu 15, Ostrava, 708 33 Czech Republic (Czech Republic); IT4Innovations Centre, VSB – Technical University of Ostrava, listopadu 15, Ostrava, 708 33 Czech Republic (Czech Republic); Legut, Dominik [IT4Innovations Centre, VSB – Technical University of Ostrava, listopadu 15, Ostrava, 708 33 Czech Republic (Czech Republic); Veis, Martin [Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Prague, 121 16 Czech Republic (Czech Republic); Pištora, Jaromír [Nanotechnology Centre, VSB – Technical University of Ostrava, listopadu 15, Ostrava, 708 33 Czech Republic (Czech Republic); Hamrle, Jaroslav, E-mail: jaroslav.hamrle@vsb.cz [IT4Innovations Centre, VSB – Technical University of Ostrava, listopadu 15, Ostrava, 708 33 Czech Republic (Czech Republic); Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, Prague, 121 16 Czech Republic (Czech Republic); Department of Physics, VSB – Technical University of Ostrava, 17. listopadu 15, Ostrava, 708 33 Czech Republic (Czech Republic)
2016-12-15
We provide unified phenomenological description of magnetooptic effects being linear and quadratic in magnetization. The description is based on few principal spectra, describing elements of permittivity tensor up to the second order in magnetization. Each permittivity tensor element for any magnetization direction and any sample surface orientation is simply determined by weighted summation of the principal spectra, where weights are given by crystallographic and magnetization orientations. The number of principal spectra depends on the symmetry of the crystal. In cubic crystals owning point symmetry we need only four principal spectra. Here, the principal spectra are expressed by ab initio calculations for bcc Fe, fcc Co and fcc Ni in optical range as well as in hard and soft x-ray energy range, i.e. at the 2p- and 3p-edges. We also express principal spectra analytically using modified Kubo formula.
Structure and energetics of nanotwins in cubic boron nitrides
Energy Technology Data Exchange (ETDEWEB)
Zheng, Shijian, E-mail: sjzheng@imr.ac.cn, E-mail: zrf@buaa.edu.cn; Ma, Xiuliang [Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016 (China); Zhang, Ruifeng, E-mail: sjzheng@imr.ac.cn, E-mail: zrf@buaa.edu.cn [School of Materials Science and Engineering, and International Research Institute for Multidisciplinary Science, Beihang University, Beijing 100191 (China); Huang, Rong [Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062 (China); Taniguchi, Takashi [National Institute for Materials Science, Tsukuba, Ibaraki 305-0044 (Japan); Ikuhara, Yuichi [Nanostructures Research Laboratory, Japan Fine Ceramics Center, Nagoya 456-8587 (Japan); Institute of Engineering Innovation, The University of Tokyo, Tokyo 113-8656 (Japan); Beyerlein, Irene J. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
2016-08-22
Recently, nanotwinned cubic boron nitrides (NT c-BN) have demonstrated extraordinary leaps in hardness. However, an understanding of the underlying mechanisms that enable nanotwins to give orders of magnitude increases in material hardness is still lacking. Here, using transmission electron microscopy, we report that the defect density of twin boundaries depends on nanotwin thickness, becoming defect-free, and hence more stable, as it decreases below 5 nm. Using ab initio density functional theory calculations, we reveal that the Shockley partials, which may dominate plastic deformation in c-BNs, show a high energetic barrier. We also report that the c-BN twin boundary has an asymmetrically charged electronic structure that would resist migration of the twin boundary under stress. These results provide important insight into possible nanotwin hardening mechanisms in c-BN, as well as how to design these nanostructured materials to reach their full potential in hardness and strength.
Pure gauge configurations and solutions to fermionic superstring field theory equations of motion
International Nuclear Information System (INIS)
Aref'eva, I Ya; Gorbachev, R V; Medvedev, P B
2009-01-01
Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of nonpolynomial and cubic string field theory are discussed. To have the possibility of dealing with both GSO(+) and GSO(-) sectors in the uniform way, a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open-string field theories truncated pure gauge configurations parametrized by wedge states play an essential role. The matrix form of this parametrization for NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equations of motion on the subspace of the wedge states. The perturbation expansion is corrected by adding extra terms that are just those necessary for the equation of motion contracted with the solution itself to be satisfied.
Multilayer gyroid cubic membrane organization in green alga Zygnema.
Zhan, Ting; Lv, Wenhua; Deng, Yuru
2017-09-01
Biological cubic membranes (CM), which are fluid membranes draped onto the 3D periodic parallel surface geometries with cubic symmetry, have been observed within subcellular organelles, including mitochondria, endoplasmic reticulum, and thylakoids. CM transition tends to occur under various stress conditions; however, multilayer CM organizations often appear associated with light stress conditions. This report is about the characterization of a projected gyroid CM in a transmission electron microscopy study of the chloroplast membranes within green alga Zygnema (LB923) whose lamellar form of thylakoid membrane started to fold into multilayer gyroid CM in the culture at the end of log phase of cell growth. Using the techniques of computer simulation of transmission electron microscopy (TEM) and a direct template matching method, we show that these CM are based on the gyroid parallel surfaces. The single, double, and multilayer gyroid CM morphologies are observed in which space is continuously divided into two, three, and more subvolumes by either one, two, or several parallel membranes. The gyroid CM are continuous with varying amount of pseudo-grana with lamellar-like morphology. The relative amount and order of these two membrane morphologies seem to vary with the age of cell culture and are insensitive to ambient light condition. In addition, thylakoid gyroid CM continuously interpenetrates the pyrenoid body through stalk, bundle-like, morphologies. Inside the pyrenoid body, the membranes re-folded into gyroid CM. The appearance of these CM rearrangements due to the consequence of Zygnema cell response to various types of environmental stresses will be discussed. These stresses include nutrient limitation, temperature fluctuation, and ultraviolet (UV) exposure.
International Nuclear Information System (INIS)
Shore, B.W.
1981-01-01
The equations of motion are discussed which describe time dependent population flows in an N-level system, reviewing the relationship between incoherent (rate) equations, coherent (Schrodinger) equations, and more general partially coherent (Bloch) equations. Approximations are discussed which replace the elaborate Bloch equations by simpler rate equations whose coefficients incorporate long-time consequences of coherence
Dian, Linghui; Yang, Zhiwen; Li, Feng; Wang, Zhouhua; Pan, Xin; Peng, Xinsheng; Huang, Xintian; Guo, Zhefei; Quan, Guilan; Shi, Xuan; Chen, Bao; Li, Ge; Wu, Chuanbin
2013-01-01
In order to improve the oral bioavailability of ibuprofen, ibuprofen-loaded cubic nanoparticles were prepared as a delivery system for aqueous formulations. The cubic inner structure was verified by cryogenic transmission electron microscopy. With an encapsulation efficiency greater than 85%, the ibuprofen-loaded cubic nanoparticles had a narrow size distribution around a mean size of 238 nm. Differential scanning calorimetry and X-ray diffraction determined that ibuprofen was in an amorphous and molecular form within the lipid matrix. The in vitro release of ibuprofen from cubic nanoparticles was greater than 80% at 24 hours, showing sustained characteristics. The pharmacokinetic study in beagle dogs showed improved absorption of ibuprofen from cubic nanoparticles compared to that of pure ibuprofen, with evidence of a longer half-life and a relative oral bioavailability of 222% (P ibuprofen-loaded cubic nanoparticles provide a promising carrier candidate with an efficient drug delivery for therapeutic treatment. PMID:23468008
Hamilton's equations for a fluid membrane
International Nuclear Information System (INIS)
Capovilla, R; Guven, J; Rojas, E
2005-01-01
Consider a homogeneous fluid membrane described by the Helfrich-Canham energy, quadratic in the mean curvature of the membrane surface. The shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature. We introduce a Hamiltonian formulation of this equation which dismantles it into a set of coupled first-order equations. This involves interpreting the Helfrich-Canham energy as an action; equilibrium surfaces are generated by the evolution of space curves. Two features complicate the implementation of a Hamiltonian framework. (i) The action involves second derivatives. This requires treating the velocity as a phase-space variable and the introduction of its conjugate momentum. The canonical Hamiltonian is constructed on this phase space. (ii) The action possesses a local symmetry-reparametrization invariance. The two labels we use to parametrize points on the surface are themselves physically irrelevant. This symmetry implies primary constraints, one for each label, that need to be implemented within the Hamiltonian. The two Lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface. The conservation of the primary constraints implies two secondary constraints, fixing the tangential components of the momentum conjugate to the position. Hamilton's equations are derived and the appropriate initial conditions on the phase-space variables are identified. Finally, it is shown how the shape equation can be reconstructed from these equations
Electromagnetic interactions in relativistic infinite component wave equations
International Nuclear Information System (INIS)
Gerry, C.C.
1979-01-01
The electromagnetic interactions of a composite system described by relativistic infinite-component wave equations are considered. The noncompact group SO(4,2) is taken as the dynamical group of the systems, and its unitary irreducible representations, which are infinite dimensional, are used to find the energy spectra and to specify the states of the systems. First the interaction mechanism is examined in the nonrelativistic SO(4,2) formulation of the hydrogen atom as a heuristic guide. A way of making a minimal relativistic generalization of the minimal ineractions in the nonrelativistic equation for the hydrogen atom is proposed. In order to calculate the effects of the relativistic minimal interactions, a covariant perturbation theory suitable for infinite-component wave equations, which is an algebraic and relativistic version of the Rayleigh-Schroedinger perturbation theory, is developed. The electric and magnetic polarizabilities for the ground state of the hydrogen atom are calculated. The results have the correct nonrelativistic limits. Next, the relativistic cross section of photon absorption by the atom is evaluated. A relativistic expression for the cross section of light scattering corresponding to the seagull diagram is derived. The Born amplitude is combusted and the role of spacelike solutions is discussed. Finally, internal electromagnetic interactions that give rise to the fine structure splittings, the Lamb shifts and the hyperfine splittings are considered. The spin effects are introduced by extending the dynamical group
Effect of Dipolar Interactions on the Magnetization of Single-Molecule Magnets in a cubic lattice
Alcantara Ortigoza, Marisol
2005-03-01
Since the one-body tunnel picture of single-molecule magnets (SMM) is not always sufficient to explain the fine structure of experimental hysteresis loops, the effect of intermolecular dipolar interactions has been investigated on an ensemble of 100 3D-systems of 5X5X4 particles, each with spin S = 5, arranged in a cubic lattice. We have solved the Landau-Lifshitz-Gilbert equation for several values of the damping constant, the field sweep rate and the lattice constant. We find that the smaller the damping constant is, the stronger the maximum field needs to be to produce hysteresis. Furthermore, the shape of the hysteresis loops also depends on the damping constant. We also find that the system magnetizes and demagnetizes faster with decreasing sweep rates, resulting in smaller hysteresis loops. Variations of the lattice constant within realistic values (1.5nm and 2.5nm) show that the dipolar interaction plays an important role in magnetic hysteresis by controlling the relaxation process. Examination of temperature dependencies (0.1K and 0.7K) of the above will be presented and compared with recent experimental data on SMM.
The effect of voids on the hardening of body-centered cubic Fe
Energy Technology Data Exchange (ETDEWEB)
Nakai, Ryosuke, E-mail: ryosuke.nakai@jupiter.qse.tohoku.ac.jp [Department of Quantum Science and Energy Engineering, Tohoku University, 6-6-01-2, Aramaki-Aza-Aoba, Aobaku, Sendai, Miyagi, 980-8579 (Japan); Yabuuchi, Kiyohiro, E-mail: k-yabuuchi@iae.kyoto-u.ac.jp [Department of Quantum Science and Energy Engineering, Tohoku University, 6-6-01-2, Aramaki-Aza-Aoba, Aobaku, Sendai, Miyagi, 980-8579 (Japan); Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, 611-0011 (Japan); Nogami, Shuhei, E-mail: shuhei.nogami@qse.tohoku.ac.jp [Department of Quantum Science and Energy Engineering, Tohoku University, 6-6-01-2, Aramaki-Aza-Aoba, Aobaku, Sendai, Miyagi, 980-8579 (Japan); Hasegawa, Akira, E-mail: akira.hasegawa@qse.tohoku.ac.jp [Department of Quantum Science and Energy Engineering, Tohoku University, 6-6-01-2, Aramaki-Aza-Aoba, Aobaku, Sendai, Miyagi, 980-8579 (Japan)
2016-04-01
The mechanical properties of metals are affected by various types of defects. Hardening is usually described through the interaction between dislocations and obstacles, in the so-called line tension theory. The strength factor in the line tension theory represents the resistance of a defect against the dislocation motion. In order to understand hardening from the viewpoint of the microstructure, an accurate determination of the strength factor of different types of defects is essential. In the present study, the strength factor of voids in body-centered cubic (BCC) Fe was investigated by two different approaches: one based on the Orowan equation to link the measured hardness with the average size and density of voids, and the other involving direct observation of the interaction between dislocations and voids by transmission electron microscope (TEM). The strength factor of voids induced by ion irradiation estimated by the Orowan equation was 0.6, whereas the strength factor estimated by the direct TEM approach was 0.8. The difference in the strength factors measured by the two approaches is due to the positional relationship between dislocations and voids: the central region of a void is stronger than the tip. Moreover, the gliding plane and the direction of dislocation may also affect the strength factor of voids. This study determined the strength factor of voids in BCC Fe accurately, and suggested that the contribution of voids to the irradiation hardening is larger than that of dislocation loops and Cu-rich precipitates. - Highlights: • The strength factor of voids in BCC Fe was experimentally investigated. • The strength factor of voids estimated by the line tension theory was 0.6. • The strength factor of voids estimated by the bowing angle of dislocations was 0.8. • The different strength factors are due to the positional relationship.
Electric quadrupole interaction in cubic BCC α-Fe
Energy Technology Data Exchange (ETDEWEB)
Błachowski, A.; Komędera, K. [Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, ul. Podchorążych 2, PL-30-084 Kraków (Poland); Ruebenbauer, K., E-mail: sfrueben@cyf-kr.edu.pl [Mössbauer Spectroscopy Division, Institute of Physics, Pedagogical University, ul. Podchorążych 2, PL-30-084 Kraków (Poland); Cios, G.; Żukrowski, J. [AGH University of Science and Technology, Academic Center for Materials and Nanotechnology, Av. A. Mickiewicza 30, PL-30-059 Kraków (Poland); Górnicki, R. [RENON, ul. Gliniana 15/15, PL-30-732 Kraków (Poland)
2016-07-15
Mössbauer transmission spectra for the 14.41-keV resonant line in {sup 57}Fe have been collected at room temperature by using {sup 57}Co(Rh) commercial source and α-Fe strain-free single crystal as an absorber. The absorber was magnetized to saturation in the absorber plane perpendicular to the γ-ray beam axis applying small external magnetic field. Spectra were collected for various orientations of the magnetizing field, the latter lying close to the [110] crystal plane. A positive electric quadrupole coupling constant was found practically independent on the field orientation. One obtains the following value V{sub zz} = +1.61(4) × 10{sup 19} Vm{sup −2} for the (average) principal component of the electric field gradient (EFG) tensor under assumption that the EFG tensor is axially symmetric and the principal axis is aligned with the magnetic hyperfine field acting on the {sup 57}Fe nucleus. The nuclear spectroscopic electric quadrupole moment for the first excited state of the {sup 57}Fe nucleus was adopted as +0.17 b. Similar measurement was performed at room temperature using as-rolled polycrystalline α-Fe foil of high purity in the zero external field. Corresponding value for the principal component of the EFG was found as V{sub zz} = +1.92(4) × 10{sup 19} Vm{sup −2}. Hence, it seems that the origin of the EFG is primarily due to the local (atomic) electronic wave function distortion caused by the spin–orbit interaction between effective electronic spin S and incompletely quenched electronic angular momentum L. It seems as well that the lowest order term proportional to the product L·λ·S dominates, as no direction dependence of the EFG principal component is seen. The lowest order term is isotropic for a cubic symmetry as one has λ=λ 1 for cubic systems with the symbol 1 denoting unit operator and λ being the coupling parameter. - Highlights: • Precision of MS the same as MAPON • Real scans versus magnetization direction • A challenge
Electric quadrupole interaction in cubic BCC α-Fe
International Nuclear Information System (INIS)
Błachowski, A.; Komędera, K.; Ruebenbauer, K.; Cios, G.; Żukrowski, J.; Górnicki, R.
2016-01-01
Mössbauer transmission spectra for the 14.41-keV resonant line in "5"7Fe have been collected at room temperature by using "5"7Co(Rh) commercial source and α-Fe strain-free single crystal as an absorber. The absorber was magnetized to saturation in the absorber plane perpendicular to the γ-ray beam axis applying small external magnetic field. Spectra were collected for various orientations of the magnetizing field, the latter lying close to the [110] crystal plane. A positive electric quadrupole coupling constant was found practically independent on the field orientation. One obtains the following value V_z_z = +1.61(4) × 10"1"9 Vm"−"2 for the (average) principal component of the electric field gradient (EFG) tensor under assumption that the EFG tensor is axially symmetric and the principal axis is aligned with the magnetic hyperfine field acting on the "5"7Fe nucleus. The nuclear spectroscopic electric quadrupole moment for the first excited state of the "5"7Fe nucleus was adopted as +0.17 b. Similar measurement was performed at room temperature using as-rolled polycrystalline α-Fe foil of high purity in the zero external field. Corresponding value for the principal component of the EFG was found as V_z_z = +1.92(4) × 10"1"9 Vm"−"2. Hence, it seems that the origin of the EFG is primarily due to the local (atomic) electronic wave function distortion caused by the spin–orbit interaction between effective electronic spin S and incompletely quenched electronic angular momentum L. It seems as well that the lowest order term proportional to the product L·λ·S dominates, as no direction dependence of the EFG principal component is seen. The lowest order term is isotropic for a cubic symmetry as one has λ=λ 1 for cubic systems with the symbol 1 denoting unit operator and λ being the coupling parameter. - Highlights: • Precision of MS the same as MAPON • Real scans versus magnetization direction • A challenge for ab initio calculations
Characterization, Microstructure, and Dielectric properties of cubic pyrochlore structural ceramics
Li, Yangyang
2013-05-01
The (BMN) bulk materials were sintered at 1050°C, 1100°C, 1150°C, 1200°C by the conventional ceramic process, and their microstructure and dielectric properties were investigated by Scanning electron microscopy (SEM), X-ray diffraction (XRD), Raman spectroscopy, Transmission electron microscopy (TEM) (including the X-ray energy dispersive spectrometry EDS and high resolution transmission electron microscopy HRTEM) and dielectric impedance analyzer. We systematically investigated the structure, dielectric properties and voltage tunable property of the ceramics prepared at different sintering temperatures. The XRD patterns demonstrated that the synthesized BMN solid solutions had cubic phase pyrochlore-type structure when sintered at 1050°C or higher, and the lattice parameter (a) of the unit cell in BMN solid solution was calculated to be about 10.56Å. The vibrational peaks observed in the Raman spectra of BMN solid solutions also confirmed the cubic phase pyrochlore-type structure of the synthesized BMN. According to the Scanning Electron Microscope (SEM) images, the grain size increased with increasing sintering temperature. Additionally, it was shown that the densities of the BMN ceramic tablets vary with sintering temperature. The calculated theoretical density for the BMN ceramic tablets sintered at different temperatures is about 6.7521 . The density of the respective measured tablets is usually amounting more than 91% and 5 approaching a maximum value of 96.5% for sintering temperature of 1150°C. The microstructure was investigated by using Scanning Transmission Electron Microscope (STEM), X-ray diffraction (XRD). Combined with the results obtained from the STEM and XRD, the impact of sintering temperature on the macroscopic and microscopic structure was discussed. The relative dielectric constant ( ) and dielectric loss ( ) of the BMN solid solutions were measured to be 161-200 and (at room temperature and 100Hz-1MHz), respectively. The BMN solid
DEFF Research Database (Denmark)
leMesurier, B.J.; Christiansen, Peter Leth; Gaididei, Yuri Borisovich
2004-01-01
The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2...... losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials....
Partial Differential Equations
1988-01-01
The volume contains a selection of papers presented at the 7th Symposium on differential geometry and differential equations (DD7) held at the Nankai Institute of Mathematics, Tianjin, China, in 1986. Most of the contributions are original research papers on topics including elliptic equations, hyperbolic equations, evolution equations, non-linear equations from differential geometry and mechanics, micro-local analysis.
A New 5-Phase Equation of State for Carbon
Energy Technology Data Exchange (ETDEWEB)
Coe, Joshua Damon [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division; Gammel, J. Tinka [Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Theoretical Division
2016-09-06
We describe the development of SESAME 7835, a new tabular equation of state (EOS) for carbon containing the diamond, bc8, simple cubic, simple hexagonal, and liquid/plasma phases. We compare the EOS against a wide variety of experimental data and simulation results, including static compression, dynamic compression, specific heat, and thermal expansion. To the extent that the reference data agree amongst themselves, the results are satisfactory in all cases.
Equating error in observed-score equating
van der Linden, Willem J.
2006-01-01
Traditionally, error in equating observed scores on two versions of a test is defined as the difference between the transformations that equate the quantiles of their distributions in the sample and population of test takers. But it is argued that if the goal of equating is to adjust the scores of
Bond-order potential for magnetic body-centered-cubic iron and its transferability
Lin, Yi-Shen; Mrovec, M.; Vitek, V.
2016-06-01
We derived and thoroughly tested a bond-order potential (BOP) for body-centered-cubic (bcc) magnetic iron that can be employed in atomistic calculations of a broad variety of crystal defects that control structural, mechanical, and thermodynamic properties of this technologically important metal. The constructed BOP reflects correctly the mixed nearly free electron and covalent bonding arising from the partially filled d band as well as the ferromagnetism that is actually responsible for the stability of the bcc structure of iron at low temperatures. The covalent part of the cohesive energy is determined within the tight-binding bond model with the Green's function of the Schrödinger equation determined using the method of continued fractions terminated at a sufficient level of the moments of the density of states. This makes the BOP an O (N ) method usable for very large numbers of particles. Only d d bonds are included explicitly, but the effect of s electrons on the covalent energy is included via their screening of the corresponding d d bonds. The magnetic part of the cohesive energy is included using the Stoner model of itinerant magnetism. The repulsive part of the cohesive energy is represented, as in any tight-binding scheme, by an empirical formula. Its functional form is physically justified by studies of the repulsion in face-centered-cubic (fcc) solid argon under very high pressure where the repulsion originates from overlapping s and p closed-shell electrons just as it does from closed-shell s electrons in transition metals squeezed into the ion core under the influence of the large covalent d bonding. Testing of the transferability of the developed BOP to environments significantly different from those of the ideal bcc lattice was carried out by studying crystal structures and magnetic states alternative to the ferromagnetic bcc lattice, vacancies, divacancies, self-interstitial atoms (SIAs), paths continuously transforming the bcc structure to
Experimental evidence of body centered cubic iron in Earth's core
Hrubiak, R.; Meng, Y.; Shen, G.
2017-12-01
The Earth's core is mainly composed of iron. While seismic evidence has shown a liquid outer core and a solid inner core, the crystalline nature of the solid iron at the core condition remains debated, largely due to the difficulties in experimental determination of exact polymorphs at corresponding pressure-temperature conditions. We have examined crystal structures of iron up to 220 GPa and 6000 K with x-ray diffraction using a double-sided laser heating system at HPCAT, Advanced Photon Source. The iron sample is confined in a small chamber surrounded by single crystal MgO. The laser power can be modulated together with temperature measurements. The modulated heating of iron in an MgO single crystal matrix allows for microstructure analysis during heating and after the sample is quenched. We present experimental evidence of a body-centered-cubic (BCC) iron from about 100 GPa and 3000 K to at least 220 GPa and 4000 K. The observed BCC phase may be consistent with a theoretically predicted BCC phase that is dynamically stable in similar pressure-temperature conditions [1]. We will discuss the stability region of the BCC phase and the melting curve of iron and their implications in the nature of the Earth's inner core. References: A. B. Belonoshko et al., Nat. Geosci., 1-6 (2017).
Cubic-quintic solitons in the checkerboard potential
International Nuclear Information System (INIS)
Driben, Rodislav; Zyss, Joseph; Malomed, Boris A.; Gubeskys, Arthur
2007-01-01
We introduce a two-dimensional (2D) model which combines a checkerboard potential, alias the Kronig-Penney (KP) lattice, with the self-focusing cubic and self-defocusing quintic nonlinear terms. The beam-splitting mechanism and soliton multistability are explored in this setting, following the recently considered 1D version of the model. Families of single- and multi-peak solitons (in particular, five- and nine-peak species naturally emerge in the 2D setting) are found in the semi-infinite gap, with both branches of bistable families being robust against perturbations. For single-peak solitons, the variational approximation (VA) is developed, providing for a qualitatively correct description of the transition from monostability to the bistability. 2D solitons found in finite band gaps are unstable. Also constructed are two different species of stable vortex solitons, arranged as four-peak patterns ('oblique' and 'straight' ones). Unlike them, compact 'crater-shaped' vortices are unstable, transforming themselves into randomly walking fundamental beams
Tunable surface configuration of skyrmion lattices in cubic helimagnets
Wan, Xuejin; Hu, Yangfan; Wang, Biao
2018-06-01
In bulk helimagnets, the presence of magnetic skyrmion lattices is always accompanied by a periodic stress field due to the intrinsic magnetoelastic coupling. The release of this nontrivial stress field at the surface causes a periodic displacement field, which characterizes a novel particle-like property of skyrmion: its surface configuration. Here, we derive the analytical solution of this displacement field for semi-infinite cubic helimagnet with the skyrmion magnetization approximated by the triple-Q representation. For MnSi, we show that the skyrmion lattices have a bumpy surface configuration characterized by periodically arranged peaks with a characteristic height of about 10‑13 m. The pattern of the peaks can be controlled by varying the strength of the applied magnetic field. Moreover, we prove that the surface configuration varies together with the motion and deformation of the skyrmion lattices. As a result, the surface configuration can be tuned by application of electric current, mechanical loads, as well as any other effective external fields for skyrmion lattices.
Plasmon polaritons in cubic lattices of spherical metallic nanoparticles
Lamowski, Simon; Mann, Charlie-Ray; Hellbach, Felicitas; Mariani, Eros; Weick, Guillaume; Pauly, Fabian
2018-03-01
We theoretically investigate plasmon polaritons in cubic lattices of spherical metallic nanoparticles. The nanoparticles, each supporting triply-degenerate localized surface plasmons, couple through the Coulomb dipole-dipole interaction, giving rise to collective plasmons that extend over the whole metamaterial. The latter hybridize with photons forming plasmon polaritons, which are the hybrid light-matter eigenmodes of the system. We derive general analytical expressions to evaluate both plasmon and plasmon-polariton dispersions and the corresponding eigenstates. These are obtained within a Hamiltonian formalism, which takes into account retardation effects in the dipolar interaction between the nanoparticles and considers the dielectric properties of the nanoparticles as well as their surrounding. Within this model we predict polaritonic splittings in the near-infrared to the visible range of the electromagnetic spectrum that depend on polarization, lattice symmetry, and wave-vector direction. Finally, we show that the predictions of our model are in excellent quantitative agreement with conventional finite-difference frequency-domain simulations, but with the advantages of analytical insight and significantly reduced computational cost.
Twinning of cubic diamond explains reported nanodiamond polymorphs
Németh, Péter; Garvie, Laurence A. J.; Buseck, Peter R.
2015-12-01
The unusual physical properties and formation conditions attributed to h-, i-, m-, and n-nanodiamond polymorphs has resulted in their receiving much attention in the materials and planetary science literature. Their identification is based on diffraction features that are absent in ordinary cubic (c-) diamond (space group: Fd-3m). We show, using ultra-high-resolution transmission electron microscope (HRTEM) images of natural and synthetic nanodiamonds, that the diffraction features attributed to the reported polymorphs are consistent with c-diamond containing abundant defects. Combinations of {113} reflection and rotation twins produce HRTEM images and d-spacings that match those attributed to h-, i-, and m-diamond. The diagnostic features of n-diamond in TEM images can arise from thickness effects of c-diamonds. Our data and interpretations strongly suggest that the reported nanodiamond polymorphs are in fact twinned c-diamond. We also report a new type of twin ( rotational), which can give rise to grains with dodecagonal symmetry. Our results show that twins are widespread in diamond nanocrystals. A high density of twins could strongly influence their applications.
Electrical leakage phenomenon in heteroepitaxial cubic silicon carbide on silicon
Pradeepkumar, Aiswarya; Zielinski, Marcin; Bosi, Matteo; Verzellesi, Giovanni; Gaskill, D. Kurt; Iacopi, Francesca
2018-06-01
Heteroepitaxial 3C-SiC films on silicon substrates are of technological interest as enablers to integrate the excellent electrical, electronic, mechanical, thermal, and epitaxial properties of bulk silicon carbide into well-established silicon technologies. One critical bottleneck of this integration is the establishment of a stable and reliable electronic junction at the heteroepitaxial interface of the n-type SiC with the silicon substrate. We have thus investigated in detail the electrical and transport properties of heteroepitaxial cubic silicon carbide films grown via different methods on low-doped and high-resistivity silicon substrates by using van der Pauw Hall and transfer length measurements as test vehicles. We have found that Si and C intermixing upon or after growth, particularly by the diffusion of carbon into the silicon matrix, creates extensive interstitial carbon traps and hampers the formation of a stable rectifying or insulating junction at the SiC/Si interface. Although a reliable p-n junction may not be realistic in the SiC/Si system, we can achieve, from a point of view of the electrical isolation of in-plane SiC structures, leakage suppression through the substrate by using a high-resistivity silicon substrate coupled with deep recess etching in between the SiC structures.
Anisotropic cubic lattice potts ferromagnet: renormalisation group treatment
International Nuclear Information System (INIS)
Tsallis, C.; Schwaccheim, G.; Silva, L.R. da; Rio Grande do Norte Univ., Natal
1983-01-01
Within a real space renormalisation group framework, the criticality of the fully anisotropic (arbitrary J sub(x), J sub(y) and J sub(z)) q-state Potts ferromagnet in simple cubic lattice is discussed. Several already known exact results for the d=1 and d=2 particular cases are recovered. Furthermore it is obtained: (i) the q-dependence of the d=3 correlation length critical exponent ν 3 (in particular, if q→0, ν 3 (q) approximatelly ν 3 (0)+ν 3 '(0)q) where the present approximate values are ν 3 (0) or approx.= 1.105 and ν 3 '(0) or approx.=-0.66; (ii) the q-dependence d=2 d=3 crossover critical exponent phi 23 (in particular, phi 23 varies as 1/√q if q Q→0); (iii) through a convenient numerical extrapolation, a quite accurate proposal for the critical temperatures corresponding to arbitrary ratios J sub(y)/ J sub(x) and J sub(z) / J sub(x) and values of q. (Author) [pt
Hyperfine interactions in the cubic semiconductor CdO
International Nuclear Information System (INIS)
Desimoni, J.; Bibiloni, A.G.; Massolo, C.P.; Renteria, M.
1990-01-01
The time-differential perturbed angular correlation technique has been applied using 111 In probes, which decay through electron capture to 111 Cd, to study the hyperfine interaction in cubic cadmium oxide, in the temperature range RT--740 degree C (RT denotes room temperature). The main fraction of probes are located in perfect-lattice sites, with null electric field gradient in agreement with crystalline-structure considerations. Around 25% of the total intensity shows an electric-field-gradient distribution around V zz =0. This corresponds to probes located in sites perturbed by the vicinity of oxygen vacancies in the lattice. The temperature-independent behavior of the measured hyperfine parameters is discussed in terms of conductivity and band-structure properties of the semiconductor. No time-dependent interaction arising from nuclear electron-capture aftereffects are seen in this experiment. This is in agreement with a previously reported model of aftereffect processes which states that only holes trapped in impurity levels inside the band gap of the semiconductor can give rise to detectable fluctuating interactions
Hyperfine interactions in the cubic semiconductor CdO
Energy Technology Data Exchange (ETDEWEB)
Desimoni, J.; Bibiloni, A.G.; Massolo, C.P.; Renteria, M. (Departamento de Fisica, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Casilla de Correo No. 67, 1900 La Plata, Argentina (AR))
1990-01-15
The time-differential perturbed angular correlation technique has been applied using {sup 111}In probes, which decay through electron capture to {sup 111}Cd, to study the hyperfine interaction in cubic cadmium oxide, in the temperature range RT--740 {degree}C (RT denotes room temperature). The main fraction of probes are located in perfect-lattice sites, with null electric field gradient in agreement with crystalline-structure considerations. Around 25% of the total intensity shows an electric-field-gradient distribution around {ital V}{sub {ital zz}}=0. This corresponds to probes located in sites perturbed by the vicinity of oxygen vacancies in the lattice. The temperature-independent behavior of the measured hyperfine parameters is discussed in terms of conductivity and band-structure properties of the semiconductor. No time-dependent interaction arising from nuclear electron-capture aftereffects are seen in this experiment. This is in agreement with a previously reported model of aftereffect processes which states that only holes trapped in impurity levels inside the band gap of the semiconductor can give rise to detectable fluctuating interactions.
Cubic Interactions of Massless Bosonic Fields in Three Dimensions
Mkrtchyan, Karapet
2018-06-01
In this Letter, we take the first step towards construction of nontrivial Lagrangian theories of higher-spin gravity in a metriclike formulation in three dimensions. The crucial feature of a metriclike formulation is that it is known how to incorporate matter interactions into the description. We derive a complete classification of cubic interactions for arbitrary triples s1 , s2 , s3 of massless fields, which are the building blocks of any interacting theory with massless higher spins. We find that there is, at most, one vertex for any given triple of spins in 3D (with one exception, s1=s2=s3=1 , which allows for two vertices). Remarkably, there are no vertices for spin values that do not respect strict triangle inequalities and contain at least two spins greater than one. This translates into selection rules for three-point functions of higher-spin conserved currents in two dimensional conformal field theory. Furthermore, universal coupling to gravity for any spin is derived. Last, we argue that this classification persists in arbitrary Einstein backgrounds.
STROPHOIDS, A FAMILY OF CUBIC CURVES WITH REMARKABLE PROPERTIES
Directory of Open Access Journals (Sweden)
STACHEL Hellmuth
2015-06-01
On each strophoid there is a symmetric relation of points, so-called ‘associated’ points, with a series of properties: The lines connecting associated points P and P’ are tangent of the negative pedal curve. Tangents at associated points intersect at a point which again lies on the cubic. For all pairs (P, P’ of associated points, the midpoints lie on a line through the node N. For any two pairs (P, P’ and (Q, Q’ of associated points, the points of intersection between the lines PQ and P’Q’ as well as between PQ’ and P’Q are again placed on the strophoid and mutually associated. The lines PQ and PQ’ are symmetric with respect to the line connecting P with the node. Thus, strophoids generalize Apollonian circles: For given non-collinear points A, A’ and N the locus of points X such that one angle bisector of the lines XA and XA’ passes through N is a strophoid.
Research of Cubic Bezier Curve NC Interpolation Signal Generator
Directory of Open Access Journals (Sweden)
Shijun Ji
2014-08-01
Full Text Available Interpolation technology is the core of the computer numerical control (CNC system, and the precision and stability of the interpolation algorithm directly affect the machining precision and speed of CNC system. Most of the existing numerical control interpolation technology can only achieve circular arc interpolation, linear interpolation or parabola interpolation, but for the numerical control (NC machining of parts with complicated surface, it needs to establish the mathematical model and generate the curved line and curved surface outline of parts and then discrete the generated parts outline into a large amount of straight line or arc to carry on the processing, which creates the complex program and a large amount of code, so it inevitably introduce into the approximation error. All these factors affect the machining accuracy, surface roughness and machining efficiency. The stepless interpolation of cubic Bezier curve controlled by analog signal is studied in this paper, the tool motion trajectory of Bezier curve can be directly planned out in CNC system by adjusting control points, and then these data were put into the control motor which can complete the precise feeding of Bezier curve. This method realized the improvement of CNC trajectory controlled ability from the simple linear and circular arc to the complex project curve, and it provides a new way for economy realizing the curve surface parts with high quality and high efficiency machining.
Nature and strength of defect interactions in cubic stabilized zirconia
International Nuclear Information System (INIS)
Bogicevic, A.; Wolverton, C.
2003-01-01
The intrinsic ordering tendencies that limit ionic conduction in doped zirconia electrolytes are fully elucidated using first-principles calculations. A detailed analysis of nearly 300 yttria- and scandia-stabilized cubic-zirconia-ordered vacancy compounds reveals a delicate balance between competing elastic and electrostatic interactions. These results explain several outstanding experimental observations and provide substantial insight needed for improving ionic conduction and enabling low-temperature operation of zirconia-based electrolytes. We show that the surprising vacancy ordering in dilute solid solutions is a consequence of repulsive electrostatic and attractive elastic interactions that balance at third-neighbor vacancy separations. In contrast, repulsive elastic vacancy-dopant interactions prevail over electrostatic attraction at all probed defect separations in YSZ and lead to very weak ordering preferences in ScSZ. The total electronic contribution to the defect interactions is shown to be strongly dominated by simple point-charge electrostatics, leaving speciation of defect ordering for a given class of aliovalent dopants to the elastic term. Thus, ion size becomes a critical parameter in controlling the ionic conductivity of doped oxide electrolytes
Cubic mesoporous Ag@CN: a high performance humidity sensor.
Tomer, Vijay K; Thangaraj, Nishanthi; Gahlot, Sweta; Kailasam, Kamalakannan
2016-12-01
The fabrication of highly responsive, rapid response/recovery and durable relative humidity (%RH) sensors that can precisely monitor humidity levels still remains a considerable challenge for realizing the next generation humidity sensing applications. Herein, we report a remarkably sensitive and rapid %RH sensor having a reversible response using a nanocasting route for synthesizing mesoporous g-CN (commonly known as g-C 3 N 4 ). The 3D replicated cubic mesostructure provides a high surface area thereby increasing the adsorption, transmission of charge carriers and desorption of water molecules across the sensor surfaces. Owing to its unique structure, the mesoporous g-CN functionalized with well dispersed catalytic Ag nanoparticles exhibits excellent sensitivity in the 11-98% RH range while retaining high stability, negligible hysteresis and superior real time %RH detection performances. Compared to conventional resistive sensors based on metal oxides, a rapid response time (3 s) and recovery time (1.4 s) were observed in the 11-98% RH range. Such impressive features originate from the planar morphology of g-CN as well as unique physical affinity and favourable electronic band positions of this material that facilitate water adsorption and charge transportation. Mesoporous g-CN with Ag nanoparticles is demonstrated to provide an effective strategy in designing high performance %RH sensors and show great promise for utilization of mesoporous 2D layered materials in the Internet of Things and next generation humidity sensing applications.
Twinning of cubic diamond explains reported nanodiamond polymorphs.
Németh, Péter; Garvie, Laurence A J; Buseck, Peter R
2015-12-16
The unusual physical properties and formation conditions attributed to h-, i-, m-, and n-nanodiamond polymorphs has resulted in their receiving much attention in the materials and planetary science literature. Their identification is based on diffraction features that are absent in ordinary cubic (c-) diamond (space group: Fd-3m). We show, using ultra-high-resolution transmission electron microscope (HRTEM) images of natural and synthetic nanodiamonds, that the diffraction features attributed to the reported polymorphs are consistent with c-diamond containing abundant defects. Combinations of {113} reflection and rotation twins produce HRTEM images and d-spacings that match those attributed to h-, i-, and m-diamond. The diagnostic features of n-diamond in TEM images can arise from thickness effects of c-diamonds. Our data and interpretations strongly suggest that the reported nanodiamond polymorphs are in fact twinned c-diamond. We also report a new type of twin ( rotational), which can give rise to grains with dodecagonal symmetry. Our results show that twins are widespread in diamond nanocrystals. A high density of twins could strongly influence their applications.
Spinning solitons in cubic-quintic nonlinear media
Indian Academy of Sciences (India)
in contrast to a recently found azimuthal instability of spinning doughnut-shaped solitons in the CQ NLS equation, their GL counterparts may be completely stable. On the other hand, a problem of fundamental interest is the possibility of the formation of fully three-dimensional (3D) optical spatiotemporal solitons, also referred ...
Defect structure of cubic solid solutions of alkaline earth and rare earth fluorides
DenHartog, HW
1996-01-01
In this paper we will consider the disorder in some cubic solid solutions consisting of one of the alkaline earth fluorides and one of the rare earth fluorides. This is an attractive group of model materials, because these materials have a rather simple overall cubic structure. We will discuss the
On the number of longest and almost longest cycles in cubic graphs
DEFF Research Database (Denmark)
Chia, Gek Ling; Thomassen, Carsten
2012-01-01
We consider the questions: How many longest cycles must a cubic graph have, and how many may it have? For each k >= 2 there are infinitely many p such that there is a cubic graph with p vertices and precisely one longest cycle of length p-k. On the other hand, if G is a graph with p vertices, all...
Cross-talk dynamics of optical solitons in a broadband Kerr nonlinear system with weak cubic loss
International Nuclear Information System (INIS)
Peleg, Avner; Nguyen, Quan M.; Chung, Yeojin
2010-01-01
We study the dynamics of fast soliton collisions in a Kerr nonlinear optical waveguide with weak cubic loss. We obtain analytic expressions for the amplitude and frequency shifts in a single two-soliton collision and show that the impact of a fast three-soliton collision is given by the sum of the two-soliton interactions. Our analytic predictions are confirmed by numerical simulations with the perturbed nonlinear Schroedinger (NLS) equation. Furthermore, we show that the deterministic collision-induced dynamics of soliton amplitudes in a broadband waveguide system with N frequency channels is described by a Lotka-Volterra model for N competing species. For a two-channel system we find that stable transmission with equal prescribed amplitudes can be achieved by a proper choice of linear amplifier gain. The predictions of the Lotka-Volterra model are confirmed by numerical solution of a perturbed coupled-NLS model.
Bhattacharya, Somnath; Mukherjee, Pradip; Roy, Amit Singha; Saha, Anirban
2018-03-01
We consider a scalar field which is generally non-minimally coupled to gravity and has a characteristic cubic Galilean-like term and a generic self-interaction, as a candidate of a Dark Energy model. The system is dynamically analyzed and novel fixed points with perturbative stability are demonstrated. Evolution of the system is numerically studied near a novel fixed point which owes its existence to the Galileon character of the model. It turns out that demanding the stability of this novel fixed point puts a strong restriction on the allowed non-minimal coupling and the choice of the self-interaction. The evolution of the equation of state parameter is studied, which shows that our model predicts an accelerated universe throughout and the phantom limit is only approached closely but never crossed. Our result thus extends the findings of Coley, Dynamical systems and cosmology. Kluwer Academic Publishers, Boston (2013) for more general NMC than linear and quadratic couplings.
Non-spherical micelles in an oil-in-water cubic phase
DEFF Research Database (Denmark)
Leaver, M.; Rajagopalan, V.; Ulf, O.
2000-01-01
phase, both with and without SDS, was established by NMR self-diffusion. In addition H-2 NMR relaxation experiments have demonstrated that the micelles in the cubic phase are non-spherical, having grown and changed shape upon formation of the cubic phase from the micellar solution. Small angle...... associated with the micellar cubic phase, Pm3n and Fd3m. The micellar volumes calculated for these space groups are similar and are consistent with a change in micellar geometry from spherical to prolate.......The cubic phase formed between the microemulsion and hexagonal phases of the ternary pentaethylene glycol dodecyl ether (C12E5)-decane-water system and that doped with small amounts of sodium dodecylsulfate (SDS) have been investigated. The presence of discrete oil-swollen micelles in the cubic...
Atomistic simulation of fatigue in face centred cubic metals
International Nuclear Information System (INIS)
Fan, Zhengxuan
2016-01-01
Fatigue is one of the major damage mechanisms of metals. It is characterized by strong environmental effects and wide lifetime dispersions which must be better understood. Different face centred cubic metals, al, Cu, Ni, and Ag are analyzed. The mechanical behaviour of surface steps naturally created by the glide of dislocations subjected to cyclic loading is examined using molecular dynamics simulations in vacuum and in air for Cu and Ni. an atomistic reconstruction phenomenon is observed at these surface steps which can induce strong irreversibility. Three different mechanisms of reconstruction are defined. Surface slip irreversibility under cyclic loading is analyzed. all surface steps are intrinsically irreversible under usual fatigue laboratory loading amplitude without the arrival of opposite sign dislocations on direct neighbor plane.With opposite sign dislocations on non direct neighbour planes, irreversibility cumulates cycle by cycle and a micro-notch is produced whose depth gradually increases.Oxygen environment affects the surface (first stage of oxidation) but does not lead to higher irreversibility as it has no major influence on the different mechanisms linked to surface relief evolution.a rough estimation of surface irreversibility is carried out for pure edge dislocations in persistent slip bands in so-called wavy materials. It gives an irreversibility fraction between 0.5 and 0.75 in copper in vacuum and in air, in agreement with recent atomic force microscopy measurements.Crack propagation mechanisms are simulated in inert environment. Cracks can propagate owing to the irreversibility of generated dislocations because of their mutual interactions up to the formation of dislocation junctions. (author) [fr
Role of Adsorption Phenomena in Cubic Tricalcium Aluminate Dissolution.
Myers, Rupert J; Geng, Guoqing; Li, Jiaqi; Rodríguez, Erich D; Ha, Juyoung; Kidkhunthod, Pinit; Sposito, Garrison; Lammers, Laura N; Kirchheim, Ana Paula; Monteiro, Paulo J M
2017-01-10
The workability of fresh Portland cement (PC) concrete critically depends on the reaction of the cubic tricalcium aluminate (C 3 A) phase in Ca- and S-rich pH >12 aqueous solution, yet its rate-controlling mechanism is poorly understood. In this article, the role of adsorption phenomena in C 3 A dissolution in aqueous Ca-, S-, and polynaphthalene sulfonate (PNS)-containing solutions is analyzed. The zeta potential and pH results are consistent with the isoelectric point of C 3 A occurring at pH ∼12 and do not show an inversion of its electric double layer potential as a function of S or Ca concentration, and PNS adsorbs onto C 3 A, reducing its zeta potential to negative values at pH >12. The S and Ca K-edge X-ray absorption spectroscopy (XAS) data obtained do not indicate the structural incorporation or specific adsorption of SO 4 2- on the partially dissolved C 3 A solids analyzed. Together with supporting X-ray ptychography and scanning electron microscopy results, a model for C 3 A dissolution inhibition in hydrated PC systems is proposed whereby the formation of an Al-rich leached layer and the complexation of Ca-S ion pairs onto this leached layer provide the key inhibiting effect(s). This model reconciles the results obtained here with the existing literature, including the inhibiting action of macromolecules such as PNS and polyphosphonic acids upon C 3 A dissolution. Therefore, this article advances the understanding of the rate-controlling mechanism in hydrated C 3 A and thus PC systems, which is important to better controlling the workability of fresh PC concrete.
Energy Technology Data Exchange (ETDEWEB)
Kong, Bo, E-mail: kong79@yeah.net, E-mail: yachao.zhang@pku.edu.cn [School of Physics and Electronic Sciences, Guizhou Education University, Guiyang 550018 (China); Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Education University, Guiyang 550018 (China); Zhang, Yachao, E-mail: kong79@yeah.net, E-mail: yachao.zhang@pku.edu.cn [Guizhou Provincial Key Laboratory of Computational Nano-Material Science, Guizhou Education University, Guiyang 550018 (China)
2016-07-07
The electronic structures of the cubic GdH{sub 3} are extensively investigated using the ab initio many-body GW calculations treating the Gd 4f electrons either in the core (4f-core) or in the valence states (4f-val). Different degrees of quasiparticle (QP) self-consistent calculations with the different starting points are used to correct the failures of the GGA/GGA + U/HSE03 calculations. In the 4f-core case, GGA + G{sub 0}W{sub 0} calculations give a fundamental band gap of 1.72 eV, while GGA+ GW{sub 0} or GGA + GW calculations present a larger band gap. In the 4f-val case, the nonlocal exchange-correlation (xc) functional HSE03 can account much better for the strong localization of the 4f states than the semilocal or Hubbard U corrected xc functional in the Kohn–Sham equation. We show that the fundamental gap of the antiferromagnetic (AFM) or ferromagnetic (FM) GdH{sub 3} can be opened up by solving the QP equation with improved starting point of eigenvalues and wave functions given by HSE03. The HSE03 + G{sub 0}W{sub 0} calculations present a fundamental band gap of 2.73 eV in the AFM configuration, and the results of the corresponding GW{sub 0} and GW calculations are 2.89 and 3.03 eV, respectively. In general, for the cubic structure, the fundamental gap from G{sub 0}W{sub 0} calculations in the 4f-core case is the closest to the real result. By G{sub 0}W{sub 0} calculations in the 4f-core case, we find that H or Gd defects can strongly affect the band structure, especially the H defects. We explain the mechanism in terms of the possible electron correlation on the hydrogen site. Under compression, the insulator-to-metal transition in the cubic GdH{sub 3} occurs around 40 GPa, which might be a satisfied prediction.
Shearman, Gemma C; Khoo, Bee J; Motherwell, Mary-Lynn; Brakke, Kenneth A; Ces, Oscar; Conn, Charlotte E; Seddon, John M; Templer, Richard H
2007-06-19
Inverse bicontinuous cubic lyotropic phases are a complex solution to the dilemma faced by all self-assembled water-amphiphile systems: how to satisfy the incompatible requirements for uniform interfacial curvature and uniform molecular packing. The solution reached in this case is for the water-amphiphile interfaces to deform hyperbolically onto triply periodic minimal surfaces. We have previously suggested that although the molecular packing in these structures is rather uniform the relative phase behavior of the gyroid, double diamond, and primitive inverse bicontinuous cubic phases can be understood in terms of subtle differences in packing frustration. In this work, we have calculated the packing frustration for these cubics under the constraint that their interfaces have constant mean curvature. We find that the relative packing stress does indeed differ between phases. The gyroid cubic has the least packing stress, and at low water volume fraction, the primitive cubic has the greatest packing stress. However, at very high water volume fraction, the double diamond cubic becomes the structure with the greatest packing stress. We have tested the model in two ways. For a system with a double diamond cubic phase in excess water, the addition of a hydrophobe may release packing frustration and preferentially stabilize the primitive cubic, since this has previously been shown to have lower curvature elastic energy. We have confirmed this prediction by adding the long chain alkane tricosane to 1-monoolein in excess water. The model also predicts that if one were able to hydrate the double diamond cubic to high water volume fractions, one should destabilize the phase with respect to the primitive cubic. We have found that such highly swollen metastable bicontinuous cubic phases can be formed within onion vesicles. Data from monoelaidin in excess water display a well-defined transition, with the primitive cubic appearing above a water volume fraction of 0.75. Both of
Blakley, G. R.
1982-01-01
Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)
Equations of State: From the Ideas of van der Waals to Association Theories
DEFF Research Database (Denmark)
Kontogeorgis, Georgios; Economou, Ioannis G.
2010-01-01
equations of state are sensitive to the mixing and combining rules used. Moreover, it is shown that previously reported deficiencies for size-asymmetric systems are more related to the van der Waals one fluid mixing rules used rather than the functionality of the cubic equation of state itself. Improved...... models for polar systems have been developed using the so-called EoS/GE mixing rules and we illustrate with the same methodology how these mixing rules should best be used for size-asymmetric systems. Despite the significant capabilities of cubic equations of state, their limitations lie especially...... in the description of complex phase behavior, e.g. liquid–liquid equilibria for highly polar and/or hydrogen bonding containing molecules. In these cases, advanced equations of state based on statistical mechanics that incorporate ideas from perturbation (e.g. SAFT and CPA), chemical (e.g. APACT) and lattice (e...
International Nuclear Information System (INIS)
Pokrivnyj, V.V.; Bekenev, V.L.
2006-01-01
Equation of states, energy band structure, electronic density of states, and bulk moduli of the boron nitride fulborenite crystals: B 12 N 12 with a diamond lattice and B 24 N 24 , B 12 N 12 with a simple cubic lattice have been calculated for the first time by FLAPW method. Calculated parameters of these compounds are as follows: equilibrium lattice parameter, the length of B-N bond, the number of atoms per conventional cell, density, bulk modulus, band gap. Hyperdiamond B 12 N 12 is shown to have the record bulk modulus B 0 = 658 GPa [ru
Handbook of integral equations
Polyanin, Andrei D
2008-01-01
This handbook contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equations that arise in mathematics, physics, engineering, the sciences, and economics. This second edition includes new chapters on mixed multidimensional equations and methods of integral equations for ODEs and PDEs, along with over 400 new equations with exact solutions. With many examples added for illustrative purposes, it presents new material on Volterra, Fredholm, singular, hypersingular, dual, and nonlinear integral equations, integral transforms, and special functions.
Enhanced nuclear magnetic resonance in a non-magnetic cubic doublet
International Nuclear Information System (INIS)
Veenendaal, E.J.
1982-01-01
In this thesis two lanthanide compounds are studied which show enhanced nuclear magnetism at low temperatures: Rb 2 NaHoF 6 and CsNaHoF 6 . Chapter II gives a description of the 4 He-circulating refrigerator, which was built to provide the low temperatures required for the polarization of the enhanced nuclear moments. This type of dilution refrigerator was chosen because of its simple design and large cooling power. Chapter III is devoted to a comparison of the different types of dilution refrigerators. A theoretical discussion is given of their performance, starting from the differential equations, which govern the temperature distribution in the refrigerator. In chapter IV the actual performance of the refrigerator, described in chapter II is discussed. In chapter V a description of the NMR-apparatus, developed for very-low-temperature NMR experiments is given. In chapter VI experimental results on the compound Rb 2 NaHoF 6 are presented. The CEF-ground state of this compound is probably the non-magnetic doublet GAMMA 3 , but at a temperature of 170 K a structural phase transition lowers the crystal symmetry from cubic to tetragonal and the doublet is split into two singlets. In chapter VII specific heat, (enhanced) nuclear magnetic resonance and magnetization measurements on the compound Cs 2 NaHoF 6 are presented which also has a GAMMA 3 -doublet ground state. In zero magnetic field the degeneracy of the doublet is removed at a temperature of 393 mK, where a phase transition is induced by quadrupolar interactions. (Auth.)
Natural convection in a cubical cavity with a coaxial heated cylinder
Energy Technology Data Exchange (ETDEWEB)
Aithal, S. M.
2018-03-01
High-resolution three-dimensional simulations were conducted to investigate the velocity and temperature fields in a cold cubical cavity due to natural convection induced by a centrally placed hot cylinder. Unsteady, incompressible Navier-Stokes equations were solved by using a spectral- element method for Rayleigh numbers ranging from 103 to 109. The effect of spanwise thermal boundary conditions, aspect ratio (radius of the cylinder to the side of the cavity), and spanwise temperature distribution of the inner cylinder on the velocity and thermal fields were investigated for each Rayleigh number. Results from two-dimensional calculations were compared with three-dimensional simulations. The 3D results indicate a complex flow structure in the vicinity of the spanwise walls. The results also show that the imposed thermal wall boundary condition impacts the flow and temperature fields strongly near the spanwise walls. The variation of the local Nusselt number on the cylinder surface and enclosure walls at various spanwise locations was also investigated. The local Nusselt number on the cylinder surface and enclosure walls at the cavity mid-plane (Z = 0) is close to 2D simulations for 103 ≤ Ra ≤ 108. Simulations also show a variation in the local Nusselt number, on both the cylinder surface and the enclosure walls, in the spanwise direction, for all Rayleigh numbers studied in this work. The results also indicate that if the enclosure walls are insulated in the spanwise direction (as opposed to a constant temperature), the peak Nusselt number on the enclosure surface occurs near the spanwise walls and is about 20% higher than the peak Nusselt number at the cavity mid-plane. The temporal characteristics of 3D flows are also different from 2D results for Ra > 108. These results suggest that 3D simulations would be more appropriate for flows with Ra > 108.
DEFF Research Database (Denmark)
Oliveira, Mariana B.; Freire, Mara G.; Marrucho, Isabel M.
2007-01-01
Fluorocarbons (FCs) are a family of chemicals that are composed primarily of carbon and fluorine. They present weak intermolecular and strong intramolecular interactions, which confers them unusual thermophysical properties. They can also solubilize large amounts of gases such as oxygen and carbon...
DEFF Research Database (Denmark)
Arya, Alay; von Solms, Nicolas; Kontogeorgis, Georgios M.
2016-01-01
Miscible and immiscible gas flooding is one of the enhanced oil recovery (EOR) techniques that has been widely used to increase the oil production. One of the critical problems with gas flooding is that it generally aggravates the asphaltene precipitation, which further creates a flow assurance...... dependency upon the saturates, aromatics, resins, and asphaltenes (SARA) analysis or molecular weight (MW) of asphaltene is also analyzed. In addition, a unique characteristic of the model for the given stock tank oil (STO) is identified, which does not change with different types and amounts of gas...... injections and also remains the same at upper and lower onset pressure boundaries. On the basis of this unique characteristic, a simple procedure to predict asphaltene phase envelope (APE) for the reservoir oil with relatively simple and few experimental data, performed on STO with n...
DEFF Research Database (Denmark)
Breil, Martin Peter; Kontogeorgis, Georgios
2009-01-01
A thorough investigation of triethylene glycol (TEG) containing systems has been performed. The introduction of a new six-site association scheme for the TEG molecule has shown to be advantageous. Glycols are often modeled using a four-site scheme (abbreviated as 4C) hence ignoring the internal...... lone pairs of oxygen. The new association scheme also takes these sites into account. The new parameters of TEG are based on the vapor pressure data, liquid density data, and liquid-liquid equilibria (LLE) data (n-heptane), and they are tested for binary systems (methane, n-octane, n-nonane, n...
Localized waves of the coupled cubic-quintic nonlinear Schrödinger equations in nonlinear optics
Xu, Tao; Chen, Yong; Lin, Ji
2017-12-01
Not Available Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11675054 and 11435005), the Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014210140).
DEFF Research Database (Denmark)
Fettouhi, André; Thomsen, Kaj
2010-01-01
A systematic investigation of the CPA model's performance within solid-liquid equilibria (SLE) in binary mixtures (methane + ethane, methane + heptane, methane + benzene, methane + CO2, ethane + heptane, ethane + CO2, 1-propanol + 1,4-dioxane, ethanol + water, 2-propanol + water) is presented. Th....... The results from the binary mixtures are used to predict SLE behaviour in ternary mixtures (methane + ethane + heptane, methane + ethane + CO2). Our results are compared with experimental data found in the literature....
Radiation response of cubic mesoporous silicate and borosilicate thin films
Manzini, Ayelén; Alurralde, Martín; Luca, Vittorio
2018-01-01
The radiation response has been studied of cubic mesoporous silicate and borosilicate thin films having different boron contents prepared using the block copolymer template Brij 58 and the dip coating technique. The degree of pore ordering of the films was analysed using low-angle X-ray diffraction and film thickness measured by X-ray reflectivity. For films calcined at 350 °C, the incorporation of boron resulted in a reproducible oscillatory variation in the d-spacing and intensity of the primary reflection as a function of boron content. A clear peak was observed in the d-spacing at 5-10 mol% boron incorporation. For borosilicate films of a given composition an overall suppression of d-spacing was observed as a function of aging time relative to films that did not contain boron. This was ascribed to a slow condensation process. The films were irradiated in pile with neutrons and with iodine ions at energies of 180 keV and 70 MeV. Neutron irradiation of the silicate thin films for periods up to 30 days and aged for 400 days resulted in little reduction in either d-spacing or intensity of the primary low-angle X-ray reflection indicating that the films retained their mesopore ordering. In contrast borosilicate films for which the B (n, α) reaction was expected to result in enhanced displacement damage showed much larger variations in X-ray parameters. For these films short irradiation times resulted in a reduction of the d-spacing and intensity of the primary reflections considerably beyond that observed through aging. It is concluded that prolonged neutron irradiation and internal α irradiation have only a small, although measurable, impact on mesoporous borosilicate thin films increasing the degree of condensation and increasing unit cell contraction. When these borosilicate films were irradiated with iodine ions, more profound changes occurred. The pore ordering of the films was significantly degraded when low energy ions were used. In some cases the degree
Study of the cubic - to - monoclinic transformation in magnesia partially stabilized zirconia
International Nuclear Information System (INIS)
Muccillo, R.
1988-01-01
The transformation of the cubic phase to the stable monoclinic phase in ZrO 2 : 3%MgO quenched from 1450 0 C to RT has been studied by X-ray diffractometry in order to explain the thermal hysteresis in the electrical conductivity. The monoclinic-to-cubic ratio has been measured for samples annealed in the 500 0 C-1000 0 C temperature range. The results show that the decrease in the cubic phase content is the main responsible for the thermal hysteresis in the electrical conductivity of the magnesia partially stabilized zirconia solid electrolytes. (author) [pt
P-union and P-intersection of neutrosophic cubic sets
Florentin Smarandache; Chang Su Kim
2015-01-01
Conditions for the P-intersection and P-intersection of falsity-external (resp. indeterminacy-external and truth-external) neutrosophic cubic sets to be an falsity-external (resp. indeterminacy-external and truth- external) neutrosophic cubic set are provided. Conditions for the P-union and the P-intersection of two truth-external (resp. indeterminacy-external and falsity-external) neutrosophic cubic sets to be a truth-internal (resp. indeterminacy-internal and falsity-internal) neutrosoph...
Structural study on cubic-tetragonal transition of CH3NH3PbI3
International Nuclear Information System (INIS)
Kawamura, Yukihiko; Mashiyama, Hiroyuki; Hasebe, Katsuhiko
2002-01-01
The cubic-tetragonal phase transition of CH 3 NH 3 PbI 3 was investigated by single crystal X-ray diffractometry. The crystal structure was refined at five temperatures in the tetragonal phase. The PbI 6 octahedron rotates around the c-axis alternatively to construct the SrTiO 3 -type tetragonal structure. A methylammonium ion is partially ordered; 24 disordered states in the cubic phase are reduced to 8. With decreasing temperature, the rotation angle of the octahedron increases monotonically, which indicates it is an order parameter of the cubic-tetragonal transition. (author)
d and f electrons in a qp-quantized cubical field
International Nuclear Information System (INIS)
Kibler, M.; Sztucki, J.
1993-03-01
A procedure for qp-quantizing a crystal-field potential V with an arbitrary symmetry G is developed. Such a procedure is applied to the case where V involves cubic components (G=0) of the degrees 4 and 6. This case corresponds to d and f electrons in a qp-quantized cubical potential. It is shown that the qp-quantization of the considered cubical potential is equivalent to a symmetry breaking of type O→D 4 . A general conjecture about this symmetry breaking phenomenon is given. (author) 21 refs
CIP - a new numerical solver for general nonlinear hyperbolic equations in multi-dimension
International Nuclear Information System (INIS)
Yabe, Takashi; Takewaki, Hideaki.
1986-12-01
A new method CIP (Cubic-Interpolated Pseudo-particle) to solve hyperbolic equations is proposed. The method gives a stable and less diffusive result for square wave propagation compared with FCT (Flux-Corrected Transport) and a better result for propagation of a sine wave with a discontinuity. The scheme is extended to nonlinear and multi-dimensional problems. (orig.) [de
Energy Technology Data Exchange (ETDEWEB)
Deluque Toro, C.E., E-mail: deluquetoro@gmail.com [Grupo de Nuevos Materiales, Universidad Popular del Cesar, Valledupar (Colombia); Rodríguez M, Jairo Arbey [Grupo de Estudios de Materiales—GEMA, Departamento de Física, Universidad Nacional de Colombia, AA 5997 Bogotá DC (Colombia); Landínez Téllez, D.A. [Grupo de Física de Nuevos Materiales, Departamento de Física, Universidad Nacional de Colombia, AA 5997 Bogotá DC (Colombia); Moreno Salazar, N.O. [Departamento de Física, Universidade Federal de Sergipe (Brazil); Roa-Rojas, J. [Grupo de Física de Nuevos Materiales, Departamento de Física, Universidad Nacional de Colombia, AA 5997 Bogotá DC (Colombia)
2014-12-15
The Ba{sub 2}YTaO{sub 6} double perovskite presents a transition from cubic (Fm−3m) to tetragonal structure (I4/m) at high temperature. In this work, we present a detailed study of the structural and electronic properties of the double perovskite Ba{sub 2}YTaO{sub 6} in space group Fm−3m and I4/m. Calculations were made with the Full-Potential Linear Augmented Plane Wave method (FP-LAPW) within the framework of the Density Functional Theory (DFT) with exchange and correlation effects in the Generalized Gradient (GGA) and Local Density (LDA) approximations. From the minimization of energy as a function of volume and the fitting of the Murnaghan equation some structural characteristics were determined as, for example, total energy, lattice parameter (a=8.50 Å in cubic phase and a=5.985 Å and c=8.576 Å in tetragonal), bulk modulus (135.6 GPa in cubic phase and 134.1 GPa in tetragonal phase) and its derivative. The study of the electronic characteristics was performed from the analysis of the electronic density of states (DOS). We find a non-metallic behavior for this with a direct band gap of approximately 3.5 eV and we found that the Ba{sub 2}YTaO{sub 6} (I4/m) phase is the most stable one. {sup ©} 2013 Elsevier Science. All rights reserved.
International Nuclear Information System (INIS)
Deluque Toro, C.E.; Rodríguez M, Jairo Arbey; Landínez Téllez, D.A.; Moreno Salazar, N.O.; Roa-Rojas, J.
2014-01-01
The Ba 2 YTaO 6 double perovskite presents a transition from cubic (Fm−3m) to tetragonal structure (I4/m) at high temperature. In this work, we present a detailed study of the structural and electronic properties of the double perovskite Ba 2 YTaO 6 in space group Fm−3m and I4/m. Calculations were made with the Full-Potential Linear Augmented Plane Wave method (FP-LAPW) within the framework of the Density Functional Theory (DFT) with exchange and correlation effects in the Generalized Gradient (GGA) and Local Density (LDA) approximations. From the minimization of energy as a function of volume and the fitting of the Murnaghan equation some structural characteristics were determined as, for example, total energy, lattice parameter (a=8.50 Å in cubic phase and a=5.985 Å and c=8.576 Å in tetragonal), bulk modulus (135.6 GPa in cubic phase and 134.1 GPa in tetragonal phase) and its derivative. The study of the electronic characteristics was performed from the analysis of the electronic density of states (DOS). We find a non-metallic behavior for this with a direct band gap of approximately 3.5 eV and we found that the Ba 2 YTaO 6 (I4/m) phase is the most stable one. © 2013 Elsevier Science. All rights reserved
Point defects and oxidation mechanism in cubic boron nitride
International Nuclear Information System (INIS)
Gorshin, A.P.; Shvajko-Shvajkovskij, V.E.
1994-01-01
A theoretical analysis of the defect formation in boron nitride by the Schottky mechanism within the framework of the quasi-chemical approximation method is carried out. On the base of solution of the disordering equations at different conditions of electroneutrality are obtained the dependences of defect concentrations in β-BN on the partial nitrogen pressure in equilibrium conditions. Experimental checking of the theoretical analysis proposed confirms the hypothesis on the presence of defects of nonstoichiometric origin in the β-BN anion sublattice
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Saturated properties prediction in critical region by a quartic equation of state
Directory of Open Access Journals (Sweden)
Yong Wang
2011-08-01
Full Text Available A diverse substance library containing extensive PVT data for 77 pure components was used to critically evaluate the performance of a quartic equation of state and other four famous cubic equations of state in critical region. The quartic EOS studied in this work was found to significantly superior to the others in both vapor pressure prediction and saturated volume prediction in vicinity of critical point.
Constructing New Discrete Integrable Coupling System for Soliton Equation by Kronecker Product
International Nuclear Information System (INIS)
Yu Fajun; Zhang Hongqing
2008-01-01
It is shown that the Kronecker product can be applied to constructing new discrete integrable coupling system of soliton equation hierarchy in this paper. A direct application to the fractional cubic Volterra lattice spectral problem leads to a novel integrable coupling system of soliton equation hierarchy. It is also indicated that the study of discrete integrable couplings by using the Kronecker product is an efficient and straightforward method. This method can be used generally
On the theory of weak turbulence for the nonlinear Schrödinger equation
Escobedo, M
2015-01-01
The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.
Hawkins, John A.; Rittenhouse, Jeffrey L.; Soper, Linda M.; Rittenhouse, Robert C.
2008-01-01
One of the most important crystal structures adopted by metals is characterized by the "abcabc"...stacking of close-packed layers. This structure is commonly referred to in textbooks as the cubic close-packed (ccp) or face-centered cubic (fcc) structure, since the entire lattice can be generated by replication of a face-centered cubic unit cell…
Explicit Gaussian quadrature rules for C^1 cubic splines with symmetrically stretched knot sequence
Ait-Haddou, Rachid; Barton, Michael; Calo, Victor M.
2015-01-01
We provide explicit expressions for quadrature rules on the space of C^1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention
Unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials
DEFF Research Database (Denmark)
Willatzen, Morten; Wang, Zhong Lin
2015-01-01
A unified treatment of coupled optical and acoustic phonons in piezoelectric cubic materials is presented whereby the lattice displacement vector and the internal ionic displacement vector are found simultaneously. It is shown that phonon couplings exist in pairs only; either between the electric...... piezoelectricity in a cubic structured material slab. First, it is shown that isolated optical phonon modes generally cannot exist in piezoelectric cubic slabs. Second, we prove that confined acousto-optical phonon modes only exist for a discrete set of in-plane wave numbers in piezoelectric cubic slabs. Third...... potential and the lattice displacement coordinate perpendicular to the phonon wave vector or between the two other lattice displacement components. The former leads to coupled acousto-optical phonons by virtue of the piezoelectric effect. We then establish three new conjectures that entirely stem from...
Physics and Technology of Transparent Ceramic Armor: Sintered Al2O3 vs Cubic Materials
National Research Council Canada - National Science Library
Krell, Andreas; Hutzler, Thomas; Klimke, Jens
2006-01-01
Sintered sub-micrometer alumina (alpha-Al2O3) is the hardest transparent armor. However, its trigonal structure gives rise to a strong thickness effect that makes thicker components translucent. Cubic ceramics (no birefringence...
Energy landscape of defects in body-centered cubic metals
International Nuclear Information System (INIS)
Alexander, Rebecca
2016-01-01
The structural materials in nuclear reactors are subjected to severe irradiation conditions, leading to changes in their mechanical properties. The aging of these materials raises important issues such as those related to the safety of existing plants and future reactors. In many cases, materials with body-centered cubic bcc crystal structure are used with iron, tungsten, vanadium and tantalum as base metal. Collisions between irradiating particles and atoms constituting materials generate point defects whose migration leads to the formation of clusters responsible for aging. In this thesis, we studied the energetic properties of point defects in the bcc metals mentioned above at the atomic scale. Modeling point defects at the atomic scale can be achieved with different methods that differ only in the quality of the description of the interaction between atoms. Studies using accurate atomic interactions such ab initio calculations are computationally costly making it impossible to directly study clusters of large sizes. The modeling of atomic interactions using semi-empirical potentials reduces the reliability of predictive calculations but allow calculations for large-sized clusters. In this thesis we have developed a unique energy model for dislocation loops as well as for three-dimensional interstitial cluster of type C15. The resulting model has no size limit and can be set entirely by ab initio calculations. To test its robustness for large sizes of clusters we also set this model with semi-empirical potentials calculations and compared the predictions of the model to atomic simulations. With our development we have determined: (i) The relative stability of interstitial dislocation loops according to their Burgers vectors. (ii) The stability of the clusters C15 compared to the type of cluster loop. We showed that the C15 type clusters are more stable when they involve less than 41 interstitials in iron. (iii) In Ta we were able to show the same stability till
Cubic and quartic planar differential systems with exact algebraic limit cycles
Directory of Open Access Journals (Sweden)
Ahmed Bendjeddou
2011-01-01
Full Text Available We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur.
Forbidden transitions in the EPR spectrum of the ferric ion cubic symmetry in magesium oxide
Energy Technology Data Exchange (ETDEWEB)
de Biasi, R S [Instituto Militar de Engenharia, Rio de Janeiro (Brazil). Secao de Engenharia e Ciencia dos Materiais
1979-03-01
The spectrum of the ..delta..m /sub s/=2 transitions of Fe/sup 3 +/ in cubic symmetry sites in MgO has been measured at 9.25GHz. The orientation dependence of the transitions is found to be consistent with a spin Hamiltonian of cubic symmetry with g=2.0037(isotropic), a=0.0205/sup +/-0.00005 cm/sup -1/.
Sridhar Budhi; Chia-Ming Wu; Dan Zhao; Ranjit T. Koodali
2015-01-01
Titania containing cubic MCM-48 mesoporous materials were synthesized successfully at room temperature by a modified Stöber method. The integrity of the cubic mesoporous phase was retained even at relatively high loadings of titania. The TiO2-MCM-48 materials were extensively characterized by a variety of physico-chemical techniques. The physico-chemical characterization indicate that Ti4+ ions can be substituted in framework tetrahedral positions. The relative amount of Ti4+ ions in tetrahe...
Introduction to differential equations
Taylor, Michael E
2011-01-01
The mathematical formulations of problems in physics, economics, biology, and other sciences are usually embodied in differential equations. The analysis of the resulting equations then provides new insight into the original problems. This book describes the tools for performing that analysis. The first chapter treats single differential equations, emphasizing linear and nonlinear first order equations, linear second order equations, and a class of nonlinear second order equations arising from Newton's laws. The first order linear theory starts with a self-contained presentation of the exponen
Uraltseva, N N
1995-01-01
This collection focuses on nonlinear problems in partial differential equations. Most of the papers are based on lectures presented at the seminar on partial differential equations and mathematical physics at St. Petersburg University. Among the topics explored are the existence and properties of solutions of various classes of nonlinear evolution equations, nonlinear imbedding theorems, bifurcations of solutions, and equations of mathematical physics (Navier-Stokes type equations and the nonlinear Schrödinger equation). The book will be useful to researchers and graduate students working in p
International Nuclear Information System (INIS)
Cheng, C.Z.
1988-12-01
A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, θ, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical β/sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab
Energy Technology Data Exchange (ETDEWEB)
Cheng, C.Z.
1988-12-01
A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, theta, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle theta and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical ..beta../sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab.
International Nuclear Information System (INIS)
Kostela, J.; Elmgren, M.; Almgren, M.
2005-01-01
The objective of this study was to investigate the electrochemical behaviour of the divalent redox active surfactant, N-cetyl-N'-methylviologen (CMV), in bicontinuous cubic and lamellar phases. The liquid crystalline phases were prepared from the system glycerolmonooleate (GMO)-water (and brine)-cationic surfactant. A comparison of the phase behaviour of GMO with the monovalent cetyltrimethylammonium bromide (CTAB) and the divalent CMV surfactant showed that the surfactants gave about the same effect at the same surface charge density. The electrochemical measurements were made with a mixture of CTAB and CMV as the surfactant. Cyclic voltammetry was used to study the electrochemistry of CMV incorporated in the cubic and lamellar phases that were spread on a gold electrode. The E 0 -values in the cubic samples were more negative (-0.55 V versus SCE) than in the lamellar samples (-0.53 V versus SCE). This can be explained by the higher charge density in the lamellar phase. The diffusion coefficients were also measured in the cubic phase. The mass transport is slowed down about fifty times in the cubic phase compared to in the pure electrolyte. The concentration dependence on the diffusion coefficient was also investigated. No electron hopping could be observed, which suggest that diffusional movement of the redox probe is the main source of charge transport. By placing the samples on a conducting glass slide, spectroelectrochemical investigations were performed. In the lamellar phase strong dimerization was detected at high concentration of viologen, but much less in the cubic phase
International Nuclear Information System (INIS)
Csenki, A.
1995-01-01
The interval reliability for a repairable system which alternates between working and repair periods is defined as the probability of the system being functional throughout a given time interval. In this paper, a set of integral equations is derived for this dependability measure, under the assumption that the system is modelled by an irreducible finite semi-Markov process. The result is applied to the semi-Markov model of a two-unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two-point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results are discussed and compared with those from simulation
FINANCIAL CRISIS, SUBSIDIES AND CLIMATE CHANGE IN THE EQUATION OF SUSTAINABLE DEVELOPMENT
Directory of Open Access Journals (Sweden)
FLORINA BRAN
2011-03-01
Full Text Available Financial crisis, subsidies and climate change in the equation ofsustainable development. An irreducible situation such as the contemporary financialcrisis creates the premises of major overthrow in decision criteria. Meanwhile,significant progresses in overcoming the ecological crisis, fueled mainly by the climatechange are also in relation with such changes. This convergence is easy to be observeddue to logical connections. If its existence was noticed at decisional levels is theoverarching question that structure the paper. Since the answer is positive, there areexplored the visions and plans of measures developed within this confrontation. Thereis applied a global approach and that is why each discussion considers also theimplications of economic globalization and of global environmental action as influencefactors on the path and direction of change.
International Nuclear Information System (INIS)
Lebedev, D.R.
1979-01-01
Benney's equations of motion of incompressible nonviscous fluid with free surface in the approximation of long waves are analyzed. The connection between the Lie algebra of Hamilton plane vector fields and the Benney's momentum equations is shown
Fractional Schroedinger equation
International Nuclear Information System (INIS)
Laskin, Nick
2002-01-01
Some properties of the fractional Schroedinger equation are studied. We prove the Hermiticity of the fractional Hamilton operator and establish the parity conservation law for fractional quantum mechanics. As physical applications of the fractional Schroedinger equation we find the energy spectra of a hydrogenlike atom (fractional 'Bohr atom') and of a fractional oscillator in the semiclassical approximation. An equation for the fractional probability current density is developed and discussed. We also discuss the relationships between the fractional and standard Schroedinger equations
Ordinary differential equations
Greenberg, Michael D
2014-01-01
Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps
Beginning partial differential equations
O'Neil, Peter V
2014-01-01
A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible,combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger's equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is or
Directory of Open Access Journals (Sweden)
R. Talebitooti
Full Text Available In this paper the effect of quadratic and cubic non-linearities of the system consisting of the crankshaft and torsional vibration damper (TVD is taken into account. TVD consists of non-linear elastomer material used for controlling the torsional vibration of crankshaft. The method of multiple scales is used to solve the governing equations of the system. Meanwhile, the frequency response of the system for both harmonic and sub-harmonic resonances is extracted. In addition, the effects of detuning parameters and other dimensionless parameters for a case of harmonic resonance are investigated. Moreover, the external forces including both inertia and gas forces are simultaneously applied into the model. Finally, in order to study the effectiveness of the parameters, the dimensionless governing equations of the system are solved, considering the state space method. Then, the effects of the torsional damper as well as all corresponding parameters of the system are discussed.
Monfared, Vahid
2018-03-01
Elastic analysis is analytically presented to predict the behaviors of the stress and displacement components in the cylindrical ring as a unit cell of a complete composite under applied stress in the complex plane using cubic polynomials. This analysis is based on the complex computation of the stress functions in the complex plane and polar coordinates. Also, suitable boundary conditions are considered and assumed to analyze along with the equilibrium equations and bi-harmonic equation. This method has some important applications in many fields of engineering such as mechanical, civil and material engineering generally. One of the applications of this research work is in composite design and designing the cylindrical devices under various loadings. Finally, it is founded that the convergence and accuracy of the results are suitable and acceptable through comparing the results.
International Nuclear Information System (INIS)
Ichiguchi, Katsuji
1998-01-01
A new reduced set of resistive MHD equations is derived by averaging the full MHD equations on specified flux coordinates, which is consistent with 3D equilibria. It is confirmed that the total energy is conserved and the linearized equations for ideal modes are self-adjoint. (author)
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
A bifurcation analysis for the Lugiato-Lefever equation
Godey, Cyril
2017-05-01
The Lugiato-Lefever equation is a cubic nonlinear Schrödinger equation, including damping, detuning and driving, which arises as a model in nonlinear optics. We study the existence of stationary waves which are found as solutions of a four-dimensional reversible dynamical system in which the evolutionary variable is the space variable. Relying upon tools from bifurcation theory and normal forms theory, we discuss the codimension 1 bifurcations. We prove the existence of various types of steady solutions, including spatially localized, periodic, or quasi-periodic solutions. Contribution to the Topical Issue: "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.
New Numerical Treatment for Solving the KDV Equation
Directory of Open Access Journals (Sweden)
khalid ali
2017-01-01
Full Text Available In the present article, a numerical method is proposed for the numerical solution of the KdV equation by using collocation method with the modified exponential cubic B-spline. In this paper we convert the KdV equation to system of two equations. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Three invariants of motion are predestined to determine the preservation properties of the problem, and the numerical scheme leads to careful and active results. Furthermore, interaction of two and three solitary waves is shown. These results show that the technique introduced here is easy to apply.
Plasma deposition of cubic boron nitride films from non-toxic material at low temperatures
International Nuclear Information System (INIS)
Karim, M.Z.; Cameron, D.C.; Murphy, M.J.; Hashmi, M.S.J.
1991-01-01
Boron nitride has become the focus of a considerable amount of interest because of its properties which relate closely to those of carbon. In particular, the cubic nitride phase has extreme hardness and very high thermal conductivity similar to the properties of diamond. The conventional methods of synthesis use the highly toxic and inflammable gas diborane (B 2 H 6 ) as the reactant material. A study has been made of the deposition of thin films of boron nitride (BN) using non-toxic material by the plasma-assisted chemical vapour deposition technique. The source material was borane-ammonia (BH 3 -NH 3 ) which is a crystalline solid at room temperature with a high vapour pressure. The BH 3 -NH 3 vapour was decomposed in a 13.56 MHz nitrogen plasma coupled either inductively or capacitively with the system. The composition of the films was assessed by measuring their IR absorption when deposited on silicon and KBr substrates. The hexagonal (graphitic) and cubic (diamond-like) allotropes can be distinguished by their characteristic absorption bands which occur at 1365 and 780 cm -1 (hexagonal) and 1070 cm -1 (cubic). We have deposited BN films consisting of a mixture of hexagonal and cubic phases; the relative content of the cubic phase was found to be directly dependent on r.f. power and substrate bias. (orig.)
International Nuclear Information System (INIS)
Rovere, Florian; Mayrhofer, Paul H; Music, Denis; Ershov, Sergey; Baben, Moritz to; Schneider, Jochen M; Fuss, Hans-Gerd
2010-01-01
The phase stability of Al-containing cubic transition metal (TM) nitrides, where Al substitutes for TM (i.e. TM 1-x Al x N), is studied as a function of the TM valence electron concentration (VEC). X-ray diffraction and thermal analyses data of magnetron sputtered Ti 1-x Al x N, V 1-x Al x N and Cr 1-x Al x N films indicate increasing phase stability of cubic TM 1-x Al x N at larger Al contents and higher temperatures with increasing TM VEC. These experimental findings can be understood based on first principle investigations of ternary cubic TM 1-x Al x N with TM = Sc, Ti, V, Cr, Y, Zr and Nb where the TM VEC and the lattice strain are systematically varied. However, our experimental data indicate that, in addition to the decomposition energetics (cubic TM 1-x Al x N → cubic TMN + hexagonal AlN), future stability models have to include nitrogen release as one of the mechanisms that critically determine the overall phase stability of TM 1-x Al x N.
Phase transformation of metastable cubic γ-phase in U-Mo alloys
International Nuclear Information System (INIS)
Sinha, V.P.; Hegde, P.V.; Prasad, G.J.; Dey, G.K.; Kamath, H.S.
2010-01-01
Over the past decade considerable efforts have been put by many fuel designers to develop low enriched uranium (LEU 235 ) base U-Mo alloy as a potential fuel for core conversion of existing research and test reactors which are running on high enriched uranium (HEU > 85%U 235 ) fuel and also for the upcoming new reactors. U-Mo alloy with minimum 8 wt% molybdenum shows excellent metastability with cubic γ-phase in cast condition. However, it is important to characterize the decomposition behaviour of metastable cubic γ-uranium in its equilibrium products for in reactor fuel performance point of view. The present paper describes the phase transformation behaviour of cubic γ-uranium phase in U-Mo alloys with three different molybdenum compositions (i.e. 8 wt%, 9 wt% and 10 wt%). U-Mo alloys were prepared in an induction melting furnace and characterized by X-ray diffraction (XRD) method for phase determination. Microstructures were developed for samples in as cast condition. The alloys were hot rolled in cubic γ-phase to break the cast structure and then they were aged at 500 o C for 68 h and 240 h, so that metastable cubic γ-uranium will undergo eutectoid decomposition to form equilibrium phases of orthorhombic α-uranium and body centered tetragonal U 2 Mo intermetallic compound. U-Mo alloy samples with different ageing history were then characterized by XRD for phase and development of microstructure.
International Nuclear Information System (INIS)
Zhalij, Alexander
2002-01-01
We classify (1+3)-dimensional Pauli equations for a spin-(1/2) particle interacting with the electro-magnetic field, that are solvable by the method of separation of variables. As a result, we obtain the 11 classes of vector-potentials of the electro-magnetic field A(t,x(vector sign))=(A 0 (t,x(vector sign)), A(vector sign)(t,x(vector sign))) providing separability of the corresponding Pauli equations. It is established, in particular, that the necessary condition for the Pauli equation to be separable into second-order matrix ordinary differential equations is its equivalence to the system of two uncoupled Schroedinger equations. In addition, the magnetic field has to be independent of spatial variables. We prove that coordinate systems and the vector-potentials of the electro-magnetic field providing the separability of the corresponding Pauli equations coincide with those for the Schroedinger equations. Furthermore, an efficient algorithm for constructing all coordinate systems providing the separability of Pauli equation with a fixed vector-potential of the electro-magnetic field is developed. Finally, we describe all vector-potentials A(t,x(vector sign)) that (a) provide the separability of Pauli equation, (b) satisfy vacuum Maxwell equations without currents, and (c) describe non-zero magnetic field
Functional equations with causal operators
Corduneanu, C
2003-01-01
Functional equations encompass most of the equations used in applied science and engineering: ordinary differential equations, integral equations of the Volterra type, equations with delayed argument, and integro-differential equations of the Volterra type. The basic theory of functional equations includes functional differential equations with causal operators. Functional Equations with Causal Operators explains the connection between equations with causal operators and the classical types of functional equations encountered by mathematicians and engineers. It details the fundamentals of linear equations and stability theory and provides several applications and examples.
International Nuclear Information System (INIS)
Senthilvelan, M; Torrisi, M; Valenti, A
2006-01-01
By using Lie's invariance infinitesimal criterion, we obtain the continuous equivalence transformations of a class of nonlinear Schroedinger equations with variable coefficients. We construct the differential invariants of order 1 starting from a special equivalence subalgebra E χ o . We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schr?dinger equations which can be mapped, by means of an equivalence transformation of E χ o , to the well-known cubic Schroedinger equation. We also provide the explicit form of the transformation
Modified wave operators for nonlinear Schrodinger equations in one and two dimensions
Directory of Open Access Journals (Sweden)
Nakao Hayashi
2004-04-01
Full Text Available We study the asymptotic behavior of solutions, in particular the scattering theory, for the nonlinear Schr"{o}dinger equations with cubic and quadratic nonlinearities in one or two space dimensions. The nonlinearities are summation of gauge invariant term and non-gauge invariant terms. The scattering problem of these equations belongs to the long range case. We prove the existence of the modified wave operators to those equations for small final data. Our result is an improvement of the previous work [13
IMPROVEMENT OF THE REDLICH-KWONG EQUATION OF STATE BY MODIFICATION OF CO-VOLUME PARAMETER
Directory of Open Access Journals (Sweden)
Ratnawati Ratnawati
2012-02-01
Full Text Available Cubic equations of state are widely used in phase-equilibrium calculations because of their simplicity and accuracy. Most equations of states are not accurate enough for predicting density of liquid and dense gas. A modification on the Redlich-Kwong (RK equation of state is developed. Parameter b is modified by introducing a new parameter,b, which is a function of molecular weight and temperature. The modification gives a significant improvement over the original RK equation for predicting density. For 6538 data points of 27 compounds, the proposed equation gives only 2.8% of average absolute deviation (AAD, while the original RK and the Soave-Redlich-Kwong (SRK equations give 11.4% and 11.7%, respectively. The proposed modification improves the performance of the RK equation for predicting vapor pressure as well. For 2829 data points of 94 compounds, the proposed modification lowers the AAD of the RK equation from 1460% down to 30.8%. It is comparable to the famous SRK equation, which give 5.8% of AAD. The advantage of the proposed equation is that it uses only critical pressure and temperature as other equations of states do, and molecular weight, which is easily calculated. Another advantage is that the proposed equation simpler than the SRK equation of state.
Partial differential equations
Evans, Lawrence C
2010-01-01
This text gives a comprehensive survey of modern techniques in the theoretical study of partial differential equations (PDEs) with particular emphasis on nonlinear equations. The exposition is divided into three parts: representation formulas for solutions; theory for linear partial differential equations; and theory for nonlinear partial differential equations. Included are complete treatments of the method of characteristics; energy methods within Sobolev spaces; regularity for second-order elliptic, parabolic, and hyperbolic equations; maximum principles; the multidimensional calculus of variations; viscosity solutions of Hamilton-Jacobi equations; shock waves and entropy criteria for conservation laws; and, much more.The author summarizes the relevant mathematics required to understand current research in PDEs, especially nonlinear PDEs. While he has reworked and simplified much of the classical theory (particularly the method of characteristics), he primarily emphasizes the modern interplay between funct...
Directory of Open Access Journals (Sweden)
Wei Khim Ng
2009-02-01
Full Text Available We construct nonlinear extensions of Dirac's relativistic electron equation that preserve its other desirable properties such as locality, separability, conservation of probability and Poincaré invariance. We determine the constraints that the nonlinear term must obey and classify the resultant non-polynomial nonlinearities in a double expansion in the degree of nonlinearity and number of derivatives. We give explicit examples of such nonlinear equations, studying their discrete symmetries and other properties. Motivated by some previously suggested applications we then consider nonlinear terms that simultaneously violate Lorentz covariance and again study various explicit examples. We contrast our equations and construction procedure with others in the literature and also show that our equations are not gauge equivalent to the linear Dirac equation. Finally we outline various physical applications for these equations.
Differential equations for dummies
Holzner, Steven
2008-01-01
The fun and easy way to understand and solve complex equations Many of the fundamental laws of physics, chemistry, biology, and economics can be formulated as differential equations. This plain-English guide explores the many applications of this mathematical tool and shows how differential equations can help us understand the world around us. Differential Equations For Dummies is the perfect companion for a college differential equations course and is an ideal supplemental resource for other calculus classes as well as science and engineering courses. It offers step-by-step techniques, practical tips, numerous exercises, and clear, concise examples to help readers improve their differential equation-solving skills and boost their test scores.
Degenerate nonlinear diffusion equations
Favini, Angelo
2012-01-01
The aim of these notes is to include in a uniform presentation style several topics related to the theory of degenerate nonlinear diffusion equations, treated in the mathematical framework of evolution equations with multivalued m-accretive operators in Hilbert spaces. The problems concern nonlinear parabolic equations involving two cases of degeneracy. More precisely, one case is due to the vanishing of the time derivative coefficient and the other is provided by the vanishing of the diffusion coefficient on subsets of positive measure of the domain. From the mathematical point of view the results presented in these notes can be considered as general results in the theory of degenerate nonlinear diffusion equations. However, this work does not seek to present an exhaustive study of degenerate diffusion equations, but rather to emphasize some rigorous and efficient techniques for approaching various problems involving degenerate nonlinear diffusion equations, such as well-posedness, periodic solutions, asympt...
International Nuclear Information System (INIS)
Wang, S.; Wang, M.P.; Chen, C.; Xiao, Z.; Jia, Y.L.; Li, Z.; Wang, Z.X.
2014-01-01
The orientation dependence of the deformation microstructure has been investigated in commercial pure molybdenum. After deformation, the dislocation boundaries of compressed molybdenum can be classified, similar to that in face-centered cubic metals, into three types: dislocation cells (Type 2), and extended planar boundaries parallel to (Type 1) or not parallel to (Type 3) a (110) trace. However, it shows a reciprocal relationship between face-centered cubic metals and body-centered cubic metals on the orientation dependence of the deformation microstructure. The higher the strain, the finer the microstructure is and the smaller the inclination angle between extended planar boundaries and the compression axis is. - Highlights: • A reciprocal relationship between FCC metals and BCC metals is confirmed. • The dislocation boundaries can be classified into three types in compressed Mo. • The dislocation characteristic of different dislocation boundaries is different
Growth of cubic InN on r-plane sapphire
International Nuclear Information System (INIS)
Cimalla, V.; Pezoldt, J.; Ecke, G.; Kosiba, R.; Ambacher, O.; Spiess, L.; Teichert, G.; Lu, H.; Schaff, W.J.
2003-01-01
InN has been grown directly on r-plane sapphire substrates by plasma-enhanced molecular-beam epitaxy. X-ray diffraction investigations have shown that the InN layers consist of a predominant zinc blende (cubic) structure along with a fraction of the wurtzite (hexagonal) phase which content increases with proceeding growth. The lattice constant for zinc blende InN was found to be a=4.986 A. For this unusual growth of a metastable cubic phase on a noncubic substrate an epitaxial relationship was proposed where the metastable zinc blende phase grows directly on the r-plane sapphire while the wurtzite phase arises as the special case of twinning in the cubic structure
Testing a generalized cubic Galileon gravity model with the Coma Cluster
Energy Technology Data Exchange (ETDEWEB)
Terukina, Ayumu; Yamamoto, Kazuhiro; Okabe, Nobuhiro [Department of Physical Sciences, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526 (Japan); Matsushita, Kyoko; Sasaki, Toru, E-mail: telkina@theo.phys.sci.hiroshima-u.ac.jp, E-mail: kazuhiro@hiroshima-u.ac.jp, E-mail: okabe@hiroshima-u.ac.jp, E-mail: matusita@rs.kagu.tus.ac.jp, E-mail: j1213703@ed.tus.ac.jp [Department of Physics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601 (Japan)
2015-10-01
We obtain a constraint on the parameters of a generalized cubic Galileon gravity model exhibiting the Vainshtein mechanism by using multi-wavelength observations of the Coma Cluster. The generalized cubic Galileon model is characterized by three parameters of the turning scale associated with the Vainshtein mechanism, and the amplitude of modifying a gravitational potential and a lensing potential. X-ray and Sunyaev-Zel'dovich (SZ) observations of the intra-cluster medium are sensitive to the gravitational potential, while the weak-lensing (WL) measurement is specified by the lensing potential. A joint fit of a complementary multi-wavelength dataset of X-ray, SZ and WL measurements enables us to simultaneously constrain these three parameters of the generalized cubic Galileon model for the first time. We also find a degeneracy between the cluster mass parameters and the gravitational modification parameters, which is influential in the limit of the weak screening of the fifth force.
Vibrational effects on surface energies and band gaps in hexagonal and cubic ice
International Nuclear Information System (INIS)
Engel, Edgar A.; Needs, Richard J.; Monserrat, Bartomeu
2016-01-01
Surface energies of hexagonal and cubic water ice are calculated using first-principles quantum mechanical methods, including an accurate description of anharmonic nuclear vibrations. We consider two proton-orderings of the hexagonal and cubic ice basal surfaces and three proton-orderings of hexagonal ice prism surfaces, finding that vibrations reduce the surface energies by more than 10%. We compare our vibrational densities of states to recent sum frequency generation absorption measurements and identify surface proton-orderings of experimental ice samples and the origins of characteristic absorption peaks. We also calculate zero point quantum vibrational corrections to the surface electronic band gaps, which range from −1.2 eV for the cubic ice basal surface up to −1.4 eV for the hexagonal ice prism surface. The vibrational corrections to the surface band gaps are up to 12% smaller than for bulk ice.
Conformal Interpolating Algorithm Based on Cubic NURBS in Aspheric Ultra-Precision Machining
International Nuclear Information System (INIS)
Li, C G; Zhang, Q R; Cao, C G; Zhao, S L
2006-01-01
Numeric control machining and on-line compensation for aspheric surface are key techniques in ultra-precision machining. In this paper, conformal cubic NURBS interpolating curve is applied to fit the character curve of aspheric surface. Its algorithm and process are also proposed and imitated by Matlab7.0 software. To evaluate the performance of the conformal cubic NURBS interpolation, we compare it with the linear interpolations. The result verifies this method can ensure smoothness of interpolating spline curve and preserve original shape characters. The surface quality interpolated by cubic NURBS is higher than by line. The algorithm is benefit to increasing the surface form precision of workpieces in ultra-precision machining
Advanced CUBIC protocols for whole-brain and whole-body clearing and imaging.
Susaki, Etsuo A; Tainaka, Kazuki; Perrin, Dimitri; Yukinaga, Hiroko; Kuno, Akihiro; Ueda, Hiroki R
2015-11-01
Here we describe a protocol for advanced CUBIC (Clear, Unobstructed Brain/Body Imaging Cocktails and Computational analysis). The CUBIC protocol enables simple and efficient organ clearing, rapid imaging by light-sheet microscopy and quantitative imaging analysis of multiple samples. The organ or body is cleared by immersion for 1-14 d, with the exact time required dependent on the sample type and the experimental purposes. A single imaging set can be completed in 30-60 min. Image processing and analysis can take whole-brain neural activities at single-cell resolution using Arc-dVenus transgenic (Tg) mice. CUBIC informatics calculated the Venus signal subtraction, comparing different brains at a whole-organ scale. These protocols provide a platform for organism-level systems biology by comprehensively detecting cells in a whole organ or body.