Particle astrophysics of nonlinear supersymmetric general relativity
Energy Technology Data Exchange (ETDEWEB)
Shima, K.; Tsuda, M. [Laboratory of Physics, Saitama Institute of Technology, Fukaya, Saitama (Japan)
2009-05-15
An explanation of relations between the large scale structure of the universe and the tiny scale structure of the particle physics, e.g. the observed mysterious relation between the (dark) energy density and the dark matter of the universe and the neutrino mass and the SUSY breaking mass scale of the particle physics may be given by the nonlinear supersymmetric general relativity (NLSUSY GR). NLSUSY GR shows that considering the physics before/of the big bang (BB) of the universe may be significant and may give new insight to unsolved problems of the low energy particle physics, cosmology and their relations. (Abstract Copyright [2009], Wiley Periodicals, Inc.)
Generalized Supersymmetric Perturbation Theory
Institute of Scientific and Technical Information of China (English)
B. G(o)n(ǖ)l
2004-01-01
@@ Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.
Generalized Kahler Geometry from supersymmetric sigma models
Bredthauer, A; Persson, J; Zabzine, M; Bredthauer, Andreas; Lindstrom, Ulf; Persson, Jonas; Zabzine, Maxim
2006-01-01
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the bi-hermitean geometry of Gates-Hull-Rocek. When cast in the language of supersymmetric sigma models, this relation maps precisely to that between the Lagrangian and the Hamiltonian formalisms. We also discuss topological twist in this context.
Supersymmetric Q-Lumps in the Grassmannian nonlinear sigma models
Bak, D; Lee, J; Oh, P; Bak, Dongsu; Hahn, Sang-Ok; Lee, Joohan; Oh, Phillial
2007-01-01
We construct the N=2 supersymmetric Grassmannian nonlinear sigma model for the massless case and extend it to massive N=2 model by adding an appropriate superpotential. We then study their BPS equations leading to supersymmetric Q-lumps carrying both topological and Noether charges. These solutions are shown to be always time dependent even sometimes involving multiple frequencies. Thus we illustrate explicitly that the time dependence is consistent with remaining supersymmetries of solitons.
Supersymmetric quantum mechanics approach to a nonlinear lattice
Energy Technology Data Exchange (ETDEWEB)
Ricotta, Regina Maria [Faculdade de Tecnologia de Sao Paulo (FATEC), SP (Brazil); Drigo Filho, Elso [Universidade Estadual Paulista Julio de Mesquita Filho (UNESP), SP (Brazil)
2011-07-01
Full text: DNA is one of the most important macromolecules of all biological system. New discoveries about it have open a vast new field of research, the physics of nonlinear DNA. A particular feature that has attracted a lot of attention is the thermal denaturation, i.e., the spontaneous separation of the two strands upon heating. In 1989 a simple lattice model for the denaturation of the DNA was proposed, the Peyrard-Bishop model, PB. The bio molecule is described by two chains of particles coupled by nonlinear springs, simulating the hydrogen bonds that connect the two basis in a pair. The potential for the hydrogen bonds is usually approximated by a Morse potential. The Hamiltonian system generates a partition function which allows the evaluation of the thermodynamical quantities such as mean strength of the basis pairs. As a byproduct the Hamiltonian system was shown to be a NLSE (nonlinear Schroedinger equation) having soliton solutions. On the other hand, a reflectionless potential with one bound state, constructed using supersymmetric quantum mechanics, SQM, can be shown to be identical to a soliton solution of the KdV equation. Thus, motivated by this Hamiltonian problem and inspired by the PB model, we consider the Hamiltonian of a reflectionless potential through SQM, in order to evaluate thermodynamical quantities of a unidimensional lattice with possible biological applications. (author)
WIEDEMANN, A; MULLERKIRSTEN, HJW
1993-01-01
Considering the N = 1 supersymmetry transformations of supersymmetric nonlinear sigma models in 1 + 1 dimensions we construct explicitly conserved Noether currents associated with supersymmetry transformations and derive the associated conserved charges in terms of the basic fields. We compare this
Energy Technology Data Exchange (ETDEWEB)
Bagger, J.A.
1984-09-01
We begin to construct the most general supersymmetric Lagrangians in one, two and four dimensions. We find that the matter couplings have a natural interpretation in the language of the nonlinear sigma model.
Locally supersymmetric D=3 non-linear sigma models
Wit, B. de; Tollsten, A. K.; Nicolai, H.
1992-01-01
We study non-linear sigma models with N local supersymmetries in three space-time dimensions. For N=1 and 2 the target space of these models is Riemannian or Kahler, respectively. All N>2 theories are associated with Einstein spaces. For N=3 the target space is quaternionic, while for N=4 it general
Nonlinear supercoherent states and geometric phases for the supersymmetric harmonic oscillator
Díaz-Bautista, Erik
2016-01-01
Nonlinear supercoherent states, which are eigenstates of nonlinear deformations of the Kornbluth-Zypman annihilation operator for the supersymmetric harmonic oscillator, will be studied. They turn out to be expressed in terms of nonlinear coherent states, associated to the corresponding deformations of the standard annihilation operator. We will discuss as well the Heisenberg uncertainty relation for a special particular case, in order to compare our results with those obtained for the Kornbluth-Zypman linear supercoherent states. As the supersymmetric harmonic oscillator executes an evolution loop, such that the evolution operator becomes the identity at a certain time, thus the linear and nonlinear supercoherent states turn out to be cyclic and the corresponding geometric phases will be evaluated.
Prolongation structures for supersymmetric equations
Roelofs, G.H.M.; Hijligenberg, van den N.W.
1990-01-01
The well known prolongation technique of Wahlquist and Estabrook (1975) for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the KdV equation of Manin-Radul. Using the theory of Kac-Moody Lie superalgebras, the explicit form of
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-10-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Generalized Nonlinear Yule Models
Lansky, Petr; Polito, Federico; Sacerdote, Laura
2016-11-01
With the aim of considering models related to random graphs growth exhibiting persistent memory, we propose a fractional nonlinear modification of the classical Yule model often studied in the context of macroevolution. Here the model is analyzed and interpreted in the framework of the development of networks such as the World Wide Web. Nonlinearity is introduced by replacing the linear birth process governing the growth of the in-links of each specific webpage with a fractional nonlinear birth process with completely general birth rates. Among the main results we derive the explicit distribution of the number of in-links of a webpage chosen uniformly at random recognizing the contribution to the asymptotics and the finite time correction. The mean value of the latter distribution is also calculated explicitly in the most general case. Furthermore, in order to show the usefulness of our results, we particularize them in the case of specific birth rates giving rise to a saturating behaviour, a property that is often observed in nature. The further specialization to the non-fractional case allows us to extend the Yule model accounting for a nonlinear growth.
Generalized symmetries of an 𝓝 = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system
Wang, Jian-Yong; Tang, Xiao-Yan; Liang, Zu-Feng; Lou, Sen-Yue
2015-05-01
The formal series symmetry approach (FSSA), a quite powerful and straightforward method to establish infinitely many generalized symmetries of classical integrable systems, has been successfully extended in the supersymmetric framework to explore series of infinitely many generalized symmetries for supersymmetric systems. Taking the 𝒩 = 1 supersymmetric Boiti-Leon-Manna-Pempinelli system as a concrete example, it is shown that the application of the extended FSSA to this supersymmetric system leads to a set of infinitely many generalized symmetries with an arbitrary function f (t). Some interesting special cases of symmetry algebras are presented, including a limit case f (t) = 1 related to the commutativity of higher order generalized symmetries. Project supported by the National Natural Science Foundation of China (Grant Nos. 11275123, 11175092, 11475052, and 11435005), the Shanghai Knowledge Service Platform for Trustworthy Internet of Things, China (Grant No. ZF1213), and the Talent Fund and K CWong Magna Fund in Ningbo University, China.
Topics on nonlinear generalized functions
Colombeau, J F
2011-01-01
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two recalls "Nonlinear generalized functions and their connections with distribution theory", "Examples of applications", and a recent development: "Locally convex topologies and compactness: a functional analysis of nonlinear generalized functions".
Towards a Supersymmetric Generalization of the Schwarzschild Black Hole
López-Domínguez, J C; Zacarías, S
2009-01-01
The Wheeler-DeWitt (WDW) equation for the Kantowski-Sachs model can also be understood as the WDW-equation corresponding to the Schwarzschild black hole due to the well known diffeomorphism between these two metrics. The WDW-equation and its solutions are ``ignorant'' of the coordinate patch one is using, only by imposing coordinate conditions we can differentiate between cosmological and black hole models. At that point, the foliation parameter $t$ or $r$ will appear in the solution of interest. In this work we supersymmetrize this WDW-equation obtaining an extra term in the potential with two possible signs. The WKB method is then applied, given rise to two classical equations. It is shown that the event horizon can never be reached because, very near to it the extra term in the potential, for each one of the equations, is more relevant than the one that corresponds to Schwarzschild. One can then study the asymptotic cases in which one of the two terms in the Hamiltonian dominates the behavior. One of them ...
Non-linear supersymmetric {sigma}-models and their gauging in the Atiyah-Ward space-time
Energy Technology Data Exchange (ETDEWEB)
Carvalho, M.; Vilar, L.C.Q.; Helayel-Neto, J.A.
1995-10-01
We present a supersymmetric non-linear {sigma}-model built up in the N 1 superspace of Atiyah-ward space-time. A manifold of the Kaehler type comes out that is restricted by a a particular decomposition of the Kaehler potential. The gauging of the {sigma}-model isometries is also accomplished in superspace. (author). 20 refs.
Loop formulation of the supersymmetric nonlinear O(N) sigma model
Steinhauer, Kyle
2013-01-01
We derive the fermion loop formulation for the supersymmetric nonlinear O$(N)$ sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For $N \\ge 3$ this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For $N=2$ we determine the critical point and present boson and fermion masses in the critical regime.
Green-Schwarz superstring. Beltrami parametrization and world-sheet supersymmetric generalization
Energy Technology Data Exchange (ETDEWEB)
Binetruy, P.; Girardi, G. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules); Grimm, R. (Karlsruhe Univ. (T.H.) (Germany, F.R.). Inst. fuer Theoretische Physik)
1989-09-28
We study a generalization of the superstring theory in which both world-sheet and space-time supersymmetries are explicit. This hybrid superstring interpolates between the Green-Schwarz and the Ramond-Neveu-Schwarz formulations. We show that the Beltrami parametrization of the world-sheet provides a natural setting for the description of {kappa}-transformations already in the Green-Schwarz string. We construct the hybrid superstring action using the (1, 1) supersymmetric version of the Beltrami parametrization. We discuss the generalization of {kappa}-transformations. (orig.).
The structure of N=2 supersymmetric nonlinear sigma models in AdS_4
Butter, Daniel
2011-01-01
We present a detailed study of the most general N=2 supersymmetric sigma models in four-dimensional anti-de Sitter space AdS_4 formulated in terms of N=1 chiral superfields. The target space is demonstrated to be a non-compact hyperkahler manifold restricted to possess a special Killing vector field which generates an SO(2) group of rotations on the two-sphere of complex structures and necessarily leaves one of them invariant. All hyperkahler cones, that is the target spaces of N=2 superconformal sigma models, prove to possess such a vector field that belongs to the Lie algebra of an isometry group SU(2) acting by rotations on the complex structures. A unique property of the N=2 sigma models constructed is that the algebra of OSp(2|4) transformations closes off the mass shell. We uncover the underlying N=2 superfield formulation for the N=2 sigma models constructed and compute the associated N=2 supercurrent. We give a special analysis of the most general systems of self-interacting N=2 tensor multiplets in A...
General N=1 supersymmetric flux vacua of massive type IIA string theory.
Behrndt, Klaus; Cvetic, Mirjam
2005-07-08
We derive conditions for the existence of four-dimensional N=1 supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly Kähler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.
Koller, Andrew; Olshanii, Maxim
2011-12-01
We present a case demonstrating the connection between supersymmetric quantum mechanics (SUSYQM), reflectionless scattering, and soliton solutions of integrable partial differential equations. We show that the members of a class of reflectionless Hamiltonians, namely, Akulin's Hamiltonians, are connected via supersymmetric chains to a potential-free Hamiltonian, explaining their reflectionless nature. While the reflectionless property in question has been mentioned in the literature for over two decades, the enabling algebraic mechanism was previously unknown. Our results indicate that the multisoliton solutions of the sine-Gordon and nonlinear Schrödinger equations can be systematically generated via the supersymmetric chains connecting Akulin's Hamiltonians. Our findings also explain a well-known but little-understood effect in laser physics: when a two-level atom, initially in the ground state, is subjected to a laser pulse of the form V(t) = (nh/τ)/cosh(t/τ), with n being an integer and τ being the pulse duration, it remains in the ground state after the pulse has been applied, for any choice of the laser detuning.
Generalized creation and annihilation operators via complex nonlinear Riccati equations
Schuch, Dieter; Castaños, Octavio; Rosas-Ortiz, Oscar
2013-06-01
Based on Gaussian wave packet solutions of the time-dependent Schrödinger equation, a generalization of the conventional creation and annihilation operators and the corresponding coherent states can be obtained. This generalization includes systems where also the width of the coherent states is time-dependent as they occur for harmonic oscillators with time-dependent frequency or systems in contact with a dissipative environment. The key point is the replacement of the frequency ω0 that occurs in the usual definition of the creation/annihilation operator by a complex time-dependent function that fulfils a nonlinear Riccati equation. This equation and its solutions depend on the system under consideration and on the (complex) initial conditions. Formal similarities also exist with supersymmetric quantum mechanics. The generalized creation and annihilation operators also allow to construct exact analytic solutions of the free motion Schrödinger equation in terms of Hermite polynomials with time-dependent variable.
Energy Technology Data Exchange (ETDEWEB)
Chau, L.L.
1983-01-01
Integrable properties, i.e., existence of linear systems, infinite number of conservation laws, Reimann-Hilbert transforms, affine Lie algebra of Kac-Moody, and Bianchi-Baecklund transformation, are discussed for the constraint equations of the supersymmetric Yang-Mills fields. For N greater than or equal to 3 these constraint equations give equations of motion of the fields. These equations of motion reduce to the ordinary Yang-Mills equations as the spinor and scalar fields are eliminated. These understandings provide a possible method to solve the full Yang-Mills equations. Connections with other non-linear systems are also discussed. 53 references.
Generalized Strongly Nonlinear Implicit Quasivariational Inequalities
Directory of Open Access Journals (Sweden)
Salahuddin
2009-01-01
Full Text Available We prove an existence theorem for solution of generalized strongly nonlinear implicit quasivariational inequality problems and convergence of iterative sequences with errors, involving Lipschitz continuous, generalized pseudocontractive and generalized -pseudocontractive mappings in Hilbert spaces.
Doped Heisenberg chains: Spin-S generalizations of the supersymmetric t-J model
Energy Technology Data Exchange (ETDEWEB)
Frahm, Holger E-mail: frahm@itp.uni-hannover.de
1999-10-25
A family of exactly solvable models describing a spin S Heisenberg chain doped with mobile spin-(S - ((1)/(2))) carriers is constructed from gl(2|1)-invariant solutions of the Yang-Baxter equation. The models are generalizations of the supersymmetric t-J model which is obtained for S ((1)/(2)). We solve the model by means of the algebraic Bethe Ansatz and present results for the zero temperature and thermodynamic properties. At low temperatures the models show spin charge separation, i.e. contain contributions of a free bosonic theory in the charge sector and an SU(2)-invariant theory describing the magnetic excitations. For small carrier concentration the latter can be decomposed further into an SU(2) level-2S Wess-Zumino-Novikov-Witten model and the minimal unitary model M{sub p} with p 2S + 1.
Generalized solutions of nonlinear partial differential equations
Rosinger, EE
1987-01-01
During the last few years, several fairly systematic nonlinear theories of generalized solutions of rather arbitrary nonlinear partial differential equations have emerged. The aim of this volume is to offer the reader a sufficiently detailed introduction to two of these recent nonlinear theories which have so far contributed most to the study of generalized solutions of nonlinear partial differential equations, bringing the reader to the level of ongoing research.The essence of the two nonlinear theories presented in this volume is the observation that much of the mathematics concernin
Energy Technology Data Exchange (ETDEWEB)
Krishna, S., E-mail: skrishna.bhu@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); Shukla, A., E-mail: ashukla038@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); Malik, R.P., E-mail: rpmalik1995@gmail.com [Physics Department, Centre of Advanced Studies, Banaras Hindu University (BHU), Varanasi-221 005 (India); DST-CIMS, Faculty of Science, BHU-Varanasi-221 005 (India)
2014-12-15
Using the supersymmetric (SUSY) invariant restrictions on the (anti-)chiral supervariables, we derive the off-shell nilpotent symmetries of the general one (0+1)-dimensional N=2 SUSY quantum mechanical (QM) model which is considered on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and θ-bar with θ{sup 2}=(θ-bar){sup 2}=0,θ(θ-bar)+(θ-bar)θ=0). We provide the geometrical meanings to the two SUSY transformations of our present theory which are valid for any arbitrary type of superpotential. We express the conserved charges and Lagrangian of the theory in terms of the supervariables (that are obtained after the application of SUSY invariant restrictions) and provide the geometrical interpretation for the nilpotency property and SUSY invariance of the Lagrangian for the general N=2 SUSY quantum theory. We also comment on the mathematical interpretation of the above symmetry transformations. - Highlights: • A novel method has been proposed for the derivation of N=2 SUSY transformations. • General N=2 SUSY quantum mechanical (QM) model with a general superpotential, is considered. • The above SUSY QM model is generalized onto a (1, 2)-dimensional supermanifold. • SUSY invariant restrictions are imposed on the (anti-)chiral supervariables. • Geometrical meaning of the nilpotency property is provided.
A note on generalized nonlinear diagonal dominance
Gan, Tai-Bin; Huang, Ting-Zhu; Gao, Jian
2006-01-01
In this paper, an open problem, proposed by A. Frommer, about nonlinear generalized diagonal dominance, is solved on some weak restriction, a counterexample is presented if such a restriction is omitted, and some new properties of nonlinear generalized diagonally dominant functions are investigated.
Supersymmetric Displaced Number States
Directory of Open Access Journals (Sweden)
Fredy R. Zypman
2015-06-01
Full Text Available We introduce, generate and study a family of supersymmetric displaced number states (SDNS that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.
Supersymmetric non conservative systems
Martínez-Pérez, N E
2015-01-01
We give the generalization of a recent variational formulation for nonconservative classical mechanics, for fermionic and sypersymmetric systems. Both cases require slightly modified boundary conditions. The supersymmetric version is given in the superfield formalism. The corresponding Noether theorem is formulated. As expected, like the energy, the supersymmetric charges are not conserved. Examples are discussed.
Noncommutative Nonlinear Supersymmetry
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2002-01-01
We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is the generalization of this lagrangian to Dirac-Born-Infeld lagrangian with nonlinear supersymmetry realized in dimensions D=2,3,4 and 6 (mod 8).
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete characterization of the approximation spaces is derived.
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...... characterization of the approximation spaces is derived....
The Geometric Nonlinear Generalized Brazier Effect
DEFF Research Database (Denmark)
Nikolajsen, Jan Ánike; Lauridsen, Peter Riddersholm; Damkilde, Lars
2016-01-01
denoted the generalized Brazier effect. The original work of Brazier dealt with very large deformations that changed the cross section significantly and hereby also the bending moment of inertia and the bending moment capacity. In this paper the aim is to describe the Brazier effect for smaller...... that the generalized Brazier effect is a local effect not influencing the overall mechanical behavior of the structure significantly. The offset is a nonlinear geometric beam-type Finite Element calculation, which takes into account the large displacements and rotations. The beam-type model defines the stresses which...... deformation not taking into account the change in moment of inertia. However, the generalized Brazier effect gives additional stresses directed perpendicular to the beam axis. In composite structures these extra stresses may influence the fatigue life significantly. The paper demonstrates a linearized method...
Constructions of vector output Boolean functions with high generalized nonlinearity
Institute of Scientific and Technical Information of China (English)
KE Pin-hui; ZHANG Sheng-yuan
2008-01-01
Carlet et al. recently introduced generalized nonlinearity to measure the ability to resist the improved correlation attack of a vector output Boolean function. This article presents a construction of vector output Boolean functions with high generalized nonlinearity using the sample space. The relation between the resilient order and generalized nonlinearity is also discussed.
A new supersymmetric classical Boussinesq equation
Institute of Scientific and Technical Information of China (English)
Zhang Meng-Xia; Liu Qing-Ping; Wang Juan; Wu Ke
2008-01-01
In this paper,we obtain a supersymmetric generalization for the classical Boussinesq equation.We show that the supersymmetric equation system passes the Painlevé test and we also calculate its one- and two-soliton solutions.
A nonlinear theory of generalized functions
1990-01-01
This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applicati...
Generalized Analytical Solutions for Nonlinear Positive-Negative Index Couplers
Directory of Open Access Journals (Sweden)
Zh. Kudyshev
2012-01-01
Full Text Available We find and analyze a generalized analytical solution for nonlinear wave propagation in waveguide couplers with opposite signs of the linear refractive index, nonzero phase mismatch between the channels, and arbitrary nonlinear coefficients.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Supersymmetric classical cosmology
Escamilla-Rivera, Celia; Urena-Lopez, L Arturo
2010-01-01
In this work a supersymmetric cosmological model is analyzed in which we consider a general superfield action of a homogeneous scalar field supermultiplet interacting with the scale factor in a supersymmetric FRW model. There appear fermionic superpartners associated with both the scale factor and the scalar field, and classical equations of motion are obtained from the super-Wheeler-DeWitt equation through the usual WKB method. The resulting supersymmetric Einstein-Klein-Gordon equations contain extra radiation and stiff matter terms, and we study their solutions in flat space for different scalar field potentials. The solutions are compared to the standard case, in particular those corresponding to the exponential potential, and their implications for the dynamics of the early Universe are discussed in turn.
Tian, Kai; Liu, Q. P.
2012-07-01
A new N=1 supersymmetric Harry Dym equation is constructed by applying supersymmetric reciprocal transformation to a trivial supersymmetric Harry Dym equation, and its recursion operator and Lax formulation are also obtained. Within the framework of symmetry approach, a class of 3rd order supersymmetric equations of Harry Dym type are considered. In addition to five known integrable equations, a new supersymmetric equation, admitting 5th order generalized symmetry, is shown to be linearizable through supersymmetric reciprocal transformation. Furthermore, its Lax representation and recursion operator are given so that the integrability of this new equation is confirmed.
ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS
Institute of Scientific and Technical Information of China (English)
GAN Zuoxin; HAN Jingqing; ZHAO Suxia; WU Yongxian
2002-01-01
In the present paper, the absolute stability of general Lurie discrete nonlinear control systems has been discussed by Lyapunov function approach. A sufficient condition of absolute stability for the general Lurie discrete nonlinear control systems is derived, and some necessary and sufficient conditions are obtained in special cases. Meanwhile, we give a simple example to illustrate the effectiveness of the results.
Khoury, Justin; Ovrut, Burt A
2011-01-01
Galileon theories are of considerable interest since they allow for stable violations of the null energy condition. Since such violations could have occurred during a high-energy regime in the history of our universe, we are motivated to study supersymmetric extensions of these theories. This is carried out in this paper, where we construct generic classes of N=1 supersymmetric Galileon Lagrangians. They are shown to admit non-equivalent stress-energy tensors and, hence, vacua manifesting differing conditions for violating the null energy condition. The temporal and spatial fluctuations of all component fields of the supermultiplet are analyzed and shown to be stable on a large number of such backgrounds. In the process, we uncover a surprising connection between conformal Galileon and ghost condensate theories, allowing for a deeper understanding of both types of theories.
Barranco, Alejandro
2012-01-01
We implement relativistic BCS superconductivity in N=1 supersymmetric field theories with a U(1)_R symmetry. The simplest model contains two chiral superfields with a Kahler potential modified by quartic terms. We study the phase diagram of the gap as a function of the temperature and the specific heat. The superconducting phase transition turns out to be first order, due to the scalar contribution to the one-loop potential. By virtue of supersymmetry, the critical curves depend logarithmically with the UV cutoff, rather than quadratically as in standard BCS theory. We comment on the difficulties in having fermion condensates when the chemical potential is instead coupled to a baryonic U(1)_B current. We also discuss supersymmetric models of BCS with canonical Kahler potential constructed by "integrating-in" chiral superfields.
Nonlinear generalization of Den Hartog's equal-peak method
Habib, G.; Detroux, T.; Viguié, R.; Kerschen, G.
2015-02-01
This study addresses the mitigation of a nonlinear resonance of a mechanical system. In view of the narrow bandwidth of the classical linear tuned vibration absorber, a nonlinear absorber, termed the nonlinear tuned vibration absorber (NLTVA), is introduced in this paper. An unconventional aspect of the NLTVA is that the mathematical form of its restoring force is tailored according to the nonlinear restoring force of the primary system. The NLTVA parameters are then determined using a nonlinear generalization of Den Hartog's equal-peak method. The mitigation of the resonant vibrations of a Duffing oscillator is considered to illustrate the proposed developments.
Instantons in four-Fermi term broken supersymmetric quantum mechanics with general potential
Energy Technology Data Exchange (ETDEWEB)
Hatzinikitas, Agapitos; Smyrnakis, Ioannis [University of Crete, Department of Applied Mathematics, L. Knosou-Ambelokipi, 71409 Iraklio, Crete (Greece)
2004-01-09
We have shown here how to find an integral representation for the solution of the Euclidean equations of motion of a quantum mechanical point particle in a general potential and in the presence of a four-Fermi term. The classical action in this theory depends explicitly on a set of four fermionic collective coordinates. The corrections to the classical action due to the presence of fermions are of topological nature in the sense that they depend only on the values of the fields at the boundary points {tau} {yields} {+-} {infinity}. As an application, the quantum mechanical sine-Gordon model with a four-Fermi term is solved explicitly and the corrections to the classical action are computed.
Robust stabilization of general nonlinear systems with structural uncertainty
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper deals with the robust stabilization and passivity of general nonlinear systems with structural uncertainty. By using Lyapunov function, it verifies that under some conditions the robust passivity implies the zero-state detectability, Furthermore, it also implies the robust stabilization for such nonlinear systems. We then establish a stabilization method for the nonlinear systems with structural uncertainty. The smooth state feedback law can be constructed with the solution of an equation. Finally, it is worth noting that the main contribution of the paper establishes the relation between robust passivity and feedback stabilization for the general nonlinear systems with structural uncertainty. The simulation shows the effectiveness of the method.
N=2 supersymmetric sigma-models in AdS
Butter, Daniel
2011-01-01
We construct the most general N=2 supersymmetric nonlinear sigma-model in four-dimensional anti-de Sitter (AdS) space in terms of N=1 chiral superfields. The target space is shown to be a non-compact hyperkahler manifold restricted to possess a special Killing vector field. A remarkable property of the sigma-model constructed is that the algebra of OSp(2|4) transformations is closed off the mass shell.
General Symmetry Approach to Solve Variable-Coefficient Nonlinear Equations
Institute of Scientific and Technical Information of China (English)
RUAN HangYu; CHEN YiXin; LOU SenYue
2001-01-01
After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schrodinger equation as a concrete example, the method is recommended in detail.``
Vibrational mechanics nonlinear dynamic effects, general approach, applications
Blekhman, Iliya I
2000-01-01
This important book deals with vibrational mechanics - the new, intensively developing section of nonlinear dynamics and the theory of nonlinear oscillations. It offers a general approach to the study of the effect of vibration on nonlinear mechanical systems.The book presents the mathematical apparatus of vibrational mechanics which is used to describe such nonlinear effects as the disappearance and appearance under vibration of stable positions of equilibrium and motions (i.e. attractors), the change of the rheological properties of the media, self-synchronization, self-balancing, the vibrat
Nearly Supersymmetric Dark Atoms
Energy Technology Data Exchange (ETDEWEB)
Behbahani, Siavosh R.; Jankowiak, Martin; /SLAC /Stanford U., ITP; Rube, Tomas; /Stanford U., ITP; Wacker, Jay G.; /SLAC /Stanford U., ITP
2011-08-12
Theories of dark matter that support bound states are an intriguing possibility for the identity of the missing mass of the Universe. This article proposes a class of models of supersymmetric composite dark matter where the interactions with the Standard Model communicate supersymmetry breaking to the dark sector. In these models supersymmetry breaking can be treated as a perturbation on the spectrum of bound states. Using a general formalism, the spectrum with leading supersymmetry effects is computed without specifying the details of the binding dynamics. The interactions of the composite states with the Standard Model are computed and several benchmark models are described. General features of non-relativistic supersymmetric bound states are emphasized.
Stability analysis of embedded nonlinear predictor neural generalized predictive controller
Directory of Open Access Journals (Sweden)
Hesham F. Abdel Ghaffar
2014-03-01
Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.
Generalized Nonlinear Proca Equation and its Free-Particle Solutions
Nobre, F D
2016-01-01
We introduce a non-linear extension of Proca's field theory for massive vector (spin $1$) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter $q$ (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit $q \\rightarrow 1$. We derive the nonlinear Proca equation from a Lagrangian that, besides the usual vectorial field $\\Psi^{\\mu}(\\vec{x},t)$, involves an additional field $\\Phi^{\\mu}(\\vec{x},t)$. We obtain exact time dependent soliton-like solutions for these fields having the...
Berry phase in a generalized nonlinear two-level system
Institute of Scientific and Technical Information of China (English)
Liu Ji-Bing; Li Jia-Hua; Song Pei-Jun; Li Wei-Bin
2008-01-01
In this paper,we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field.Both the field nonlinearity and the atom-field coupling nonlinearity are considered.We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case.In addition,we also find that the geometric phase may be easily observed when the field nonlinearity is not considered.The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered.We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Castaños, Octavio; Schuch, Dieter; Rosas-Ortiz, Oscar
2013-02-01
Based on the Gaussian wave packet solution for the harmonic oscillator and the corresponding creation and annihilation operators, a generalization is presented that also applies for wave packets with time-dependent width as they occur for systems with different initial conditions, time-dependent frequency or in contact with a dissipative environment. In all these cases, the corresponding coherent states, position and momentum uncertainties and quantum mechanical energy contributions can be obtained in the same form if the creation and annihilation operators are expressed in terms of a complex variable that fulfils a nonlinear Riccati equation which determines the time-evolution of the wave packet width. The solutions of this Riccati equation depend on the physical system under consideration and on the (complex) initial conditions and have close formal similarities with general superpotentials leading to isospectral potentials in supersymmetric quantum mechanics. The definition of the generalized creation and annihilation operator is also in agreement with a factorization of the operator corresponding to the Ermakov invariant that exists in all cases considered.
Completely generalized multivalued nonlinear quasi-variational inclusions
Directory of Open Access Journals (Sweden)
Zeqing Liu
2002-01-01
Full Text Available We introduce and study a new class of completely generalized multivalued nonlinear quasi-variational inclusions. Using the resolvent operator technique for maximal monotone mappings, we suggest two kinds of iterative algorithms for solving the completely generalized multivalued nonlinear quasi-variational inclusions. We establish both four existence theorems of solutions for the class of completely generalized multivalued nonlinear quasi-variational inclusions involving strongly monotone, relaxed Lipschitz, and generalized pseudocontractive mappings, and obtain a few convergence results of iterative sequences generated by the algorithms. The results presented in this paper extend, improve, and unify a lot of results due to Adly, Huang, Jou-Yao, Kazmi, Noor, Noor-Al-Said, Noor-Noor, Noor-Noor-Rassias, Shim-Kang-Huang-Cho, Siddiqi-Ansari, Verma, Yao, and Zhang.
Stability properties of a general class of nonlinear dynamical systems
Energy Technology Data Exchange (ETDEWEB)
Gleria, I.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: iram@ucb.br; Figueiredo, A. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: annibal@helium.fis.unb.br; Rocha, T.M. [Filho Instituto de Fisica, Universidade de Brasilia, Campus Universitario Darcy Ribeiro, Brasilia (Brazil). E-mail: marciano@helium.fis.unb.br
2001-05-04
We establish sufficient conditions for the boundedness of the trajectories and the stability of the fixed points in a class of general nonlinear systems, the so-called quasi-polynomial vector fields, with the help of a natural embedding of such systems in a family of generalized Lotka-Volterra (LV) equations. A purely algebraic procedure is developed to determine such conditions. We apply our method to obtain new results for LV systems, by a reparametrization in time variable, and to study general nonlinear vector fields, originally far from the LV format. (author)
Generalized Mass Action Law and Thermodynamics of Nonlinear Markov Processes
Gorban, A N
2015-01-01
The nonlinear Markov processes are the measure-valued dynamical systems which preserve positivity. They can be represented as the law of large numbers limits of general Markov models of interacting particles. In physics, the kinetic equations allow Lyapunov functionals (entropy, free energy, etc.). This may be considered as a sort of inheritance of the Lyapunov functionals from the microscopic master equations. We study nonlinear Markov processes that inherit thermodynamic properties from the microscopic linear Markov processes. We develop the thermodynamics of nonlinear Markov processes and analyze the asymptotic assumption, which are sufficient for this inheritance.
A generalization error estimate for nonlinear systems
DEFF Research Database (Denmark)
Larsen, Jan
1992-01-01
models of linear and simple neural network systems. Within the linear system GEN is compared to the final prediction error criterion and the leave-one-out cross-validation technique. It was found that the GEN estimate of the true generalization error is less biased on the average. It is concluded...
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Duality in supersymmetric Yang-Mills theory
Energy Technology Data Exchange (ETDEWEB)
Peskin, M.E.
1997-02-01
These lectures provide an introduction to the behavior of strongly-coupled supersymmetric gauge theories. After a discussion of the effective Lagrangian in nonsupersymmetric and supersymmetric field theories, the author analyzes the qualitative behavior of the simplest illustrative models. These include supersymmetric QCD for N{sub f} < N{sub c}, in which the superpotential is generated nonperturbatively, N = 2 SU(2) Yang-Mills theory (the Seiberg-Witten model), in which the nonperturbative behavior of the effect coupling is described geometrically, and supersymmetric QCD for N{sub f} large, in which the theory illustrates a non-Abelian generalization of electric-magnetic duality. 75 refs., 12 figs.
Aleixo, A. N. F.; Balantekin, A. B.
2015-12-01
We resolve the normal ordering problem for symmetric ( D ˆ + D ˆ - ) n and asymmetric ( Dˆ + r D ˆ - ) n strings of the nonlinear deformed ladder operators D ˆ ± for supersymmetric and shape-invariant potential systems, where r and n are positive integers. We provide exact and explicit expressions for their normal forms N { ( D ˆ + D ˆ - ) n } and N { ( Dˆ + r D ˆ - ) n } , where in N { . . . } all D ˆ - are at the right side. We find that the solutions involve sequence of expansion coefficients which, for r, n > 1, corresponds to the f-deformed generalization of the classical Stirling and Bell numbers of the second kind. We apply the general formalism for the translational shape-invariant potential systems as well as for the particular case of the harmonic oscillator potential system. We show that these numbers are obtained for families of polynomial expressions generated with the deformations parameters and the parameters related to the forms of the supersymmetric partner potentials.
Modulation instability of broad optical beams in nonlinear media with general nonlinearity
Institute of Scientific and Technical Information of China (English)
Hongcheng Wang; Weilong She
2006-01-01
@@ The modulation instability of quasi-plane-wave optical beams is investigated in the frame of generalized Schr(o)dinger equation with the nonlinear term of a general form. General expressions are derived for the dispersion relation, the critical transverse spatial frequency, as well as the instability growth rate.The analysis generalizes the known results reported previously. A detailed discussion on the modulation instability in biased centrosymmetric photorefractive media is also given.
A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem
Directory of Open Access Journals (Sweden)
Meixia Li
2012-01-01
Full Text Available Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.
General difference schemes with intrinsic parallelism for nonlinear parabolic systems
Institute of Scientific and Technical Information of China (English)
周毓麟; 袁光伟
1997-01-01
The boundary value problem for nonlinear parabolic system is solved by the finite difference method with intrinsic parallelism. The existence of the discrete vector solution for the general finite difference schemes with intrinsic parallelism is proved by the fixed-point technique in finite-dimensional Euclidean space. The convergence and stability theorems of the discrete vector solutions of the nonlinear difference system with intrinsic parallelism are proved. The limitation vector function is just the unique generalized solution of the original problem for the parabolic system.
Colombeau, J. F.
2007-01-01
We present numerical techniques based on generalized functions adapted to nonlinear calculations. They concern main numerical engineering problems ruled by-or issued from-nonlinear equations of continuum mechanics. The aim of this text is to invite the readers in applying these techniques in their own work without significant prerequisites by presenting their use on a sample of elementary applications from engineering. Pure mathematicians can read it easily since the numerical techniques are ...
Ilinskii, K N; Melezhik, V S; Ilinski, K N; Kalinin, G V; Melezhik, V V
1994-01-01
We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (supersymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry index) is determined. As the examples of suggested concept of supersymmetric adiabatic evolution the Holomorphic quantum mechanics on complex plane and Meromorphic quantum mechanics on Riemann surface are considered. The supersymmetric Berry indexes for the models are calculated.
Supersymmetric R4-actions in ten dimensions
Roo, M. de; Suelmann, H.; Wiedemann, A.
1992-01-01
We construct supersymmetric R+R4-actions in ten dimensions. Two invariants, of which the bosonic parts are known from string amplitude and sigma model calculations, are obtained. One of these invariants can be generalized to an R+F2+F4-invariant for supersymmetric Yang-Mills theory coupled to superg
Supersymmetric vacua in random supergravity
Bachlechner, Thomas C.; Marsh, David; McAllister, Liam; Wrase, Timm
2013-01-01
We determine the spectrum of scalar masses in a supersymmetric vacuum of a general mathcal{N}=1 supergravity theory, with the Kähler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P=exp left( {{{{-2{N^2}{{{left| W right|}}^2}}} left/ {{m_{susy}^2}} right.}} right) , with W denoting the superpotential and m susy the supersymmetric mass scale; for more general distributions of the entries, our result is accurate when N ≫ 1. We conclude that for left| W right|gtrsim {{{{m_{susy}}}} left/ {N} right.} , tachyonic instabilities are ubiquitous in configurations obtained by uplifting supersymmetric vacua.
The Supersymmetric Effective Field Theory of Inflation
Delacretaz, Luca V; Senatore, Leonardo
2016-01-01
We construct the Supersymmetric Effective Field Theory of Inflation, that is the most general theory of inflationary fluctuations when time-translations and supersymmetry are spontaneously broken. The non-linear realization of these invariances allows us to define a complete SUGRA multiplet containing the graviton, the gravitino, the Goldstone of time translations and the Goldstino, with no auxiliary fields. Going to a unitary gauge where only the graviton and the gravitino are present, we write the most general Lagrangian built out of the fluctuations of these fields, invariant under time-dependent spatial diffeomorphisms, but softly-breaking time diffeomorphisms and gauged SUSY. With a suitable St\\"uckelberg transformation, we introduce the Goldstone boson of time translation and the Goldstino of SUSY. No additional dynamical light field is needed. In the high energy limit, larger than the inflationary Hubble scale for the Goldstino, these fields decouple from the graviton and the gravitino, greatly simplif...
Energy Technology Data Exchange (ETDEWEB)
Xie, Xi-Yang; Tian, Bo, E-mail: tian_bupt@163.com; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-15
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
RF Circuit linearity optimization using a general weak nonlinearity model
Cheng, W.; Oude Alink, M.S.; Annema, Anne J.; Croon, Jeroen A.; Nauta, Bram
2012-01-01
This paper focuses on optimizing the linearity in known RF circuits, by exploring the circuit design space that is usually available in today’s deep submicron CMOS technologies. Instead of using brute force numerical optimizers we apply a generalized weak nonlinearity model that only involves AC
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
qualities. The controller is a non-linear version of the well-known generalized predictive controller developed in linear control theory. It involves minimization of a cost function which in the present case has to be done numerically. Therefore, we develop the numerical algorithms necessary in substantial...
Generalized nonlinear Proca equation and its free-particle solutions
Energy Technology Data Exchange (ETDEWEB)
Nobre, F.D. [Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems, Rio de Janeiro, RJ (Brazil); Plastino, A.R. [Universidad Nacional Buenos Aires-Noreoeste, CeBio y Secretaria de Investigacion, Junin (Argentina)
2016-06-15
We introduce a nonlinear extension of Proca's field theory for massive vector (spin 1) bosons. The associated relativistic nonlinear wave equation is related to recently advanced nonlinear extensions of the Schroedinger, Dirac, and Klein-Gordon equations inspired on the non-extensive generalized thermostatistics. This is a theoretical framework that has been applied in recent years to several problems in nuclear and particle physics, gravitational physics, and quantum field theory. The nonlinear Proca equation investigated here has a power-law nonlinearity characterized by a real parameter q (formally corresponding to the Tsallis entropic parameter) in such a way that the standard linear Proca wave equation is recovered in the limit q → 1. We derive the nonlinear Proca equation from a Lagrangian, which, besides the usual vectorial field Ψ{sup μ}(vector x,t), involves an additional field Φ{sup μ}(vector x,t). We obtain exact time-dependent soliton-like solutions for these fields having the form of a q-plane wave, and we show that both field equations lead to the relativistic energy-momentum relation E{sup 2} = p{sup 2}c{sup 2} + m{sup 2}c{sup 4} for all values of q. This suggests that the present nonlinear theory constitutes a new field theoretical representation of particle dynamics. In the limit of massless particles the present q-generalized Proca theory reduces to Maxwell electromagnetism, and the q-plane waves yield localized, transverse solutions of Maxwell equations. Physical consequences and possible applications are discussed. (orig.)
A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING
Institute of Scientific and Technical Information of China (English)
Xin-wei Liu; Ya-xiang Yuan
2001-01-01
The trust region approach has been extended to solving nonlinear constrained optimization. Most of these extensions consider only equality constraints and require strong global regularity assumptions. In this paper, a trust region algorithm for solving general nonlinear programming is presented, which solves an unconstrained piecewise quadratic trust region subproblem and a quadratic programming trust region subproblem at each iteration. A new technique for updating the penalty parameter is introduced. Under very mild conditions, the global convergence results are proved. Some local convergence results are also proved. Preliminary numerical results are also reported.
The holographic supersymmetric Casimir energy
Benetti Genolini, Pietro; Cassani, Davide; Martelli, Dario; Sparks, James
2017-01-01
We consider a general class of asymptotically locally AdS5 solutions of minimal gauged supergravity, which are dual to superconformal field theories on curved backgrounds S1×M3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S1×R4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory supersymmetric relation between charges.
Geometry and duality in Supersymmetric $\\sigma$-Models
Curtright, T L; Zachos, C K; Curtright, Thomas; Uematsu, Tsuneo; Zachos, Cosmas
1996-01-01
The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear sigma-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the Boson-Fermion Symphysis of the dual transition, and on the new geometry of the DSM.
Generalized non-linear strength theory and transformed stress space
Institute of Scientific and Technical Information of China (English)
YAO Yangping; LU Dechun; ZHOU Annan; ZOU Bo
2004-01-01
Based on the test data of frictional materials and previous research achievements in this field, a generalized non-linear strength theory (GNST) is proposed. It describes non-linear strength properties on the π-plane and the meridian plane using a unified formula, and it includes almost all the present non-linear strength theories, which can be used in just one material. The shape of failure function of the GNST is a smooth curve between the SMP criterion and the Mises criterion on the π-plane, and an exponential curve on the meridian plane. Through the transformed stress space based on the GNST, the combination of the GNST and various constitutive models using p and q as stress parameters can be realized simply and rationally in three-dimensional stress state.
General expression for linear and nonlinear time series models
Institute of Scientific and Technical Information of China (English)
Ren HUANG; Feiyun XU; Ruwen CHEN
2009-01-01
The typical time series models such as ARMA, AR, and MA are founded on the normality and stationarity of a system and expressed by a linear difference equation; therefore, they are strictly limited to the linear system. However, some nonlinear factors are within the practical system; thus, it is difficult to fit the model for real systems with the above models. This paper proposes a general expression for linear and nonlinear auto-regressive time series models (GNAR). With the gradient optimization method and modified AIC information criteria integrated with the prediction error, the parameter estimation and order determination are achieved. The model simulation and experiments show that the GNAR model can accurately approximate to the dynamic characteristics of the most nonlinear models applied in academics and engineering. The modeling and prediction accuracy of the GNAR model is superior to the classical time series models. The proposed GNAR model is flexible and effective.
Neural Generalized Predictive Control of a non-linear Process
DEFF Research Database (Denmark)
Sørensen, Paul Haase; Nørgård, Peter Magnus; Ravn, Ole
1998-01-01
The use of neural network in non-linear control is made difficult by the fact the stability and robustness is not guaranteed and that the implementation in real time is non-trivial. In this paper we introduce a predictive controller based on a neural network model which has promising stability...... detail and discuss the implementation difficulties. The neural generalized predictive controller is tested on a pneumatic servo sys-tem....
Exploring the Supersymmetric $\\sigma$ Model
De Oliveira-Imbiriba, B C
1999-01-01
The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological nature, and its association with the torsion. It is also shown that to cancel the quantum conformal anomaly the model should obey the Einstein equations. We provide a quick introduction about supersymmetry in chapter 2 to help the understanding the supersymmetric extension of the model. In the last chapter we present the supersymmetric model and its equations of motion. Finally we work-out the two-supersymmetry case, introducing the chiral as well as the twisted chiral fields, expliciting the very specific $SU(2)\\otimes U(1)$ case.
Supersymmetric Vacua in Random Supergravity
Bachlechner, Thomas C; McAllister, Liam; Wrase, Timm
2012-01-01
We determine the spectrum of scalar masses in a supersymmetric vacuum of a general N=1 supergravity theory, with the Kahler potential and superpotential taken to be random functions of N complex scalar fields. We derive a random matrix model for the Hessian matrix and compute the eigenvalue spectrum. Tachyons consistent with the Breitenlohner-Freedman bound are generically present, and although these tachyons cannot destabilize the supersymmetric vacuum, they do influence the likelihood of the existence of an `uplift' to a metastable vacuum with positive cosmological constant. We show that the probability that a supersymmetric AdS vacuum has no tachyons is formally equivalent to the probability of a large fluctuation of the smallest eigenvalue of a certain real Wishart matrix. For normally-distributed matrix entries and any N, this probability is given exactly by P = exp(-2N^2|W|^2/m_{susy}^2), with W denoting the superpotential and m_{susy} the supersymmetric mass scale; for more general distributions of the...
Solution of Second Order Supersymmetrical Intertwining Relations in Minkowski Plane
Ioffe, M V; Nishnianidze, D N
2016-01-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the itertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest - constant - ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Solution of second order supersymmetrical intertwining relations in Minkowski plane
Ioffe, M. V.; Kolevatova, E. V.; Nishnianidze, D. N.
2016-08-01
Supersymmetrical (SUSY) intertwining relations are generalized to the case of quantum Hamiltonians in Minkowski space. For intertwining operators (supercharges) of second order in derivatives, the intertwined Hamiltonians correspond to completely integrable systems with the symmetry operators of fourth order in momenta. In terms of components, the intertwining relations correspond to the system of nonlinear differential equations which are solvable with the simplest—constant—ansatzes for the "metric" matrix in second order part of the supercharges. The corresponding potentials are built explicitly both for diagonalizable and nondiagonalizable form of "metric" matrices, and their properties are discussed.
Liu, Chang
2015-01-01
The nonlinear frequency shift is derived in a transparent asymptotic form for intense Langmuir waves in general collisionless plasma. The formula describes both fluid and kinetic effects simultaneously. The fluid nonlinearity is expressed, for the ?first time, through the plasma dielectric function, and the kinetic nonlinearity accounts for both smooth distributions and trapped-particle beams. Various known limiting scalings are reproduced as special cases. The calculation avoids differential equations and can be extended straightforwardly to other nonlinear plasma waves.
Chaos Control in Nonlinear Systems Using the Generalized Backstopping Method
Directory of Open Access Journals (Sweden)
A. R. Sahab
2008-01-01
Full Text Available One of the most important nonlinear systems for checking the abilities of control methods is chaos. In this study chaos in Lorenz system was used for checking abilities of new control method. This new method to control nonlinear systems was called Generalized Backstepping method because of its similarity to Backstepping but its abilities to control more systems than Backstepping. This new method was applied to Lorenz system in three ways: 1.Stabilized states of equations. 2. Track step response. 3. Track sinusoidal response. In every way, simulations proved abilities of method. Comparing this new method with Backstepping showed that in this method, states stabilize at zero in shorter time than Backstepping and input control is more limited. So new method not only is used in more systems but also has better response.
Periodic Wave Solutions of Generalized Derivative Nonlinear Schr(o)dinger Equation
Institute of Scientific and Technical Information of China (English)
ZHA Qi-Lao; LI Zhi-Bin
2008-01-01
A Darboux transformation of the generalized derivative nonlinear Schr(o)dinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schr(o)dinger equation are explicitly given.
Supersymmetric Open Wilson Lines
Baker, Edward B
2011-01-01
In this paper we study Open Wilson Lines (OWL's) in the context of two Supersymmetric Yang Mills theories. First we consider four dimensional N=2 Supersymmetric Yang Mills Theory with hypermultiplets transforming in the fundamental representation of the gauge group, and find supersymmetric OWL's only in the superconformal versions of these theories. We then consider four dimensional N=4 SYM coupled to a three dimensional defect hypermultiplet. Here there is a semi-circular supersymmetric OWL, which is related to the ray by a conformal transformation. We perform a perturbative calculation of the operators in both theories, and discuss using localization to compute them non-perturbatively.
The supersymmetric flavor problem
Dimopoulos, Savas K; Dimopoulos, Savas; Sutter, Dave
1995-01-01
The supersymmetric SU(3)\\times SU(2)\\times U(1) theory with minimal particle content and general soft supersymmetry breaking terms has 110 physical parameters in its flavor sector: 30 masses, 39 real mixing angles and 41 phases. The absence of an experimental indication for the plethora of new parameters places severe constraints on theories posessing Planck or GUT-mass particles and suggests that theories of flavor conflict with naturalness. We illustrate the problem by studying the processes \\mu \\rightarrow e + \\gamma and K^0 - \\bar{K}^0 mixing which are very sensitive probes of Planckian physics: a single Planck mass particle coupled to the electron or the muon with a Yukawa coupling comparable to the gauge coupling typically leads to a rate for \\mu \\rightarrow e + \\gamma exceeding the present experimental limits. A possible solution is that the messengers which transmit supersymmetry breaking to the ordinary particles are much lighter than M_{\\rm Planck}.
New approaches to generalized Hamiltonian realization of autonomous nonlinear systems
Institute of Scientific and Technical Information of China (English)
王玉振; 李春文; 程代展
2003-01-01
The Hamiltonian function method plays an important role in stability analysis and stabilization. The key point in applying the method is to express the system under consideration as the form of dissipative Hamiltonian systems, which yields the problem of generalized Hamiltonian realization. This paper deals with the generalized Hamiltonian realization of autonomous nonlinear systems. First, this paper investigates the relation between traditional Hamiltonian realizations and first integrals, proposes a new method of generalized Hamiltonian realization called the orthogonal decomposition method, and gives the dissipative realization form of passive systems. This paper has proved that an arbitrary system has an orthogonal decomposition realization and an arbitrary asymptotically stable system has a strict dissipative realization. Then this paper studies the feedback dissipative realization problem and proposes a control-switching method for the realization. Finally,this paper proposes several sufficient conditions for feedback dissipative realization.
New variable separation solutions for the generalized nonlinear diffusion equations
Fei-Yu, Ji; Shun-Li, Zhang
2016-03-01
The functionally generalized variable separation of the generalized nonlinear diffusion equations ut = A(u,ux)uxx + B(u,ux) is studied by using the conditional Lie-Bäcklund symmetry method. The variant forms of the considered equations, which admit the corresponding conditional Lie-Bäcklund symmetries, are characterized. To construct functionally generalized separable solutions, several concrete examples defined on the exponential and trigonometric invariant subspaces are provided. Project supported by the National Natural Science Foundation of China (Grant Nos. 11371293, 11401458, and 11501438), the National Natural Science Foundation of China, Tian Yuan Special Foundation (Grant No. 11426169), and the Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2015JQ1014).
Lotka-Volterra representation of general nonlinear systems.
Hernández-Bermejo, B; Fairén, V
1997-02-01
In this article we elaborate on the structure of the generalized Lotka-Volterra (GLV) form for nonlinear differential equations. We discuss here the algebraic properties of the GLV family, such as the invariance under quasimonomial transformations and the underlying structure of classes of equivalence. Each class possesses a unique representative under the classical quadratic Lotka-Volterra form. We show how other standard modeling forms of biological interest, such as S-systems or mass-action systems, are naturally embedded into the GLV form, which thus provides a formal framework for their comparison and for the establishment of transformation rules. We also focus on the issue of recasting of general nonlinear systems into the GLV format. We present a procedure for doing so and point at possible sources of ambiguity that could make the resulting Lotka-Volterra system dependent on the path followed. We then provide some general theorems that define the operational and algorithmic framework in which this is not the case.
Nonlinear viscoelasticity and generalized failure criterion for biopolymer gels
Divoux, Thibaut; Keshavarz, Bavand; Manneville, Sébastien; McKinley, Gareth
2016-11-01
Biopolymer gels display a multiscale microstructure that is responsible for their solid-like properties. Upon external deformation, these soft viscoelastic solids exhibit a generic nonlinear mechanical response characterized by pronounced stress- or strain-stiffening prior to irreversible damage and failure, most often through macroscopic fractures. Here we show on a model acid-induced protein gel that the nonlinear viscoelastic properties of the gel can be described in terms of a 'damping function' which predicts the gel mechanical response quantitatively up to the onset of macroscopic failure. Using a nonlinear integral constitutive equation built upon the experimentally-measured damping function in conjunction with power-law linear viscoelastic response, we derive the form of the stress growth in the gel following the start up of steady shear. We also couple the shear stress response with Bailey's durability criteria for brittle solids in order to predict the critical values of the stress σc and strain γc for failure of the gel, and how they scale with the applied shear rate. This provides a generalized failure criterion for biopolymer gels in a range of different deformation histories. This work was funded by the MIT-France seed fund and by the CNRS PICS-USA scheme (#36939). BK acknowledges financial support from Axalta Coating Systems.
Generalized Ghost Dark Energy with Non-Linear Interaction
Ebrahimi, E; Mehrabi, A; Movahed, S M S
2016-01-01
In this paper we investigate ghost dark energy model in the presence of non-linear interaction between dark energy and dark matter. The functional form of dark energy density in the generalized ghost dark energy (GGDE) model is $\\rho_D\\equiv f(H, H^2)$ with coefficient of $H^2$ represented by $\\zeta$ and the model contains three free parameters as $\\Omega_D, \\zeta$ and $b^2$ (the coupling coefficient of interactions). We propose three kinds of non-linear interaction terms and discuss the behavior of equation of state, deceleration and dark energy density parameters of the model. We also find the squared sound speed and search for signs of stability of the model. To compare the interacting GGDE model with observational data sets, we use more recent observational outcomes, namely SNIa, gamma-ray bursts, baryonic acoustic oscillation and the most relevant CMB parameters including, the position of acoustic peaks, shift parameters and redshift to recombination. For GGDE with the first non-linear interaction, the j...
A General Nonlinear Optimization Algorithm for Lower Bound Limit Analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...
Karagiannakis, N; Pallis, C
2015-01-01
We analyze the parametric space of the constrained minimal supersymmetric standard model with mu>0 supplemented by a generalized asymptotic Yukawa coupling quasi-unification condition which yields acceptable masses for the fermions of the third family. We impose constraints from the cold dark matter abundance in the universe and its direct detection experiments, the B-physics, as well as the masses of the sparticles and the lightest neutral CP-even Higgs boson. Fixing the mass of the latter to its central value from the LHC and taking 40<=tanbeta<=50, we find a relatively wide allowed parameter space with -11<=A_0/M_{1/2}<=15 and mass of the lightest sparticle in the range (0.09-1.1) TeV. This sparticle is possibly detectable by the present cold dark matter direct search experiments. The required fine-tuning for the electroweak symmetry breaking is much milder than the one needed in the neutralino-stau coannihilation region of the same model.
Modelling Nonlinearities and Reference Dependence in General Practitioners' Income Preferences.
Holte, Jon Helgheim; Sivey, Peter; Abelsen, Birgit; Olsen, Jan Abel
2016-08-01
This paper tests for the existence of nonlinearity and reference dependence in income preferences for general practitioners. Confirming the theory of reference dependent utility within the context of a discrete choice experiment, we find that losses loom larger than gains in income for Norwegian general practitioners, i.e. they value losses from their current income level around three times higher than the equivalent gains. Our results are validated by comparison with equivalent contingent valuation values for marginal willingness to pay and marginal willingness to accept compensation for changes in job characteristics. Physicians' income preferences determine the effectiveness of 'pay for performance' and other incentive schemes. Our results may explain the relative ineffectiveness of financial incentive schemes that rely on increasing physicians' incomes. Copyright © 2015 John Wiley & Sons, Ltd.
Renormalizability of Supersymmetric Group Field Cosmology
Upadhyay, Sudhaker
2014-01-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
Renormalizability of supersymmetric group field cosmology
Upadhyay, Sudhaker
2014-03-01
In this paper we consider the gauge invariant third quantized model of supersymmetric group field cosmology. The supersymmetric BRST invariance for such theory in non-linear gauge is also analysed. The path integral formulation to the case of a multiverse made up of homogeneous and isotropic spacetimes filled with a perfect fluid is presented. The renormalizability for the scattering of universes in multiverse are established with suitably constructed master equations for connected diagrams and proper vertices. The Slavnov-Taylor identities for this theory hold to all orders of radiative corrections.
Solitonlike solutions of the generalized discrete nonlinear Schrödinger equation
DEFF Research Database (Denmark)
Rasmussen, Kim; Henning, D.; Gabriel, H.
1996-01-01
We investigate the solution properties oi. a generalized discrete nonlinear Schrodinger equation describing a nonlinear lattice chain. The generalized equation interpolates between the integrable discrete Ablowitz-Ladik equation and the nonintegrable discrete Schrodinger equation. Special interest...... nonlinear Schrodinger equation. In this way eve are able to construct coherent solitonlike structures of profile determined by the map parameters....
Instability of supersymmetric microstate geometries
Eperon, Felicity C; Santos, Jorge E
2016-01-01
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an "evanescent ergosurface": a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Instability of supersymmetric microstate geometries
Energy Technology Data Exchange (ETDEWEB)
Eperon, Felicity C.; Reall, Harvey S.; Santos, Jorge E. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
2016-10-07
We investigate the classical stability of supersymmetric, asymptotically flat, microstate geometries with five non-compact dimensions. Such geometries admit an “evanescent ergosurface”: a timelike hypersurface of infinite redshift. On such a surface, there are null geodesics with zero energy relative to infinity. These geodesics are stably trapped in the potential well near the ergosurface. We present a heuristic argument indicating that this feature is likely to lead to a nonlinear instability of these solutions. We argue that the precursor of such an instability can be seen in the behaviour of linear perturbations: nonlinear stability would require that all linear perturbations decay sufficiently rapidly but the stable trapping implies that some linear perturbation decay very slowly. We study this in detail for the most symmetric microstate geometries. By constructing quasinormal modes of these geometries we show that generic linear perturbations decay slower than any inverse power of time.
Supersymmetric Spacetimes from Curved Superspace
Kuzenko, Sergei M
2015-01-01
We review the superspace technique to determine supersymmetric spacetimes in the framework of off-shell formulations for supergravity in diverse dimensions using the case of 3D N=2 supergravity theories as an illustrative example. This geometric formalism has several advantages over other approaches advocated in the last four years. Firstly, the infinitesimal isometry transformations of a given curved superspace form, by construction, a finite-dimensional Lie superalgebra, with its odd part corresponding to the rigid supersymmetry transformations. Secondly, the generalised Killing spinor equation, which must be obeyed by the supersymmetry parameters, is a consequence of the more fundamental superfield Killing equation. Thirdly, general rigid supersymmetric theories on a curved spacetime are readily constructed in superspace by making use of the known off-shell supergravity-matter couplings and restricting them to the background chosen. It is the superspace techniques which make it possible to generate arbitra...
$\\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
Aprile, Francesco
2016-01-01
General half-BPS A-type boundary conditions are formulated for N=2 supersymmetric field theories on compact 3-manifolds with boundary. We observe that under suitable conditions manifolds of the real A-type admitting two complex supersymmetries (related by charge conjugation) possess, besides a contact structure, a natural integrable toric foliation. A boundary, or a general co-dimension-1 defect, can be inserted along any leaf of this preferred foliation to produce manifolds with boundary that have the topology of a solid torus. We show that supersymmetric field theories on such manifolds can be endowed with half-BPS A-type boundary conditions. We specify the natural curved space generalization of the A-type projection of bulk supersymmetries and analyze the resulting A-type boundary conditions in generic 3d non-linear sigma models and YM/CS-matter theories.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
Dynamic behavior of a nonlinear rational difference equation and generalization
Directory of Open Access Journals (Sweden)
Shi Qihong
2011-01-01
Full Text Available Abstract This paper is concerned about the dynamic behavior for the following high order nonlinear difference equation x n = (x n-k + x n-m + x n-l /(x n-k x n-m + x n-m x n-l +1 with the initial data { x - l , x - l + 1 , … , x - 1 } ∈ ℝ + l and 1 ≤ k ≤ m ≤ l. The convergence of solution to this equation is investigated by introducing a new sequence, which extends and includes corresponding results obtained in the references (Li in J Math Anal Appl 312:103-111, 2005; Berenhaut et al. Appl. Math. Lett. 20:54-58, 2007; Papaschinopoulos and Schinas J Math Anal Appl 294:614-620, 2004 to a large extent. In addition, some propositions for generalized equations are reported.
Supersymmetric invariant theories
Esipova, S R; Radchenko, O V
2013-01-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Supersymmetric invariant theories
Esipova, S. R.; Lavrov, P. M.; Radchenko, O. V.
2014-04-01
We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is a direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
Exact Solution of a Generalized Nonlinear Schrodinger Equation Dimer
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Maniadis, P.; Tsironis, G.P.
1998-01-01
We present exact solutions for a nonlinear dimer system defined throught a discrete nonlinear Schrodinger equation that contains also an integrable Ablowitz-Ladik term. The solutions are obtained throught a transformation that maps the dimer into a double Sine-Gordon like ordinary nonlinear...... differential equation....
Supersymmetric Color Superconductivity
Harnik, R; Murayama, H; Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi
2004-01-01
Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N_c) gauge theories with N_f flavors of quarks in the presence of a baryon chemical potential mu, and describe the global symmetry breaking patterns at low energy. Our analysis requires mu mu_c. We also give a qualitative description of the phases in the `conformal window', 3/2 N_c < N_f < 3N_c, at finite density.
Renormalization of supersymmetric theories
Energy Technology Data Exchange (ETDEWEB)
Pierce, D.M.
1998-06-01
The author reviews the renormalization of the electroweak sector of the standard model. The derivation also applies to the minimal supersymmetric standard model. He discusses regularization, and the relation between the threshold corrections and the renormalization group equations. He considers the corrections to many precision observables, including M{sub W} and sin{sup 2}{theta}{sup eff}. He shows that global fits to the data exclude regions of supersymmetric model parameter space and lead to lower bounds on superpartner masses.
A generalization of the power law distribution with nonlinear exponent
Prieto, Faustino; Sarabia, José María
2017-01-01
The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called Generalized Power Law (GPL), which can be useful for modeling data in all the range and possess power law tails. To do that, we model the exponent of the power law using a non-linear function which depends on data and two parameters. Then, we provide some basic properties and some specific models of that new family of distributions. After that, we study a relevant model of the family, with special emphasis on the quantile and hazard functions, and the corresponding estimation and testing methods. Finally, as an empirical evidence, we study how the debt is distributed across municipalities in Spain. We check that power law model is only valid in the upper tail; we show analytically and graphically the competence of the new model with municipal debt data in the whole range; and we compare the new distribution with other well-known distributions including the Lognormal, the Generalized Pareto, the Fisk, the Burr type XII and the Dagum models.
Fun with supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Freedman, B.; Cooper, F.
1984-04-01
One reason for studying supersymmetric quantum mechanics is that there are a class of superpotentials W(x) which behave at large x as x/sup ..cap alpha../ for which we know from general arguments whether SUSY is broken or unbroken. Thus one can use these superpotentials to test various ideas about how to see if supersymmetry is broken in an arbitrary model. Recently, Witten proposed a topological invariant, the Witten index ..delta.. which counts the number of bosons minus the number of fermions having ground state energy zero. Since if supersymmetry is broken, the ground state energy cannot be zero, one expects if ..delta.. is not zero, SUSY is preserved and the theory is not a good candidate for a realistic model. In this study we evaluate ..delta.. for several examples, and show some unexpected peculiarities of the Witten index for certain choice of superpotentials W(x). We also discuss two other nonperturbative methods of studying supersymmetry breakdown. One involves relating supersymmetric quantum mechanics to a stochastic classical problem and the other involves considering a discrete (but not supersymmetric) version of the theory and studying its behavior as one removes the lattice cuttoff. In this survey we review the Hamiltonian and path integral approaches to supersymmetric quantum mechanics. We then discuss the related path integrals for the Witten Index and for stochastic processes and show how they are indications for supersymmetry breakdown. We then discuss a system where the superpotential W(x) has assymetrical values at +-infinity. We finally discuss nonperturbative strategies for studying supersymmetry breakdown based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed. 17 references.
Supersymmetric color superconductivity
Energy Technology Data Exchange (ETDEWEB)
Harnik, Roni; Larson, Daniel T.; Murayama, Hitoshi
2003-09-18
Recent interest in novel phases in high density QCD motivates the study of high density supersymmetric QCD (SQCD), where powerful exact results for supersymmetric gauge theories can be brought to bear in the strongly coupled regime. We begin by describing how a chemical potential can be incorporated into a supersymmetric theory as a spurion vector superfield. We then study supersymmetric SU(N{sub c}) gauge theories with N{sub f} flavors of quarks in the presence of a baryon chemical potential {mu}, and describe the global symmetry breaking patterns at low energy. Our analysis requires {mu} < {Lambda} and is thus complementary to the variational approach that has been successful for {mu} >> {Lambda}. We find that for N{sub F} < N{sub c} a modified U(1){sub B} symmetry is preserved, analogous to the non-supersymmetric 2SC phase, whereas for N{sub f} = N{sub c} there is a critical chemical potential above which the U(1){sub B} is broken, as it is in the non-supersymmetric CFL phase. We further analyze the cases with N{sub c} + 1 {le} N{sub f} < 3/2 N{sub c} and find that baryon number is broken dynamically for {mu} > {mu}{sub c}. We also give a qualitative description of the phases in the ''conformal window'', 3/2 N{sub c} < N{sub f} < 3N{sub c}, at finite density.
Ouari, Kamel; Rekioua, Toufik; Ouhrouche, Mohand
2014-01-01
In order to make a wind power generation truly cost-effective and reliable, an advanced control techniques must be used. In this paper, we develop a new control strategy, using nonlinear generalized predictive control (NGPC) approach, for DFIG-based wind turbine. The proposed control law is based on two points: NGPC-based torque-current control loop generating the rotor reference voltage and NGPC-based speed control loop that provides the torque reference. In order to enhance the robustness of the controller, a disturbance observer is designed to estimate the aerodynamic torque which is considered as an unknown perturbation. Finally, a real-time simulation is carried out to illustrate the performance of the proposed controller.
Non-renormalization theorems andN=2 supersymmetric backgrounds
Energy Technology Data Exchange (ETDEWEB)
Butter, Daniel [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Wit, Bernard de [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands); Institute for Theoretical Physics, Utrecht University,Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Lodato, Ivano [Nikhef, Science Park 105, 1098 XG Amsterdam (Netherlands)
2014-03-28
The conditions for fully supersymmetric backgrounds of general N = 2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.
Non-renormalization theorems and N=2 supersymmetric backgrounds
Butter, Daniel; Lodato, Ivano
2014-01-01
The conditions for fully supersymmetric backgrounds of general N=2 locally supersymmetric theories are derived based on the off-shell superconformal multiplet calculus. This enables the derivation of a non-renormalization theorem for a large class of supersymmetric invariants with higher-derivative couplings. The theorem implies that the invariant and its first order variation must vanish in a fully supersymmetric background. The conjectured relation of one particular higher-derivative invariant with a specific five-dimensional invariant containing the mixed gauge-gravitational Chern-Simons term is confirmed.
Robust Absolute Stability of General Interval Lur'e Type Nonlinear Control Systems
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, Lyapunov function method isused to study the robust absolute stability of general interval Lur'e type nonlinear control systems. As a result, algebraically sufficient conditions with interval matrix inequality form are obtained for the general interval Lur'e type nonlinear control systems, thus the relationship between the stability of symmetrical interval matrix and the robust absolute stability of general interval Lur'e type nonlinear control systems is established.
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Fu, Wenbo; Maldacena, Juan; Sachdev, Subir
2016-01-01
We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The ${\\cal N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$, but non-perturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$. We also compute the large $N$ spectrum of "singlet" operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an ${\\cal N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we disc...
Supersymmetric compactifications of heterotic strings with fluxes and condensates
Energy Technology Data Exchange (ETDEWEB)
Manousselis, Pantelis [Department of Engineering Sciences, University of Patras, GR-26110 Patras (Greece)]. E-mail: pantelis@upatras.gr; Prezas, Nikolaos [Institut de Physique, Universite de Neuchatel, CH-2000 Neuchatel (Switzerland)]. E-mail: nikolaos.prezas@unine.ch; Zoupanos, George [Physics Department, National Technical University of Athens, GR-15780 University Campus, Athens (Greece)]. E-mail: zoupanos@mail.cern.ch
2006-04-03
We discuss supersymmetric compactifications of heterotic strings in the presence of H-flux and general condensates using the formalism of G-structures and intrinsic torsion. We revisit the examples based on nearly-Kaehler coset spaces and show that supersymmetric solutions, where the Bianchi identity is satisfied, can be obtained when both gaugino and dilatino condensates are present.
Supersymmetric Wilson Loops and Super Non-Abelian Stokes Theorem
Karp, R L; Karp, Robert L.; Mansouri, Freydoon
2000-01-01
We generalize the standard product integral formalism to incorporateGrassmann valued matrices and show that the resulting supersymmetric productintegrals provide a natural framework for describing supersymmetric Wilsonlines and Wilson loops. We use this formalism to establish the supersymmetricversion of the non-Abelian Stokes Theorem.
Institute of Scientific and Technical Information of China (English)
Chang Jing; Gao Yi-xian; Cai Hua
2014-01-01
In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher’s equation, the nonlinear schr¨odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.
Adding momentum to supersymmetric geometries
Energy Technology Data Exchange (ETDEWEB)
Lunin, Oleg, E-mail: olunin@albany.edu [Department of Physics, University at Albany (SUNY), Albany, NY 12222 (United States); Mathur, Samir D., E-mail: mathur.16@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States); Turton, David, E-mail: turton.7@osu.edu [Department of Physics, Ohio State University, Columbus, OH 43210 (United States)
2013-03-11
We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a traveling wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T{sup 4}. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.
Adding momentum to supersymmetric geometries
Lunin, Oleg; Turton, David
2012-01-01
We consider general supersymmetric solutions to minimal supergravity in six dimensions, trivially lifted to IIB supergravity. To any such solution we add a travelling-wave deformation involving the additional directions. The deformed solution is given in terms of a function which is harmonic in the background geometry. We also present a family of explicit examples describing microstates of the D1-D5 system on T^4. In the case where the background contains a large AdS region, the deformation is identified as corresponding to an action of a U(1) current of the D1-D5 orbifold CFT on a given state.
The holographic supersymmetric Casimir energy
Genolini, Pietro Benetti; Martelli, Dario; Sparks, James
2016-01-01
We consider a general class of asymptotically locally AdS_5 solutions of minimal gauged supergravity, that are dual to superconformal field theories on curved backgrounds S^1 x M_3 preserving two supercharges. We demonstrate that standard holographic renormalization corresponds to a scheme that breaks supersymmetry. We propose new boundary terms that restore supersymmetry, and show that for smooth solutions with topology S^1 x R^4 the improved on-shell action reproduces both the supersymmetric Casimir energy and the field theory BPS relation between charges.
Barbosa-Cendejas, Nandinii; Kanakoglou, Konstantinos; Paschalis, Joannis E
2011-01-01
In this paper we recall a simple formulation of the stationary electrovacuum theory in terms of the famous complex Ernst potentials, a pair of functions which allows one to generate new exact solutions from known ones by means of the so-called nonlinear hidden symmetries of Lie-Backlund type. This formalism turned out to be very useful to perform a complete classification of all 4D solutions which present two spacetime symmetries or possess two Killing vectors. Curiously enough, the Ernst formalism can be extended and applied to stationary General Relativity as well as the effective heterotic string theory reduced down to three spatial dimensions by means of a (real) matrix generalization of the Ernst potentials. Thus, in this theory one can also make use of nonlinear matrix hidden symmetries in order to generate new exact solutions from seed ones. Due to the explicit independence of the matrix Ernst potential formalism of the original theory (prior to dimensional reduction) on the dimension D, in the case wh...
The Supersymmetric Particle Spectrum
Barger, V; Ohmann, P
1994-01-01
We examine the spectrum of supersymmetric particles predicted by grand unified theoretical (GUT) models where the electroweak symmetry breaking is accomplished radiatively. We evolve the soft supersymmetry breaking parameters according to the renormalization group equations (RGE). The minimization of the Higgs potential is conveniently described by means of tadpole diagrams. We present complete one-loop expressions for these minimization conditions, including contributions from the matter and the gauge sectors. We concentrate on the low $\\tan \\beta$ fixed point region (that provides a natural explanation of a large top quark mass) for which we find solutions to the RGE satisfying both experimental bounds and fine-tuning criteria. We also find that the constraint from the consideration of the lightest supersymmetric particle as the dark matter of the universe is accommodated in much of parameter space where the lightest neutralino is predominantly gaugino. The supersymmetric mass spectrum displays correlations...
Generalized Supersymetric Boundary State
1999-01-01
Following our previous paper (hep-th/9909027), we generalize a supersymmetric boundary state so that arbitrary configuration of the gauge field coupled to the boundary of the worldsheet is incorpolated. This generalized boundary state is BRST invariant and satisfy the non-linear boundary conditions with non-constant gauge field strength. This boundary state contains divergence which is identical with the loop divergence in a superstring sigma model. Hence vanishing of the beta function in the...
Planarizable Supersymmetric Quantum Toboggans
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Miloslav Znojil
2011-02-01
Full Text Available In supersymmetric quantum mechanics the emergence of a singularity may lead to the breakdown of isospectrality between partner potentials. One of the regularization recipes is based on a topologically nontrivial, multisheeted complex deformations of the line of coordinate x giving the so called quantum toboggan models (QTM. The consistent theoretical background of this recipe is briefly reviewed. Then, certain supersymmetric QTM pairs are shown exceptional and reducible to doublets of non-singular ordinary differential equations a.k.a. Sturm-Schrödinger equations containing a weighted energy E→EW(x and living in single complex plane.
Supersymmetric Optical Structures
Miri, Mohammad-Ali; El-Ganainy, Ramy; Christodoulides, Demetrios N
2013-01-01
We show that supersymmetry can provide a versatile platform in synthesizing a new class of optical structures with desired properties and functionalities. By exploiting the intimate relationship between superpatners, one can systematically construct index potentials capable of exhibiting the same scattering and guided wave characteristics. In particular, in the Helmholtz regime, we demonstrate that one-dimensional supersymmetric pairs display identical reflectivities and transmittivities for any angle of incidence. Optical SUSY is then extended to two-dimensional systems where a link between specific azimuthal mode subsets is established. Finally we explore supersymmetric photonic lattices where discreteness can be utilized to design lossless integrated mode filtering arrangements.
Koehn, Michael
2015-01-01
In supersymmetric theories, topological defects can have nontrivial behaviors determined purely by whether or not supersymmetry is restored in the defect core. A well-known example of this is that some supersymmetric cosmic strings are automatically superconducting, leading to important cosmological effects and constraints. We investigate the impact of nontrivial kinetic interactions, present in a number of particle physics models of interest in cosmology, on the relationship between supersymmetry and supercurrents on strings. We find that in some cases it is possible for superconductivity to be disrupted by the extra interactions.
Supersymmetric Perturbations of the M5 brane
Niarchos, Vasilis
2014-01-01
We study long-wavelength supersymmetric deformations of brane solutions in supergravity using an extension of previous ideas within the general scheme of the blackfold approach. As a concrete example, we consider long-wavelength perturbations of the planar M2-M5 bound state solution in eleven-dimensional supergravity. We propose a specific ansatz for the first order deformation of the supergravity fields and explore how this deformation perturbs the Killing spinor equations. We find that a special part of these equations gives a projection equation on the Killing spinors that has the same structure as the $\\kappa$-symmetry condition of the abelian M5 brane theory. Requiring a match between supergravity and gauge theory implies a specific non-linear gauge-gravity map between the bosonic fields of the abelian M5 brane theory and the gravity-induced fluid-like degrees of freedom of the blackfold equations that control the perturbative gravity solution. This observation sheds new light on the SUGRA/DBI correspond...
New supersymmetric localizations from topological gravity
Bae, Jinbeom; Imbimbo, Camillo; Rey, Soo-Jong; Rosa, Dario
2016-03-01
Supersymmetric field theories can be studied exactly on off-shell "localizing" supergravity backgrounds. We show that these supergravity configurations can be identified with BRST invariant configurations of background topological gravity coupled to background topological gauge multiplets. We apply this topological point of view to two-dimensional {N}=left(2,2right) supersymmetric matter theories to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. We recover all known localizing backgrounds and (infinitely) many more that have not been explored so far. The newly found localizing backgrounds are characterized by quantized fluxes for both graviphotons of the {N}=left(2,2right) supergravity multiplet. The BRST invariant topological backgrounds are parametrized by both Killing vectors and {{S}}^1 -equivariant cohomology of the two-dimensional spacetime. We completely reconstruct the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are composite, in that they are nonlinear functionals of topological fields. Moreover, we show that the supersymmetric Ω-deformation is nothing but the background value of the ghost-for-ghost of topological gravity, a result which holds for higher dimensions too.
Softly Broken Supersymmetric Gauge Theories through Compactifications
Takenaga, K
1998-01-01
Effects of boundary conditions of fields for compactified space directions on the supersymmetric gauge theories are discussed. For general and possible boundary conditions the supersymmetry is explicitly broken to yield universal soft supersymmetry breaking terms, and the gauge symmetry of the theory can also be broken through the dynamics of non-integrable phases, depending on number and the representation under the gauge group of matters. The 4-dimensional supersymmetric QCD is studied as a toy model when one of the space coordinates is compactified on $S^1$.
Spectral properties in supersymmetric matrix models
Energy Technology Data Exchange (ETDEWEB)
Boulton, Lyonell, E-mail: L.Boulton@hw.ac.uk [Department of Mathematics and Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Garcia del Moral, Maria Pilar, E-mail: garciamormaria@uniovi.es [Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain); Restuccia, Alvaro, E-mail: arestu@usb.ve [Departamento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas (Venezuela, Bolivarian Republic of); Departamento de Fisica, Universidad de Oviedo, Avda Calvo Sotelo 18, 33007 Oviedo (Spain)
2012-03-21
We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-supersymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge.
Supersymmetric extension of the Snyder algebra
Energy Technology Data Exchange (ETDEWEB)
Gouba, L., E-mail: lgouba@ictp.it [Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34014 Trieste (Italy); Stern, A., E-mail: astern@bama.ua.edu [Dept. of Physics and Astronomy, Univ. of Alabama, Tuscaloosa, Al 35487 (United States)
2012-04-11
We obtain a minimal supersymmetric extension of the Snyder algebra and study its representations. The construction differs from the general approach given in Hatsuda and Siegel ( (arXiv:hep-th/0311002)) and does not utilize super-de Sitter groups. The spectra of the position operators are discrete, implying a lattice description of space, and the lattice is compatible with supersymmetry transformations. -- Highlights: Black-Right-Pointing-Pointer A new supersymmetric extension of the Snyder algebra is constructed. Black-Right-Pointing-Pointer The extension is minimal and the construction does not involve supersymmetric de Sitter algebras. Black-Right-Pointing-Pointer An involution is defined for the system and discrete representations are constructed. Black-Right-Pointing-Pointer The representations imply a spatial lattice and the lattice spacing is half that of the bosonic case. Black-Right-Pointing-Pointer A differential operator representation is given for fields on super-momentum space.
Supersymmetric heterotic string backgrounds
Gran, U.; Papadopoulos, G.; Roest, D.; Cvetič, M.
2007-01-01
We present the main features of the solution of the gravitino and dilatino Killing spinor equations derived in hep-th/0510176 and hep-th/0703143 which have led to the classification of geometric types of all type I backgrounds. We then apply these results to the supersymmetric backgrounds of the het
Gudnason, Sven Bjarke; Sasaki, Shin
2015-01-01
Construction of a supersymmetric extension of the Skyrme term was a long-standing problem because of the auxiliary field problem; that is, the auxiliary field may propagate and cannot be eliminated, and the problem of having fourth-order time derivative terms. In this paper, we construct for the first time a supersymmetric extension of the Skyrme term in four spacetime dimensions, in the manifestly supersymmetric superfield formalism that does not suffer from the auxiliary field problem. Chiral symmetry breaking in supersymmetric theories results not only in Nambu-Goldstone (NG) bosons (pions) but also in the same number of quasi-NG bosons so that the low-energy theory is described by an SL(N,C)-valued matrix field instead of SU(N) for NG bosons. The solution of auxiliary fields is trivial on the canonical branch of the auxiliary field equation, in which case our model results in a fourth-order derivative term that is not the Skyrme term. For the case of SL(2,C), we find explicitly a nontrivial solution to th...
On supersymmetric geometric flows and R2 inflation from scale invariant supergravity
Rajpoot, Subhash; Vacaru, Sergiu I.
2017-09-01
Models of geometric flows pertaining to R2 scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic to the Kählerian spaces Mn = SU(1 , 1 + k) / U(1) × SU(1 + k) as generalizations of the non-supersymmetric analogs with SO(1 , 1 + k) / SO(1 + k) manifolds. For curved superspaces with geometric evolution of physical objects, a complete supersymmetric theory has to be elaborated on nonholonomic (super) manifolds and bundles determined by non-integrable superdistributions with additional constraints on (super) field dynamics and geometric evolution equations. We also consider generalizations of Perelman's functionals using such nonholonomic variables which result in the decoupling of geometric flow equations and Ricci soliton equations with supergravity modifications of the R2 gravity theory. As such, it is possible to construct exact non-homogeneous and locally anisotropic cosmological solutions for various types of (super) gravity theories modeled as modified Ricci soliton configurations. Such solutions are defined by employing the general ansatz encompassing coefficients of generic off-diagonal metrics and generalized connections that depend generically on all spacetime coordinates. We consider nonholonomic constraints resulting in diagonal homogeneous configurations encoding contributions from possible nonlinear parametric geometric evolution scenarios, off-diagonal interactions and anisotropic polarization/modification of physical constants. In particular, we analyze small parametric deformations when the underlying scale symmetry is preserved and the nontrivial anisotropic vacuum corresponds to generalized de Sitter spaces. Such configurations may mimic quantum effects whenever transitions to flat space are possible. Our approach allows us to generate solutions with scale violating terms induced by geometric flows, off
Freezing of nonlinear Bloch oscillations in the generalized discrete nonlinear Schrödinger equation.
Cao, F J
2004-09-01
The dynamics in a nonlinear Schrödinger chain in a homogeneous electric field is studied. We show that discrete translational invariant integrability-breaking terms can freeze the Bloch nonlinear oscillations and introduce new faster frequencies in their dynamics. These phenomena are studied by direct numerical integration and through an adiabatic approximation. The adiabatic approximation allows a description in terms of an effective potential that greatly clarifies the phenomena.
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Directory of Open Access Journals (Sweden)
Süleyman Öğrekçi
2015-01-01
Full Text Available We propose an efficient analytic method for solving nonlinear differential equations of fractional order. The fractional derivative is defined in the sense of modified Riemann-Liouville derivative. A new technique for calculating the generalized Taylor series coefficients (also known as “generalized differential transforms,” GDTs of nonlinear functions and a new approach of the generalized Taylor series method (GTSM are presented. This new method offers a simple algorithm for computing GDTs of nonlinear functions and avoids massive computational work that usually arises in the standard method. Several illustrative examples are demonstrated to show effectiveness of the proposed method.
New Supersymmetric Localizations from Topological Gravity
Bae, Jinbeom; Rey, Soo-Jong; Rosa, Dario
2015-01-01
Supersymmetric field theories can be studied exactly on suitable off-shell supergravity backgrounds. We show that in two dimensions such backgrounds are identifiable with BRST invariant backgrounds of topological gravity coupled to an abelian topological gauge multiplet. This latter background is required for the consistent coupling of the topological `matter' YM theory to topological gravity. We make use of this topological point of view to obtain, in a simple and straightforward way, a complete classification of localizing supersymmetric backgrounds in two dimensions. The BRST invariant topological backgrounds are parametrized by both Killing vectors and $S^1$-equivariant cohomology of the 2-dimensional world-sheet. We reconstruct completely the supergravity backgrounds from the topological data: some of the supergravity fields are twisted versions of the topological backgrounds, but others are "composite", i.e. they are non-linear functionals of them. We recover all the known localizing 2-dimensional backg...
Global stabilizer of a general class of feedback nonlinear systems and its exponential convergence
Institute of Scientific and Technical Information of China (English)
Runing MA; Jundi DIAN
2005-01-01
We discuss the global stabilization procedure which renders a general class of feedback nonlinear systems exponential convergent. Our stabilizer consists of a nested saturation function, which is a nonlinear combination of satrration functions. Here we prove the exponential convergence of the stabilizer for the first time and give numerical examples to illustrate the efficiency of the result given above.
Quasi-periodic Solutions of the General Nonlinear Beam Equations
Institute of Scientific and Technical Information of China (English)
GAO YI-XIAN
2012-01-01
In this paper,one-dimensional (1D) nonlinear beam equations of the form utt - uxx + uxxxx + mu = f(u)with Dirichlet boundary conditions are considered,where the nonlinearity f is an analytic,odd function and f(u) = O(u3).It is proved that for all m ∈ (0,M*] (∈) R(M* is a fixed large number),but a set of small Lebesgue measure,the above equations admit small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori for an associated infinite dimensional dynamical system.The proof is based on an infinite dimensional KAM theory and a partial Birkhoff normal form technique.
N=2 supersymmetric extension of l-conformal Galilei algebra
Energy Technology Data Exchange (ETDEWEB)
Masterov, Ivan [Laboratory of Mathematical Physics, Tomsk Polytechnic University, 634050 Tomsk, Lenin Ave. 30 (Russian Federation)
2012-07-15
N=2 supersymmetric extension of the l-conformal Galilei algebra is constructed. A relation between its representations in flat spacetime and in Newton-Hooke spacetime is discussed. An infinite-dimensional generalization of the superalgebra is given.
Institute of Scientific and Technical Information of China (English)
LIN Xiangguo; LIANG Yong
2005-01-01
The processing of nonlinear data was one of hot topics in surveying and mapping field in recent years.As a result, many linear methods and nonlinear methods have been developed.But the methods for processing generalized nonlinear surveying and mapping data, especially for different data types and including unknown parameters with random or nonrandom, are seldom noticed.A new algorithm model is presented in this paper for processing nonlinear dynamic multiple-period and multiple-accuracy data derived from deformation monitoring network.
Gukov, S G
1997-01-01
The evidently supersymmetric four-dimensional Wess-Zumino model with quenched disorder is considered at the one-loop level. The infrared fixed points of a beta-function form the moduli space $M = RP^2$ where two types of phases were found: with and without replica symmetry. While the former phase possesses only a trivial fixed point, this point become unstable in the latter phase which may be interpreted as a spin glass phase.
Generalized dromions of the （2＋1）—dimensional nonlinear Schroedinger equations
Institute of Scientific and Technical Information of China (English)
JiefangZHANG
2001-01-01
We derive the generalized dromions of the (2+1)-dimensional nonlinear Schroedinger equations besides the basic dromion solutions by sutably ustilising the arbitrary function in the bilinearized equatins.The rich dromion structures for this system are revealed.
Generalized Dromion Structures of New (2 + 1)-Dimensional Nonlinear EvolutionEquation
Institute of Scientific and Technical Information of China (English)
ZHANG Jie-Fang
2001-01-01
We derive the generalized dromions of the new (2 + 1)-dimensional nonlinear evolution equation by the arbitrary function presented in the bilinearized linear equations. The rich soliton and dromion structures for this system are released.
Institute of Scientific and Technical Information of China (English)
Wei-zhong Dai; Raja Nassar
2000-01-01
A finite difference scheme for the generalized nonlinear Schrodinger equation with variable coefficients is developed. The scheme is shown to satisfy two conser vation laws. Numerical results show that the scheme is accurate and efficient.
Decoupling of supersymmetric particles
Dobado, A; Peñaranda, S
1999-01-01
The possibility of a heavy supersymmetric spectrum at the Minimal Supersymmetric Standard Model is considered and the decoupling from the low energy electroweak scale is analyzed in detail. The formal proof of decoupling of supersymmetric particles from low energy physics is stated in terms of the effective action for the particles of the Standard Model that results by integrating out all the sparticles in the limit where their masses are larger than the electroweak scale. The computation of the effective action for the standard electroweak gauge bosons W^{+-}, Z and \\gamma is performed by integrating out all the squarks, sleptons, charginos and neutralinos to one-loop. The Higgs sector is not considered in this paper. The large sparticle masses limit is also analyzed in detail. Explicit analytical formulae for the two-point functions of the electroweak gauge bosons to be valid in that limit are presented. Finally, the decoupling of sparticles in the S, T and U parameters is studied analitically. A discussion...
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
Directory of Open Access Journals (Sweden)
Zeid I. A. Al-Muhiameed
2011-01-01
Full Text Available With the help of the generalized Jacobi elliptic function, an improved Jacobi elliptic function method is used to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Lin equation are investigated, and the exact solutions are derived with the aid of the homogenous balance principle.
Institute of Scientific and Technical Information of China (English)
ZhangTiande; CaoQingjie; PriceG.W.; DjidjeliK.; TwizellE.H.
1999-01-01
Spatial soliton solutions of a class of generalized nonlinear Schrodinger equations in N-space are discussed analytically and numerically. This achieved using a traveling wavemethod to formulate one-soliton solution and the P-R method is employed to the numerlcal solutions and the interactions between the solirons for the generalized nonlinear systems in Z-pace.The results presented show that the soliton phenomena are characteristics associated with the nonlinearhies of the dynamical systems.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2014-10-01
Full Text Available In this article, new extension of the generalized and improved (G′/G-expansion method is proposed for constructing more general and a rich class of new exact traveling wave solutions of nonlinear evolution equations. To demonstrate the novelty and motivation of the proposed method, we implement it to the Korteweg-de Vries (KdV equation. The new method is oriented toward the ease of utilize and capability of computer algebraic system and provides a more systematic, convenient handling of the solution process of nonlinear equations. Further, obtained solutions disclose a wider range of applicability for handling a large variety of nonlinear partial differential equations.
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue; GUO Jin-yun
2005-01-01
The unknown parameter's variance-covariance propagation and calculation in the generalized nonlinear least squares remain to be studied now,which didn't appear in the internal and external referencing documents. The unknown parameter's variance-covariance propagation formula, considering the two-power terms, was concluded used to evaluate the accuracy of unknown parameter estimators in the generalized nonlinear least squares problem. It is a new variance-covariance formula and opens up a new way to evaluate the accuracy when processing data which have the multi-source,multi-dimensional, multi-type, multi-time-state, different accuracy and nonlinearity.
ON THE NONLINEAR RIEMANN PROBLEMS FOR GENERAL FIRST ELLIPTIC SYSTEMS IN THE PLANE
Institute of Scientific and Technical Information of China (English)
李明忠; 宋洁
2005-01-01
The nonlinear Riemann problem for general systems of the first-order linear and quasi-linear equations in the plane are considered. It translates them to singular integral equations and proves the existence of the solution by means of contract principle or. general contract principle. The known results are generalized.
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2012-01-01
Full Text Available We obtain the classification of exact solutions, including soliton, rational, and elliptic solutions, to the one-dimensional general improved Camassa Holm KP equation and KdV equation by the complete discrimination system for polynomial method. In discussion, we propose a more general trial equation method for nonlinear partial differential equations with generalized evolution.
Supersymmetric Descendants of Self-Adjointly Extended Quantum Mechanical Hamiltonians
Al-Hashimi, M H; Shalaby, A; Wiese, U -J
2013-01-01
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant.
Supersymmetric P(X,phi) and the Ghost Condensate
Khoury, Justin; Ovrut, Burt
2010-01-01
We show how to construct supersymmetric actions for higher-derivative scalar field theories of the form P(X,phi), within the context of d=4, N=1 supersymmetry. This construction is of general use, and is applied to write a supersymmetric version of the Dirac-Born-Infeld action. Our principal application of this formalism is to construct the supersymmetric extension of the ghost condensate. This allows us to study the interplay between supersymmetry, time-dependent backgrounds and violations of the null energy condition.
Generalized Hyperbolic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
Directory of Open Access Journals (Sweden)
Zeid I. A. Al-Muhiameed
2012-01-01
Full Text Available With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are investigated and the exact solutions are derived with the aid of the homogenous balance principle and generalized hyperbolic functions. We study the effect of the generalized hyperbolic function parameters p and q in the obtained solutions by using the computer simulation.
Non-Supersymmetric Stringy Attractors
Dominic, Pramod
2011-01-01
In this paper we examine the stability of non-supersymmetric attractors in type IIA supergravity compactified on a Calabi-Yau manifold, in the presence of sub-leading corrections to the N=$ pre-potential. We study black hole configurations carrying D0-D6 and D0-D4 charges. We consider the O(1) corrections to the pre-potential given by the Euler number of the Calabi-Yau manifold. We argue that such corrections in general can not lift the zero modes for the D0-D6 attractors. However, for the attractors carrying the D0-D4 charges, they affect the zero modes in the vector multiplet sector. We show that, in the presence of such O(1) corrections, the D0-D4 attractors can either be stable or unstable depending on the geometry of the underlying Calabi-Yau manifold, and on the specific values of the charges they carry.
Currents in supersymmetric field theories
Derendinger, Jean-Pierre
2016-01-01
A general formalism to construct and improve supercurrents and source or anomaly superfields in two-derivative N=1 supersymmetric theories is presented. It includes arbitrary gauge and chiral superfields and a linear superfield coupled to gauge fields. These families of supercurrent structures are characterized by their energy-momentum tensors and R currents and they display a specific relation to the dilatation current of the theory. The linear superfield is introduced in order to describe the gauge coupling as a background (or propagating) field. Supersymmetry does not constrain the dependence on this gauge coupling field of gauge kinetic terms and holomorphicity restrictions are absent. Applying these results to an effective (Wilson) description of super-Yang-Mills theory, matching or cancellation of anomalies leads to an algebraic derivation of the all-order NSVZ beta function.
BRST Invariant Theory Of A Generalized 1+1 Dimensional Nonlinear Sigma Model With Topological Term
Huang, Yong-Chang; Lee, Xi-Guo
2006-01-01
We give a generalized Lagrangian density of 1+1 Dimensional O(3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter originating from the freedom degree of BRST transformation in a general O(3) nonlinear sigma model, and we gain the general commutation relations of ghost field.
Nonlinear generalized source method for modeling second-harmonic generation in diffraction gratings
Weismann, Martin; Panoiu, Nicolae C
2015-01-01
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source method to nonlinear optical interactions by incorporating the contribution of nonlinear polarization sources to the diffracted field in the algorithm. We derive the mathematical formalism underlying the numerical method and introduce the Fourier-factorization suitable for nonlinear calculations. The numerical efficiency and runtime characteristics of the method are investigated in a set of benchmark calculations: the results corresponding to the fundamental frequency are compared to those obtained from a reference method and the beneficial effects of the modified Fourier-factorization rule on the accuracy of the nonlinear computations is demonstrated. In order to illustrate the capabilities of our method, we employ it to demonstrate strong enhancement of second-harmonic genera...
Harnik, R
2004-01-01
Supersymmetric models have traditionally been assumed to be perturbative up to high scales due to the requirement of calculable unification. In this note I review the recently proposed `Fat Higgs' model which relaxes the requirement of perturbativity. In this framework, an NMSSM-like trilinear coupling becomes strong at some intermediate scale. The NMSSM Higgses are meson composites of an asymptotically-free gauge theory. This allows us to raise the mass of the Higgs, thus alleviating the MSSM of its fine tuning problem. Despite the strong coupling at an intermediate scale, the UV completion allows us to maintain gauge coupling unification.
Supersymmetric Electroweak Baryogenesis
Rius, N; Rius, Nuria; Sanz, Veronica
2000-01-01
We calculate the baryon asymmetry generated at the electroweak phase transition in the minimal supersymmetric standard model, using a new method to compute the CP-violating asymmetry in the Higgsino flux reflected into the unbroken phase. The method is based on a Higgs insertion expansion. We find that the CP asymmetry at leading order is proportional to the change in $\\tan next-to-leading order this suppression factor disappears. These results explain previous discrepancies among different calculations, and may enhance the final baryon asymmetry generated during the electroweak phase transition.
Generalizing Fisher's “reproductive value”: Nonlinear, homogeneous, biparental systems*
Samuelson, Paul A.
1977-01-01
Biparental demographic models violate linearity. However, in their early “dilute” stages before limited environment resources bring need for competitive selection, first-degree-homogeneous relations obtain. For them, a reproductive-value function of the initial coordinates is defined to recapitulate their contribution to the asymptotically dominating mode of exponential growth: now the generalized Fisher reproductive value of one sex is altered by relative numbers of the other sex. The new reproductive-value function is also derived for general systems of homogeneous-first-degree differential and difference equations, and is shown to grow from the start at the asymptotic growth rate. PMID:16592475
New solutions for two integrable cases of a generalized fifth-order nonlinear equation
Wazwaz, Abdul-Majid
2015-05-01
Multiple-complexiton solutions for a new generalized fifth-order nonlinear integrable equation are constructed with the help of the Hirota's method and the simplified Hirota's method. By extending the real parameters into complex parameters, nonsingular complexiton solutions are obtained for two specific coefficients of the new generalized equation.
2011-01-01
International audience; In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization~: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show ...
A new integrable discrete generalized nonlinear Schrodinger equation and its reductions
Li, Hongmin; Li, Yuqi; Chen, Yong
2013-01-01
A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical discrete nonlinear Schrodinger (NLS) equation. To show the complete integrability of the discrete GNLS equation, the recursion operator, symmetries and conservation quantities are obtained. Furthermore, all of reductions for the discrete GNLS equation are give...
Institute of Scientific and Technical Information of China (English)
TAO Hua-xue (陶华学); GUO Jin-yun (郭金运)
2003-01-01
Data are very important to build the digital mine. Data come from many sources, have different types and temporal states. Relations between one class of data and the other one, or between data and unknown parameters are more nonlinear. The unknown parameters are non-random or random, among which the random parameters often dynamically vary with time. Therefore it is not accurate and reliable to process the data in building the digital mine with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method to process data in building the digital mine is put forward. In the meantime, the corresponding mathematical model is also given. The generalized nonlinear least squares problem is more complex than the common nonlinear least squares problem and its solution is more difficultly obtained because the dimensions of data and parameters in the former are bigger. So a new solution model and the method are put forward to solve the generalized nonlinear dynamic least squares problem. In fact, the problem can be converted to two sub-problems, each of which has a single variable. That is to say, a complex problem can be separated and then solved. So the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations. The method lessens the calculating load and opens up a new way to process the data in building the digital mine, which have more sources, different types and more temporal states.
Pulsed Laser Nonlinear Thomson Scattering for General Scattering Geometries
Energy Technology Data Exchange (ETDEWEB)
Geoffrey Krafft; A. Doyuran; James Rosenzweig
2005-05-01
In a recent paper it has been shown that single electron Thomson backscatter calculations can be performed including the effects of pulsed high intensity lasers. In this paper we present a more detailed treatment of the problem and present results for more general scattering geometries. In particular, we present new results for 90 degree Thomson scattering. Such geometries have been increasingly studied as X-ray sources of short-pulse radiation. Also, we present a clearer physical basis for these different cases.
Consistent gravitino couplings in non-supersymmetric strings
Dudas, E A
2001-01-01
The massless spectrum of the ten dimensional USp(32) type I string has an N=1 supergravity multiplet coupled to non-supersymmetric matter. This raises the question of the consistency of the gravitino interactions. We resolve this apparent puzzle by arguing for the existence of a local supersymmetry which is non-linearly realised in the open sector. We determine the leading order low energy effective Lagrangian. Similar results are expected to apply to lower dimensional type I models where supergravity is coupled to non-supersymmetric branes.
Cosmological nonlinear structure formation in full general relativity
Torres, Jose M; Diez-Tejedor, Alberto; Nunez, Dario
2014-01-01
We perform numerical evolutions of cosmological scenarios using a standard general relativistic code in spherical symmetry. We concentrate on two different situations: initial matter distributions that are homogeneous and isotropic, and perturbations to those that respect the spherical symmetry. As matter models we consider the case of a pressureless perfect fluid, i.e. dust, and the case of a real massive scalar field oscillating around the minimum of the potential. Both types of matter have been considered as possible dark matter candidates in the cosmology literature, dust being closely related to the standard cold dark matter paradigm. We confirm that in the linear regime the perturbations associated with these types of matter grow in essentially the same way, the main difference being that in the case of a scalar field the dynamics introduce a cut-off in the power spectrum of the density perturbations at scales comparable with the Compton wavelength of the field. We also follow the evolutions well beyond...
Energy Technology Data Exchange (ETDEWEB)
Zhang, Sheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China)]. E-mail: zhshaeng@yahoo.com.cn; Xia, Tiecheng [Department of Mathematics, Bohai University, Jinzhou 121000 (China); Department of Mathematics, Shanghai University, Shanghai 200444 (China)
2007-04-09
In this Letter, a generalized new auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the combined KdV-mKdV equation and the (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equations to illustrate the validity and advantages of the method. As a result, many new and more general exact solutions are obtained.
Generalized similarity, renormalization groups, and nonlinear clocks for multiscaling.
Park, M; O'Malley, D; Cushman, J H
2014-04-01
Fixed points of the renormalization group operator Rp,rX(t)≡X(rt)/rp are said to be p-self-similar. Here X(t) is an arbitrary stochastic process. The concept of a p-self-similar process is generalized via the renormalization group operator RF,GX(t)=F[X(G(t))], where F and G are bijections on (-∞,∞) and [0,∞), respectively. If X(t) is a fixed point of RF,G, then X(t) is said to be (F,G)-self-similar. We say Y(t) is (F,G)-X(t)-similar if RF,GX(t)=Y(t) in distribution. Exit time distributions and finite-size Lyapunov exponents were obtained for these latter processes. A power law multiscaling process is defined with a multipower-law clock. This process is employed to statistically represent diffusion in a nanopore, a monolayer fluid confined between atomically structured surfaces. The tools presented provide a straightforward method to statistically represent any multiscaling process in time.
On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.
Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba
2013-01-01
Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ (d) , and the dictionary is learned from the training data using the vector space structure of ℝ (d) and its Euclidean L(2)-metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.
Supersymmetrizing Massive Gravity
Malaeb, Ola
2013-01-01
When four scalar fields with global Lorentz symmetry are coupled to gravity and take a vacuum expectation value breaking diffeomorphism invariance spontaneously, the graviton becomes massive. This model is supersymmetrized by considering four N=1 chiral superfields with global Lorentz symmetry. When the scalar components of the chiral multiplets z^A acquire a vacuum expectation value, both diffeomorphism invariance and local supersymmetry are broken spontaneously. The global Lorentz index A becomes identified with the space-time Lorentz index making the scalar fields z^A vectors and the chiral spinors \\psi^A spin-3/2 Rarita-Schwinger fields. The global supersymmetry is promoted to a local one using the rules of tensor calculus of coupling the N=1 supergravity Lagrangian to the four chiral multiplets. We show that the spectrum of the model in the broken phase consists of a massive spin-2 field, two massive spin-3/2 fields with different mass and a massive vector.
Supersymmetric mode converters
Heinrich, Matthias; Miri, Mohammad-Ali; Stützer, Simon; Nolte, Stefan; Szameit, Alexander; Christodoulides, Demetrios N.
2015-08-01
In recent years, the ever-increasing demand for high-capacity transmission systems has driven remarkable advances in technologies that encode information on an optical signal. Mode-division multiplexing makes use of individual modes supported by an optical waveguide as mutually orthogonal channels. The key requirement in this approach is the capability to selectively populate and extract specific modes. Optical supersymmetry (SUSY) has recently been proposed as a particularly elegant way to resolve this design challenge in a manner that is inherently scalable, and at the same time maintains compatibility with existing multiplexing strategies. Supersymmetric partners of multimode waveguides are characterized by the fact that they share all of their effective indices with the original waveguide. The crucial exception is the fundamental mode, which is absent from the spectrum of the partner waveguide. Here, we demonstrate experimentally how this global phase-matching property can be exploited for efficient mode conversion. Multimode structures and their superpartners are experimentally realized in coupled networks of femtosecond laser-written waveguides, and the corresponding light dynamics are directly observed by means of fluorescence microscopy. We show that SUSY transformations can readily facilitate the removal of the fundamental mode from multimode optical structures. In turn, hierarchical sequences of such SUSY partners naturally implement the conversion between modes of adjacent order. Our experiments illustrate just one of the many possibilities of how SUSY may serve as a building block for integrated mode-division multiplexing arrangements. Supersymmetric notions may enrich and expand integrated photonics by versatile optical components and desirable, yet previously unattainable, functionalities.
Supersymmetric Quantum Mechanics and Topology
Directory of Open Access Journals (Sweden)
Muhammad Abdul Wasay
2016-01-01
Full Text Available Supersymmetric quantum mechanical models are computed by the path integral approach. In the β→0 limit, the integrals localize to the zero modes. This allows us to perform the index computations exactly because of supersymmetric localization, and we will show how the geometry of target space enters the physics of sigma models resulting in the relationship between the supersymmetric model and the geometry of the target space in the form of topological invariants. Explicit computation details are given for the Euler characteristics of the target manifold and the index of Dirac operator for the model on a spin manifold.
Directory of Open Access Journals (Sweden)
Yusuf Pandir
2013-01-01
Full Text Available We firstly give some new functions called generalized hyperbolic functions. By the using of the generalized hyperbolic functions, new kinds of transformations are defined to discover the exact approximate solutions of nonlinear partial differential equations. Based on the generalized hyperbolic function transformation of the generalized KdV equation and the coupled equal width wave equations (CEWE, we find new exact solutions of two equations and analyze the properties of them by taking different parameter values of the generalized hyperbolic functions. We think that these solutions are very important to explain some physical phenomena.
Cubic generalized B-splines for interpolation and nonlinear filtering of images
Tshughuryan, Heghine
1997-04-01
This paper presents the introduction and using of the generalized or parametric B-splines, namely the cubic generalized B-splines, in various signal processing applications. The theory of generalized B-splines is briefly reviewed and also some important properties of generalized B-splines are investigated. In this paper it is shown the use of generalized B-splines as a tool to solve the quasioptimal algorithm problem for nonlinear filtering. Finally, the experimental results are presented for oscillatory and other signals and images.
Generalized exponential input-to-state stability of nonlinear systems with time delay
Sun, Fenglan; Gao, Lingxia; Zhu, Wei; Liu, Feng
2017-03-01
This paper studies the general input-to-state stability problem of the nonlinear delay systems. By employing Lypaunov-Razumikhin technique, several general input-to-state stability concepts, that is generalized globally exponential integral input-to-state stability (GGE-iISS), generalized globally integral exponential integral input-to-state stability (GGIE-iISS), and eλt-weighted generalized globally integral exponential integral input-to-state stability (eλt-weighted GGIE-iISS) are studied. An example is given to illustrate the correctness of the obtained theoretical results.
Small numbers in supersymmetric theories of nature
Energy Technology Data Exchange (ETDEWEB)
Graesser, Michael Lawrence [Univ. of California, Berkeley, CA (United States)
1999-05-01
The Standard Model of particle interactions is a successful theory for describing the interactions of quarks, leptons and gauge bosons at microscopic distance scales. Despite these successes, the theory contains many unsatisfactory features. The origin of particle masses is a central mystery that has eluded experimental elucidation. In the Standard Model the known particles obtain their mass from the condensate of the so-called Higgs particle. Quantum corrections to the Higgs mass require an unnatural fine tuning in the Higgs mass of one part in 10^{-32} to obtain the correct mass scale of electroweak physics. In addition, the origin of the vast hierarchy between the mass scales of the electroweak and quantum gravity physics is not explained in the current theory. Supersymmetric extensions to the Standard Model are not plagued by this fine tuning issue and may therefore be relevant in Nature. In the minimal supersymmetric Standard Model there is also a natural explanation for electroweak symmetry breaking. Supersymmetric Grand Unified Theories also correctly predict a parameter of the Standard Model. This provides non-trivial indirect evidence for these theories. The most general supersymmetric extension to the Standard Model however, is excluded by many physical processes, such as rare flavor changing processes, and the non-observation of the instability of the proton. These processes provide important information about the possible structure such a theory. In particular, certain parameters in this theory must be rather small. A physics explanation for why this is the case would be desirable. It is striking that the gauge couplings of the Standard Model unify if there is supersymmetry close to the weak scale. This suggests that at high energies Nature is described by a supersymmetric Grand Unified Theory. But the mass scale of unification must be introduced into the theory since it does not coincide with the probable mass scale of strong quantum gravity
Parallel Solutions for Large—Scale General Sparse Nonlinear Systems of Equations
Institute of Scientific and Technical Information of China (English)
胡承毅
1996-01-01
In solving application problems,many large-scale nonlinear systems of equaions result in sparse Jacobian matrices.Such nonlinear systems are called sparse nonlinear systems.The irregularity of the locations of nonzrero elements of a general sparse matrix makes it very difficult to generally map sparse matrix computations to multiprocessors for parallel processing in a well balanced manner.To overcome this difficulty,we define a new storage scheme for general sparse matrices in this paper,With the new storage scheme,we develop parallel algorithms to solve large-scale general sparse systems of equations by interval Newton/Generalized bisection methods which reliably find all numerical solutions within a given domain.I n Section 1,we provide an introduction to the addressed problem and the interval Newton's methods.In Section 2,some currently used storage schemes for sparse systems are reviewed.In Section 3,new index schemes to store general sparse matrices are reported.In Section 4,we present a parallel algorithm to evaluate a general sparse Jacobian matrix.In Section 5,we present a parallel algorithm to solve the corresponding interval linear system by the all-row preconditioned scheme.Conclusions and future work are discussed in Section 6.
Higher Order Mean Squared Error of Generalized Method of Moments Estimators for Nonlinear Models
Directory of Open Access Journals (Sweden)
Yi Hu
2014-01-01
Full Text Available Generalized method of moments (GMM has been widely applied for estimation of nonlinear models in economics and finance. Although generalized method of moments has good asymptotic properties under fairly moderate regularity conditions, its finite sample performance is not very well. In order to improve the finite sample performance of generalized method of moments estimators, this paper studies higher-order mean squared error of two-step efficient generalized method of moments estimators for nonlinear models. Specially, we consider a general nonlinear regression model with endogeneity and derive the higher-order asymptotic mean square error for two-step efficient generalized method of moments estimator for this model using iterative techniques and higher-order asymptotic theories. Our theoretical results allow the number of moments to grow with sample size, and are suitable for general moment restriction models, which contains conditional moment restriction models as special cases. The higher-order mean square error can be used to compare different estimators and to construct the selection criteria for improving estimator’s finite sample performance.
Blow-up in nonlinear Schroedinger equations. I. A general review
DEFF Research Database (Denmark)
Juul Rasmussen, Jens; Rypdal, K.
1986-01-01
The general properties of a class of nonlinear Schroedinger equations: iut + p:∇∇u + f(|u|2)u = 0 are reviewed. Conditions for existence, uniqueness, and stability of solitary wave solutions are presented, along with conditions for blow-up and global existence for the Cauchy problem....
Institute of Scientific and Technical Information of China (English)
CHEN Jiang; HE Hong-Sheng; YANG Kong-Qing
2005-01-01
A generalized F-expansion method is introduced and applied to (3+ 1)-dimensional Kadomstev-Petviashvili(KP) equation. As a result, some new Jacobi elliptic function solutions of the equation are found, from which the trigonometric function solutions and the solitary wave solutions can be obtained. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
Conservation laws of the generalized nonlocal nonlinear Schr(o)dinger equation
Institute of Scientific and Technical Information of China (English)
Ouyang Shi-Gen; Quo Qi; Wu Li-Jun; Lan Sheng
2007-01-01
The derivations of several conservation laws of the generalized nonlocal nonlinear Schr(o)dinger equation are presented. These invariants are the number of particles, the momentum, the angular momentum and the Hamiltonian in the quantum mechanical analogy. The Lagrangian is also presented.
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
Institute of Scientific and Technical Information of China (English)
Mo Jia-Qi; Lin Su-Rong
2009-01-01
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method,it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping,it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method,it possesses a good accuracy.
Asymptotic Behavior of Global Solution for Nonlinear Generalized Euler-Possion-Darboux Equation
Institute of Scientific and Technical Information of China (English)
LIANGBao-song; CHENZhen
2004-01-01
J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.
General treatment of the non-linear Rsub(Xi) gauge condition
Energy Technology Data Exchange (ETDEWEB)
Girardi, G.; Malleville, C.; Sorba, P. (Grenoble-1 Univ., 74 - Annecy (France). Lab. de Physique des Particules)
1982-11-04
It is shown that the non-linear Rsub(xi) gauge condition already introduced for the standard SU(2)xU(1) model can be generalized for any gauge model with the same type of simplification, namely the suppression of any coupling of the form: (massless gauge boson)x(massive gauge boson)x(unphysical Higgs).
Supersymmetric quantum mechanics and paraquantization
Energy Technology Data Exchange (ETDEWEB)
Morchedi, O.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
The paraquantum Hamiltonian of a free particle is shown to be supersymmetric. Depending on the space-time dimension, the corresponding N=1 and N=2 supercharges are constructed and the related Hamiltonians are derived.
Supersymmetric quantum mechanics with reflections
Energy Technology Data Exchange (ETDEWEB)
Post, Sarah; Vinet, Luc [Centre de Recherches Mathematiques, Universite de Montreal, Montreal CP6128 (QC) H3C 3J7 (Canada); Zhedanov, Alexei, E-mail: post@crm.umontreal.ca, E-mail: luc.vinet@umontreal.ca, E-mail: zhedanov@fti.dn.ua [Donetsk Institute for Physics and Technology, Donetsk 83114 (Ukraine)
2011-10-28
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q {yields} -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wavefunctions of extended Scarf I potentials with different parameters are presented. (paper)
Nonlinear Observer Design of the Generalized Rössler Hyperchaotic Systems via DIL Methodology
Directory of Open Access Journals (Sweden)
Yeong-Jeu Sun
2012-01-01
Full Text Available The generalized Rössler hyperchaotic systems are presented, and the state observation problem of such systems is investigated. Based on the differential inequality with Lyapunov methodology (DIL methodology, a nonlinear observer design for the generalized Rössler hyperchaotic systems is developed to guarantee the global exponential stability of the resulting error system. Meanwhile, the guaranteed exponential decay rate can be accurately estimated. Finally, numerical simulations are provided to illustrate the feasibility and effectiveness of proposed approach.
Supersymmetric branes on curved spaces and fluxes
Triendl, Hagen
2015-01-01
We discuss general supersymmetric brane configurations in flux backgrounds of string and M-theory and derive a necessary condition for the worldvolume theory to be supersymmetric on a given curved manifold. This condition resembles very much the conditions found from coupling a supersymmetric field theory to off-shell supergravity but can be derived in any dimension and for up to sixteen supercharges. Apart from the topological twist, all couplings appearing in the supersymmetry condition are linked to fluxes in the bulk. We explicitly derive the condition for D3-, M2- and M5-branes, in which case the results are also useful for constructing holographic duals to the corresponding field theories. In $N=1$ setups we compare the supersymmetry conditions to those that arise by coupling the field theory to off-shell supergravity. We find that the couplings of both old and new minimal supergravity are simultaneously realized, indicating that off-shell supergravity should be coupled via the S-multiplet of 16/16 supe...
A New Generalization of Extended Tanh-Function Method for Solving Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHENG Xue-Dong; CHEN Yong; LI Biao; ZHANG Hong-Qing
2003-01-01
Making use of a new generalized ansatze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations.As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extendedtanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain othernew and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profilesolitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.
General complex envelope solutions of coupled-mode optics with quadratic or cubic nonlinearity
Hesketh, Graham D
2015-01-01
The analytic general solutions for the complex field envelopes are derived using Weierstrass elliptic functions for two and three mode systems of differential equations coupled via quadratic $\\chi_2$ type nonlinearity as well as two mode systems coupled via cubic $\\chi_3$ type nonlinearity. For the first time, a compact form of the solutions is given involving simple ratios of Weierstrass sigma functions (or equivalently Jacobi theta functions). A Fourier series is also given. All possible launch states are considered. The models describe sum and difference frequency generation, polarization dynamics, parity-time dynamics and optical processing applications.
Generalized Kudryashov method for solving some (3+1-dimensional nonlinear evolution equations
Directory of Open Access Journals (Sweden)
Md. Shafiqul Islam
2015-06-01
Full Text Available In this work, we have applied the generalized Kudryashov methods to obtain the exact travelling wave solutions for the (3+1-dimensional Jimbo-Miwa (JM equation, the (3+1-dimensional Kadomtsev-Petviashvili (KP equation and the (3+1-dimensional Zakharov-Kuznetsov (ZK. The attained solutions show distinct physical configurations. The constraints that will guarantee the existence of specific solutions will be investigated. These solutions may be useful and desirable for enlightening specific nonlinear physical phenomena in genuinely nonlinear dynamical systems.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
BiHermitian supersymmetric quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Zucchini, Roberto [Dipartimento di Fisica, Universita degli Studi di Bologna, V Irnerio 46, I-40126 Bologna (Italy)
2007-04-21
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian Supersymmetric Quantum Mechanics
Zucchini, R
2006-01-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2,2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kaehler manifolds recently developed by Gualtieri. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li.
BiHermitian supersymmetric quantum mechanics
Zucchini, Roberto
2007-04-01
BiHermitian geometry, discovered long ago by Gates, Hull and Rocek, is the most general sigma model target space geometry allowing for (2, 2) world sheet supersymmetry. In this paper, we work out supersymmetric quantum mechanics for a biHermitian target space. We display the full supersymmetry of the model and illustrate in detail its quantization procedure. Finally, we show that the quantized model reproduces the Hodge theory for compact twisted generalized Kähler manifolds recently developed by Gualtieri in [33]. This allows us to recover and put in a broader context the results on the biHermitian topological sigma models obtained by Kapustin and Li in [9].
Directory of Open Access Journals (Sweden)
T. D. Frank
2016-12-01
Full Text Available In physics, several attempts have been made to apply the concepts and tools of physics to the life sciences. In this context, a thermostatistic framework for active Nambu systems is proposed. The so-called free energy Fokker–Planck equation approach is used to describe stochastic aspects of active Nambu systems. Different thermostatistic settings are considered that are characterized by appropriately-defined entropy measures, such as the Boltzmann–Gibbs–Shannon entropy and the Tsallis entropy. In general, the free energy Fokker–Planck equations associated with these generalized entropy measures correspond to nonlinear partial differential equations. Irrespective of the entropy-related nonlinearities occurring in these nonlinear partial differential equations, it is shown that semi-analytical solutions for the stationary probability densities of the active Nambu systems can be obtained provided that the pumping mechanisms of the active systems assume the so-called canonical-dissipative form and depend explicitly only on Nambu invariants. Applications are presented both for purely-dissipative and for active systems illustrating that the proposed framework includes as a special case stochastic equilibrium systems.
The Supersymmetric Standard Model
Fayet, Pierre
2016-10-01
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a neutralino, is expected to be stable and a possible candidate for dark matter. The electroweak breaking requires two doublets, leading to several charged and neutral Brout-Englert-Higgs bosons. This also leads to gauge/Higgs unification by providing extra spin-0 partners for the spin-1 W± and Z. It offers the possibility to view, up to a mixing angle, the new 125 GeV boson as the spin-0 partner of the Z under two supersymmetry transformations, i.e. as a Z that would be deprived of its spin. Supersymmetry then relates two existing particles of different spins, in spite of their different gauge symmetry properties, through supersymmetry transformations acting on physical fields in a non-polynomial way. We also discuss how the compactification of extra dimensions, relying on R-parity and other discrete symmetries, may determine both the supersymmetrybreaking and grand-unification scales.
The Supersymmetric Standard Model
Fayet, Pierre
2016-01-01
The Standard Model may be included within a supersymmetric theory, postulating new sparticles that differ by half-a-unit of spin from their standard model partners, and by a new quantum number called R-parity. The lightest one, usually a neutralino, is expected to be stable and a possible candidate for dark matter. The electroweak breaking requires two doublets, leading to several charged and neutral Brout- Englert-Higgs bosons. This also leads to gauge/Higgs unification by providing extra spin-0 partners for the spin-1 W$^\\pm$ and Z. It offers the possibility to view, up to a mixing angle, the new 125 GeV boson as the spin-0 partner of the Z under two supersymmetry transformations, i.e. as a Z that would be deprived of its spin. Supersymmetry then relates two existing particles of different spins, in spite of their different gauge symmetry properties, through supersymmetry transformations acting on physical fields in a non-polynomial way. We also discuss how the compactification of extra dimensions, relying ...
Nonlinear continuous-time generalized predictive control of solar power plant
Directory of Open Access Journals (Sweden)
Khoukhi Billal
2015-01-01
Full Text Available This paper presents an application of nonlinear continuous-time generalized predictive control (GPC to the distributed collector field of a solar power plant. The major characteristic of a solar power plant is that the primary energy source, solar radiation, cannot be manipulated. Solar radiation varies throughout the day, causing changes in plant dynamics and strong perturbations in the process. A brief description of the solar power plant and its simulator is given. After that, basic concepts of predictive control and continuous-time generalized predictive control are introduced. A new control strategy, named nonlinear continuous-time generalized predictive control (NCGPC, is then derived to control the process. The simulation results show that the NCGPC gives a greater flexibility to achieve performance goals and better perturbation rejection than classical control.
Barker, Blake; Noble, Pascal; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized (integrable) perturbations. Our analysis is based upon detailed estimates of the linearized solution operator, which are complicated by the fact that the (necessarily essential) spectrum of the associated linearization intersects the imaginary axis at the origin. We carry out a numerical Evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves, in close agreement with previous numerical studies of Frisch-She-Thual, Bar-Nepomnyashchy, Chang-Demekhin-Kopelevich, and others carried out by other techniques. We also compare predictions of the associated Whitham modulation equations, which formally describe the dynamics of weak large s...
Shen, Mouquan; Park, Ju H; Ye, Dan
2016-09-01
This paper is devoted to the control of Markov jump nonlinear systems with general transition probabilities (TPs) allowed to be known, uncertain, and unknown. With the help of the S-procedure to dispose the system nonlinearities and the TP property to eliminate the coupling between unknown TP and Lyapunov variable, an extended bounded real lemma for the considered system to be stochastically stable with the prescribed H∞ performance is established in the framework of linear matrix inequalities. To handle the nonlinearity incurred by uncertain TP for controller synthesis, a separated method is proposed to decouple the interconnection between Lyapunov variables and controller gains. A numerical example is given to show the effectiveness of the proposed method.
Generalized Two-State Theory for an Atom Laser with Nonlinear Couplings
Institute of Scientific and Technical Information of China (English)
JING Hui; TIAN Li-Jun
2002-01-01
We present a generalized two-state theory to investigate the quantum dynamics and statistics of an atom laser with nonlinear couplings. The rotating wave approximate Hamiltonian of the system is proved to be analytically solvable. The fraction of output atoms is then showed to exhibit an interesting collapse and revival phenomenon with respect to the evolution time, a sign of nonlinear couplings. Several nonclassical effects, such as sub-Poissonian distribution, quadrature squeezing effects, second-order cross-correlation and accompanied violation of Cauchy-Schwartz inequality are also revealed for the output matter wave. The initial global phase of the trapped condensate, in weak nonlinear coupling limits, is found to exert an interesting impact on the quantum statistical properties of the propagating atom laser beam.
Kinetic treatment of nonlinear magnetized plasma motions - General geometry and parallel waves
Khabibrakhmanov, I. KH.; Galinskii, V. L.; Verheest, F.
1992-01-01
The expansion of kinetic equations in the limit of a strong magnetic field is presented. This gives a natural description of the motions of magnetized plasmas, which are slow compared to the particle gyroperiods and gyroradii. Although the approach is 3D, this very general result is used only to focus on the parallel propagation of nonlinear Alfven waves. The derivative nonlinear Schroedinger-like equation is obtained. Two new terms occur compared to earlier treatments, a nonlinear term proportional to the heat flux along the magnetic field line and a higher-order dispersive term. It is shown that kinetic description avoids the singularities occurring in magnetohydrodynamic or multifluid approaches, which correspond to the degenerate case of sound speeds equal to the Alfven speed, and that parallel heat fluxes cannot be neglected, not even in the case of low parallel plasma beta. A truly stationary soliton solution is derived.
Wave packet dynamics in one-dimensional linear and nonlinear generalized Fibonacci lattices.
Zhang, Zhenjun; Tong, Peiqing; Gong, Jiangbin; Li, Baowen
2011-05-01
The spreading of an initially localized wave packet in one-dimensional linear and nonlinear generalized Fibonacci (GF) lattices is studied numerically. The GF lattices can be classified into two classes depending on whether or not the lattice possesses the Pisot-Vijayaraghavan property. For linear GF lattices of the first class, both the second moment and the participation number grow with time. For linear GF lattices of the second class, in the regime of a weak on-site potential, wave packet spreading is close to ballistic diffusion, whereas in the regime of a strong on-site potential, it displays stairlike growth in both the second moment and the participation number. Nonlinear GF lattices are then investigated in parallel. For the first class of nonlinear GF lattices, the second moment of the wave packet still grows with time, but the corresponding participation number does not grow simultaneously. For the second class of nonlinear GF lattices, an analogous phenomenon is observed for the weak on-site potential only. For a strong on-site potential that leads to an enhanced nonlinear self-trapping effect, neither the second moment nor the participation number grows with time. The results can be useful in guiding experiments on the expansion of noninteracting or interacting cold atoms in quasiperiodic optical lattices.
Lu, Bao-Liang; Ito, Koji
2003-09-01
In this paper we present a method for converting general nonlinear programming (NLP) problems into separable programming (SP) problems by using feedforward neural networks (FNNs). The basic idea behind the method is to use two useful features of FNNs: their ability to approximate arbitrary continuous nonlinear functions with a desired degree of accuracy and their ability to express nonlinear functions in terms of parameterized compositions of functions of single variables. According to these two features, any nonseparable objective functions and/or constraints in NLP problems can be approximately expressed as separable functions with FNNs. Therefore, any NLP problems can be converted into SP problems. The proposed method has three prominent features. (a) It is more general than existing transformation techniques; (b) it can be used to formulate optimization problems as SP problems even when their precise analytic objective function and/or constraints are unknown; (c) the SP problems obtained by the proposed method may highly facilitate the selection of grid points for piecewise linear approximation of nonlinear functions. We analyze the computational complexity of the proposed method and compare it with an existing transformation approach. We also present several examples to demonstrate the method and the performance of the simplex method with the restricted basis entry rule for solving SP problems.
General job stress: a unidimensional measure and its non-linear relations with outcome variables.
Yankelevich, Maya; Broadfoot, Alison; Gillespie, Jennifer Z; Gillespie, Michael A; Guidroz, Ashley
2012-04-01
This article aims to examine the non-linear relations between a general measure of job stress [Stress in General (SIG)] and two outcome variables: intentions to quit and job satisfaction. In so doing, we also re-examine the factor structure of the SIG and determine that, as a two-factor scale, it obscures non-linear relations with outcomes. Thus, in this research, we not only test for non-linear relations between stress and outcome variables but also present an updated version of the SIG scale. Using two distinct samples of working adults (sample 1, N = 589; sample 2, N = 4322), results indicate that a more parsimonious eight-item SIG has better model-data fit than the 15-item two-factor SIG and that the eight-item SIG has non-linear relations with job satisfaction and intentions to quit. Specifically, the revised SIG has an inverted curvilinear J-shaped relation with job satisfaction such that job satisfaction drops precipitously after a certain level of stress; the SIG has a J-shaped curvilinear relation with intentions to quit such that turnover intentions increase exponentially after a certain level of stress.
Nonlinear q-Generalizations of Quantum Equations: Homogeneous and Nonhomogeneous Cases—An Overview
Directory of Open Access Journals (Sweden)
Fernando D. Nobre
2017-01-01
Full Text Available Recent developments on the generalizations of two important equations of quantum physics, namely the Schroedinger and Klein–Gordon equations, are reviewed. These generalizations present nonlinear terms, characterized by exponents depending on an index q, in such a way that the standard linear equations are recovered in the limit q → 1 . Interestingly, these equations present a common, soliton-like, traveling solution, which is written in terms of the q-exponential function that naturally emerges within nonextensive statistical mechanics. In both cases, the corresponding well-known Einstein energy-momentum relations, as well as the Planck and the de Broglie ones, are preserved for arbitrary values of q. In order to deal appropriately with the continuity equation, a classical field theory has been developed, where besides the usual Ψ ( x → , t , a new field Φ ( x → , t must be introduced; this latter field becomes Ψ * ( x → , t only when q → 1 . A class of linear nonhomogeneous Schroedinger equations, characterized by position-dependent masses, for which the extra field Φ ( x → , t becomes necessary, is also investigated. In this case, an appropriate transformation connecting Ψ ( x → , t and Φ ( x → , t is proposed, opening the possibility for finding a connection between these fields in the nonlinear cases. The solutions presented herein are potential candidates for applications to nonlinear excitations in plasma physics, nonlinear optics, in structures, such as those of graphene, as well as in shallow and deep water waves.
Energy Technology Data Exchange (ETDEWEB)
Krivoshchekov, V.L.; Slavnov, A.A.; Chekhov, L.O.
1988-01-01
An effective meson action is constructed for supersymmetric quantum chromodynamics (SUSY-QCD) in the framework of the 1/N expansion. It is shown that there is no dynamical spontaneous breaking of the supersymmetry. The explicit expression obtained for the low-energy action with allowance for the anomaly is the supersymmetric generalization of the Weinberg-Wess-Zumino-Witten action.
Institute of Scientific and Technical Information of China (English)
R.Mokhtari; A.Samadi Toodar; N.G.Chegini
2011-01-01
@@ We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schr(o)dinger equations.The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method.The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly.Some comparisons with the methods applied in the literature are carried out.%We the extend application of the generalized differential quadrature method (GDQM) to solve some coupled nonlinear Schrodinger equations. The cosine-based GDQM is employed and the obtained system of ordinary differential equations is solved via the fourth order Runge-Kutta method. The numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.
Yang, Jianke
2012-01-01
Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schroedinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. It is shown that the smooth solution branch switches stability at the bifurcation point. In addition, the two bifurcated solution branches and the smooth branch have the opposite (same) stability when their power slopes have the same (opposite) sign. One unusual feature on the stability of these pitchfork bifurcations is that the smooth and bifurcated solution branches can be both stable or both unstable, which contrasts such bifurcations in finite-dimensional dynamical systems where the smooth and bifurcated branches generally have opposite stability. For the special case of positive solitary waves, stronger and more explicit stab...
A Quadratic precision generalized nonlinear global optimization migration velocity inversion method
Institute of Scientific and Technical Information of China (English)
Zhao Taiyin; Hu Guangmin; He Zhenhua; Huang Deji
2009-01-01
An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.
Conservation Laws and Traveling Wave Solutions of a Generalized Nonlinear ZK-BBM Equation
Directory of Open Access Journals (Sweden)
Khadijo Rashid Adem
2014-01-01
Full Text Available We study a generalized two-dimensional nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK-BBM equation, which is in fact Benjamin-Bona-Mahony equation formulated in the ZK sense. Conservation laws for this equation are constructed by using the new conservation theorem due to Ibragimov and the multiplier method. Furthermore, traveling wave solutions are obtained by employing the (G'/G-expansion method.
Kutev, N.; Kolkovska, N.; Dimova, M.
2013-10-01
The Cauchy problem to the generalized Boussinesq equation with Bernoulli type nonlinearities is studied. Global solvability of the solutions with sub-critical initial energy is proved by means of different techniques - nonstandard potential well method and method of the conservation low of the energy. In the framework of the nonstandard potential well method a new critical energy constant is introduced and estimated. The performed numerical experiments support the theoretical results.
Indian Academy of Sciences (India)
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
Can there be a general nonlinear PDE theory for the existence of solutions ?
2004-01-01
Contrary to widespread perception, there is ever since 1994 a unified, general type independent theory for the existence of solutions for very large classes of nonlinear systems of PDEs. This solution method is based on the Dedekind order completion of suitable spaces of piece-wise smooth functions on the Euclidean domains of definition of the respective PDEs. The method can also deal with associated initial and/or boundary value problems. The solutions obtained can be assimilated with usual ...
A NONMONOTONE TRUST REGION ALGORITHM FOR NONLINEAR OPTIMIZATION SUBJECT TO GENERAL CONSTRAINTS
Institute of Scientific and Technical Information of China (English)
Hongchao Zhang
2003-01-01
In this paper we present a nonmonotone trust region algorithm for general nonlinear constrained optimization problems. The main idea of this paper is to combine Yuan's technique[1] with a nonmonotone method similar to Ke and Han [2]. This new algorithm may not only keep the robust properties of the algorithm given by Yuan, but also have some advantages led by the nonmonotone technique. Under very mild conditions, global convergence for the algorithm is given. Numerical experiments demonstrate the efficiency of the algorithm.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
We analyze the blowup problems to the nonlinear Schrodinger equation with har-monic potential. This equation always models the Bose-Einstein condensation in lower dimensions. It is known that the mass of the blowup solutions from radially symmet-ric initial data can concentrate on the point of blowup. In this paper based on the refined compactness lemma, we extend the result to general data.
Well-posedness for a generalized derivative nonlinear Schrödinger equation
Hayashi, Masayuki; Ozawa, Tohru
2016-11-01
We study the Cauchy problem for a generalized derivative nonlinear Schrödinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces H1 and H2. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space H1.
Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang
2017-09-01
A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 1, then the system remains permanent in the mean.
Supersymmetric black holes in string theory
Energy Technology Data Exchange (ETDEWEB)
Mohaupt, T. [Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL (United Kingdom)
2007-05-15
We review recent developments concerning supersymmetric black holes in string theory. After a general introduction to the laws of black hole mechanics and to black hole entropy in string theory, we discuss black hole solutions in N=2 supergravity, special geometry, the black hole attractor equations and the underlying variational principle. Special attention is payed to the crucial role of higher derivative corrections. Finally we discuss black hole partition functions and their relation with the topological string, mainly from the supergravity perspective. We summarize the state of art and discuss various open questions and problems. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Supersymmetric q-deformed quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Traikia, M. H.; Mebarki, N. [Laboratoire de Physique Mathematique et Subatomique, Mentouri University, Constantine (Algeria)
2012-06-27
A supersymmetric q-deformed quantum mechanics is studied in the weak deformation approximation of the Weyl-Heisenberg algebra. The corresponding supersymmetric q-deformed hamiltonians and charges are constructed explicitly.
Directory of Open Access Journals (Sweden)
Da-Guang Zhang
2015-10-01
Full Text Available For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Da-Guang; Li, Meng-Han; Zhou, Hao-Miao, E-mail: zhouhm@cjlu.edu.cn [College of Information Engineering, China Jiliang University, 310018, Hangzhou (China)
2015-10-15
For magnetostrictive rods under combined axial pre-stress and magnetic field, a general one-dimension nonlinear magneto-elastic coupled constitutive model was built in this paper. First, the elastic Gibbs free energy was expanded into polynomial, and the relationship between stress and strain and the relationship between magnetization and magnetic field with the polynomial form were obtained with the help of thermodynamic relations. Then according to microscopic magneto-elastic coupling mechanism and some physical facts of magnetostrictive materials, a nonlinear magneto-elastic constitutive with concise form was obtained when the relations of nonlinear strain and magnetization in the polynomial constitutive were instead with transcendental functions. The comparisons between the prediction and the experimental data of different magnetostrictive materials, such as Terfenol-D, Metglas and Ni showed that the predicted magnetostrictive strain and magnetization curves were consistent with experimental results under different pre-stresses whether in the region of low and moderate field or high field. Moreover, the model can fully reflect the nonlinear magneto-mechanical coupling characteristics between magnetic, magnetostriction and elasticity, and it can effectively predict the changes of material parameters with pre-stress and bias field, which is useful in practical applications.
Bednarik, Michal; Konicek, Petr
2002-07-01
This paper deals with using the generalized Burgers equation for description of nonlinear waves in circular ducts. Two new approximate solutions of the generalized Burgers equation (GBE) are presented. These solutions take into account the boundary layer effects. The first solution is valid for the preshock region and gives more precise results than the Fubini solution, whereas the second one is valid for the postshock (sawtooth) region and provides better results than the Fay solution. The approximate solutions are compared with numerical results of the GBE. Furthermore, the limits of validity of the used model equation are discussed with respect to boundary conditions and radius of a circular duct.
An SIR Epidemic Model with Time Delay and General Nonlinear Incidence Rate
Directory of Open Access Journals (Sweden)
Mingming Li
2014-01-01
Full Text Available An SIR epidemic model with nonlinear incidence rate and time delay is investigated. The disease transmission function and the rate that infected individuals recovered from the infected compartment are assumed to be governed by general functions F(S,I and G(I, respectively. By constructing Lyapunov functionals and using the Lyapunov-LaSalle invariance principle, the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is obtained. It is shown that the global properties of the system depend on both the properties of these general functions and the basic reproductive number R0.
Multi-Order Exact Solutions for a generalized shallow water wave equation and other nonlinear PDEs
Bagchi, Bijan; Ganguly, Asish
2011-01-01
We seek multi-order exact solutions of a generalized shallow water wave equation along with those corresponding to a class of nonlinear systems described by the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. We employ a modified version of a generalized Lame equation and subject it to a perturbative treatment identifying the solutions order by order in terms of Jacobi elliptic functions. Our solutions are new and hold the key feature that they are expressible in terms of an auxiliary function f in a generic way. For appropriate choices of f we recover the previous results reported in the literature.
Chavanis, Pierre-Henri
2008-01-01
We consider a generalized class of Keller-Segel models describing the chemotaxis of biological populations (bacteria, amoebae, endothelial cells, social insects,...). We show the analogy with nonlinear mean field Fokker-Planck equations and generalized thermodynamics. As an illustration, we introduce a new model of chemotaxis incorporating both effects of anomalous diffusion and exclusion principle (volume filling). We also discuss the analogy between biological populations described by the Keller-Segel model and self-gravitating Brownian particles described by the Smoluchowski-Poisson system.
n = 4 supersymmetric FRW model
Energy Technology Data Exchange (ETDEWEB)
Rosales, J.J.; Pashnev, A. [Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, 141980 (Russian Federation); Tkach, V.I. [Instituto de Fisica, Universidad de Guanajuato, 05315-970 Leon, 66318 Guanajuato (Mexico)]. e-mail: juan@ifug3.ugto.mx, pashnev@thsun1.jinr.ru, vladimir@ifug3.ugto.mx
2003-07-01
In this work we have constructed the n = 4 extended local conformal time supersymmetry for the Friedmann-Robertson-Walker cosmological models. This is based on the superfield construction of the action, which is invariant under world line local n = 4 supersymmetry with SU(2){sub local} X SU(2){sub global} internal subgroup. It is shown that the supersymmetric action has the form of the localized (or superconformal) version of the action for n = 4 supersymmetric quantum mechanics. This superfield procedure provides a well defined scheme for including super matter. (Author)
Bilinear approach to the supersymmetric Gardner equation
Babalic, C. N.; Carstea, A. S.
2016-08-01
We study a supersymmetric version of the Gardner equation (both focusing and defocusing) using the superbilinear formalism. This equation is new and cannot be obtained from the supersymmetric modified Korteweg-de Vries equation with a nonzero boundary condition. We construct supersymmetric solitons and then by passing to the long-wave limit in the focusing case obtain rational nonsingular solutions. We also discuss the supersymmetric version of the defocusing equation and the dynamics of its solutions.
Institute of Scientific and Technical Information of China (English)
朱海平
2012-01-01
We construct analytical self-similar solutions for the generalized （3＋1）-dimensional nonlinear Schrdinger equation with polynomial nonlinearity of arbitrary order. As an example, we list self-similar solutions of quintic nonlinear Schrdinger equation with distributed dispersion and distributed linear gain, including bright similariton solution, fractional and combined Jacobian elliptic function solutions. Moreover, we discuss self-similar evolutional dynamic behaviors of these solutions in the dispersion decreasing fiber and the periodic distributed amplification system.
Energy Technology Data Exchange (ETDEWEB)
Wang, Hailing [Institute of Applied Mathematics, Chongqing University of Posts and Telecommunications, Chongqing 400065 (China); Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong); Chung, Kwok-wai, E-mail: makchung@cityu.edu.hk [Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon (Hong Kong)
2012-02-27
The analytical solutions of nonlinear oscillators obtained from most perturbation or approximate methods usually have poor accuracy near homoclinic/heteroclinic (HH) orbits. In this Letter, we propose a nonlinear time transformation method to overcome such difficulty. In particular, we apply such method with Padé approximation to find analytical solutions of a generalized Duffing-harmonic oscillator having a rational form for the potential energy. For some parametric ranges, HH orbits exist in such an oscillator. For analytical approximation of periodic solution obtained from the present method, it is shown that the relative error of period with respect to the exact period tends to zero when the amplitude of periodic solution tends to either zero or infinity. The relative error is still very small even near to HH orbits. Furthermore, analytical approximate of HH orbits can also be obtained. From the illustrative examples, the phase portraits are in excellent agreement with the exact HH orbits. The results from the present method are compared with the exact solutions and that from the cubication method. -- Highlights: ► A nonlinear transformation is proposed for a generalized Duffing-harmonic oscillator. ► The relative error of period with respect to the exact one is always very small. ► Approximate solution of homoclinic/heteroclinic orbits can be obtained. ► Phase portraits are in excellent agreement even at homoclinic/heteroclinic orbits.
Linear and nonlinear associations between general intelligence and personality in Project TALENT.
Major, Jason T; Johnson, Wendy; Deary, Ian J
2014-04-01
Research on the relations of personality traits to intelligence has primarily been concerned with linear associations. Yet, there are no a priori reasons why linear relations should be expected over nonlinear ones, which represent a much larger set of all possible associations. Using 2 techniques, quadratic and generalized additive models, we tested for linear and nonlinear associations of general intelligence (g) with 10 personality scales from Project TALENT (PT), a nationally representative sample of approximately 400,000 American high school students from 1960, divided into 4 grade samples (Flanagan et al., 1962). We departed from previous studies, including one with PT (Reeve, Meyer, & Bonaccio, 2006), by modeling latent quadratic effects directly, controlling the influence of the common factor in the personality scales, and assuming a direction of effect from g to personality. On the basis of the literature, we made 17 directional hypotheses for the linear and quadratic associations. Of these, 53% were supported in all 4 male grades and 58% in all 4 female grades. Quadratic associations explained substantive variance above and beyond linear effects (mean R² between 1.8% and 3.6%) for Sociability, Maturity, Vigor, and Leadership in males and Sociability, Maturity, and Tidiness in females; linear associations were predominant for other traits. We discuss how suited current theories of the personality-intelligence interface are to explain these associations, and how research on intellectually gifted samples may provide a unique way of understanding them. We conclude that nonlinear models can provide incremental detail regarding personality and intelligence associations.
Ge, Hao; Qian, Hong
2017-01-01
This paper studies a mathematical formalism of nonequilibrium thermodynamics for chemical reaction models with N species, M reactions, and general rate law. We establish a mathematical basis for J. W. Gibbs' macroscopic chemical thermodynamics under G. N. Lewis' kinetic law of entire equilibrium (detailed balance in nonlinear chemical kinetics). In doing so, the equilibrium thermodynamics is then naturally generalized to nonequilibrium settings without detailed balance. The kinetic models are represented by a Markovian jumping process. A generalized macroscopic chemical free energy function and its associated balance equation with nonnegative source and sink are the major discoveries. The proof is based on the large deviation principle of this type of Markov processes. A general fluctuation dissipation theorem for stochastic reaction kinetics is also proved. The mathematical theory illustrates how a novel macroscopic dynamic law can emerges from the mesoscopic kinetics in a multi-scale system.
Supersymmetric quantum mechanics for two-dimensional disk
Indian Academy of Sciences (India)
Akira Suzuki; Ranabir Dutt; Rajat K Bahaduri
2005-07-01
The infinite square well potential in one dimension has a smooth supersymmetric partner potential which is shape invariant. In this paper, we study the generalization of this to two dimensions by constructing the supersymmetric partner of the disk billiard. We find that the property of shape invariance is lost in this case. Nevertheless, the WKB results are significantly improved when SWKB calculations are performed with the square of the superpotential. We also study the effect of inserting a singular flux line through the center of the disk.
Supersymmetric Casimir Energy and $SL(3,\\mathbb{Z})$ Transformations
Brünner, Frederic; Spiridonov, Vyacheslav P
2016-01-01
We provide a recipe to extract the supersymmetric Casimir energy of theories defined on primary Hopf surfaces directly from the superconformal index. It involves an $SL(3,\\mathbb{Z})$ transformation acting on the complex structure moduli of the background geometry. In particular, the known relation between Casimir energy, index and partition function emerges naturally from this framework, allowing rewriting of the latter as a modified elliptic hypergeometric integral. We show this explicitly for $\\mathcal{N}=1$ SQCD and $\\mathcal{N}=4$ supersymmetric Yang-Mills theory for all classical gauge groups, and conjecture that it holds more generally.
Extended Supersymmetric BMS$_3$ algebras and Their Free Field Realisations
Banerjee, Nabamita; Lodato, Ivano; Mukhi, Sunil; Neogi, Turmoli
2016-01-01
We study $N=(2,4,8)$ supersymmetric extensions of the three dimensional BMS algebra (BMS$_3$) with most generic possible central extensions. We find that $N$-extended supersymmetric BMS$_3$ algebras can be derived by a suitable contraction of two copies of the extended superconformal algebras. Extended algebras from all the consistent contractions are obtained by scaling left-moving and right-moving supersymmetry generators symmetrically, while Virasoro and R-symmetry generators are scaled asymmetrically. On the way, we find that the BMS/GCA correspondence does not in general hold for supersymmetric systems. Using the $\\beta$-$\\gamma$ and the ${\\mathfrak b}$-${\\mathfrak c}$ systems, we construct free field realisations of all the extended super-BMS$_3$ algebras.
D-brane Solitons in Supersymmetric Sigma-Models
Gauntlett, J P; Tong, D; Townsend, P K; Gauntlett, Jerome P.; Portugues, Rubén; Tong, David; Townsend, Paul K.
2001-01-01
Massive D=4 N=2 supersymmetric sigma models typically admit domain wall (Q-kink) solutions and string (Q-lump) solutions, both preserving 1/2 supersymmetry. We exhibit a new static 1/4 supersymmetric `kink-lump' solution in which a string ends on a wall, and show that it has an effective realization as a BIon of the D=4 super DBI-action. It is also shown to have a time-dependent Q-kink-lump generalization which reduces to the Q-lump in a limit corresponding to infinite BI magnetic field. All these 1/4 supersymmetric sigma-model solitons are shown to be realized in M-theory as calibrated, or `Q-calibrated', M5-branes in an M-monopole background.
Nonlinear Propagation in Multimode and Multicore Fibers: Generalization of the Manakov Equations
Mumtaz, Sami; Agrawal, Govind P
2012-01-01
This paper starts by an investigation of nonlinear transmission in space-division multiplexed (SDM) systems using multimode fibers exhibiting a rapidly varying birefringence. A primary objective is to generalize the Manakov equations, well known in the case of single-mode fibers. We first investigate a reference case where linear coupling among the spatial modes of the fiber is weak and after averaging over birefringence fluctuations, we obtain new Manakov equations for multimode fibers. Such an averaging reduces the number of intermodal nonlinear terms drastically since all four-wave-mixing terms average out. Cross-phase modulation terms still affect multimode transmission but their effectiveness is reduced. We then verify the accuracy of our new Manakov equations by transmitting multiple PDM-QPSK signals over different modes of a multimode fiber and comparing the numerical results with those obtained by solving the full stochastic equation. The agreement is excellent in all cases studied. A great benefit of...
Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces
Directory of Open Access Journals (Sweden)
Cho Yeol
2011-01-01
Full Text Available Abstract In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed variational inequalities problems, it is clear that it cannot be directly applied to the problems that we have considered in this paper because of φ and g. 2000 AMS Subject Classification: 47H05; 47H09; 47J25; 65J15.
Cooperative Output Regulation of Nonlinear Multiagent Systems under a General Directed Graph
Directory of Open Access Journals (Sweden)
Dingcai Huang
2015-01-01
Full Text Available This paper studies the cooperative output regulation problem for a class of nonlinear multiagent systems modeled by nonlinear dynamics under a general directed communication topology. A type of distributed internal model is introduced to convert the cooperative output regulation problem into a robust stabilization problem of a so-called augmented system. Based on the Lyapunov stability theorem and M-matrix theorem, a kind of distributed output feedback controller only using the relative outputs of neighboring agents together with its stability analysis is further proposed with the aid of the backstepping technology, under which the outputs of the followers will asymptotically converge to that of the leader if, for each follower, there exists at least a directed path from the leader to the follower. Finally, a numerical example is provided to illustrate the effectiveness of the analytic results.
A general non-linear optimization algorithm for lower bound limit analysis
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Damkilde, Lars
2003-01-01
The non-linear programming problem associated with the discrete lower bound limit analysis problem is treated by means of an algorithm where the need to linearize the yield criteria is avoided. The algorithm is an interior point method and is completely general in the sense that no particular...... finite element discretization or yield criterion is required. As with interior point methods for linear programming the number of iterations is affected only little by the problem size. Some practical implementation issues are discussed with reference to the special structure of the common lower bound...... load optimization problem. and finally the efficiency and accuracy of the method is demonstrated by means of examples of plate and slab structures obeying different non-linear yield criteria. Copyright (C) 2002 John Wiley Sons. Ltd....
Consistent supersymmetric decoupling in cosmology
Sousa Sánchez, Kepa
2012-01-01
The present work discusses several problems related to the stability of ground states with broken supersymmetry in supergravity, and to the existence and stability of cosmic strings in various supersymmetric models. In particular we study the necessary conditions to truncate consistently a sector o
Introduction to Supersymmetric Gauge Theories
Piguet, O
1997-01-01
In these lectures I present a basic introduction to supersymmetry, especially to N=1 supersymmetric gauge theories and their renormalization, in the Wess-Zumino gauge. I also discuss the various ways supersymmetry may be broken in order to account for the lack of exact supersymmetry in the actual world of elementary particles.
Supersymmetric classical mechanics: free case
Energy Technology Data Exchange (ETDEWEB)
Rodrigues, R. de Lima [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza]. E-mail: rafael@cfp.ufpb.br; Almeida, W. Pires de [Paraiba Univ., Cajazeiras, PB (Brazil). Dept. de Ciencias Exatas e da Natureza; Fonseca Neto, I. [Paraiba Univ., Campina Grande, PB (Brazil). Dept. de Fisica
2001-06-01
We present a review work on Supersymmetric Classical Mechanics in the context of a Lagrangian formalism, with N = 1-supersymmetry. We show that the N = 1 supersymmetry does not allow the introduction of a potencial energy term depending on a single commuting supercoordinate, {phi}(t;{theta}). (author)
Supersymmetric Langevin equation to explore free-energy landscapes.
Mossa, Alessandro; Clementi, Cecilia
2007-04-01
The recently discovered supersymmetric generalizations of the Langevin dynamics and Kramers equation can be utilized for the exploration of free-energy landscapes of systems whose large time-scale separation hampers the usefulness of standard molecular dynamics techniques. The first realistic application is here presented. The system chosen is a minimalist model for a short alanine peptide exhibiting a helix-coil transition.
Two-loop beta functions for supersymmetric gauge theories
Energy Technology Data Exchange (ETDEWEB)
Jack, I. (Imperial Coll. of Science and Technology, London (UK). Blackett Lab.)
1984-11-15
The two-loop ..beta.. functions in the dimensional regularisation framework for a general gauge theory coupled to scalar and spinor fields are presented and by means of a finite transformation of the couplings are converted into a form which vanishes for special cases corresponding to supersymmetric gauge theories.
The $N=2$ supersymmetric unconstrained matrix GNLS hierarchies
Sorin, A.S.; Kersten, P.H.M.
2002-01-01
The generalization of the $N=2$ supersymmetric chiral matrix $(k|n,m)$--GNLS hierarchy to the case when matrix entries are bosonic and fermionic unconstrained $N=2$ superfields is proposed. This is done by exhibiting the corresponding matrix Lax--pair representation in terms of $N=2$ unconstrained s
Supersymmetric AdS{sub 6} solutions of type IIB supergravity
Energy Technology Data Exchange (ETDEWEB)
Kim, Hyojoong, E-mail: h.kim@khu.ac.kr; Kim, Nakwoo, E-mail: nkim@khu.ac.kr [Department of Physics and Research Institute of Basic Science, Kyung Hee University, 130-701, Seoul (Korea, Republic of); Suh, Minwoo, E-mail: minsuh@usc.edu [Department of Physics, Sogang University, 121-742, Seoul (Korea, Republic of)
2015-10-11
We study the general requirement for supersymmetric AdS{sub 6} solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the canonical form of the solutions. Our result agrees precisely with the work of Apruzzi et al. (JHEP 1411:099, 2014), which used the pure spinor technique. Hoping to identify the geometry of the problem, we also computed four-dimensional theory through the dimensional reduction of type IIB supergravity on AdS{sub 6}. This effective action is essentially a non-linear sigma model with five scalar fields parametrizing SL(3,ℝ)/SO(2,1), modified by a scalar potential and coupled to Einstein gravity in Euclidean signature. We argue that the scalar potential can be explained by a subgroup CSO(1,1,1) ⊂SL(3,ℝ) in a way analogous to gauged supergravity.
Supersymmetric AdS{sub 6} solutions of type IIB supergravity
Energy Technology Data Exchange (ETDEWEB)
Kim, Hyojoong; Kim, Nakwoo [Kyung Hee University, Department of Physics and Research Institute of Basic Science, Seoul (Korea, Republic of); Suh, Minwoo [Sogang University, Department of Physics, Seoul (Korea, Republic of)
2015-10-15
We study the general requirement for supersymmetric AdS{sub 6} solutions in type IIB supergravity. We employ the Killing spinor technique and study the differential and algebraic relations among various Killing spinor bilinears to find the canonical form of the solutions. Our result agrees precisely with the work of Apruzzi et al. (JHEP 1411:099, 2014), which used the pure spinor technique. Hoping to identify the geometry of the problem, we also computed four-dimensional theory through the dimensional reduction of type IIB supergravity on AdS{sub 6}. This effective action is essentially a non-linear sigma model with five scalar fields parametrizing SL(3,R)/ SO(2,1), modified by a scalar potential and coupled to Einstein gravity in Euclidean signature. We argue that the scalar potential can be explained by a subgroup CSO(1,1,1) is contained in SL(3,R) in a way analogous to gauged supergravity. (orig.)
Solutions to the Painlevé V equation through supersymmetric quantum mechanics
Bermudez, David; Fernández C, David J.; Negro, Javier
2016-08-01
In this paper we shall use the algebraic method known as supersymmetric quantum mechanics (SUSY QM) to obtain solutions to the Painlevé V (PV) equation, a second-order nonlinear ordinary differential equation. For this purpose, we will apply first the SUSY QM treatment to the radial oscillator. In addition, we will revisit the polynomial Heisenberg algebras (PHAs) and we will study the general systems ruled by them: for first-order PHAs we obtain the radial oscillator while for third-order PHAs the potential will be determined by solutions to the PV equation. This connection allows us to introduce a simple technique for generating solutions of the PV equation expressed in terms of confluent hypergeometric functions. Finally, we will classify them into several solution hierarchies.
Quantum spectral curve of the N=6 supersymmetric Chern-Simons theory.
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-11
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N=6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Quantum Spectral Curve of the N =6 Supersymmetric Chern-Simons Theory
Cavaglià, Andrea; Fioravanti, Davide; Gromov, Nikolay; Tateo, Roberto
2014-07-01
Recently, it was shown that the spectrum of anomalous dimensions and other important observables in planar N=4 supersymmetric Yang-Mills theory are encoded into a simple nonlinear Riemann-Hilbert problem: the Pμ system or quantum spectral curve. In this Letter, we extend this formulation to the N =6 supersymmetric Chern-Simons theory introduced by Aharony, Bergman, Jafferis, and Maldacena. This may be an important step towards the exact determination of the interpolating function h(λ) characterizing the integrability of this model. We also discuss a surprising relation between the quantum spectral curves for the N=4 supersymmetric Yang-Mills theory and the N=6 supersymmetric Chern-Simons theory considered here.
Supersymmetric Sigma Model Geometry
Ulf Lindström
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Supersymmetric Sigma Model geometry
Lindström, Ulf
2012-01-01
This is a review of how sigma models formulated in Superspace have become important tools for understanding geometry. Topics included are: The (hyper)k\\"ahler reduction; projective superspace; the generalized Legendre construction; generalized K\\"ahler geometry and constructions of hyperk\\"ahler metrics on Hermitean symmetric spaces.
Directory of Open Access Journals (Sweden)
Xuming Huang
2009-01-01
Full Text Available We study the permanence of periodic predator-prey system with general nonlinear functional responses and stage structure for both predator and prey and obtain that the predator and the prey species are permanent.
Yan, Zhenya
2013-01-01
The higher-order dispersive and nonlinear effects (alias {\\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse propagation. We consider optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schr\\"odinger (NLS) equation with space- and time-modulated parameters. A proper transformation is presented to reduce the generalized higher-order NLS equation to the integrable Hirota equation with constant coefficients. This transformation allows us to relate certain class of exact solutions of the generalized higher-order NLS equation to the variety of solutions of the integrable Hirota equation. In particular, we illustrate the approach in terms of two lowest-order rational solutions of the Hirota equation as seeding functions to generate rogue wave solutions localized in time that have complicated evolution in space with or without the differential gain or lo...
A generalized nonlinear model-based mixed multinomial logit approach for crash data analysis.
Zeng, Ziqiang; Zhu, Wenbo; Ke, Ruimin; Ash, John; Wang, Yinhai; Xu, Jiuping; Xu, Xinxin
2017-02-01
The mixed multinomial logit (MNL) approach, which can account for unobserved heterogeneity, is a promising unordered model that has been employed in analyzing the effect of factors contributing to crash severity. However, its basic assumption of using a linear function to explore the relationship between the probability of crash severity and its contributing factors can be violated in reality. This paper develops a generalized nonlinear model-based mixed MNL approach which is capable of capturing non-monotonic relationships by developing nonlinear predictors for the contributing factors in the context of unobserved heterogeneity. The crash data on seven Interstate freeways in Washington between January 2011 and December 2014 are collected to develop the nonlinear predictors in the model. Thirteen contributing factors in terms of traffic characteristics, roadway geometric characteristics, and weather conditions are identified to have significant mixed (fixed or random) effects on the crash density in three crash severity levels: fatal, injury, and property damage only. The proposed model is compared with the standard mixed MNL model. The comparison results suggest a slight superiority of the new approach in terms of model fit measured by the Akaike Information Criterion (12.06 percent decrease) and Bayesian Information Criterion (9.11 percent decrease). The predicted crash densities for all three levels of crash severities of the new approach are also closer (on average) to the observations than the ones predicted by the standard mixed MNL model. Finally, the significance and impacts of the contributing factors are analyzed.
Supersymmetric descendants of self-adjointly extended quantum mechanical Hamiltonians
Energy Technology Data Exchange (ETDEWEB)
Al-Hashimi, M.H., E-mail: hashimi@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Salman, M., E-mail: msalman@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Shalaby, A., E-mail: amshalab@qu.edu.qa [Department of Mathematics, Statistics, and Physics, Qatar University, Al Tarfa, Doha 2713 (Qatar); Physics Department, Faculty of Science, Mansoura University (Egypt); Wiese, U.-J., E-mail: wiese@itp.unibe.ch [Albert Einstein Center for Fundamental Physics, Institute for Theoretical Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern (Switzerland); Center for Theoretical Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA (United States)
2013-10-15
We consider the descendants of self-adjointly extended Hamiltonians in supersymmetric quantum mechanics on a half-line, on an interval, and on a punctured line or interval. While there is a 4-parameter family of self-adjointly extended Hamiltonians on a punctured line, only a 3-parameter sub-family has supersymmetric descendants that are themselves self-adjoint. We also address the self-adjointness of an operator related to the supercharge, and point out that only a sub-class of its most general self-adjoint extensions is physical. Besides a general characterization of self-adjoint extensions and their supersymmetric descendants, we explicitly consider concrete examples, including a particle in a box with general boundary conditions, with and without an additional point interaction. We also discuss bulk-boundary resonances and their manifestation in the supersymmetric descendant. -- Highlights: •Self-adjoint extension theory and contact interactions. •Application of self-adjoint extensions to supersymmetry. •Contact interactions in finite volume with Robin boundary condition.
General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques
Lytel, Rick; Kuzyk, Mark G
2016-01-01
We develop an algorithm to apply the Dalgarno-Lewis (DL) perturbation theory to quantum graphs with multiple, connected edges. We use it to calculate the nonlinear optical hyperpolarizability tensors for graphs and show that it replicates the sum over states computations, but executes ten to fifty times faster. DL requires only knowledge of the ground state of the graph, eliminating the requirement to determine all possible degeneracies of a complex network. The algorithm is general and may be applied to any quantum graph.
Solving the Generalized Nonlinear Schrödinger Equation via Quartic Spline Approximation
Sheng, Q.; Khaliq, A. Q. M.; Al-Said, E. A.
2001-01-01
This paper is concerned with a new conservative finite difference method for solving the generalized nonlinear Schrödinger (GNLS) equation iut+uxx+f(⊢u⊢2)u=0. The numerical scheme is constructed through the semidiscretization and an application of the quartic spline approximation. Central difference and extrapolation formulae are used for approximating the Neumann boundary conditions introduced. Both continuous and discrete energy conservation and the stability property are investigated. The numerical method provides an efficient and reliable way for computing long-time solitary solutions given by the GNLS equation. Numerical examples are given to demonstrate our conclusions.
Breathers and Soliton Solutions for a Generalization of the Nonlinear Schrödinger Equation
Directory of Open Access Journals (Sweden)
Hai-Feng Zhang
2013-01-01
Full Text Available A generalized nonlinear Schrödinger equation, which describes the propagation of the femtosecond pulse in single mode optical silica fiber, is analytically investigated. By virtue of the Darboux transformation method, some new soliton solutions are generated: the bright one-soliton solution on the zero background, the dark one-soliton solution on the continuous wave background, the Akhmediev breather which delineates the modulation instability process, and the breather evolving periodically along the straight line with a certain angle of x-axis and t-axis. Those results might be useful in the study of the femtosecond pulse in single mode optical silica fiber.
DEFF Research Database (Denmark)
Blekhman, I. I.; Sorokin, V. S.
2016-01-01
A general approach to study effects produced by oscillations applied to nonlinear dynamic systems is developed. It implies a transition from initial governing equations of motion to much more simple equations describing only the main slow component of motions (the vibro-transformed dynamics...... equations). The approach is named as the oscillatory strobodynamics, since motions are perceived as under a stroboscopic light. The vibro-transformed dynamics equations comprise terms that capture the averaged effect of oscillations. The method of direct separation of motions appears to be an efficient...
Oscillation of solutions to second-order nonlinear differential equations of generalized Euler type
Directory of Open Access Journals (Sweden)
Asadollah Aghajani
2013-08-01
Full Text Available We are concerned with the oscillatory behavior of the solutions of a generalized Euler differential equation where the nonlinearities satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super linearity are assumed. Some implicit necessary and sufficient conditions and some explicit sufficient conditions are given for all nontrivial solutions of this equation to be oscillatory or nonoscillatory. Also, it is proved that solutions of the equation are all oscillatory or all nonoscillatory and cannot be both.
Zhang, L.; Yu, C.; Sun, J. Q.
2015-03-01
It is difficult to simulate the dynamical behavior of actual financial markets indexes effectively, especially when they have nonlinear characteristics. So it is significant to propose a mathematical model with these characteristics. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension D where 2 > D > 1.5 and Hurst exponent (H) where 1 > H > 0.5 firstly. And then we study the dynamical behavior of H for WMF as D and the spectrum of the time series γ change in three-dimensional space, respectively. Because WMF and the actual stock market indexes have two common features: fractal behavior using fractal dimension and long memory effect by Hurst exponent, we study the relationship between WMF and the actual stock market indexes. We choose a random value of γ and fixed value of D for WMF to simulate the S&P 500 indexes at different time ranges. As shown in the simulation results of three-dimensional space, we find that γ is important in WMF model and different γ may have the same effect for the nonlinearity of WMF. Then we calculate the skewness and kurtosis of actual Daily S&P 500 index in different time ranges which can be used to choose the value of γ. Based on these results, we choose appropriate γ, D and initial value into WMF to simulate Daily S&P 500 indexes. Using the fit line method in two-dimensional space for the simulated values, we find that the generalized WMF model is effective for simulating different actual stock market indexes in different time ranges. It may be useful for understanding the dynamical behavior of many different financial markets.
Towards a Non-Supersymmetric String Phenomenology
Abel, Steven; Mavroudi, Eirini
2015-01-01
Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively little work studying the phenomenologies associated with their non-supersymmetric counterparts. The primary reason for this relative lack of attention is the fact that strings without spacetime supersymmetry are generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper, we demonstrate that this hurdle can be overcome in a class of tachyon-free four-dimensional string models realized through coordinate-dependent compactifications. Moreover, as we shall see, it is possible to construct models in this class whose low-lying states resemble the Standard Model (or even potential unified extensions thereof) --- all without any light superpartners, and indeed without supersymmetry at any energy scale. The existence of such models thus opens the door to general stu...
Kelly, John V.; O'Brien, Jeff; O'Neill, Feidhlim T.; Gleeson, Michael R.; Sheridan, John T.
2004-10-01
Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is non-local as it is assumed that monomers are polymerised to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The numerical method of solution typically involves retaining either two or four harmonics of the Fourier series of monomer concentration in the calculation. In this paper a general set of equations is derived which allows inclusion of higher number of harmonics for any response function. The numerical convergence for varying number of harmonics retained is investigated with special care being taken to note the effect of the; non-local material variance s, the power law degree k, and the rates of diffusion, D, and polymerisation F0. General non-linear material responses are also included.
Energy Technology Data Exchange (ETDEWEB)
Wang, Shi-bing, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn [School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236041 (China); Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 (China); Wang, Xing-yuan, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn [Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024 (China); Wang, Xiu-you [School of Computer and Information Engineering, Fuyang Normal University, Fuyang 236041 (China); Zhou, Yu-fei [College of Electrical Engineering and Automation, Anhui University, Hefei 230601 (China)
2016-04-15
With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters. On the basis of Lyapunov stability theory and adaptive control, an AGCCS controller and parameter update laws are derived to achieve synchronization and parameter identification of two real drive systems and a complex response system, as well as two complex drive systems and a real response system. Two simulation examples, namely, ACGCS for chaotic real Lorenz and Chen systems driving a hyperchaotic complex Lü system, and hyperchaotic complex Lorenz and Chen systems driving a real chaotic Lü system, are presented to verify the feasibility and effectiveness of the proposed scheme.
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, Nail H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Meleshko, Sergey V [School of Mathematics, Institute of Science, Suranaree University of Technology, Nakhon Ratchasima 30000 (Thailand); Rudenko, Oleg V, E-mail: nib@bth.se, E-mail: sergey@math.sut.ac.th, E-mail: rudenko@acs366.phys.msu.ru [Department of Physics, Moscow State University, 119991 Moscow (Russian Federation)
2011-08-05
The paper deals with an evolutionary integro-differential equation describing nonlinear waves. A particular choice of the kernel in the integral leads to well-known equations such as the Khokhlov-Zabolotskaya equation, the Kadomtsev-Petviashvili equation and others. Since the solutions of these equations describe many physical phenomena, the analysis of the general model studied in this paper is important. One of the methods for obtaining solutions of differential equations is provided by the Lie group analysis. However, this method is not applicable to integro-differential equations. Therefore, we discuss new approaches developed in modern group analysis and apply them to the general model considered in this paper. Reduced equations and exact solutions are also presented.
A general derivation of the subharmonic threshold for non-linear bubble oscillations.
Prosperetti, Andrea
2013-06-01
The paper describes an approximate but rather general derivation of the acoustic threshold for a subharmonic component to be possible in the sound scattered by an insonified gas bubble. The general result is illustrated with several specific models for the mechanical behavior of the surface coating of bubbles used as acoustic contrast agents. The approximate results are found to be in satisfactory agreement with fully non-linear numerical results in the literature. The amplitude of the first harmonic is also found by the same method. A fundamental feature identified by the analysis is that the subharmonic threshold can be considerably lowered with respect to that of an uncoated free bubble if the mechanical response of the coating varies rapidly in the neighborhood of certain specific values of the bubble radius, e.g., because of buckling.
Huang, Z; Huang, Zheng; Suzuki, Mahiko
1996-01-01
We obtain the general analytic solutions of the nonlinear \\sigma-model in 3+1 dimensions as the candidates for the disoriented chiral condensate (DCC). The nonuniformly isospin-orientated solutions are shown to be related to the uniformly oriented ones through the chiral (axial) rotations. We discuss the pion charge distribution arising from these solutions. The distribution dP/df=1/(2\\sqrt{f}) holds for the uniform solutions in general and the nonuniform solutions in the 1+1 boost invariant case. For the nonuniform solution in 1+1 without a boost-invariance and in higher dimensions, the distribution does not hold in the integrated form. However, it is applicable to the pions selected from a small segment in the momentum phase space. We suggest that the nonuniform DCC's may correspond to the mini-Centauro events.
On timelike supersymmetric solutions of gauged minimal 5-dimensional supergravity
Chimento, Samuele
2016-01-01
We analyze the timelike supersymmetric solutions of minimal gauged 5-dimensional supergravity for the case in which the K\\"ahler base manifold admits a holomorphic isometry and depends on two real functions satisfying a simple second-order differential equation. Using this general form of the base space, the equations satisfied by the building blocks of the solutions become of, at most, fourth degree and can be solved by simple polynomic ansatzs. In this way we construct two 3-parameter families of solutions that contain almost all the timelike supersymmetric solutions of this theory with one angular momentum known so far and a few more: the (singular) supersymmetric Reissner-Nordstr\\"om-AdS solutions, the three exact supersymmetric solutions describing the three near-horizon geometries found by Gutowski and Reall, three 1-parameter asymptotically-AdS$_{5}$ black-hole solutions with those three near-horizon geometries (Gutowski and Reall's black hole being one of them), three generalizations of the G\\"odel un...
Signals of Supersymmetric Dark Matter
Abbas, A
2000-01-01
The Lightest Supersymmetric Particle predicted in most of the supersymmetric scenarios is an ideal candidate for the dark matter of cosmology. Their detection is of extreme significance today. Recently there have been intriguing signals of a 59 Gev neutralino dark matter at DAMA in Gran Sasso. We look at other possible signatures of dark matter in astrophysical and geological frameworks. The passage of the earth through dense clumps of dark matter would produce large quantities of heat in the interior of this planet through the capture and subsequent annihilation of dark matter particles. This heat would lead to large-scale volcanism which could in turn have caused mass extinctions. The periodicity of such volcanic outbursts agrees with the frequency of palaeontological mass extinctions as well as the observed periodicity in the occurrence of the largest flood basalt provinces on the globe. Binary character of these extinctions is another unique aspect of this signature of dark matter. In addition dark matter...
Supersymmetric Higgs Bosons and Beyond
Energy Technology Data Exchange (ETDEWEB)
Carena, Marcela; /Fermilab /Chicago U., EFI; Kong, Kyoungchul; /Fermilab /SLAC; Ponton, Eduardo; /Columbia U.; Zurita, Jose; /Fermilab /Buenos Aires U.
2010-08-26
We consider supersymmetric models that include particles beyond the Minimal Supersymmetric Standard Model (MSSM) with masses in the TeV range, and that couple significantly to the MSSM Higgs sector. We perform a model-independent analysis of the spectrum and couplings of the MSSM Higgs fields, based on an effective theory of the MSSM degrees of freedom. The tree-level mass of the lightest CP-even state can easily be above the LEP bound of 114 GeV, thus allowing for a relatively light spectrum of superpartners, restricted only by direct searches. The Higgs spectrum and couplings can be significantly modified compared to the MSSM ones, often allowing for interesting new decay modes. We also observe that the gluon fusion production cross section of the SM-like Higgs can be enhanced with respect to both the Standard Model and the MSSM.
BERGSHOEFF, EA; KALLOSH, R; ORTIN, T
1993-01-01
We present plane-wave-type solutions of the lowest-order superstring effective action which have unbroken space-time supersymmetries. They are given by a stringy generalization of the Brinkmann metric, dilaton, axion, and gauge fields. Some conspiracy between the metric and the axion field is requir
BERGSHOEFF, E
1994-01-01
We present plane-wave-type solutions to the superstring effective action which have unbroken space-time supersymmetries. They describe dilaton, axion and gauge fields in a generalization of the Brinkmann metric. A crucial property of the solutions is a conspiracy between the metric and the axion fie
Fun with supersymmetric quantum mechanics
Freedman, B.; Cooper, F.
1984-04-01
The Hamiltonian and path integral approaches to supersymmetric quantum mechanics were reviewed. The related path integrals for the Witten Index and for stochastic processes were discussed and shown to be indications for supersymmetry breakdown. A system where in the superpotential W(x) has assymetrical values at + or - infinity was considered. Nonperturbative strategies for studying supersymmetry breakdown were described. These strategies are based on introducing a lattice and studying the behavior of the ground state energy as the lattice cutoff is removed.
Quantum integrability and supersymmetric vacua
Nekrasov, Nikita A.; Shatashvili, Samson L.
2009-01-01
This is an announcement of some of the results of a longer paper where the supersymmetric vacua of two dimensional N=2 susy gauge theories with matter are shown to be in one-to-one correspondence with the eigenstates of integrable spin chain Hamiltonians. The correspondence between the Heisenberg spin chain and the two dimensional U(N) theory with fundamental hypermultiplets is reviewed in detail. We demonstrate the isomorphism of the equivariant quantum cohomology of the cotangent bundle to ...
Nonlinear Bogolyubov-Valatin transformations: 2 modes
Scharnhorst, K
2010-01-01
Extending our earlier study of nonlinear Bogolyubov-Valatin transformations (canonical transformations for fermions) for one fermionic mode, in the present paper we perform a thorough study of general (nonlinear) canonical transformations for two fermionic modes. We find that the Bogolyubov-Valatin group for n=2 fermionic modes which can be implemented by means of unitary SU(2^n = 4) transformations is isomorphic to SO(6;R)/Z_2. The investigation touches on a number of subjects. As a novelty from a mathematical point of view, we study the structure of nonlinear basis transformations in a Clifford algebra [specifically, in the Clifford algebra C(0,4)] entailing (supersymmetric) transformations among multivectors of different grades. A prominent algebraic role in this context is being played by biparavectors (products of Dirac matrices, quadriquaternions, sedenions) and spin bivectors (antisymmetric complex matrices). The studied biparavectors are equivalent to Eddington's E-numbers and can be understood in ter...
Lorentz violation in supersymmetric field theories.
Nibbelink, Stefan Groot; Pospelov, Maxim
2005-03-04
We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric standard model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultraviolet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications of dispersion relations at high energies thereby escaping constraints from astrophysical searches for Lorentz violation.
Supersymmetric theories on squashed five-sphere
Imamura, Yosuke
2012-01-01
We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing equation by dimensional reduction from 6d, and use Noether procedure to construct actions. The supersymmetric Yang-Mills action is straightforwardly obtained from the supersymmetric Chern-Simons action by using a supersymmetry preserving constant vector multiplet.
Institute of Scientific and Technical Information of China (English)
陶华学; 郭金运
2003-01-01
Data coming from different sources have different types and temporal states. Relations between one type of data and another ones, or between data and unknown parameters are almost nonlinear. It is not accurate and reliable to process the data in building the digital earth with the classical least squares method or the method of the common nonlinear least squares. So a generalized nonlinear dynamic least squares method was put forward to process data in building the digital earth. A separating solution model and the iterative calculation method were used to solve the generalized nonlinear dynamic least squares problem. In fact, a complex problem can be separated and then solved by converting to two sub-problems, each of which has a single variable. Therefore the dimension of unknown parameters can be reduced to its half, which simplifies the original high dimensional equations.
A new LES model derived from generalized Navier-Stokes equations with nonlinear viscosity
Rodríguez, José M
2015-01-01
Large Eddy Simulation (LES) is a very useful tool when simulating turbulent flows if we are only interested in its "larger" scales. One of the possible ways to derive the LES equations is to apply a filter operator to the Navier-Stokes equations, obtaining a new equation governing the behavior of the filtered velocity. This approach introduces in the equations the so called subgrid-scale tensor, that must be expressed in terms of the filtered velocity to close the problem. One of the most popular models is that proposed by Smagorinsky, where the subgrid-scale tensor is modeled by introducing an eddy viscosity. In this work, we shall propose a new approximation to this problem by applying the filter, not to the Navier-Stokes equations, but to a generalized version of them with nonlinear viscosity. That is, we shall introduce a nonlinear viscosity, not as a procedure to close the subgrid-scale tensor, but as part of the model itself (see below). Consequently, we shall need a different method to close the subgri...
Energy Technology Data Exchange (ETDEWEB)
Zhang, Jianxin; Zhang, Zhenjun [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Tong, Peiqing, E-mail: pqtong@njnu.edu.cn [Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023 (China); Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023 (China)
2013-07-15
We investigate the spreading of an initially localized wave packet in one-dimensional generalized Fibonacci (GF) lattices by solving numerically the discrete nonlinear Schrödinger equation (DNLSE) with a delayed cubic nonlinear term. It is found that for short delay time, the wave packet is self-trapping in first class of GF lattices, that is, the second moment grows with time, but the corresponding participation number does not grow. However, both the second moment and the participation number grow with time for large delay time. This illuminates that the wave packet is delocalized. For the second class of GF lattices, the dynamic behaviors of wave packet depend on the strength of on-site potential. For a weak on-site potential, the results are similar to the case of the first class. For a strong on-site potential, both the second moment and the participation number does not grow with time in the regime of short delay time. In the regime of large delay time, both the second moment and the participation number exhibit stair-like growth.
Park, Y. C.; Chang, M. H.; Lee, T.-Y.
2007-06-01
A deterministic global optimization method that is applicable to general nonlinear programming problems composed of twice-differentiable objective and constraint functions is proposed. The method hybridizes the branch-and-bound algorithm and a convex cut function (CCF). For a given subregion, the difference of a convex underestimator that does not need an iterative local optimizer to determine the lower bound of the objective function is generated. If the obtained lower bound is located in an infeasible region, then the CCF is generated for constraints to cut this region. The cutting region generated by the CCF forms a hyperellipsoid and serves as the basis of a discarding rule for the selected subregion. However, the convergence rate decreases as the number of cutting regions increases. To accelerate the convergence rate, an inclusion relation between two hyperellipsoids should be applied in order to reduce the number of cutting regions. It is shown that the two-hyperellipsoid inclusion relation is determined by maximizing a quadratic function over a sphere, which is a special case of a trust region subproblem. The proposed method is applied to twelve nonlinear programming test problems and five engineering design problems. Numerical results show that the proposed method converges in a finite calculation time and produces accurate solutions.
Instanton Corrected Non-Supersymmetric Attractors
Dominic, Pramod
2010-01-01
We discuss non-supersymmetric attractors with an instanton correction in Type IIA string theory compactified on a Calabi-Yau three-fold at large volume. For a stable non-supersymmetric black hole, the attractor point must minimize the effective black hole potential. We study the supersymmetric as well as non-supersymmetric attractors for the D0-D4 system with instanton corrections. We show that in simple models, like the STU model, the flat directions of the mass matrix can be lifted by a suitable choice of the instanton parameters.
Stable Non-Supersymmetric Throats in String Theory
Energy Technology Data Exchange (ETDEWEB)
Kachru, Shamit; Simic, Dusan; /Stanford U., ITP /SLAC /Santa Barbara, KITP; Trivedi, Sandip P.; /Tata Inst. /Stanford U., ITP /SLAC
2011-06-28
We construct a large class of non-supersymmetric AdS-like throat geometries in string theory by taking non-supersymmetric orbifolds of supersymmetric backgrounds. The scale of SUSY breaking is the AdS radius, and the dual field theory has explicitly broken supersymmetry. The large hierarchy of energy scales in these geometries is stable. We establish this by showing that the dual gauge theories do not have any relevant operators which are singlets under the global symmetries. When the geometries are embedded in a compact internal space, a large enough discrete subgroup of the global symmetries can still survive to prevent any singlet relevant operators from arising. We illustrate this by embedding one case in a non-supersymmetric orbifold of a Calabi-Yau manifold. These examples can serve as a starting point for obtaining Randall-Sundrum models in string theory, and more generally for constructing composite Higgs or technicolor-like models where strongly coupled dynamics leads to the breaking of electro-weak symmetry. Towards the end of the paper, we briefly discuss how bulk gauge fields can be incorporated by introducing D7-branes in the bulk, and also show how the strongly coupled dynamics can lead to an emergent weakly coupled gauge theory in the IR with matter fields including scalars.
Institute of Scientific and Technical Information of China (English)
JIANG Zhi-ping
2012-01-01
With the help of the variable-coefficient generalized projected Ricatti equation expansion method,we present exact solutions for the generalized (2+1)-dimensional nonlinear Schr(o)dinger equation with variable coefficients.These solutions include solitary wave solutions,soliton-like solutions and trigonometric function solutions.Among these solutions,some are found for the first time.
Institute of Scientific and Technical Information of China (English)
Liu Xiao-Bei; Li Biao
2011-01-01
We present three families of soliton solutions to the generalized (3+1)-dimensional nonlinear Schr(o)dinger equation with distributed coefficients. We investigate the dynamics of these solitons in nonlinear optics with some selected parameters.Different shapes of bright solitons,a train of bright solitons and dark solitons are observed.The obtained results may raise the possibilities of relevant experiments and potential applications.
Ma, Yaping; Xiao, Yegui; Wei, Guo; Sun, Jinwei
2016-01-01
In this paper, a multichannel nonlinear adaptive noise canceller (ANC) based on the generalized functional link artificial neural network (FLANN, GFLANN) is proposed for fetal electrocardiogram (FECG) extraction. A FIR filter and a GFLANN are equipped in parallel in each reference channel to respectively approximate the linearity and nonlinearity between the maternal ECG (MECG) and the composite abdominal ECG (AECG). A fast scheme is also introduced to reduce the computational cost of the FLANN and the GFLANN. Two (2) sets of ECG time sequences, one synthetic and one real, are utilized to demonstrate the improved effectiveness of the proposed nonlinear ANC. The real dataset is derived from the Physionet non-invasive FECG database (PNIFECGDB) including 55 multichannel recordings taken from a pregnant woman. It contains two subdatasets that consist of 14 and 8 recordings, respectively, with each recording being 90 s long. Simulation results based on these two datasets reveal, on the whole, that the proposed ANC does enjoy higher capability to deal with nonlinearity between MECG and AECG as compared with previous ANCs in terms of fetal QRS (FQRS)-related statistics and morphology of the extracted FECG waveforms. In particular, for the second real subdataset, the F1-measure results produced by the PCA-based template subtraction (TSpca) technique and six (6) single-reference channel ANCs using LMS- and RLS-based FIR filters, Volterra filter, FLANN, GFLANN, and adaptive echo state neural network (ESN a ) are 92.47%, 93.70%, 94.07%, 94.22%, 94.90%, 94.90%, and 95.46%, respectively. The same F1-measure statistical results from five (5) multi-reference channel ANCs (LMS- and RLS-based FIR filters, Volterra filter, FLANN, and GFLANN) for the second real subdataset turn out to be 94.08%, 94.29%, 94.68%, 94.91%, and 94.96%, respectively. These results indicate that the ESN a and GFLANN perform best, with the ESN a being slightly better than the GFLANN but about four times more
Simple supersymmetric strongly coupled preon model
Fajfer, S.; Tadić, D.
1988-08-01
This supersymmetric-SU(5) composite model is a natural generalization of the usual strong-coupling models. Preon superfields are in representations 5* and 10. The product representations 5*×10, 5×10, 5×5, and 5*×5 contain only those strongly hypercolor bound states which are needed in the standard electroweak theory. There are no superfluous quarklike states. The neutrino is massless. Only one strongly hypercolor bound singlet (10×10*) can exist as a free particle. At higher energies one should expect to see a plethora of new particles. Grand unification happens at the scale M~1014 GeV. Cabibbo mixing can be incorporated by using a transposed Kobayashi-Maskawa mixing matrix.
Supersymmetric Scenarios with Dominant Radiative Neutralino Decay
Ambrosanio, S; Ambrosanio, Sandro; Mele, Barbara
1997-01-01
The radiative decay of the next-to-lightest neutralino into a lightest neutralino and a photon is analyzed in the MSSM. We find that significant regions of the supersymmetric parameter space with large radiative BR's (up to about 100%) do exist. The radiative channel turns out to be enhanced when the neutralino tree-level decays are suppressed either `kinematically' or `dynamically'. In general, in the regions allowed by LEP data and not characterized by asymptotic values of the SuSy parameters, the radiative enhancement requires tan beta ~= 1 and/or M_1 ~= M_2, and negative values of relaxing the usual relation M_1=(5/3)*tan^2(th_W)*M_2, i.e. gaugino mass unification at the GUT scale. The influence of varying the stop masses and mixing angle when the radiative decay is enhanced is also considered. Some phenomenological consequences of the above picture are discussed.
Supersymmetric quantum mechanics and Painleve equations
Bermudez, David
2013-01-01
In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order PHA the potential is determined by solutions to Painleve IV (PIV) and Painleve V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
Area law violations in a supersymmetric model
Huijse, Liza; Swingle, Brian
2013-01-01
We study the structure of entanglement in a supersymmetric lattice model of fermions on certain types of decorated graphs with quenched disorder. In particular, we construct models with controllable ground-state degeneracy protected by supersymmetry and the choice of Hilbert space. We show that in certain special limits, these degenerate ground states are associated with local impurities and that there exists a basis of the ground-state manifold in which every basis element satisfies a boundary law for entanglement entropy. On the other hand, by considering incoherent mixtures or coherent superpositions of these localized ground states, we can find regions that violate the boundary law for entanglement entropy over a wide range of length scales. More generally, we discuss various criteria for constructing violations of the boundary law for entanglement entropy and discuss possible relations of our work to recent holographic studies.
SU(2|2) supersymmetric mechanics
Ivanov, Evgeny; Sidorov, Stepan
2016-01-01
We introduce a new kind of non-relativistic ${\\cal N}{=}\\,8$ supersymmetric mechanics, associated with worldline realizations of the supergroup $SU(2|2)$ treated as a deformation of flat ${\\cal N}{=}\\,8$, $d{=}1$ supersymmetry. Various worldline $SU(2|2)$ superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell $SU(2|2)$ multiplets $({\\bf 3,8,5})$, $({\\bf 4,8,4})$ and $({\\bf 5,8,3})$, we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group $OSp(4^*|4)$ in the conformal cases. For the simplest $({\\bf 5, 8, 3})$ model the quantization is performed.
Supersymmetric Wilson loops at two loops
Bassetto, Antonio; Pucci, Fabrizio; Seminara, Domenico
2008-01-01
We study the quantum properties of certain BPS Wilson loops in ${\\cal N}=4$ supersymmetric Yang-Mills theory. They belong to a general family, introduced recently, in which the addition of particular scalar couplings endows generic loops on $S^3$ with a fraction of supersymmetry. When restricted to $S^2$, their quantum average has been further conjectured to be exactly computed by the matrix model governing the zero-instanton sector of YM$_2$ on the sphere. We perform a complete two-loop analysis on a class of cusped Wilson loops lying on a two-dimensional sphere, finding perfect agreement with the conjecture. The perturbative computation reproduces the matrix-model expectation through a highly non-trivial interplay between ladder diagrams and self-energies/vertex contributions, suggesting the existence of a localization procedure.
Effective Action of Softly Broken Supersymmetric Theories
Nibbelink, S G; Nibbelink, Stefan Groot; Nyawelo, Tino S.
2007-01-01
We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions are parameterized using spurion insertions. We comment on the uniqueness of this parameterization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To preform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to non-commutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kaehler potential.
SU(2|2) supersymmetric mechanics
Energy Technology Data Exchange (ETDEWEB)
Ivanov, Evgeny [Joint Institute for Nuclear Research,Dubna, Moscow Region, 141980 (Russian Federation); Lechtenfeld, Olaf [Institut für Theoretische Physik and Riemann Center for Geometry and Physics,Leibniz Universität Hannover,Appelstraße 2, 30167 Hannover (Germany); Sidorov, Stepan [Joint Institute for Nuclear Research,Dubna, Moscow Region, 141980 (Russian Federation)
2016-11-07
We introduce a new kind of non-relativistic N= 8 supersymmetric mechanics, associated with worldline realizations of the supergroup SU(2|2) treated as a deformation of flat N= 8, d=1 supersymmetry. Various worldline SU(2|2) superspaces are constructed as coset manifolds of this supergroup, and the corresponding superfield techniques are developed. For the off-shell SU(2|2) multiplets (3,8,5), (4,8,4) and (5,8,3), we construct and analyze the most general superfield and component actions. Common features are mass oscillator-type terms proportional to the deformation parameter and a trigonometric realization of the superconformal group OSp(4{sup ∗}|4) in the conformal cases. For the simplest (5,8,3) model the quantization is performed.
Nonlinear Schrödinger equation from generalized exact uncertainty principle
Rudnicki, Łukasz
2016-09-01
Inspired by the generalized uncertainty principle, which adds gravitational effects to the standard description of quantum uncertainty, we extend the exact uncertainty principle approach by Hall and Reginatto (2002 J. Phys. A: Math. Gen. 35 3289), and obtain a (quasi)nonlinear Schrödinger equation. This quantum evolution equation of unusual form, enjoys several desired properties like separation of non-interacting subsystems or plane-wave solutions for free particles. Starting with the harmonic oscillator example, we show that every solution of this equation respects the gravitationally induced minimal position uncertainty proportional to the Planck length. Quite surprisingly, our result successfully merges the core of classical physics with non-relativistic quantum mechanics in its extremal form. We predict that the commonly accepted phenomenon, namely a modification of a free-particle dispersion relation due to quantum gravity might not occur in reality.
Generalized projective synchronization in time-delayed systems: nonlinear observer approach.
Ghosh, Dibakar
2009-03-01
In this paper, we consider the projective-anticipating, projective, and projective-lag synchronization in a unified coupled time-delay system via nonlinear observer design. A new sufficient condition for generalized projective synchronization is derived analytically with the help of Krasovskii-Lyapunov theory for constant and variable time-delay systems. The analytical treatment can give stable synchronization (anticipatory and lag) for a large class of time-delayed systems in which the response system's trajectory is forced to have an amplitude proportional to the drive system. The constant of proportionality is determined by the control law, not by the initial conditions. The proposed technique has been applied to synchronize Ikeda and prototype models by numerical simulation.
Han, Qun; Xu, Wei; Sun, Jian-Qiao
2016-09-01
The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.
Institute of Scientific and Technical Information of China (English)
ZHANG Suying; DENG Zichen
2005-01-01
Based on Magnus or Fer expansion for solving linear differential equation and operator semi-group theory, Lie group integration methods for general nonlinear dynamic equation are studied. Approximate schemes of Magnus type of 4th, 6th and 8th order are constructed which involve only 1, 4 and 10 different commutators, and the time-symmetry properties of the schemes are proved. In the meantime, the integration methods based on Fer expansion are presented. Then by connecting the Fer expansion methods with Magnus expansion methods some techniques are given to simplify the construction of Fer expansion methods. Furthermore time-symmetric integrators of Fer type are constructed. These methods belong to the category of geometric integration methods and can preserve many qualitative properties of the original dynamic system.
Directory of Open Access Journals (Sweden)
Christopher Heine
2014-08-01
Full Text Available A detailed description of the rubber parts’ properties is gaining in importance in the current simulation models of multi-body simulation. One application example is a multi-body simulation of the washing machine movement. Inside the washing machine, there are different force transmission elements, which consist completely or partly of rubber. Rubber parts or, generally, elastomers usually have amplitude-dependant and frequency-dependent force transmission properties. Rheological models are used to describe these properties. A method for characterization of the amplitude and frequency dependence of such a rheological model is presented within this paper. Within this method, the used rheological model can be reduced or expanded in order to illustrate various non-linear effects. An original result is given with the automated parameter identification. It is fully implemented in Matlab. Such identified rheological models are intended for subsequent implementation in a multi-body model. This allows a significant enhancement of the overall model quality.
Generalized nonlinear models applied to the prediction of basal area and volume of Eucalyptus sp
Directory of Open Access Journals (Sweden)
Samuel de Pádua Chaves e Carvalho
2011-12-01
Full Text Available This paper aims to propose the use of generalized nonlinear models for prediction of basal area growth and yield of total volume of the hybrid Eucalyptus urocamaldulensis, in a stand situation in a central region in state of Minas Gerais. The used methodology allows to work with data in its original form without the necessity of transformation of variables, and generate highly accurate models. To evaluate the fitting quality, it was proposed the Bayesian information criterion, of the Akaike, and test the maximum likelihood, beyond the standard error of estimate, and residual graphics. The models were used with a good performance, highly accurate and parsimonious estimates of the variables proposed, with errors reduced to 12% for basal area and 4% for prediction of the volume.
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The formulations of the finite-field approach to calculate the linear and non-linear optical coefficients mi, aij, bijk and gijkl of a molecular system with different symmetries have been deduced and summarized. The possible choices of the energy sets of the 48 frequent point groups have been optimized and categorized into 11 classes. With the restriction of symmetry operators, a minimum of 9, no more than 21 energy points have to be calculated in order to determine the coefficients, except in the case of the first class to which C1 point group belongs and in which the 34 non-relative energy points selected in our uniform and general scheme are all needed. The symmetric operators that cause some of the tensor components to vanish have been demonstrated as well.
Soliton and similarity solutions of N=2,4 supersymmetric equations
Delisle, Laurent
2012-01-01
We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg-de Vries and modified KdV equations. We give new representations of the $\\tau$-functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
Soliton and Similarity Solutions of Ν = 2, 4 Supersymmetric Equations
Directory of Open Access Journals (Sweden)
Laurent Delisle
2012-08-01
Full Text Available We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.
A Nonlinear Coupled-Mode System for Water Waves over a General Bathymetry
Athanassoulis, G. A.; Belibassakis, K. A.
2003-04-01
In the present work we consider the problem of non-linear gravity waves propagating over a general bathymetry. The simpler two dimensional problem (one horizontal dimension) is first examined. An essential feature of this problem is that the wave field is not spatially periodic. Extra difficulties are introduced by the fact that we wish to drop the assumptions of smallness of the free-surface and bottom slope. The interaction of free-surface gravity waves with uneven bottom topography requires, in principle, the solution of a complicated nonlinear boundary value problem. Under the assumptions of incompressibility and irrotationality, the problem of evolution of water waves, over a variable bathymetry region, admits of at least two different varia-tional formulations: A Hamiltonian one, proposed by Petrov (1964) and exploited further by Zakharov (1968) and various other authors thenceforth, and an unconstrained one, proposed by Luke (1967). Our main concern herewith is to develop a non-linear theory for the case of a smooth, generally shaped bathymetry, without imposing any mild-slope type assumptions neither on the free-surface nor on the bottom boundary. The present development is based on Luke's variational principle, in which the admissible fields are free of essential conditions, except, of course, for the smoothness and completeness (compatibility) prerequisites. The vertical structure of the wave field is exactly represented by means of a modal-type series expansion of the wave potential (Athanassoulis and Belibassakis 2000). This series expansion contains the usual propagating and evanescent modes, plus two additional modes, called the free-surface mode and the sloping-bottom mode, introduced in order to consistently treat the non-vertical end-conditions at the free-surface and the bottom boundaries. A similar technique has been successfully applied to the solution of the linearised (Athanassoulis and Belibassakis 1999) and the second-order (Belibassakis and
Supersymmetric dark matter above the W mass
Griest, Kim; Kamionkowski, Marc; Turner, Michael S.
1989-01-01
The cosmological consequences are studied for the minimal supersymmetric extension of the standard model in the case that the neutralino is heavier than W. The cross section was calculated for annihilation of heavy neutralinos into final states containing gauge and Higgs bosons (XX yields WW, ZZ, HH, HW, HZ), where X is the lightest, nth neutralino and the results are compared with the results with those previously obtained for annihilation into fermions to find the relic cosmological abundance for the most general neutralino. The new channels are particularly important for the Higgsino-like and mixed-state neutralinos, but are sub-dominant (to the fermion-antifermion annihilation channels) in the case that the neutralino is mostly a gaugino. The effect of the top quark mass is also considered. Using these cross sections and the cosmological constraint omega(sub X)h squared is less than or approximately 1, the entire range of cosmologically acceptable supersymmetric parameter space is mapped and a very general bound on the neutralino mass is discovered. For a top quark mass of less than 180 GeV, neutralinos heavier than 3200 GeV are cosmologically inconsistent, and if the top quark mass is less than 120 GeV, the bound is lowered to 2600 GeV. Neutralino states that are mostly gaugino are constrained to be lighter than 550 GeV. It is found that a heavy neutralino that contributes omega(sub X) is approximately 1 arises for a very wide range of model parameters and makes, therefore, a very natural and attractive dark matter candidate.
Geloun, Joseph Ben; Scholtz, Frederik G
2009-01-01
The N=1 supersymmetric invariant Landau problem is constructed and solved. By considering Landau level projections remaining non trivial under N=1 supersymmetry transformations, the algebraic structures of the N=1 supersymmetric covariant non(anti)commutative superplane analogue of the ordinary N=0 noncommutative Moyal-Voros plane are identified.
Rahman, T.
2009-01-01
In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is oft
Directory of Open Access Journals (Sweden)
Pongsakorn Sunthrayuth
2012-01-01
Full Text Available We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the purposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results. The results obtained in this paper extend the recent ones announced by many others.
Supersymmetric Adler Functions and Holography
Iwanaga, Masaya; Sakai, Tadakatsu
2016-01-01
We perform several tests on a recent proposal by Shifman and Stepanyantz for an exact expression for the current correlation functions in supersymmetric gauge theories. We clarify the meaning of the relation in superconformal theories. In particular we show that it automatically follows from known relations between the current correlation functions and anomalies. It therefore also automatically matches between different dual realizations of the same superconformal theory. We use holographic examples as well as calculations in free theories to show that the proposed relation fails in theories with mass terms.
Electroweak breaking in supersymmetric models
Ibáñez, L E
1992-01-01
We discuss the mechanism for electroweak symmetry breaking in supersymmetric versions of the standard model. After briefly reviewing the possible sources of supersymmetry breaking, we show how the required pattern of symmetry breaking can automatically result from the structure of quantum corrections in the theory. We demonstrate that this radiative breaking mechanism works well for a heavy top quark and can be combined in unified versions of the theory with excellent predictions for the running couplings of the model. (To be published in ``Perspectives in Higgs Physics'', G. Kane editor.)
Supersymmetric photonic signals at LEP
López, J; Zichichi, Antonino
1996-01-01
We explore and contrast the single-photon and diphoton signals expected at LEP 2, that arise from neutralino-gravitino (e^+ e^- -> chi + gravitino -> gamma + E_miss) and neutralino-neutralino (e^+ e^- -> chi + chi -> gamma + gamma + E_miss) production in supersymmetric models with a light gravitino. LEP 1 limits imply that one may observe either one, but not both, of these signals at LEP 2, depending on the values of the neutralino and gravitino masses: single-photons for m_chi > Mz and m_gravitino < 3 x 10^-5 eV; diphotons for m_chi < Mz and all allowed values of m_gravitino.
A nonlinear generalized continuum approach for electro-elasticity including scale effects
Skatulla, S.; Arockiarajan, A.; Sansour, C.
2009-01-01
Materials characterized by an electro-mechanically coupled behaviour fall into the category of so-called smart materials. In particular, electro-active polymers (EAP) recently attracted much interest, because, upon electrical loading, EAP exhibit a large amount of deformation while sustaining large forces. This property can be utilized for actuators in electro-mechanical systems, artificial muscles and so forth. When it comes to smaller structures, it is a well-known fact that the mechanical response deviates from the prediction of classical mechanics theory. These scale effects are due to the fact that the size of the microscopic material constituents of such structures cannot be considered to be negligible small anymore compared to the structure's overall dimensions. In this context so-called generalized continuum formulations have been proven to account for the micro-structural influence to the macroscopic material response. Here, we want to adopt a strain gradient approach based on a generalized continuum framework [Sansour, C., 1998. A unified concept of elastic-viscoplastic Cosserat and micromorphic continua. J. Phys. IV Proc. 8, 341-348; Sansour, C., Skatulla, S., 2007. A higher gradient formulation and meshfree-based computation for elastic rock. Geomech. Geoeng. 2, 3-15] and extend it to also encompass the electro-mechanically coupled behaviour of EAP. The approach introduces new strain and stress measures which lead to the formulation of a corresponding generalized variational principle. The theory is completed by Dirichlet boundary conditions for the displacement field and its derivatives normal to the boundary as well as the electric potential. The basic idea behind this generalized continuum theory is the consideration of a micro- and a macro-space which together span the generalized space. As all quantities are defined in this generalized space, also the constitutive law, which is in this work conventional electro-mechanically coupled nonlinear
Supersymmetric features of Maxwell fisheye lens
Rosu, H C; Wolf, K B; Obregón, O; Rosu, Haret C; Reyes, M; Wolf, K B; Obregon, O
1995-01-01
Following L\\'evai, we apply a Natanzon-type supersymmetric analysis to the Maxwell fisheye wave problem at zero energy. Working in the so-called R_{0}=0 sector, we obtain the corresponding superpartner (fermionic) fisheye scattering potential within the standard one-dimensional (radial) supersymmetric procedure.
N=1 Supersymmetric Boundary Bootstrap
Toth, G Z
2004-01-01
We investigate the boundary bootstrap programme for finding exact reflection matrices of integrable boundary quantum field theories with N=1 boundary supersymmetry. The bulk S-matrix and the reflection matrix are assumed to take the form S=S_1S_0, R=R_1R_0, where S_0 and R_0 are the S-matrix and reflection matrix of some integrable non-supersymmetric boundary theory that is assumed to be known, and S_1 and R_1 describe the mixing of supersymmetric indices. Under the assumption that the bulk particles transform in the kink and boson/fermion representations and the ground state is a singlet we present rules by which the supersymmetry representations and reflection factors for excited boundary bound states can be determined. We apply these rules to the boundary sine-Gordon model, to the boundary a_2^(1) and a_4^(1) affine Toda field theories, to the boundary sinh-Gordon model and to the free particle.
A Maximally Supersymmetric Kondo Model
Energy Technology Data Exchange (ETDEWEB)
Harrison, Sarah; Kachru, Shamit; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2012-02-17
We study the maximally supersymmetric Kondo model obtained by adding a fermionic impurity to N = 4 supersymmetric Yang-Mills theory. While the original Kondo problem describes a defect interacting with a free Fermi liquid of itinerant electrons, here the ambient theory is an interacting CFT, and this introduces qualitatively new features into the system. The model arises in string theory by considering the intersection of a stack of M D5-branes with a stack of N D3-branes, at a point in the D3 worldvolume. We analyze the theory holographically, and propose a dictionary between the Kondo problem and antisymmetric Wilson loops in N = 4 SYM. We perform an explicit calculation of the D5 fluctuations in the D3 geometry and determine the spectrum of defect operators. This establishes the stability of the Kondo fixed point together with its basic thermodynamic properties. Known supergravity solutions for Wilson loops allow us to go beyond the probe approximation: the D5s disappear and are replaced by three-form flux piercing a new topologically non-trivial S3 in the corrected geometry. This describes the Kondo model in terms of a geometric transition. A dual matrix model reflects the basic properties of the corrected gravity solution in its eigenvalue distribution.
The supersymmetric Higgs boson with flavoured A-terms
Directory of Open Access Journals (Sweden)
Andrea Brignole
2015-09-01
Full Text Available We consider a supersymmetric scenario with large flavour violating A-terms in the stop/scharm sector and study their impact on the Higgs mass, the electroweak ρ parameter and the effective Higgs couplings to gluons, photons and charm quarks. For each observable we present explicit analytical expressions which exhibit the relevant parametric dependences, both in the general case and in specific limits. We find significant effects and comment on phenomenological implications for the LHC and future colliders.
An introduction to supersymmetric field theories in curved space
Dumitrescu, Thomas T
2016-01-01
In this review, we give a pedagogical introduction to a systematic framework for constructing and analyzing supersymmetric field theories on curved spacetime manifolds. The framework is based on the use of off-shell supergravity background fields. We present the general principles, which broadly apply to theories with different amounts of supersymmetry in diverse dimensions, as well as specific applications to N=1 theories in four dimensions and their three-dimensional cousins with N=2 supersymmetry.
Energy Technology Data Exchange (ETDEWEB)
Chen Yong E-mail: chenyong@dlut.edu.cn; Li Biao E-mail: libiao@dlut.edu.cn
2004-03-01
Applying the improved generalized method, which is a direct and unified algebraic method for constructing multiple travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the KdV-type equations and KdV-Burgers-type equations with nonlinear terms of any order. As a result, we can not only successfully recover the previously known travelling wave solutions found by existing various tanh methods and other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions.
Burg, van der Eeke; Leeuw, de Jan
1988-01-01
In this paper we discuss the estimation of mean and standard errors of the eigenvalues and category quantifications in generalized non-linear canonical correlation analysis (OVERALS). Starting points are the delta method equations, but the jack-knife and bootstrap are used to provide finite differen
Institute of Scientific and Technical Information of China (English)
张卫国
2003-01-01
In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.
Directory of Open Access Journals (Sweden)
Zhen Chen
2016-01-01
Full Text Available Accelerated degradation test (ADT has been widely used to assess highly reliable products’ lifetime. To conduct an ADT, an appropriate degradation model and test plan should be determined in advance. Although many historical studies have proposed quite a few models, there is still room for improvement. Hence we propose a Nonlinear Generalized Wiener Process (NGWP model with consideration of the effects of stress level, product-to-product variability, and measurement errors for a higher estimation accuracy and a wider range of use. Then under the constraints of sample size, test duration, and test cost, the plans of constant-stress ADT (CSADT with multiple stress levels based on the NGWP are designed by minimizing the asymptotic variance of the reliability estimation of the products under normal operation conditions. An optimization algorithm is developed to determine the optimal stress levels, the number of units allocated to each level, inspection frequency, and measurement times simultaneously. In addition, a comparison based on degradation data of LEDs is made to show better goodness-of-fit of the NGWP than that of other models. Finally, optimal two-level and three-level CSADT plans under various constraints and a detailed sensitivity analysis are demonstrated through examples in this paper.
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
Energy Technology Data Exchange (ETDEWEB)
Norton, S.J. [Oak Ridge National Lab., TN (United States)
1997-04-01
Iterative approaches to the nonlinear inverse transport problem are described, which give rise to the structure that best predicts a set of transport observations. Such methods are based on minimizing a global error functional measuring the discrepancy between predicted and observed transport data. Required for this minimization is the functional gradient (Frechet derivative) of the global error evaluated with respect to a set of unknown material parameters (specifying boundary locations, scattering cross sections, etc.) which are to be determined. It is shown how this functional gradient is obtained from numerical solutions to the forward and adjoint transport problems computed once per iteration. This approach is not only far more efficient, but also more accurate, than a finite-difference method for computing the gradient of the global error. The general technique can be applied to inverse-transport problems of all descriptions, provided only that solutions to the forward and adjoint problems can be found numerically. As an illustration, two inverse problems are treated: the reconstruction of an anisotropic scattering function in a one-dimensional homogeneous slab and the two-dimensional imaging of a spatially-varying scattering cross section.
Estimation of land surface evaporation using a generalized nonlinear complementary relationship
Zhang, Lu; Cheng, Lei; Brutsaert, Wilfried
2017-02-01
Evaporation is a key component of the hydrological cycle and affects regional water resources. Although the physics of evaporation is well understood, its estimation in practice remains a challenge. Among available methods for estimating it, the complementary principle of Bouchet has the potential to provide a practical tool for regional water resources assessment. In this study, the generalized nonlinear formulation of this principle by Brutsaert (2015) was tested against evaporation measurements from four flux stations in Australia under different climatic and vegetation conditions. The method was implemented using meteorological data and Class A pan evaporation measurements. After calibration the estimated daily evaporation values were in good agreement with flux station measurements with a mean correlation coefficient of 0.83 and a bias of 4% on average. More accurate estimates of daily evaporation were obtained when the evaporative demand or apparent potential evaporation was determined from the Penman equation instead of from pan evaporation. The obtained parameter values were found to lie well within the ranges of reported values in the literature. Advantages of the method are that only routine meteorological data are required and that it can be used to estimate long-term evaporation trends.
Institute of Scientific and Technical Information of China (English)
ZHENGChun-Long; ZHANGJie-Fang; CHENLi-Qun
2003-01-01
Starting from a special Baecklund transform and a variable separation approach, a quite general variable separation solution of the generalized ( 2 + 1 )-dimensional perturbed nonlinear Schroedinger system is obtained. In addition to the single-valued localized coherent soliron excitations like dromions, breathers, instantons, peakons, and previously revealed chaotic localized solution, a new type of multi-valued (folded) localized excitation is derived by introducing some appropriate lower-dimensional multiple valued functions.
Detection of supersymmetric dark matter.
Xinrui, Hou; Li, Xueqian; Xinhe, Meng; Zhijian, Tao
1997-10-01
A re-analysis of a heavy charged particle production event observed at the cloudy chamber of the Yunnan Cosmic Ray Station (YCRS) in 1972 indicates that the mysterious heavy particle may be identified as a supersymmetric (SUSY) particle produced by bombarding a neutral SUSY cosmic ray particle on a proton. Based on the assumption, following literature studies that the neutral SUSY particle which constitutes the main fraction of the cold dark matter is a scalar neutrino (sneutrino) or neutralino (photino), the authors evaluate the flux of such SUSY particles which gain sufficient energies via elastic scattering with charged cosmic particles on the way to an Earth detector and the capture rates in both the sneutrino and photino cases respectively. The errors appearing in the study are briefly discussed and this work may provide a basis of designing cosmic ray detectors to search for SUSY particles.
Supersymmetric Sneutrino-Higgs Inflation
Deen, Rehan; Purves, Austin
2016-01-01
It is shown that in the phenomenologically realistic supersymmetric $B-L$ MSSM theory, a linear combination of the neutral, up Higgs field with the third family left-and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order $10^{13}~\\mathrm{GeV}$, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a "robust" set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements.
Supersymmetric unification at the millennium
Indian Academy of Sciences (India)
Charanjit S Aulakh
2000-07-01
We argue that the discovery of neutrino mass effects at super-Kamiokande implies a clear logical chain leading from the Standard Model, through the MSSM and the recently developed minimal left right supersymmetric models with a renormalizable see-saw mechanism for neutrino mass, to left right symmetric SUSY GUTS: in particular, SO(10) and SU(2)× SU(2) × SU(4). The progress in constructing such GUTS explicitly is reviewed and their testability/falsiﬁability by lepton ﬂavour violation and proton decay measurements emphasized. SUSY violations of the survival principle and the interplay between third generation Yukawa coupling uniﬁcation and the structurally stable IR attractive features of the RG ﬂow in SUSY GUTS are also discussed.
Supersymmetric Sneutrino-Higgs inflation
Deen, Rehan; Ovrut, Burt A.; Purves, Austin
2016-11-01
It is shown that in the phenomenologically realistic supersymmetric B - L MSSM theory, a linear combination of the neutral, up Higgs field with the third family left- and right-handed sneutrinos can play the role of the cosmological inflaton. Assuming that supersymmetry is softly broken at a mass scale of order 1013 GeV, the potential energy associated with this field allows for 60 e-foldings of inflation with the cosmological parameters being consistent with all Planck2015 data. The theory does not require any non-standard coupling to gravity and the physical fields are all sub-Planckian during the inflationary epoch. It will be shown that there is a "robust" set of initial conditions which, in addition to satisfying the Planck data, simultaneously are consistent with all present LHC phenomenological requirements.
Perturbation Theory in Supersymmetric QED: Infrared Divergences and Gauge Invariance
Dine, Michael; Haber, Howard E; Haskins, Laurel Stephenson
2016-01-01
We study some aspects of perturbation theory in $N=1$ supersymmetric abelian gauge theories with massive charged matter. In general gauges, infrared (IR) divergences and nonlocal behavior arise in 1PI diagrams, associated with a $1/k^4$ term in the propagator for the vector superfield. We examine this structure in supersymmetric QED. The IR divergences are gauge-dependent and must cancel in physical quantities like the electron pole mass. We demonstrate that cancellation takes place in a nontrivial way, amounting to a reorganization of the perturbative series from powers of $e^2$ to powers of $e$. We also show how these complications are avoided in cases where a Wilsonian effective action can be defined.
Supersymmetric quantum spin chains and classical integrable systems
Tsuboi, Zengo; Zabrodin, Anton; Zotov, Andrei
2015-05-01
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y( gl( N| M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.
Supersymmetric quantum spin chains and classical integrable systems
Tsuboi, Zengo; Zotov, Andrei
2014-01-01
For integrable inhomogeneous supersymmetric spin chains (generalized graded magnets) constructed employing Y(gl(N|M))-invariant R-matrices in finite-dimensional representations we introduce the master T-operator which is a sort of generating function for the family of commuting quantum transfer matrices. Any eigenvalue of the master T-operator is the tau-function of the classical mKP hierarchy. It is a polynomial in the spectral parameter which is identified with the 0-th time of the hierarchy. This implies a remarkable relation between the quantum supersymmetric spin chains and classical many-body integrable systems of particles of the Ruijsenaars-Schneider type. As an outcome, we obtain a system of algebraic equations for the spectrum of the spin chain Hamiltonians.
Cluster-like coordinates in supersymmetric quantum field theory.
Neitzke, Andrew
2014-07-08
Recently it has become apparent that N = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.
Modified Lagrangian and Least Root Approaches for General Nonlinear Optimization Problems
Institute of Scientific and Technical Information of China (English)
W. Oettli; X.Q. Yang
2002-01-01
In this paper we study nonlinear Lagrangian methods for optimization problems with side constraints.Nonlinear Lagrangian dual problems are introduced and their relations with the original problem are established.Moreover, a least root approach is investigated for these optimization problems.
Supersymmetric counterterms from new minimal supergravity
Assel, Benjamin; Martelli, Dario
2014-01-01
We present a systematic classification of counterterms of four-dimensional supersymmetric field theories on curved space, obtained as the rigid limit of new minimal supergravity. These are supergravity invariants constructed using the field theory background fields. We demonstrate that if the background preserves two supercharges of opposite chirality, then all dimensionless counterterms vanish. This implies that a supersymmetric renormalisation scheme is free of ambiguities. When only one Euclidean supercharge is preserved, we describe the ambiguities that appear in supersymmetric observables, in particular in the dependence on marginal couplings.
Phenomenology of non-minimal supersymmetric models at linear colliders
Energy Technology Data Exchange (ETDEWEB)
Porto, Stefano
2015-06-15
The focus of this thesis is on the phenomenology of several non-minimal supersymmetric models in the context of future linear colliders (LCs). Extensions of the minimal supersymmetric Standard Model (MSSM) may accommodate the observed Higgs boson mass at about 125 GeV in a more natural way than the MSSM, with a richer phenomenology. We consider both F-term extensions of the MSSM, as for instance the non-minimal supersymmetric Standard Model (NMSSM), as well as D-terms extensions arising at low energies from gauge extended supersymmetric models. The NMSSM offers a solution to the μ-problem with an additional gauge singlet supermultiplet. The enlarged neutralino sector of the NMSSM can be accurately studied at a LC and used to distinguish the model from the MSSM. We show that exploiting the power of the polarised beams of a LC can be used to reconstruct the neutralino and chargino sector and eventually distinguish the NMSSM even considering challenging scenarios that resemble the MSSM. Non-decoupling D-terms extensions of the MSSM can raise the tree-level Higgs mass with respect to the MSSM. This is done through additional contributions to the Higgs quartic potential, effectively generated by an extended gauge group. We study how this can happen and we show how these additional non-decoupling D-terms affect the SM-like Higgs boson couplings to fermions and gauge bosons. We estimate how the deviations from the SM couplings can be spotted at the Large Hadron Collider (LHC) and at the International Linear Collider (ILC), showing how the ILC would be suitable for the model identication. Since our results prove that a linear collider is a fundamental machine for studying supersymmetry phenomenology at a high level of precision, we argue that also a thorough comprehension of the physics at the interaction point (IP) of a LC is needed. Therefore, we finally consider the possibility of observing intense electromagnetic field effects and nonlinear quantum electrodynamics
Tamma, Kumar K.; Railkar, Sudhir B.
1987-01-01
The present paper describes the development of a new hybrid computational approach for applicability for nonlinear/linear thermal structural analysis. The proposed transfinite element approach is a hybrid scheme as it combines the modeling versatility of contemporary finite elements in conjunction with transform methods and the classical Bubnov-Galerkin schemes. Applicability of the proposed formulations for nonlinear analysis is also developed. Several test cases are presented to include nonlinear/linear unified thermal-stress and thermal-stress wave propagations. Comparative results validate the fundamental capablities of the proposed hybrid transfinite element methodology.
Das, Debottam; Ellwanger, Ulrich; Teixeira, Ana M.
2012-03-01
The code NMSDECAY allows to compute widths and branching ratios of sparticle decays in the Next-to-Minimal Supersymmetric Standard Model. It is based on a generalization of SDECAY, to include the extended Higgs and neutralino sectors of the NMSSM. Slepton 3-body decays, possibly relevant in the case of a singlino-like lightest supersymmetric particle, have been added. NMSDECAY will be part of the NMSSMTools package, which computes Higgs, sparticle masses and Higgs decays in the NMSSM. Program summaryProgram title: NMSDECAY Catalogue identifier: AELC_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELC_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 188 177 No. of bytes in distributed program, including test data, etc.: 1 896 478 Distribution format: tar.gz Programming language: FORTRAN77 Computer: All supporting g77, gfortran, ifort Operating system: All supporting g77, gfortran, ifort Classification: 11.1 External routines: Routines in the NMSSMTools package: At least one of the routines in the directory main (e.g. nmhdecay.f), all routines in the directory sources. (All software is included in the distribution package.) Nature of problem: Calculation of all decay widths and decay branching fractions of all particles in the Next-to-Minimal Supersymmetric Standard Model. Solution method: Suitable generalization of the code SDECAY [1] including the extended Higgs and neutralino sector of the Next-to-Minimal Supersymmetric Standard Model, and slepton 3-body decays. Additional comments: NMSDECAY is interfaced with NMSSMTools, available on the web page http://www.th.u-psud.fr/NMHDECAY/nmssmtools.html. Running time: On an Intel Core i7 with 2.8 GHZ: about 2 seconds per point in parameter space, if all flags flagqcd, flagmulti and flagloop are switched on.
Supersymmetric partition functions and the three-dimensional A-twist arXiv
Closset, Cyril; Willett, Brian
We study three-dimensional $\\mathcal{N}=2$ supersymmetric gauge theories on $\\mathcal{M}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, $\\Sigma_g$. We compute the $\\mathcal{M}_{g,p}$ supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called "fibering operator" on $S^2 \\times S^1$ with a topological twist. More generally, we show that the 3d $\\mathcal{N}=2$ supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on $\\mathcal{M}_{g,p}$ are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimens...
Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model
Wang, Lei; Jiang, Dong-Yang; Qi, Feng-Hua; Shi, Yu-Ying; Zhao, Yin-Chuan
2017-01-01
Under investigation in this paper is a generalized mixed nonlinear Schrödinger equation (GMNLSE) which arises in several physical areas including the quantum field theory, weakly nonlinear dispersive water waves, and nonlinear optics. The linear stability analysis is performed and the instability zones as well as the modulational instability gain are obtained and discussed. Higher-order rogue waves (RWs) in terms of the determinants for the GMNLSE model are constructed by the N-fold Darboux transformation. Several patterns of the RWs are illustrated, such as the fundamental pattern, triangular pattern, circular pattern, pentagon pattern, circular-triangular pattern, and circular-fundamental pattern. Effects of the nonlinear parameters on the RWs are discussed. It is found that the nonlinear terms affect the widths and velocities of the RWs, although the amplitudes of these waves remain unchanged. The semirational RW solution, which is a combination of rational and exponential functions, is derived to describe the interaction between the RW and multi-breather.
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Hayashi, T; Okuyama, K; Suzuki, H; Hayashi, Takuya; Ohshima, Yoshihisa; Okuyama, Kiyoshi; Suzuki, Hiroshi
1998-01-01
We formulate a manifestly supersymmetric gauge-covariant regularization of supersymmetric chiral gauge theories. In our scheme, the effective action in the superfield background-field method above one-loop is always supersymmetric and gauge invariant. The gauge anomaly has the covariant form and can emerge only in one-loop diagrams with all the external lines are the background gauge superfield. We also present several illustrative applications in the one-loop approximation: The self-energy part of the chiral multiplet and the gauge multiplet; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and the anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
The Minimal Supersymmetric Fat Higgs Model
Harnik, R; Larson, D T; Murayama, H; Harnik, Roni; Kribs, Graham D.; Larson, Daniel T.; Murayama, Hitoshi
2003-01-01
We present a calculable supersymmetric theory of a composite ``fat'' Higgs boson. Electroweak symmetry is broken dynamically through a new gauge interaction that becomes strong at an intermediate scale. The Higgs mass can easily be 200-450 GeV along with the superpartner masses, solving the supersymmetric little hierarchy problem. We explicitly verify that the model is consistent with precision electroweak data without fine-tuning. Gauge coupling unification can be maintained despite the inherently strong dynamics involved in electroweak symmetry breaking. Supersymmetrizing the Standard Model therefore does not imply a light Higgs mass, contrary to the lore in the literature. The Higgs sector of the minimal Fat Higgs model has a mass spectrum that is distinctly different from the Minimal Supersymmetric Standard Model.
Bosonization of supersymmetric KdV equation
Energy Technology Data Exchange (ETDEWEB)
Gao Xiaonan [Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 (China); Lou, S.Y., E-mail: sylou@sjtu.edu.cn [Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 (China); Faculty of Science, Ningbo University, Ningbo, 315211 (China); School of Mathematics, Fudan University, Shanghai, 200433 (China)
2012-01-16
Bosonization approach to the classical supersymmetric systems is presented. By introducing the multi-fermionic parameters in the expansions of the superfields, the N=1 supersymmetric KdV (sKdV) system is transformed to a system of coupled bosonic equations. The method can be applied to any fermionic systems. By solving the coupled bosonic equations, some novel types of exact solutions can be explicitly obtained. Especially, the richness of the localized excitations of the supersymmetric integrable system is discovered. The rich multi-soliton solutions obtained here have not yet been obtained by using other methods. However, the traditional known multi-soliton solutions can also not be obtained by the bosonization approach of this Letter. Some open problems on the bosonization of the supersymmetric integrable models are proposed in the both classical and quantum levels.
Proton Decay in Minimal Supersymmetric SU(5)
Bajc, Borut; Perez, Pavel Fileviez; Senjanovic, Goran
2002-01-01
We systematically study proton decay in the minimal supersymmetric SU(5) grand unified theory. We find that although the available parameter space of soft masses and mixings is quite constrained, the theory is still in accord with experiment.
Bubbles of Nothing and Supersymmetric Compactifications
Blanco-Pillado, Jose J; Sousa, Kepa; Urrestilla, Jon
2016-01-01
We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such "topologically unobstructed" cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to $M_3 \\times S_1$ presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this dec...
Patterns of flavor signals in supersymmetric models
Energy Technology Data Exchange (ETDEWEB)
Goto, T. [KEK National High Energy Physics, Tsukuba (Japan)]|[Kyoto Univ. (Japan). YITP; Okada, Y. [KEK National High Energy Physics, Tsukuba (Japan)]|[Graduate Univ. for Advanced Studies, Tsukuba (Japan). Dept. of Particle and Nucelar Physics; Shindou, T. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)]|[International School for Advanced Studies, Trieste (Italy); Tanaka, M. [Osaka Univ., Toyonaka (Japan). Dept. of Physics
2007-11-15
Quark and lepton flavor signals are studied in four supersymmetric models, namely the minimal supergravity model, the minimal supersymmetric standard model with right-handed neutrinos, SU(5) supersymmetric grand unified theory with right-handed neutrinos and the minimal supersymmetric standard model with U(2) flavor symmetry. We calculate b{yields}s(d) transition observables in B{sub d} and B{sub s} decays, taking the constraint from the B{sub s}- anti B{sub s} mixing recently observed at Tevatron into account. We also calculate lepton flavor violating processes {mu} {yields} e{gamma}, {tau} {yields} {mu}{gamma} and {tau} {yields} e{gamma} for the models with right-handed neutrinos. We investigate possibilities to distinguish the flavor structure of the supersymmetry breaking sector with use of patterns of various flavor signals which are expected to be measured in experiments such as MEG, LHCb and a future Super B Factory. (orig.)
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...
Das, A; Das, A; Wotzasek, C
1995-01-01
We study a supersymmetric 2-dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2\\vert1) formulate it on the superspace, and discuss its physical spectrum.
POSITIVE SOLUTIONS OF FULLY NONLINEAR ELLIPTIC EQUATIONS ON GENERAL BOUNDED DOMAINS
Institute of Scientific and Technical Information of China (English)
Li Meisheng; Bao Jiguang
2001-01-01
We prove the refined ABP maximum principle, comparison principle, and related existence and uniqueness theorem for the positive solutions of the Dirich let problems of second order fully nonlinear elliptic equations on arbitrary bounded domains.
National Research Council Canada - National Science Library
Naher, Hasibun; Abdullah, Farah Aini
2013-01-01
In this article, new (G′/G)-expansion method and new generalized (G′/G)-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations...
NEW EXACTLY SOLVABLE SUPERSYMMETRIC PERIODIC POTENTIALS
Institute of Scientific and Technical Information of China (English)
LIU KE-JIA; HE LI; ZHOU GUO-LI; WU YU-JIAO
2001-01-01
Using the formalism of supersymmetric quantum mechanics, we give an exact solution for a family of onedimensional periodic potentials, which are the supersymmetric partners of the potential proportional to the trigonometric function cos(2x) such that the Schrodinger equation for this potential is named the Mathieu equation mathematically.We show that the new potentials are distinctly different from their original ones. However, both have the same energy band structure. All the potentials obtained in this paper are free of singularities.
On the uniqueness of supersymmetric attractors
Directory of Open Access Journals (Sweden)
Taniya Mandal
2015-10-01
Full Text Available In this paper we discuss the uniqueness of supersymmetric attractors in four-dimensional N=2 supergravity theories coupled to n vector multiplets. We prove that for a given charge configuration the supersymmetry preserving axion free attractors are unique. We generalise the analysis to axionic attractors and state the conditions for uniqueness explicitly. We consider the example of a two-parameter model and find all solutions to the supersymmetric attractor equations and discuss their uniqueness.
(2+1)-dimensional supersymmetric integrable equations
Yan, Zhao-Wen; Tala; Chen, Fang; Liu, Tao-Ran; Han, Jing-Min
2017-09-01
By means of two different approaches, we construct the (2+1)-dimensional supersymmetric integrable equations based on the super Lie algebra osp(3/2). We relax the constraint condition of homogenous space of super Lie algebra osp(3/2) in the first approach. In another one, the technique of extending the dimension of the systems is used. Furthermore for the (2 + 1)-dimensional supersymmetric integrable equations, we also derive their Bäcklund transformations.
Neutral Supersymmetric Higgs Boson Searches
Energy Technology Data Exchange (ETDEWEB)
Robinson, Stephen Luke [Imperial College, London (United Kingdom)
2008-07-01
In some Supersymmetric extensions of the Standard Model, including the Minimal Supersymmetric Standard Model (MSSM), the coupling of Higgs bosons to b-quarks is enhanced. This enhancement makes the associated production of the Higgs with b-quarks an interesting search channel for the Higgs and Supersymmetry at D0. The identification of b-quarks, both online and offline, is essential to this search effort. This thesis describes the author's involvement in the development of both types of b-tagging and in the application of these techniques to the MSSM Higgs search. Work was carried out on the Level-3 trigger b-tagging algorithms. The impact parameter (IP) b-tagger was retuned and the effects of increased instantaneous luminosity on the tagger were studied. An extension of the IP-tagger to use the z-tracking information was developed. A new b-tagger using secondary vertices was developed and commissioned. A tool was developed to allow the use of large multi-run samples for trigger studies involving b-quarks. Offline, a neural network (NN) b-tagger was trained combining the existing offline lifetime based b-tagging tools. The efficiency and fake rate of the NN b-tagger were measured in data and MC. This b-tagger was internally reviewed and certified by the Collaboration and now provides the official b-tagging for all analyses using the Run IIa dataset at D0. A search was performed for neutral MSSM Higgs bosons decaying to a b{bar b} pair and produced in association with one or more b-quarks. Limits are set on the cross-section times the branching ratio for such a process. The limits were interpreted in various MSSM scenarios. This analysis uses the NN b-tagger and was the first to use this tool. The analysis also relies on triggers using the Level-3 IP b-tagging tool described previously. A likelihood discriminant was used to improve the analysis and a neural network was developed to cross-check this technique. The result of the analysis has been submitted to PRL
Lectures on Supersymmetric Yang-Mills Theory and Integrable Systems
D'Hoker, Eric; Phong, D. H.
Introduction Supersymmetry and the Standard Model Supersymmetry and Unification of Forces Supersymmetric Yang-Mills Dynamics Supersymmetric Yang-Mills in 4 Dimensions Supersymmetry Algebra Massless Particle Representations Massive Particle Representations Field Contents of Supersymmetric Field Theories N = 1 Supersymmetric Lagrangians N = 1 Superfield Methods Irreducible Superfields of N = 1 General N = 1 Susy Lagrangians via Superfields Renormalizable N = 2,4 Susy Lagrangians N = 2 Superfield Methods: Unconstrained Superspace N = 2 Superfield Methods: Harmonic/Analytic Superspaces Seiberg-Witten Theory Wilson Effective Couplings and Actions Holomorphicity and Nonrenormalization Low Energy Dynamics of N = 2 Super-Yang-Mills Particle and Field Contents Form of the N = 2 Low Energy Effective Lagrangian Physical Properties of the Prepotential Electric-Magnetic Duality Monodromy via Elliptic Curves for SU(2) Gauge Group Physical Interpretation of Singularities Hypergeometric Function Representation More General Gauge Groups, Hypermultiplets Model of Riemann Surfaces Identifying Seiberg-Witten and Riemann Surface Data SU(N) Gauge Algebras, Fundamental Hypermultiplets Classical Gauge Algebras, Fundamental Hypermultiplets Mechanical Integrable Systems Lax Pairs with Spectral Parameter-Spectral Curves The Toda Systems The Calogero-Moser Systems for SU(N) Relation between Calogero-Moser and Toda for SU(N) Relations with KdV and KP Systems Calogero-Moser Systems for General Lie Algebras Scaling of Calogero-Moser to Toda for General Lie Algebras Calogero-Moser Lax Pairs for General Lie Algebras Lax Pairs with Spectral Parameter for Classical Lie Algebras The General Ansatz Lax Pairs for Untwisted Calogero-Moser Systems Lax Pairs for Twisted Calogero-Moser Systems Scaling Limits of Lax Pairs Super-Yang-Mills and Calogero-Moser Systems Correspondence of Seiberg-Witten and Integrable Systems Calogero-Moser and Seiberg-Witten Theory for SU(N) Four Fundamental Theorems Partial
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of the ferromagnetic elastic medium, a nonlinear coupling theoretical modeling for a ferromagnetic thin shell is developed. All governing equations and boundary conditions for the ferromagnetic shell are obtained from the variational manipulations on the magnetic scalar potential, temperature and the elastic displacement related to the total energy functional. The multi-field couplings and geometrical nonlinearity of the ferromagnetic thin shell are taken into account in the modeling. The general modeling can be further deduced to existing models of the magneto-elasticity and the thermo-elasticity of a ferromagnetic shell and magneto-thermo-elasticity of a ferromagnetic plate, which axe coincident with the ones in literature.
Institute of Scientific and Technical Information of China (English)
Huang Xiujie; Zhang Jixun; Yang Ling; Yang Shikou; Wang Xingli
2016-01-01
The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range, the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.
The Supersymmetric origin of matter
Energy Technology Data Exchange (ETDEWEB)
Balazs, C.; /Argonne; Carena, M.; /Fermilab; Menon, A.; Morrissey, D.E.; Wagner, C.E.M.; /Argonne /Chicago U., EFI
2004-12-01
The Minimal Supersymmetric extension of the Standard Model (MSSM) can provide the correct neutralino relic abundance and baryon number asymmetry of the universe. Both may be efficiently generated in the presence of CP violating phases, light charginos and neutralinos, and a light top squark. Due to the coannihilation of the neutralino with the light stop, we find a large region of parameter space in which the neutralino relic density is consistent with WMAP and SDSS data. We perform a detailed study of the additional constraints induced when CP violating phases, consistent with the ones required for baryogenesis, are included. We explore the possible tests of this scenario from present and future electron Electric Dipole Moment (EDM) measurements, direct neutralino detection experiments, collider searches and the b {yields} s{gamma} decay rate. We find that the EDM constraints are quite severe and that electron EDM experiments, together with stop searches at the Tevatron and Higgs searches at the LHC, will provide a definite test of our scenario of electroweak baryogenesis in the next few years.
Quantum Supersymmetric Bianchi IX Cosmology
Damour, Thibault
2014-01-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing to one timelike dimension the action of D=4 simple supergravity for a Bianchi IX cosmological model. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a spinor of Spin(8,4) depending on the three squashing parameters, which satisfies Dirac, and Klein-Gordon-like, wave equations describing the propagation of a quantum spinning particle reflecting off spin-dependent potential walls. The algebra of the susy constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3. The (quartic-in-fermions) squared-mass term entering the Klein-Gordon-like equation has several remarkable properties: 1)it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; 2)it is a quad...
On maximally supersymmetric Yang-Mills theories
Movshev, M
2004-01-01
We consider ten-dimensional supersymmetric Yang-Mills theory (10D SUSY YM theory) and its dimensional reductions, in particular, BFSS and IKKT models. We formulate these theories using algebraic techniques based on application of differential graded Lie algebras and associative algebras as well as of more general objects, L_{\\infty}- and A_{\\infty}- algebras. We show that using pure spinor formulation of 10D SUSY YM theory equations of motion and isotwistor formalism one can interpret these equations as Maurer-Cartan equations for some differential Lie algebra. This statement can be used to write BV action functional of 10D SUSY YM theory in Chern-Simons form. The differential Lie algebra we constructed is closely related to differential associative algebra Omega of (0, k)-forms on some supermanifold; the Lie algebra is tensor product of Omega and matrix algebra . We construct several other algebras that are quasiisomorphic to Omega and, therefore, also can be used to give BV formulation of 10D SUSY YM theory...
New Dualities in Supersymmetric Chiral Gauge Theories
Energy Technology Data Exchange (ETDEWEB)
Craig, Nathaniel; /Princeton, Inst. Advanced Study /Rutgers U., Piscataway; Essig, Rouven; Hook, Anson; Torroba, Gonzalo; /Stanford U., Phys. Dept. /SLAC
2011-08-15
We analyze the phase structure of supersymmetric chiral gauge theories with gauge group SU(N), an antisymmetric, and F {le} N + 3 flavors, in the presence of a cubic superpotential. When F = N + 3 the theory flows to a superconformal fixed point in the infrared, and new dual descriptions of this theory are uncovered. The theory with odd N admits a self-dual magnetic description. For general N, we find an infinite family of magnetic dual descriptions, characterized by arbitrarily large gauge groups and additional classical global symmetries that are truncated by nonperturbative effects. The infrared dynamics of these theories are analyzed using a-maximization, which supports the claim that all these theories flow to the same superconformal fixed point. A very rich phase structure is found when the number of flavors is reduced below N + 3, including a new self-dual point, transitions from conformal to confining, and a nonperturbative instability for F {le} N. We also give examples of chiral theories with antisymmetrics that have nonchiral duals.
Kengne, Emmanuel; Saydé, Michel; Ben Hamouda, Fathi; Lakhssassi, Ahmed
2013-11-01
Analytical entire traveling wave solutions to the 1+1 density-dependent nonlinear reaction-diffusion equation via the extended generalized Riccati equation mapping method are presented in this paper. This equation can be regarded as an extension case of the Fisher-Kolmogoroff equation, which is used for studying insect and animal dispersal with growth dynamics. The analytical solutions are then used to investigate the effect of equation parameters on the population distribution.
Institute of Scientific and Technical Information of China (English)
Deng Xi-Jun; Yan Zi-Zong; Han Li-Bo
2009-01-01
In this paper,the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied.By using the first integral method,which is based on the divisor theorem,some exact explicit travelling solitary wave solutions for the above equation are obtained.As a result,some minor errors and some known results in the previousl literature are clarified and improved.
General decay of solutions of a nonlinear system of viscoelastic wave equations
Said-Houari, Belkacem
2011-04-16
This work is concerned with a system of two viscoelastic wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we prove that, for certain class of relaxation functions and for some restrictions on the initial data, the rate of decay of the total energy depends on those of the relaxation functions. This result improves many results in the literature, such as the ones in Messaoudi and Tatar (Appl. Anal. 87(3):247-263, 2008) and Liu (Nonlinear Anal. 71:2257-2267, 2009) in which only the exponential and polynomial decay rates are considered. © 2011 Springer Basel AG.
Static solution of the general relativistic nonlinear $\\sigma$model equation
Lee, C H; Lee, H K; Lee, Chul H; Kim, Joon Ha; Lee, Hyun Kyu
1994-01-01
The nonlinear \\sigma-model is considered to be useful in describing hadrons (Skyrmions) in low energy hadron physics and the approximate behavior of the global texture. Here we investigate the properties of the static solution of the nonlinear \\sigma-model equation coupled with gravity. As in the case where gravity is ignored, there is still no scale parameter that determines the size of the static solution and the winding number of the solution is 1/2. The geometry of the spatial hyperspace in the asymptotic region of large r is explicitly shown to be that of a flat space with some missing solid angle.
Institute of Scientific and Technical Information of China (English)
杨灵娥
2003-01-01
In this paper, we prove that in the inviscid limit the solution of the gen eralized derivative Ginzburg-Landau equations converges to the solution of derivative nonlinear Schrodinger equation, we also give the convergence rates for the difference of the solution.
Nonlinear Collapse of General Thin-Walled Cross-Sections Under Pure Bending
DEFF Research Database (Denmark)
Couturier, Philippe; Krenk, Steen
2016-01-01
Thin-walled beams exhibit a nonlinear response to bending moments due to the progressive flattening of the crosssection, a behavior commonly referred to as the Brazier effect. Most approaches to model this effect are limited to either circular cross-sections or to cross-sections made of isotropic...
A general U-block model-based design procedure for nonlinear polynomial control systems
Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua
2016-10-01
The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.
Bubbles of nothing and supersymmetric compactifications
Energy Technology Data Exchange (ETDEWEB)
Blanco-Pillado, Jose J. [IKERBASQUE, Basque Foundation for Science, 48011, Bilbao (Spain); Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Shlaer, Benjamin [Department of Physics, University of Auckland,Private Bag 92019, Auckland (New Zealand); Institute of Cosmology, Department of Physics and Astronomy,Tufts University, Medford, MA 02155 (United States); Sousa, Kepa [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain); Instituto de Fisica Teorica UAM-CSIC, Universidad Autonoma de Madrid,Cantoblanco, 28049 Madrid (Spain); Urrestilla, Jon [Department of Theoretical Physics, University of the Basque Country UPV/EHU,48080 Bilbao (Spain)
2016-10-03
We investigate the non-perturbative stability of supersymmetric compactifications with respect to decay via a bubble of nothing. We show examples where this kind of instability is not prohibited by the spin structure, i.e., periodicity of fermions about the extra dimension. However, such “topologically unobstructed” cases do exhibit an extra-dimensional analog of the well-known Coleman-De Luccia suppression mechanism, which prohibits the decay of supersymmetric vacua. We demonstrate this explicitly in a four dimensional Abelian-Higgs toy model coupled to supergravity. The compactification of this model to M{sub 3}×S{sub 1} presents the possibility of vacua with different windings for the scalar field. Away from the supersymmetric limit, these states decay by the formation of a bubble of nothing, dressed with an Abelian-Higgs vortex. We show how, as one approaches the supersymmetric limit, the circumference of the topologically unobstructed bubble becomes infinite, thereby preventing the realization of this decay. This demonstrates the dynamical origin of the decay suppression, as opposed to the more familiar argument based on the spin structure. We conjecture that this is a generic mechanism that enforces stability of any topologically unobstructed supersymmetric compactification.
On Supersymmetric Geometric Flows and $\\mathcal{R}^2$ Inflation From Scale Invariant Supergravity
Rajpoot, Subhash
2016-01-01
Models of geometric flows pertaining to $\\mathcal{R}^2$ scale invariant (super) gravity theories coupled to conformally invariant matter fields are investigated. Related to this work are supersymmetric scalar manifolds that are isomorphic to the K\\"{a}hlerian spaces $\\mathcal{M}_n=SU(1,1+k)/U(1)\\times SU(1+k)$ as generalizations of the non-supersymmetric analogs with $SO(1,1+k)/SO(1+k)$ manifolds. For curved superspaces with geometric evolution of physical objects, a complete supersymmetric theory has to be elaborated on nonholonomic (super) manifolds and bundles determined by non-integrable superdistributions with additional constraints on (super) field dynamics and geometric evolution equations. We also consider generalizations of Perelman's functionals using such nonholonomic variables which result in the decoupling of geometric flow equations and Ricci soliton equations with supergravity modifications of the $R^2$ gravity theory. As such, it is possible to construct exact non-homogeneous and locally aniso...
Koch, Herbert; Vişan, Monica
2014-01-01
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ide...
Directory of Open Access Journals (Sweden)
Ahmad Molabahrami
2013-09-01
Full Text Available In this paper, the integral mean value method is employed to handle the general nonlinear Fredholm integro-differential equations under the mixed conditions. The application of the method is based on the integral mean value theorem for integrals. By using the integral mean value method, an integro-differential equation is transformed to an ordinary differential equation, then by solving it, the obtained solution is transformed to a system of nonlinear algebraic equations to calculate the unknown values. The efficiency of the approach will be shown by applying the procedure on some examples. In this respect, a comparison with series pattern solutions, obtained by some analytic methods, is given. For the approximate solution given by integral mean value method, the bounds of the absolute errors are given. The Mathematica program of the integral mean value method based on the procedure in this paper is designed.
Foo, Lee Kien; McGree, James; Duffull, Stephen
2012-01-01
Optimal design methods have been proposed to determine the best sampling times when sparse blood sampling is required in clinical pharmacokinetic studies. However, the optimal blood sampling time points may not be feasible in clinical practice. Sampling windows, a time interval for blood sample collection, have been proposed to provide flexibility in blood sampling times while preserving efficient parameter estimation. Because of the complexity of the population pharmacokinetic models, which are generally nonlinear mixed effects models, there is no analytical solution available to determine sampling windows. We propose a method for determination of sampling windows based on MCMC sampling techniques. The proposed method attains a stationary distribution rapidly and provides time-sensitive windows around the optimal design points. The proposed method is applicable to determine sampling windows for any nonlinear mixed effects model although our work focuses on an application to population pharmacokinetic models. Copyright © 2012 John Wiley & Sons, Ltd.
On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
Koroteev, Peter
2016-01-01
In this note we further develop the duality between supersymmetric gauge theories in various dimensions and elliptic integrable systems such as Ruijsenaars-Schneider model and periodic intermediate long wave hydrodynamics. These models arise in instanton counting problems and are described by certain elliptic algebras. We discuss the correspondence between the two types of models by employing the large-n limit of the dual gauge theory. In particular we provide non-Abelian generalization of our previous result on the intermediate long wave model.
Non-supersymmetric black rings as thermally excited supertubes
Energy Technology Data Exchange (ETDEWEB)
Elvang, Henriette [Department of Physics, University of California, Santa Barbara, CA 93106-9530 (United States); Emparan, Roberto [Institucio Catalana de Recerca i Estudis Avancats (ICREA) (Spain); Departament de Fisica Fonamental and C.E.R. en Astrofisica, Fisica de Particules i Cosmologia, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)]. E-mail: emparan@ub.edu; Figueras, Pau [Departament de Fisica Fonamental and C.E.R. en Astrofisica, Fisica de Particules i Cosmologia, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona (Spain)
2005-02-01
We construct a seven-parameter family of supergravity solutions that describe non-supersymmetric black rings and black tubes with three charges, three dipoles and two angular momenta. The black rings have regular horizons and non-zero temperature. They are naturally interpreted as the supergravity descriptions of thermally excited configurations of supertubes, specifically of supertubes with two charges and one dipole, and of supertubes with three charges and two dipoles. In order to fully describe thermal excitations near supersymmetry of the black supertubes with three charges and three dipoles a more general family of black ring solutions is required. (author)
Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions
Noma, Y
2006-01-01
We derive the relation between the Hilbert space of certain geometries under the Bohr-Sommerfeld quantization and the perturbative prepotentials for the supersymmetric five-dimensional SU(N) gauge theories with massive fundamental matters and with one massive adjoint matter. The gauge theory with one adjoint matter shows interesting features. A five-dimensional generalization of Nekrasov's partition function can be written as a correlation function of two-dimensional chiral bosons and as a partition function of a statistical model of partitions. From a ground state of the statistical model we reproduce the polyhedron which characterizes the Hilbert space.
N=2 supersymmetric dynamics for pedestrians
Tachikawa, Yuji
2015-01-01
Understanding the dynamics of gauge theories is crucial, given the fact that all known interactions are based on the principle of local gauge symmetry. Beyond the perturbative regime, however, this is a notoriously difficult problem. Requiring invariance under supersymmetry turns out to be a suitable tool for analyzing supersymmetric gauge theories over a larger region of the space of parameters. Supersymmetric quantum field theories in four dimensions with extended N=2 supersymmetry are further constrained and have therefore been a fertile field of research in theoretical physics for quite some time. Moreover, there are far-reaching mathematical ramifications that have led to a successful dialogue with differential and algebraic geometry. These lecture notes aim to introduce students of modern theoretical physics to the fascinating developments in the understanding of N=2 supersymmetric gauge theories in a coherent fashion. Starting with a gentle introduction to electric-magnetic duality, the author guides r...
New dualities of supersymmetric gauge theories
2016-01-01
This book reviews a number of spectacular advances that have been made in the study of supersymmetric quantum field theories in the last few years. Highlights include exact calculations of Wilson loop expectation values, and highly nontrivial quantitative checks of the long-standing electric-magnetic duality conjectures. The book starts with an introductory article presenting a survey of recent advances, aimed at a wide audience with a background and interest in theoretical physics. The following articles are written for advanced students and researchers in quantum field theory, string theory and mathematical physics, our goal being to familiarize these readers with the forefront of current research. The topics covered include recent advances in the classification and vacuum structure of large families of N=2 supersymmetric field theories, followed by an extensive discussion of the localisation method, one of the most powerful tools for exact studies of supersymmetric field theories. The quantities that have ...
Superconformal Algebras and Supersymmetric Integrable Flows
Sachse, Christoph; Devchand, Chandrasekhar
2009-01-01
After a comprehensive review of superconformal algebras, super-diffeomorphisms and supervector fields on supercircles S^{1|n} we study various supersymmetric extensions of the KdV and Camassa-Holm equations. We describe their (super) Hamiltonian structures and their connection to bihamiltonian geometry. These are interpreted as geodesic flows on various superconformal groups. We also give an example of superintegrable systems of Ramond type. The one-parameter family of equations shown by Degasperis, Holm and Hone (DHH) to possess multi-peakon solutions is identified as a geodesic flow equation on a one-parameter deformation of the group of diffeomorphisms of the circle, with respect to a right-invariant Sobolev H^1--metric. A supersymmetrisation of the algebra of deformed vector fields on S^1 yields supersymmetric DHH equations (also known as b-field equations), which include the supersymmetric Camassa--Holm equation as a special case.
Supersymmetric defect models and mirror symmetry
Energy Technology Data Exchange (ETDEWEB)
Hook, Anson; Kachru, Shamit; Torroba, Gonzalo
2013-11-01
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d NN = 4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d NN = 2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of NN = 4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.
Supersymmetric Defect Models and Mirror Symmetry
Hook, Anson; Torroba, Gonzalo
2013-01-01
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d N=4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d N=2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of N=4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.
Gauging isometries in N=4 supersymmetric mechanics
Delduc, F
2008-01-01
This talk summarizes the study of superfield gaugings of isometries of extended supersymmetric mechanics in hep-th/0605211, hep-th/0611247 and arXiv:0706.0706. The gauging procedure provides a manifestly supersymmetric realization of d=1 automorphic dualities which interrelate various irreducible off-shell multiplets of d=1 extended supersymmetry featuring the same number of physical fermions but different divisions of bosonic fields into the physical and auxiliary subsets. We concentrate on the most interesting N=4 case and demonstrate that, with a suitable choice of the symmetry to be gauged, all such multiplets of N=4 supersymmetric mechanics and their generic superfield actions can be obtained from the "root" multiplet (4,4,0) and the appropriate gauged subclasses of the generic superfield action of the latter by a simple universal recipe.
Decoupling of Supersymmetric Particles in the MSSM
Dobado, A; Peñaranda, S
1998-01-01
A heavy supersymmetric spectrum at the Minimal Supersymmetric Standard Model is considered and the decoupling from the low energy electroweak scale is analyzed. A formal and partial proof of decoupling of supersymmetric particles in the limit where their masses are larger than the electroweak scale is performed by integrating out all the sparticles to one loop and by evaluating the effective action for the standard electroweak gauge bosons $W^{\\pm}, Z$ and two-point functions of the electroweak gauge bosons and the $S, T$ and $U$ parameters, to be valid in that limit, are also presented. A discussion on how the decoupling takes place in terms of both the physical sparticle masses and the non-physical mass parameters as the $\\mu$-parameter and the soft-breaking parameters is included.
Generalized Equations and Their Solutions. Part 2. Applications to Nonlinear Programming
1980-03-01
Bolivar, Caracas, Venezuela, with support from the United Nations Educational, Scientific and Cultural Organization under Proyecto UNESCO VEN-77-002. The...tional, Scientific and Cultural Crganization under Proyecto UNESCO VEN-77-0 02. Vhe author greatly appreciates the hospitality and support extended...condition is satisfied by the linearizations of the nonlinear problem, then the latter has, at least locally, an upper Lipschitzian inverse (which, of
Quantum supersymmetric Bianchi IX cosmology
Damour, Thibault; Spindel, Philippe
2014-11-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle
Invariant Regularization of Supersymmetric Chiral Gauge Theory
Suzuki, H
1999-01-01
We present a regularization scheme which respects the supersymmetry and the maximal background gauge covariance in supersymmetric chiral gauge theories. When the anomaly cancellation condition is satisfied, the effective action in the superfield background field method automatically restores the gauge invariance without counterterms. The scheme also provides a background gauge covariant definition of composite operators that is especially useful in analyzing anomalies. We present several applications: The minimal consistent gauge anomaly; the super-chiral anomaly and the superconformal anomaly; as the corresponding anomalous commutators, the Konishi anomaly and an anomalous supersymmetric transformation law of the supercurrent (the ``central extension'' of N=1 supersymmetry algebra) and of the R-current.
Just so oscillations in supersymmetric standard model
Joshipura, A S; Anjan S Joshipura; Marek Nowakowski
1995-01-01
We analyze the spectrum and mixing among neutrinos in the minimal supersymmetric standard model with explicit breaking of R parity. It is shown that ({\\em i}) the mixing among neutrinos is naturally large and ({\\em ii}) the non zero neutrino mass is constrained to be \\leq 10^{-5} eV from arguments based on baryogenesis. Thus vacuum oscillations of neutrinos in this model may offer a solution of the solar neutrino problem. The allowed space of the supersymmetric parameters consistent with this solution is determined.
Supersymmetric asymptotic safety is not guaranteed
DEFF Research Database (Denmark)
Intriligator, Kenneth; Sannino, Francesco
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety...... in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those...
Supersymmetric radiative corrections at large tan {beta}
Energy Technology Data Exchange (ETDEWEB)
Logan, H.E.
2001-02-20
In the minimal supersymmetric extension of the Standard Model (MSSM), fermion masses and Yukawa couplings receive radiative corrections at one loop from diagrams involving the supersymmetric particles. The corrections to the relation between down-type fermion masses and Yukawa couplings are enhanced by tan {beta}, which makes them potentially very significant at large tan {beta}. These corrections affect a wide range of processes in the MSSM, including neutral and charged Higgs phenomenology, rare B meson decays, and renormalization of the CKM matrix. We give a pedagogical review of the sources and phenomenological effects of these corrections.
Supersymmetric asymptotic safety is not guaranteed
Intriligator, Kenneth
2015-01-01
It was recently shown that certain perturbatively accessible, non-supersymmetric gauge-Yukawa theories have UV asymptotic safety, without asymptotic freedom: the UV theory is an interacting RG fixed point, and the IR theory is free. We here investigate the possibility of asymptotic safety in supersymmetric theories, and use unitarity bounds, and the a-theorem, to rule it out in broad classes of theories. The arguments apply without assuming perturbation theory. Therefore, the UV completion of a non-asymptotically free susy theory must have additional, non-obvious degrees of freedom, such as those of an asymptotically free (perhaps magnetic dual) extension.
Angular Momentum of Supersymmetric Non-isotropic Traps
Institute of Scientific and Technical Information of China (English)
XU Qiang
2001-01-01
A simple way to explain quantum behavior of supersymmetric non-isotropic traps is proposed in the framework of sermiunitary formulation of supersymmetric quantum mechanics. Using semiunitary formulation we can simultaneously supersymmetrize the complete set of observables, especially including angular moment.
5D Maximally Supersymmetric Yang-Mills on the Lattice
Joseph, Anosh
2016-01-01
We provide details of the lattice construction of five-dimensional maximally supersymmetric Yang-Mills theory. The lattice theory is supersymmetric, gauge invariant and free from spectrum doublers. Such a supersymmetric lattice formulation is interesting as it can be used for non-perturbative explorations of the five-dimensional theory, which has a known gravitational dual.
Vock, David M; Davidian, Marie; Tsiatis, Anastasios A
2014-01-01
Generalized linear and nonlinear mixed models (GMMMs and NLMMs) are commonly used to represent non-Gaussian or nonlinear longitudinal or clustered data. A common assumption is that the random effects are Gaussian. However, this assumption may be unrealistic in some applications, and misspecification of the random effects density may lead to maximum likelihood parameter estimators that are inconsistent, biased, and inefficient. Because testing if the random effects are Gaussian is difficult, previous research has recommended using a flexible random effects density. However, computational limitations have precluded widespread use of flexible random effects densities for GLMMs and NLMMs. We develop a SAS macro, SNP_NLMM, that overcomes the computational challenges to fit GLMMs and NLMMs where the random effects are assumed to follow a smooth density that can be represented by the seminonparametric formulation proposed by Gallant and Nychka (1987). The macro is flexible enough to allow for any density of the response conditional on the random effects and any nonlinear mean trajectory. We demonstrate the SNP_NLMM macro on a GLMM of the disease progression of toenail infection and on a NLMM of intravenous drug concentration over time.
Shulkind, Gal; Nazarathy, Moshe
2012-11-05
DFT-spread (DFT-S) coherent optical OFDM was numerically and experimentally shown to provide improved nonlinear tolerance over an optically amplified dispersion uncompensated fiber link, relative to both conventional coherent OFDM and single-carrier transmission. Here we provide an analytic model rigorously accounting for this numerical result and precisely predicting the optimal bandwidth per DFT-S sub-band (or equivalently the optimal number of sub-bands per optical channel) required in order to maximize the link non-linear tolerance (NLT). The NLT advantage of DFT-S OFDM is traced to the particular statistical dependency introduced among the OFDM sub-carriers by means of the DFT spreading operation. We further extend DFT-S to a unitary-spread generalized modulation format which includes as special cases the DFT-S scheme as well as a new format which we refer to as wavelet-spread (WAV-S) OFDM, replacing the spreading DFTs by Hadamard matrices which have elements +/-1 hence are multiplier-free. The extra complexity incurred in the spreading operation is almost negligible, however the performance improvement with WAV-S relative to plain OFDM is more modest than that achieved by DFT-S, which remains the preferred format for nonlinear tolerance improvement, outperforming both plain OFDM and single-carrier schemes.
Prediction of nonlinear optical properties of organic materials. General theoretical considerations
Cardelino, B.; Moore, C.; Zutaut, S.
1993-01-01
The prediction of nonlinear optical properties of organic materials is geared to assist materials scientists in the selection of good candidate molecules. A brief summary of the quantum mechanical methods used for estimating hyperpolarizabilities will be presented. The advantages and limitations of each technique will be discussed. Particular attention will be given to the finite-field method for calculating first and second order hyperpolarizabilities, since this method is better suited for large molecules. Corrections for dynamic fields and bulk effects will be discussed in detail, focusing on solvent effects, conformational isomerization, core effects, dispersion, and hydrogen bonding. Several results will be compared with data obtained from third-harmonic-generation (THG) and dc-induced second harmonic generation (EFISH) measurements. These comparisons will demonstrate the qualitative ability of the method to predict the relative strengths of hyperpolarizabilities of a class of compounds. The future application of molecular mechanics, as well as other techniques, in the study of bulk properties and solid state defects will be addressed. The relationship between large values for nonlinear optical properties and large conjugation lengths is well known, and is particularly important for third-order processes. For this reason, the materials with the largest observed nonresonant third-order properties are conjugated polymers. An example of this type of polymer is polydiacetylene. One of the problems in dealing with polydiacetylene is that substituents which may enhance its nonlinear properties may ultimately prevent it from polymerizing. A model which attempts to predict the likelihood of solid-state polymerization is considered, along with the implications of the assumptions that are used. Calculations of the third-order optical properties and their relationship to first-order properties and energy gaps will be discussed. The relationship between monomeric and
Theesar, S Jeeva Sathya; Balasubramaniam, P; Banerjee, Santo
2012-09-01
In Chaos 19, 013102 (2009), the author proposed generalized projective synchronization for time delay systems using nonlinear observer and obtained sufficient condition to ensure projective synchronization for modulated time varying delay. There are concerns with the obtained conditions as the result was applicable only to trivial case of time varying delay τ[over dot](1)(t)=dτ(1)(t)/dt<1. In this paper, we note the drawbacks of the proposed sufficient condition. The new improved sufficient condition for ensuring the projective synchronization of time varying delayed systems is presented. The proposed new criteria have been verified by adopting the Ikeda system.
Yang, Jianke
2012-03-01
Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that stability of solitary waves does not switch at saddle-node bifurcations. This analytical result is confirmed by numerical examples where both soliton branches are stable at saddle-node bifurcations.
Chou, Shih-Wei; Lin, Ying-Chieh
2017-08-01
In this paper, we investigate the Cauchy problem for a nonlinear hyperbolic system of balance laws with sources ax g and at h. To get the approximate solutions of our problem, we consider a version of generalized Riemann problem that concentrates the variation of a on a thin T-shaped region of each grid. A new version of Glimm scheme is introduced to construct the approximate solutions and its stability is proved by considering two types of conditions on a. Finally, we verify the consistency of the scheme and the entropy inequality to establish the global existence of entropy solutions.
Richard, Jacques C.
1995-01-01
This paper presents a dynamic model of an internal combustion engine coupled to a variable pitch propeller. The low-order, nonlinear time-dependent model is useful for simulating the propulsion system of general aviation single-engine light aircraft. This model is suitable for investigating engine diagnostics and monitoring and for control design and development. Furthermore, the model may be extended to provide a tool for the study of engine emissions, fuel economy, component effects, alternative fuels, alternative engine cycles, flight simulators, sensors, and actuators. Results show that the model provides a reasonable representation of the propulsion system dynamics from zero to 10 Hertz.
DEFF Research Database (Denmark)
Abrahamsen, Trine Julie; Hansen, Lars Kai
2011-01-01
We investigate sparse non-linear denoising of functional brain images by kernel Principal Component Analysis (kernel PCA). The main challenge is the mapping of denoised feature space points back into input space, also referred to as ”the pre-image problem”. Since the feature space mapping...... sparse pre-image reconstruction by Lasso regularization. We find that sparse estimation provides better brain state decoding accuracy and a more reproducible pre-image. These two important metrics are combined in an evaluation framework which allow us to optimize both the degree of sparsity and the non...
On the Supersymmetric Index of the M-theory 5-brane and Little String Theory
Bonelli, G
2001-01-01
We propose a six-dimensional framework to calculate the supersymmetric index of M-theory 5-branes wrapped on a six-manifold with product topology $M_4\\times T^2$, where $M_4$ is a holomorphic 4-cycle in a Calabi-Yau three-fold. This is obtained by zero-modes counting of the self-dual tensor contribution plus ``little'' string states and correctly reproduces the known results which can be obtained by shrinking or blowing the $T^2$ volume parameter. We also extract the geometric moduli space of the multi M5-brane system and infer the generic structure of the supersymmetric index for more general geometries.
Solving the Hierarchy Problem with a Light Singlet and Supersymmetric Mass Terms
Delgado, Antonio; de la Puente, Alejandro
2011-01-01
A generalization of the Next-to-Minimal Supersymmetric Model (NMSSM) is studied in which an explicit \\mu-term as well as a small supersymmetric mass term for the singlet superfield are incorporated. We study the possibility of raising the Standard Model-like Higgs mass at tree level through its mixing with a light, mostly-singlet, CP-even scalar. We are able to generate Higgs boson masses up to 145 GeV with top squarks below 1.1 TeV and without the need to fine tune parameters in the scalar potential. This model yields light singlet-like scalars and pseudoscalars passing all collider constraints.
Solving the little hierarchy problem with a light singlet and supersymmetric mass terms
Energy Technology Data Exchange (ETDEWEB)
Delgado, Antonio, E-mail: antonio.delgado@nd.edu [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Kolda, Christopher [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Puente, Alejandro de la [Department of Physics, University of Notre Dame, Notre Dame, IN 46556 (United States); Fermi National Accelerator Laboratory, P.O. Box 500, Batavia, IL 60510 (United States)
2012-04-12
A generalization of the Next-to-Minimal Supersymmetric Model (NMSSM) is studied in which an explicit {mu}-term as well as a small supersymmetric mass term for the singlet superfield are incorporated. We study the possibility of raising the Standard Model-like Higgs mass at tree level through its mixing with a light, mostly-singlet, CP-even scalar. We are able to generate Higgs boson masses up to 145 GeV with top squarks below 1.1 TeV and without the need to fine tune parameters in the scalar potential. This model yields light singlet-like scalars and pseudoscalars passing all collider constraints.
Directory of Open Access Journals (Sweden)
Hasibun Naher
2013-03-01
Full Text Available In this article, new (G′/G-expansion method and new generalized (G′/G-expansion method is proposed to generate more general and abundant new exact traveling wave solutions of nonlinear evolution equations. The novelty and advantages of these methods is exemplified by its implementation to the KdV equation. The results emphasize the power of proposed methods in providing distinct solutions of different physical structures in nonlinear science. Moreover, these methods could be more effectively used to deal with higher dimensional and higher order nonlinear evolution equations which frequently arise in many scientific real time application fields.
Computing Maximally Supersymmetric Scattering Amplitudes
Stankowicz, James Michael, Jr.
This dissertation reviews work in computing N = 4 super-Yang--Mills (sYM) and N = 8 maximally supersymmetric gravity (mSUGRA) scattering amplitudes in D = 4 spacetime dimensions in novel ways. After a brief introduction and overview in Ch. 1, the various techniques used to construct amplitudes in the remainder of the dissertation are discussed in Ch. 2. This includes several new concepts such as d log and pure integrand bases, as well as how to construct the amplitude using exactly one kinematic point where it vanishes. Also included in this chapter is an outline of the Mathematica package on shell diagrams and numerics.m (osdn) that was developed for the computations herein. The rest of the dissertation is devoted to explicit examples. In Ch. 3, the starting point is tree-level sYM amplitudes that have integral representations with residues that obey amplitude relations. These residues are shown to have corresponding residue numerators that allow a double copy prescription that results in mSUGRA residues. In Ch. 4, the two-loop four-point sYM amplitude is constructed in several ways, showcasing many of the techniques of Ch. 2; this includes an example of how to use osdn. The two-loop five-point amplitude is also presented in a pure integrand representation with comments on how it was constructed from one homogeneous cut of the amplitude. On-going work on the two-loop n-point amplitude is presented at the end of Ch. 4. In Ch. 5, the three-loop four-point amplitude is presented in the d log representation and in the pure integrand representation. In Ch. 6, there are several examples of four- through seven-loop planar diagrams that illustrate how considerations of the singularity structure of the amplitude underpin dual-conformal invariance. Taken with the previous examples, this is additional evidence that the structure known to exist in the planar sector extends to the full theory. At the end of this chapter is a proof that all mSUGRA amplitudes have a pole at
Asymptotic iteration approach to supersymmetric bistable potentials
Institute of Scientific and Technical Information of China (English)
H. Ciftci; O. ozer; P. Roy
2012-01-01
We examine quasi exactly solvable bistable potentials and their supersymmetric partners within the framework of the asymptotic iteration method (AIM).It is shown that the AIM produces excellent approximate spectra and that sometimes it is found to be more useful to use the partner potential for computation. We also discuss the direct application of the AIM to the Fokker-Planck equation.
Photon structure function in supersymmetric QCD revisited
Energy Technology Data Exchange (ETDEWEB)
Sahara, Ryo, E-mail: sahara@scphys.kyoto-u.ac.jp [Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa, Kyoto 606-8502 (Japan); Uematsu, Tsuneo, E-mail: uematsu@scphys.kyoto-u.ac.jp [Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa, Kyoto 606-8502 (Japan); Kitadono, Yoshio, E-mail: kitadono@phys.sinica.edu.tw [Institute of Physics, Academia Sinica, Taipei, Taiwan (China)
2012-02-07
We investigate the virtual photon structure function in the supersymmetric QCD (SQCD), where we have squarks and gluinos in addition to the quarks and gluons. Taking into account the heavy particle mass effects to the leading order in QCD and SQCD we evaluate the photon structure function and numerically study its behavior for the QCD and SQCD cases.
Photon Structure Function in Supersymmetric QCD Revisited
Sahara, Ryo; Kitadono, Yoshio
2011-01-01
We investigate the virtual photon structure function in the supersymmetric QCD (SQCD), where we have squarks and gluinos in addition to the quarks and gluons. Taking into account the heavy particle mass effects to the leading order in QCD and SQCD we evaluate the photon structure function and numerically study its behavior for the QCD and SQCD cases.
Neutrino masses and mixing in supersymmetric theories
Indian Academy of Sciences (India)
Sudhir K Vempati
2000-07-01
It has been known for sometime that supersymmetric theories with -parity violation provide a natural framework where small neutrino masses can be generated. We discuss neutrino masses and mixing in these theories in the presence of trilinear lepton number violating couplings. It will be shown that simultaneous solutions to solar and atmospheric neutrino problems can be realized in these models.
Spectral properties of supersymmetric shape invariant potentials
Indian Academy of Sciences (India)
Barnali Chakrabarti
2008-01-01
We present the spectral properties of supersymmetric shape invariant potentials (SIPs). Although the folded spectrum is completely random, unfolded spectrum shows that energy levels are highly correlated and absolutely rigid. All the SIPs exhibit harmonic oscillator-type spectral statistics in the unfolded spectrum. We conjecture that this is the reflection of shape invariant symmetry.
Partition functions for supersymmetric black holes
Manschot, J.
2008-01-01
This thesis presents a number of results on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view. Such a microscopic explanation was desired after the association of a
Supersymmetric integrable scattering theories with unstable particles
Fring, A
2005-01-01
We propose scattering matrices for N=1 supersymmetric integrable quantum field theories in 1+1 dimensions which involve unstable particles in their spectra. By means of the thermodynamic Bethe ansatz we analyze the ultraviolet behaviour of some of these theories and identify the effective Virasoro central charge of the underlying conformal field theories.
Geometry of all supersymmetric type I backgrounds
Gran, Ulf; Papadopoulos, George; Sloane, Peter; Roest, Diederik
2007-01-01
We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9, 1), while th
A renormalizable supersymmetric SO(10) model
Chen, Ying-Kang
2015-01-01
A realistic grand unified model has never been constructed in the literature due to three major difficulties: the seesaw mechanism without spoiling gauge coupling unification, the doublet-triplet splitting and the proton decay suppression. We propose a renormalizable supersymmetric SO(10) model with all these difficulties solved naturally.
The spinorial method of classifying supersymmetric backgrounds
Gran, U.; Gutowski, J.; Papadopoulos, G.; Roest, D.
2006-01-01
We review how the classification of all supersymmetric backgrounds of IIB supergravity can be reduced to the evaluation of the Killing spinor equations and their integrability conditions, which contain the field equations, on five types of spinors. This is an extension of the work [hep-th/0503046] t
Effective action for supersymmetric chiral anomaly
Energy Technology Data Exchange (ETDEWEB)
Krivoshchekov, V.K.; Chekhov, L.O.
1987-05-01
It is shown that consistency conditions of the type of the Wess-Zumino conditions are necessary and sufficient conditions for local integrability of the supersymmetric chiral anomaly. It follows from the requirement of global integrability that the coefficient of the anomalous action is discrete. Explicit expressions are obtained for consistent anomalies and the corresponding functionals, which depend on superfields of various types.
Electric dipole moments in supersymmetric theories
Romanino, Andrea
1996-01-01
Intrinsic EDMs in microscopic systems at a level of sensitivity achievable in experiments under way or foreseen are predicted in supersymmetric unified theories. I describe this and other sources of measurable EDMs and I show how these sources can be distinguished through experiments in different systems.
The geometry of supermanifolds and new supersymmetric actions
Energy Technology Data Exchange (ETDEWEB)
Castellani, L., E-mail: leonardo.castellani@mfn.unipmn.it [Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel, 11, 15121 Alessandria (Italy); INFN, Sezione di Torino, via P. Giuria 1, 10125 Torino (Italy); Catenacci, R., E-mail: roberto.catenacci@mfn.unipmn.it [Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel, 11, 15121 Alessandria (Italy); Gruppo Nazionale di Fisica Matematica, INdAM, P.le Aldo Moro 5, 00185 Roma (Italy); Grassi, P.A., E-mail: pietro.grassi@mfn.unipmn.it [Dipartimento di Scienze e Innovazione Tecnologica, Università del Piemonte Orientale, Viale T. Michel, 11, 15121 Alessandria (Italy); INFN, Sezione di Torino, via P. Giuria 1, 10125 Torino (Italy)
2015-10-15
This is the first of two papers in which we construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In this paper we introduce the fundamental concepts and a method for computing Hodge duals in simple cases. We refer to a subsequent publication [12] for a more general approach and the required mathematical details. In the case of supermanifolds it is known that superforms are not sufficient to construct a consistent integration theory and that integral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and super forms in a new way which can be easily generalized to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.
The geometry of supermanifolds and new supersymmetric actions
Directory of Open Access Journals (Sweden)
L. Castellani
2015-10-01
Full Text Available This is the first of two papers in which we construct the Hodge dual for supermanifolds by means of the Grassmannian Fourier transform of superforms. In this paper we introduce the fundamental concepts and a method for computing Hodge duals in simple cases. We refer to a subsequent publication [12] for a more general approach and the required mathematical details. In the case of supermanifolds it is known that superforms are not sufficient to construct a consistent integration theory and that integral forms are needed. They are distribution-like forms which can be integrated on supermanifolds as a top form can be integrated on a conventional manifold. In our construction of the Hodge dual of superforms they arise naturally. The compatibility between Hodge duality and supersymmetry is exploited and applied to several examples. We define the irreducible representations of supersymmetry in terms of integral and super forms in a new way which can be easily generalized to several models in different dimensions. The construction of supersymmetric actions based on the Hodge duality is presented and new supersymmetric actions with higher derivative terms are found. These terms are required by the invertibility of the Hodge operator.
Leech Lattice Extension of the Non-linear Schrodinger Equation Theory of Einstein spaces
Chapline, George
2015-01-01
Although the nonlinear Schrodinger equation description of Einstein spaces has provided insights into how quantum mechanics might modify the classical general relativistic description of space-time, an exact quantum description of space-times with matter has remained elusive. In this note we outline how the nonlinear Schrodinger equation theory of Einstein spaces might be generalized to include matter by transplanting the theory to the 25+1 dimensional Lorentzian Leech lattice. Remarkably when a hexagonal section of the Leech lattice is set aside as the stage for the nonlinear Schrodinger equation, the discrete automorphism group of the complex Leech lattice with one complex direction fixed can be lifted to continuous Lie group symmetries. In this setting the wave function becomes an 11x11 complex matrix which represents matter degrees of freedom consisting of a 2-form abelian gauge field and vector nonabelian SU(3)xE6 gauge fields together with their supersymmetric partners. The lagrangian field equations fo...
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
A general-purpose contact detection algorithm for nonlinear structural analysis codes
Energy Technology Data Exchange (ETDEWEB)
Heinstein, M.W.; Attaway, S.W.; Swegle, J.W.; Mello, F.J.
1993-05-01
A new contact detection algorithm has been developed to address difficulties associated with the numerical simulation of contact in nonlinear finite element structural analysis codes. Problems including accurate and efficient detection of contact for self-contacting surfaces, tearing and eroding surfaces, and multi-body impact are addressed. The proposed algorithm is portable between dynamic and quasi-static codes and can efficiently model contact between a variety of finite element types including shells, bricks, beams and particles. The algorithm is composed of (1) a location strategy that uses a global search to decide which slave nodes are in proximity to a master surface and (2) an accurate detailed contact check that uses the projected motions of both master surface and slave node. In this report, currently used contact detection algorithms and their associated difficulties are discussed. Then the proposed algorithm and how it addresses these problems is described. Finally, the capability of the new algorithm is illustrated with several example problems.
Directory of Open Access Journals (Sweden)
Dan Ye
2013-01-01
Full Text Available This paper is concerned with delay-dependent stochastic stability for time-delay Markovian jump systems (MJSs with sector-bounded nonlinearities and more general transition probabilities. Different from the previous results where the transition probability matrix is completely known, a more general transition probability matrix is considered which includes completely known elements, boundary known elements, and completely unknown ones. In order to get less conservative criterion, the state and transition probability information is used as much as possible to construct the Lyapunov-Krasovskii functional and deal with stability analysis. The delay-dependent sufficient conditions are derived in terms of linear matrix inequalities to guarantee the stability of systems. Finally, numerical examples are exploited to demonstrate the effectiveness of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Huang, Z. [Department of Physics, University of Arizona, Tucson, Arizona 85741 (United States); Suzuki, M. [Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720 (United States)
1996-01-01
We obtain the general solutions of the nonlinear {sigma} model in 3+1 dimensions as the candidates for the disoriented chiral condensate (DCC). The nonuniformly isospin-oriented solutions are shown to be related to the uniformly oriented ones through the chiral (axial) rotations. We discuss the pion charge distribution arising from these solutions. The distribution {ital dP}/{ital d}{ital f}=1/(2 {radical}{ital f} ) holds for the uniform solutions in general and the nonuniform solutions in the 1+1 boost-invariant case. For the nonuniform solution in 1+1 without boost invariance and in higher dimensions, the distribution does not hold in the integrated form. However, it is applicable to the pions selected from a small segment in the momentum phase space. We suggest that the nonuniform DCC{close_quote}s may correspond to the mini-Centauro events. {copyright} {ital 1996 The American Physical Society.}
Czachor, Marek
1994-01-01
A new version of NLQM is formulated in terms of the generalized Nambu dynamics. The generalization is free from the difficulties of earlier approaches. The paper is a second part of "Elements of NLQM (I): NL Schrodinger equation and two-level atoms".
A general derivation of the subharmonic threshold for non-linear bubble oscillations
Prosperetti, A.
2013-01-01
The paper describes an approximate but rather general derivation of the acoustic threshold for a subharmonic component to be possible in the sound scattered by an insonified gas bubble. The general result is illustrated with several specific models for the mechanical behavior of the surface coating
Generalized Forecast Error Variance Decomposition for Linear and Nonlinear Multivariate Models
DEFF Research Database (Denmark)
Lanne, Markku; Nyberg, Henri
We propose a new generalized forecast error variance decomposition with the property that the proportions of the impact accounted for by innovations in each variable sum to unity. Our decomposition is based on the well-established concept of the generalized impulse response function. The use...
Non-minimal supersymmetric models. LHC phenomenolgy and model discrimination
Energy Technology Data Exchange (ETDEWEB)
Krauss, Manuel Ernst
2015-12-18
It is generally agreed upon the fact that the Standard Model of particle physics can only be viewed as an effective theory that needs to be extended as it leaves some essential questions unanswered. The exact realization of the necessary extension is subject to discussion. Supersymmetry is among the most promising approaches to physics beyond the Standard Model as it can simultaneously solve the hierarchy problem and provide an explanation for the dark matter abundance in the universe. Despite further virtues like gauge coupling unification and radiative electroweak symmetry breaking, minimal supersymmetric models cannot be the ultimate answer to the open questions of the Standard Model as they still do not incorporate neutrino masses and are besides heavily constrained by LHC data. This does, however, not derogate the beauty of the concept of supersymmetry. It is therefore time to explore non-minimal supersymmetric models which are able to close these gaps, review their consistency, test them against experimental data and provide prospects for future experiments. The goal of this thesis is to contribute to this process by exploring an extraordinarily well motivated class of models which bases upon a left-right symmetric gauge group. While relaxing the tension with LHC data, those models automatically include the ingredients for neutrino masses. We start with a left-right supersymmetric model at the TeV scale in which scalar SU(2){sub R} triplets are responsible for the breaking of left-right symmetry as well as for the generation of neutrino masses. Although a tachyonic doubly-charged scalar is present at tree-level in this kind of models, we show by performing the first complete one-loop evaluation that it gains a real mass at the loop level. The constraints on the predicted additional charged gauge bosons are then evaluated using LHC data, and we find that we can explain small excesses in the data of which the current LHC run will reveal if they are actual new
Yang, Cheng-Hsiung; Wu, Cheng-Lin
2014-01-01
An adaptive control scheme is developed to study the generalized adaptive chaos synchronization with uncertain chaotic parameters behavior between two identical chaotic dynamic systems. This generalized adaptive chaos synchronization controller is designed based on Lyapunov stability theory and an analytic expression of the adaptive controller with its update laws of uncertain chaotic parameters is shown. The generalized adaptive synchronization with uncertain parameters between two identical new Lorenz-Stenflo systems is taken as three examples to show the effectiveness of the proposed method. The numerical simulations are shown to verify the results.
Thailert, E.; Suksern, S.
2014-01-01
We discuss the linearization problem of third-order ordinary differential equation under the generalized linearizing transformation. We identify the form of the linearizable equations and the conditions which allow the third-order ordinary differential equation to be transformed into the simplest linear equation. We also illustrate how to construct the generalized linearizing transformation. Some examples of linearizable equation are provided to demonstrate our procedure.
Energy Technology Data Exchange (ETDEWEB)
Zenchuk, A I, E-mail: zenchuk@itp.ac.r [Institute of Problems of Chemical Physics, RAS Acad. Semenov av., 1 Chernogolovka, Moscow region 142432 (Russian Federation)
2010-06-18
We develop a new integration technique allowing one to construct a rich manifold of particular solutions to multidimensional generalizations of classical C- and S-integrable partial differential equations (PDEs). Generalizations of (1+1)-dimensional C-integrable and (2+1)-dimensional S-integrable N-wave equations are derived among examples. Examples of multidimensional second-order PDEs are represented as well.
Generalizing a nonlinear geophysical flood theory to medium-sized river networks
Gupta, Vijay K.; Mantilla, Ricardo; Troutman, Brent M.; Dawdy, David; Krajewski, Witold F.
2010-01-01
The central hypothesis of a nonlinear geophysical flood theory postulates that, given space-time rainfall intensity for a rainfall-runoff event, solutions of coupled mass and momentum conservation differential equations governing runoff generation and transport in a self-similar river network produce spatial scaling, or a power law, relation between peak discharge and drainage area in the limit of large area. The excellent fit of a power law for the destructive flood event of June 2008 in the 32,400-km2 Iowa River basin over four orders of magnitude variation in drainage areas supports the central hypothesis. The challenge of predicting observed scaling exponent and intercept from physical processes is explained. We show scaling in mean annual peak discharges, and briefly discuss that it is physically connected with scaling in multiple rainfall-runoff events. Scaling in peak discharges would hold in a non-stationary climate due to global warming but its slope and intercept would change.
Supersymmetric Quantum Mechanics and Super-Lichnerowicz Algebras
Hallowell, K; 10.1007/s00220-007-0393-1
2008-01-01
We present supersymmetric, curved space, quantum mechanical models based on deformations of a parabolic subalgebra of osp(2p+2|Q). The dynamics are governed by a spinning particle action whose internal coordinates are Lorentz vectors labeled by the fundamental representation of osp(2p|Q). The states of the theory are tensors or spinor-tensors on the curved background while conserved charges correspond to the various differential geometry operators acting on these. The Hamiltonian generalizes Lichnerowicz's wave/Laplace operator. It is central, and the models are supersymmetric whenever the background is a symmetric space, although there is an osp(2p|Q) superalgebra for any curved background. The lowest purely bosonic example (2p,Q)=(2,0) corresponds to a deformed Jacobi group and describes Lichnerowicz's original algebra of constant curvature, differential geometric operators acting on symmetric tensors. The case (2p,Q)=(0,1) is simply the {\\cal N}=1 superparticle whose supercharge amounts to the Dirac operat...
Energy Technology Data Exchange (ETDEWEB)
Carvalho, L. Faria; Toppan, F., E-mail: leofc@cbpf.b, E-mail: toppan@cbpf.b [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil); Kuznetsova, Z., E-mail: zhanna.kuznetsova@ufabc.edu.b [Universidade Federal do ABC (UFABC), Santo Andre, SP (Brazil)
2009-07-01
We discuss four off-shell N = 4 D = 1 supersymmetry transformations, their associated one-dimensional -models and their mutual relations. They are given by I - the (4, 4){sub lin} linear 'root' supermultiplet (supersymmetric extension of R{sup 4}), II - the (3, 4, 1){sub lin} linear supermultiplet (supersymmetric extension of R3), III - the (3, 4, 1){sub nl} non-linear supermultiplet living on S{sup 3} and IV - the (2, 4, 2){sub nl} non-linear supermultiplet living on S{sup 2}. The I {yields} II map is the supersymmetric extension of the R4 {yields} R3 bilinear map, while the II {yields} IV map is the supersymmetric extension of the S{sup 3} {yields} S{sup 2} first Hopf fibration. The restrictions on the S{sup 3}, S{sup 2} spheres are expressed in terms of the stereo graphic projections. The non-linear supermultiplets, whose super transformations are local differential polynomials, are not equivalent to the linear supermultiplets with the same field content. The -models are determined in terms of an unconstrained pre potential of the target coordinates. The Uniformization Problem requires solving an inverse problem for the pre potential. The basic features of the supersymmetric extension of the second and third Hopf maps are briefly sketched. Finally, the Schur's lemma (i.e. the real, complex or quaternionic property) is extended to all minimal linear supermultiplets up to N {<=} 8. (author)
Minimal Generalized Lyapunov Function Theorems for Nonlinear Systems%非线性系统的最小广义Lyapunov函数定理
Institute of Scientific and Technical Information of China (English)
玉强; 吴保卫
2014-01-01
利用Zorn引理和LaSalle不变原理，研究一般非线性系统最小广义 Lyapunov 函数的存在性，证明了最小(非负)广义 Lyapunov 函数和最小(非负)强广义 Lyapunov 函数的存在性定理。%Based on Zorn’s lemma and LaSalle’s invariance principle,the existence of the minimal generalized Lyapunov function for nonlinear systems was considered. We developed the minimal generalized Lyapunov function theorems and the minimal strong generalized Lyapunov function theorems for nonlinear dynamical systems.
Coward, Adrian V.; Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.
1994-01-01
In this paper the nonlinear stability of two-phase core-annular flow in a pipe is examined when the acting pressure gradient is modulated by time harmonic oscillations and viscosity stratification and interfacial tension is present. An exact solution of the Navier-Stokes equations is used as the background state to develop an asymptotic theory valid for thin annular layers, which leads to a novel nonlinear evolution describing the spatio-temporal evolution of the interface. The evolution equation is an extension of the equation found for constant pressure gradients and generalizes the Kuramoto-Sivashinsky equation with dispersive effects found by Papageorgiou, Maldarelli & Rumschitzki, Phys. Fluids A 2(3), 1990, pp. 340-352, to a similar system with time periodic coefficients. The distinct regimes of slow and moderate flow are considered and the corresponding evolution is derived. Certain solutions are described analytically in the neighborhood of the first bifurcation point by use of multiple scales asymptotics. Extensive numerical experiments, using dynamical systems ideas, are carried out in order to evaluate the effect of the oscillatory pressure gradient on the solutions in the presence of a constant pressure gradient.
Duality and Superconvergence Relation in Supersymmetric Gauge Theories
Tachibana, M
1998-01-01
We investigate the phase structures of various N=1 supersymmetric gauge theories including even the exceptional gauge group from the viewpoint of superconvergence of the gauge field propagator. Especially we analyze in detail whether a new type of duality recently discovered by Oehme in $SU(N_c)$ gauge theory coupled to fundamental matter fields can be found in more general gauge theories with more general matter representations or not. The result is that in the cases of theories including matter fields in only the fundamental representation, Oehme's duality holds but otherwise it does not. In the former case, superconvergence relation might give good criterion to describe the interacting non-Abelian Coulomb phase without using some information from dual magnetic theory.
General Trimmed Estimation : Robust Approach to Nonlinear and Limited Dependent Variable Models
Cizek, P.
2004-01-01
High breakdown-point regression estimators protect against large errors and data con- tamination. Motivated by some { the least trimmed squares and maximum trimmed like- lihood estimators { we propose a general trimmed estimator, which unifies and extends many existing robust procedures. We derive
Characters of the Solutions to a Generalized Nonlinear Max-type Difference Equation
Institute of Scientific and Technical Information of China (English)
SHI Qi-hong; SU Xing; YUAN Guo-qiang; XIAO Qian
2013-01-01
This paper is concerned with the boundedness and asymptotic behavior of positive solutions for a generalized difference equation arising from automatic control theory.The main results improve and extend the ones in the previous works to a large extent.One in particular is that Rouche's theorem is available to prove the convergence of solutions.
Ye, Jian
In Part I, we first study an iso-spectral deformation of general matrix which is a natural generalization of the nonperiodic Toda lattice equation. This deformation is equivalent to the Cholesky flow. We prove the integrability of the deformation, and give an explicit formula for the solution to the initial value problem. The formula is obtained by generalizing the orthogonalization procedure of Szego. Using the formula, the solution to the LU factorization can be constructed explicitly. Based on the root spaces for simple Lie algebras, we consider several reductions of the equation. This leads to generalized Toda equations related to other classical semi-simple Lie algebra which include the integrable systems studied by Bogoyavlensky and Kostant. We show these systems can be solved explicitly in a unified way. Based on the explicit solutions, we then consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with distinct real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda lattice equations introduced by Kodama and Ye. These Toda lattices consist of 2N-1 different systems with hamiltonians H = [[1]/over[2
A generalization of the MDS method by mixed integer linear and nonlinear mathematical models
Directory of Open Access Journals (Sweden)
Sadegh Niroomand
2014-09-01
Full Text Available The Multi-Dimensional Scaling (MDS method is used in statistics to detect hidden interrelations among multi-dimensional data and it has a wide range of applications. The method’s input is a matrix that describes the similarity/dissimilarity among objects of unknown dimension. The objects are generally reconstructed as points of a lower dimensional space to reveal the geometric configuration of the objects. The original MDS method uses Euclidean distance, for measuring both the distance of the reconstructed points and the bias of the reconstructed distances from the original similarity values. In this paper, these distances are distinguished, and distances other than Euclidean are also used, generalizing the MDS method. Two different distances may be used for the two different purposes. Therefore the instances of the generalized MDS model are denoted as model, where the first distance is the type of distance of the reconstructed points and the second one measures the bias of the reconstructed distances and the similarity values. In the case of and distances mixed-integer programming models are provided. The computational experiences show that the generalized model can catch the key properties of the original configuration, if any exist. Keywords: Multivariate Analysis; Multi-Dimensional Scaling; Optimization; Mixed Integer Linear Programming; Statistics.
Institute of Scientific and Technical Information of China (English)
宋丽娜; 王维国
2012-01-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Song, Li-Na; Wang, Wei-Guo
2012-08-01
By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.
Measuring And Explaining The Supersymmetric Lagrangian
Wang, L
2002-01-01
The issues of measuring the supersymmetric Lagrangian once data is available, and making the connections between the low energy effective Lagrangian and fundamental theory, are considered. After a brief introduction to the fundamentals of supersymmetry and overview of Minimal Supersymmetric Standard Model (MSSM), case studies in ways of measuring different parameters in the low energy MSSM Lagrangian are presented. They include: measuring CP violation phases and LSP masses in gluino decay; Higgs production and detection; flavor and CP violation in b → sγ processes; signature of cold dark matter in the cosmic rays. Potential ambiguities in the process of recovering the high energy effective Lagrangian from low energy data are discussed. A new basis, which is explicitly independent of unphysical parameters, is proposed to write the renormalization group equations. After a brief survey of some basic issues of string theory phenomenology, a string theory motivated Pati-Salam like model is const...
A constrained supersymmetric left-right model
Hirsch, Martin; Opferkuch, Toby; Porod, Werner; Staub, Florian
2016-01-01
We present a supersymmetric left-right model which predicts gauge coupling unification close to the string scale and extra vector bosons at the TeV scale. The subtleties in constructing a model which is in agreement with the measured quark masses and mixing for such a low left-right breaking scale are discussed. It is shown that in the constrained version of this model radiative breaking of the gauge symmetries is possible and a SM-like Higgs is obtained. Additional CP-even scalars of a similar mass or even much lighter are possible. The expected mass hierarchies for the supersymmetric states differ clearly from those of the constrained MSSM. In particular, the lightest down-type squark, which is a mixture of the sbottom and extra vector-like states, is always lighter than the stop. We also comment on the model's capability to explain current anomalies observed at the LHC.
A supersymmetric consistent truncation for conifold solutions
Cassani, Davide
2010-01-01
We establish a supersymmetric consistent truncation of type IIB supergravity on the T^{1,1} coset space, based on extending the Papadopoulos-Tseytlin ansatz to the full set of SU(2)xSU(2) invariant Kaluza-Klein modes. The five-dimensional model is a gauged N=4 supergravity with three vector multiplets, which incorporates various conifold solutions and is suitable for the study of their dynamics. By analysing the scalar potential we find a family of new non-supersymmetric AdS_5 extrema interpolating between a solution obtained long ago by Romans and a solution employing an Einstein metric on T^{1,1} different from the standard one. Finally, we discuss some simple consistent subtruncations preserving N=2 supersymmetry. One of them is compatible with the inclusion of smeared D7-branes.
Bound States Of Supersymmetric Black Holes
Britto-Pacumio, R A
2002-01-01
The quantum mechanics of N slowly-moving supersymmetric black holes in five dimensions is considered. A divergent continuum of states describing arbitrarily closely bound black holes with arbitrarily small excitation energies is found. A superconformal structure appears at low energies and can be used to define a topological index counting the weighted number of supersymmetric bound states. It is shown that the index is determined from the dimensions of certain cohomology classes on the symmetric product of N copies of R4. This bound state index is computed exactly for two and three black holes. The required regulator for the infrared continuum of near-coincident black holes is chosen in accord with the enhanced superconformal symmetry.
Phenomenology of the Utilitarian Supersymmetric Standard Model
Fraser, Sean; Ma, Ernest; Pollard, Nicholas; Popov, Oleg; Zakeri, Mohammadreza
2016-01-01
We study the 2010 specific version of the 2002 proposed $U(1)_X$ extension of the supersymmetric standard model, which has no $\\mu$ term and conserves baryon number and lepton number separately and automatically. We consider in detail the scalar sector as well as the extra $Z_X$ gauge boson, and their interactions with the necessary extra color-triplet particles of this model, which behave as leptoquarks. We show how the diphoton excess at 750 GeV, recently observed at the LHC, may be explained within this context. We identify a new fermion dark-matter candidate and discuss its properties. An important byproduct of this study is the discovery of relaxed supersymmetric constraints on the Higgs boson's mass of 125 GeV.
Phenomenology of the utilitarian supersymmetric standard model
Fraser, Sean; Kownacki, Corey; Ma, Ernest; Pollard, Nicholas; Popov, Oleg; Zakeri, Mohammadreza
2016-08-01
We study the 2010 specific version of the 2002 proposed U(1)X extension of the supersymmetric standard model, which has no μ term and conserves baryon number and lepton number separately and automatically. We consider in detail the scalar sector as well as the extra ZX gauge boson, and their interactions with the necessary extra color-triplet particles of this model, which behave as leptoquarks. We show how the diphoton excess at 750 GeV, recently observed at the LHC, may be explained within this context. We identify a new fermion dark-matter candidate and discuss its properties. An important byproduct of this study is the discovery of relaxed supersymmetric constraints on the Higgs boson's mass of 125 GeV.
Supersymmetric QCD: Exact Results and Strong Coupling
Dine, Michael; Pack, Lawrence; Park, Chang-Soon; Ubaldi, Lorenzo; Wu, Weitao
2011-01-01
We revisit two longstanding puzzles in supersymmetric gauge theories. The first concerns the question of the holomorphy of the coupling, and related to this the possible definition of an exact (NSVZ) beta function. The second concerns instantons in pure gluodynamics, which appear to give sensible, exact results for certain correlation functions, which nonetheless differ from those obtained using systematic weak coupling expansions. For the first question, we extend an earlier proposal of Arkani-Hamed and Murayama, showing that if their regulated action is written suitably, the holomorphy of the couplings is manifest, and it is easy to determine the renormalization scheme for which the NSVZ formula holds. This scheme, however, is seen to be one of an infinite class of schemes, each leading to an exact beta function; the NSVZ scheme, while simple, is not selected by any compelling physical consideration. For the second question, we explain why the instanton computation in the pure supersymmetric gauge theory is...
Selecting Supersymmetric String Scenarios From Sparticle Spectra
Allanach, Benjamin C; Quevedo, Fernando
2002-01-01
We approach the following question: if supersymmetry is discovered, how can we select among different supersymmetric extensions of the Standard Model? In particular, we perform an analysis of the sparticle spectrum in low-energy string effective theories, asking which observables best distinguish various scenarios. We examine scenarios differing by the fundamental string scale and concentrate on GUT and intermediate scale models. We scan over all parameters (two goldstino angles, tan beta and the gravitino mass) in each scenario, finding ratios of sparticle masses that provide the maximum discrimination between them. The necessary accuracy for discrimination is determined in each case. We find that the required accuracy on various sparticle mass ratios is at the few percent level, a precision that may be achieved in future linear colliders. We place phenomenological constraints on the parameter space and determine the supersymmetric contribution to the muon anomalous magnetic moment.
Galoisian Approach to Supersymmetric Quantum Mechanics
Acosta-Humanez, Primitivo B
2009-01-01
This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\\"odinger equation, specially the integrable cases in the sense of the Picard-Vessiot theory and the main algorithmic tools used here are the Kovacic algorithm and the \\emph{algebrization method} to obtain linear differential equations with rational coefficients. We analyze the Darboux transformations, Crum iterations and supersymmetric quantum mechanics with their \\emph{algebrized} versions from a Galoisian approach. Applying the algebrization method and the Kovacic's algorithm we obtain the ground state, the set of eigenvalues, eigenfunctions, the differential Galois groups and eigenrings of some Schr\\"odinger equation with potentials such as exactly solvable and shape invariant potentials. Finally, we introduce one methodology to find exactly solvable potentials: to construct other potentials, we apply the algebrization alg...
The gravitino problem in supersymmetric warm inflation
Sanchez, Juan C Bueno; Berera, Arjun; Dimopoulos, Konstantinos; Kohri, Kazunori
2010-01-01
The warm inflation paradigm considers the continuous production of radiation during inflation due to dissipative effects. In its strong dissipation limit, warm inflation gives way to a radiation dominated Universe. High scale inflation then yields a high reheating temperature, which then poses a severe gravitino overproduction problem for the supersymmetric realisations of warm inflation. In this paper we show that in certain class of supersymmetric models the dissipative dynamics of the inflaton is such that the field can avoid its complete decay after inflation. In some cases, the residual energy density stored in the field oscillations may come to dominate over the radiation bath at a later epoch. If the inflaton field finally decays much later than the onset of the matter dominated phase, the entropy produced in its decay may be sufficient to counteract the excess of gravitinos produced during the last stages of warm inflation.
Supersymmetric composite gauge fields with compensators
Nishino, Hitoshi; Rajpoot, Subhash
2016-06-01
We study supersymmetric composite gauge theory, supplemented with compensator mechanism. As our first example, we give the formulation of N = 1 supersymmetric non-Abelian composite gauge theory without the kinetic term of a non-Abelian gauge field. The important ingredient is the Proca-Stueckelberg-type compensator scalar field that makes the gauge-boson field equation non-singular, i.e., the field equation can be solved for the gauge field algebraically as a perturbative expansion. As our second example, we perform the gauging of chiral-symmetry for N = 1 supersymmetry in four dimensions by a composite gauge field. These results provide supporting evidence for the consistency of the mechanism that combines the composite gauge field formulations and compensator formulations, all unified under supersymmetry.
Flavor Mixing Phenomenology in Supersymmetric Models
Rehman, Muhammad
2016-01-01
This dissertation investigates the flavor mixing effects in supersymmetric models on electroweak precision observables, Higgs boson mass predictions, B-physics observables, quark flavor violating Higgs decays, lepton flavor violating charged lepton decays and lepton flavor violating Higgs decays. The flavor mixing effects are studied in model independent way i.e. by putting off-diagonal entries in the sfermion mass matrix by hand as well as in the minimal flavor violating constrained MSSM, where mixing can originate from CKM matrix in the case of squarks and from PMNS matrix in the case of sleptons. We found that flavor mixing can have large impact to some observables, enabling us to put new constraints on parameter space in supersymmetric models.
Topological solitons in the supersymmetric Skyrme model
Gudnason, Sven Bjarke; Sasaki, Shin
2016-01-01
A supersymmetric extension of the Skyrme model was obtained recently, which consists of only the Skyrme term in the Nambu-Goldstone (pion) sector complemented by the same number of quasi-Nambu-Goldstone bosons. Scherk-Schwarz dimensional reduction yields a kinetic term in three or lower dimensions and a potential term in two dimensions, preserving supersymmetry. Euclidean solitons (instantons) are constructed in the supersymmetric Skyrme model. In four dimensions, the soliton is an instanton first found by Speight. Scherk-Schwarz dimensional reduction is then performed once to get a 3-dimensional theory in which a 3d Skyrmion-instanton is found and then once more to get a 2d theory in which a 2d vortex-instanton is obtained. Although the last one is a global vortex it has finite action in contrast to conventional theory. All of them are non-BPS states breaking all supersymmetries.
Planar Gravitational Corrections For Supersymmetric Gauge Theories
Dijkgraaf, R; Ooguri, H; Vafa, C; Zanon, D
2004-01-01
In this paper we discuss the contribution of planar diagrams to gravitational F-terms for N=1 supersymmetric gauge theories admitting a large N description. We show how the planar diagrams lead to a universal contribution at the extremum of the glueball superpotential, leaving only the genus one contributions, as was previously conjectured. We also discuss the physical meaning of gravitational F-terms.
Approximate Flavor Symmetry in Supersymmetric Model
Tao, Zhijian
1998-01-01
We investigate the maximal approximate flavor symmetry in the framework of generic minimal supersymmetric standard model. We consider the low energy effective theory of the flavor physics with all the possible operators included. Spontaneous flavor symmetry breaking leads to the approximate flavor symmetry in Yukawa sector and the supersymmetry breaking sector. Fermion mass and mixing hierachies are the results of the hierachy of the flavor symmetry breaking. It is found that in this theory i...
Utilitarian Supersymmetric Gauge Model of Particle Interactions
Ma, Ernest
2010-01-01
A remarkable U(1) gauge extension of the supersymmetric standard model was proposed eight years ago. It is anomaly-free, has no mu term, and conserves baryon and lepton numbers automatically. The phenomenology of a specific version of this model is discussed. In particular, leptoquarks are predicted, with couplings to the heavy singlet neutrinos, the scalar partners of which may be components of dark matter. The Majorana neutrino mass matrix itself may have two zero subdeterminants.
Renormalizable supersymmetric gauge theory in six dimensions
Energy Technology Data Exchange (ETDEWEB)
Ivanov, E.A. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)]. E-mail: eivanov@theor.jinr.ru; Smilga, A.V. [SUBATECH, Universite de Nantes, 4 rue Alfred Kastler, BP 20722, Nantes 44307 (France)]. E-mail: smilga@subatech.in2p3.fr; Zupnik, B.M. [Bogoliubov Laboratory of Theoretical Physics, JINR, 141980 Dubna (Russian Federation)]. E-mail: zupnik@theor.jinr.ru
2005-10-17
We construct and discuss a 6D supersymmetric gauge theory involving four derivatives in the action. The theory involves a dimensionless coupling constant and is renormalizable. At the tree level, it enjoys N=(1,0) superconformal symmetry, but the latter is broken by quantum anomaly. Our study should be considered as preparatory for seeking an extended version of this theory which would hopefully preserve conformal symmetry at the full quantum level and be ultraviolet-finite.
Supersymmetric solutions for non-relativistic holography
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Blackett Laboratory, Imperial College, London (United Kingdom)]|[Institute for Mathematical Sciences, Imperial College, London (United Kingdom)
2009-01-15
We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z{>=}4 and z{>=}3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively. (orig.)
Simple supersymmetric methods in neutron diffusion
1996-01-01
We present the supersymmetric Witten and double Darboux (strictly isospectral) constructions as applied to the diffusion of thermal neutrons from an infinitely long line source. While the Witten construction is just a mathematical scheme, the double Darboux method introduces a one-parameter family of diffusion solutions which are strictly isospectral to the stationary solution. They correspond to a Darboux-transformed diffusion length which is flux dependent
Li, Shukai; Yang, Lixing; Gao, Ziyou; Li, Keping
2014-11-01
In this paper, the stabilization strategies of a general nonlinear car-following model with reaction-time delay of the drivers are investigated. The reaction-time delay of the driver is time varying and bounded. By using the Lyapunov stability theory, the sufficient condition for the existence of the state feedback control strategy for the stability of the car-following model is given in the form of linear matrix inequality, under which the traffic jam can be well suppressed with respect to the varying reaction-time delay. Moreover, by considering the external disturbance for the running cars, the robust state feedback control strategy is designed, which ensures robust stability and a smaller prescribed H∞ disturbance attenuation level for the traffic flow. Numerical examples are given to illustrate the effectiveness of the proposed methods.
On quasi-periodic solutions for generalized Boussinesq equation with quadratic nonlinearity
Shi, Yanling; Xu, Junxiang; Xu, Xindong
2015-02-01
In this paper, one-dimensional generalized Boussinesq equation: utt - uxx + (u2 + uxx)xx = 0 with boundary conditions ux(0, t) = ux(π, t) = uxxx(0, t) = uxxx(π, t) = 0 is considered. It is proved that the equation admits a Whitney smooth family of small-amplitude quasi-periodic solutions with 2-dimensional Diophantine frequencies. The proof is based on an infinite dimensional Kolmogorov-Arnold-Moser theorem and Birkhoff normal form.
Galaxy Bias and non-Linear Structure Formation in General Relativity
Baldauf, Tobias; Senatore, Leonardo; Zaldarriaga, Matias
2011-01-01
Length scales probed by large scale structure surveys are becoming closer to the horizon scale. Further, it has been recently understood that non-Gaussianity in the initial conditions could show up in a scale dependence of the bias of galaxies at the largest distances. It is therefore important to include General Relativistic effects. Here we provide a General Relativistic generalization of the bias, valid both for Gaussian and non-Gaussian initial conditions. The collapse of objects happens on very small scales, while long-wavelength modes are always in the quasi linear regime. Around every collapsing region, it is therefore possible to find a reference frame that is valid for all times and where the space time is almost flat: the Fermi frame. Here the Newtonian approximation is applicable and the equations of motion are the ones of the N-body codes. The effects of long-wavelength modes are encoded in the mapping from the cosmological frame to the local frame. For the linear bias, the effect of the long-wave...
Cosmological consequences of supersymmetric flat directions
Riva, Francesco; Sarkar, Subir; Giudice, Gian
In this work we analyze various implications of the presence of large field vacum expectation values (VEVs) along supersymmetric flat direct ions during the early universe. First, we discuss supersymmetric leptogenesis and the grav itino bound. Supersym- metric thermal leptogenesis with a hierarchical right-han ded neutrino mass spectrum normally requires the mass of the lightest right-handed neu trino to be heavier than about 10 9 GeV. This is in conflict with the upper bound on the reheating t empera- ture which is found by imposing that the gravitinos generate d during the reheating stage after inflation do not jeopardize successful nucleosy nthesis. We show that a solution to this tension is actually already incorporated i n the framework, because of the presence of flat directions in the supersymmetric scalar potential. Massive right- handed neutrinos are efficiently produced non-thermally and the observed baryon asymmetry can be explained even for a reheating temperature respecting the grav- itino bound...
Non-supersymmetric Orientifolds of Gepner Models
Gato-Rivera, B
2008-01-01
Starting from a previously collected set of tachyon-free closed strings, we search for N=2 minimal model orientifold spectra which contain the standard model and are free of tachyons and tadpoles at lowest order. For each class of tachyon-free closed strings -- bulk supersymmetry, automorphism invariants or Klein bottle projection -- we do indeed find non-supersymmetric and tachyon free chiral brane configurations that contain the standard model. However, a tadpole-cancelling hidden sector could only be found in the case of bulk supersymmetry. Although about half of the examples we have found make use of branes that break the bulk space-time supersymmetry, the resulting massless open string spectra are nevertheless supersymmetric in all cases. Dropping the requirement that the standard model be contained in the spectrum, we find chiral tachyon and tadpole-free solutions in all three cases, although in the case of bulk supersymmetry all massless spectra are supersymmetric. In the other two cases we find truly ...
Likelihood Analysis of Supersymmetric SU(5) GUTs
Energy Technology Data Exchange (ETDEWEB)
Bagnaschi, E. [DESY; Costa, J. C. [Imperial Coll., London; Sakurai, K. [Warsaw U.; Borsato, M. [Santiago de Compostela U.; Buchmueller, O. [Imperial Coll., London; Cavanaugh, R. [Illinois U., Chicago; Chobanova, V. [Santiago de Compostela U.; Citron, M. [Imperial Coll., London; De Roeck, A. [Antwerp U.; Dolan, M. J. [Melbourne U.; Ellis, J. R. [King' s Coll. London; Flächer, H. [Bristol U.; Heinemeyer, S. [Madrid, IFT; Isidori, G. [Zurich U.; Lucio, M. [Santiago de Compostela U.; Martínez Santos, D. [Santiago de Compostela U.; Olive, K. A. [Minnesota U., Theor. Phys. Inst.; Richards, A. [Imperial Coll., London; de Vries, K. J. [Imperial Coll., London; Weiglein, G. [DESY
2016-10-31
We perform a likelihood analysis of the constraints from accelerator experiments and astrophysical observations on supersymmetric (SUSY) models with SU(5) boundary conditions on soft SUSY-breaking parameters at the GUT scale. The parameter space of the models studied has 7 parameters: a universal gaugino mass $m_{1/2}$, distinct masses for the scalar partners of matter fermions in five- and ten-dimensional representations of SU(5), $m_5$ and $m_{10}$, and for the $\\mathbf{5}$ and $\\mathbf{\\bar 5}$ Higgs representations $m_{H_u}$ and $m_{H_d}$, a universal trilinear soft SUSY-breaking parameter $A_0$, and the ratio of Higgs vevs $\\tan \\beta$. In addition to previous constraints from direct sparticle searches, low-energy and flavour observables, we incorporate constraints based on preliminary results from 13 TeV LHC searches for jets + MET events and long-lived particles, as well as the latest PandaX-II and LUX searches for direct Dark Matter detection. In addition to previously-identified mechanisms for bringing the supersymmetric relic density into the range allowed by cosmology, we identify a novel ${\\tilde u_R}/{\\tilde c_R} - \\tilde{\\chi}^0_1$ coannihilation mechanism that appears in the supersymmetric SU(5) GUT model and discuss the role of ${\\tilde \
PBH tests for nonlinear systems
Kawano, Yu; Ohtsuka, Toshiyuki
2017-01-01
Recently, concepts of nonlinear eigenvalues and eigenvectors are introduced. In this paper, we establish connections between the nonlinear eigenvalues and nonlinear accessibility/observability. In particular, we provide a generalization of Popov- Belevitch-Hautus (PBH) test to nonlinear accessibilit
A General Nonlinear Fluid Model for Reacting Plasma-Neutral Mixtures
Energy Technology Data Exchange (ETDEWEB)
Meier, E T; Shumlak, U
2012-04-06
A generalized, computationally tractable fluid model for capturing the effects of neutral particles in plasmas is derived. The model derivation begins with Boltzmann equations for singly charged ions, electrons, and a single neutral species. Electron-impact ionization, radiative recombination, and resonant charge exchange reactions are included. Moments of the reaction collision terms are detailed. Moments of the Boltzmann equations for electron, ion, and neutral species are combined to yield a two-component plasma-neutral fluid model. Separate density, momentum, and energy equations, each including reaction transfer terms, are produced for the plasma and neutral equations. The required closures for the plasma-neutral model are discussed.
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Bilinear approach to N=2 supersymmetric KdV equations
Institute of Scientific and Technical Information of China (English)
2009-01-01
The N=2 supersymmetric KdV equations are studied within the framework of Hirota bilinear method. For two such equations, namely N=2, a=4 and N=2, a=1 supersymmetric KdV equations, we obtain the corresponding bilinear formulations. Using them, we construct particular solutions for both cases. In particular, a bilinear Bcklund transformation is given for the N=2, a=1 supersymmetric KdV equation.
Vertex Operators for Irregular Conformal Blocks: Supersymmetric Case
Polyakov, Dimitri
2016-01-01
We construct supersymmetric irregular vertex operators of arbitrary rank, appearing in the colliding limit of primary fields. We find that the structure of the supersymmetric irregular vertices differs significantly from the bosonic case: upon supersymmetrization, the irregular operators are no longer the eigenstates of positive Virasoro and $W_N$ generators but block-diagonalize them. We relate the block-diagonal structure of the irregular vertices to contributions of the Ramond sector to the colliding limit.
On supersymmetric Chern-Simons-type theories in five dimensions
Kuzenko, Sergei M
2014-01-01
We present a closed-form expression for the supersymmetric non-Abelian Chern-Simons action in conventional five-dimensional N=1 superspace. Our construction makes use of the superform formalism to generate supersymmetric invariants. Similar ideas are applied to construct supersymmetric actions for off-shell supermultiplets with an intrinsic central charge. In particular, the large tensor multiplet is described in superspace for the first time.
Lee, Shiu-Hang; Nagataki, Shigehiro
2012-01-01
To better model the efficient production of cosmic rays (CRs) in supernova remnants (SNRs) with the associated coupling between CR production and SNR dynamics, we have generalized an existing cr-hydro-NEI code (i.e., Ellison et al. 2012) to include the following processes: (1) an explicit calculation of the upstream precursor structure including the position dependent flow speed, density, temperature, and magnetic field strength; (2) a momentum and space dependent CR diffusion coefficient; (3) an explicit calculation of magnetic field amplification (MFA); (4) calculation of the maximum CR momentum using the amplified magnetic field; (5) a finite Alfven speed for the particle scattering centers; and (6) the ability to accelerate a superthermal seed population of CRs as well as the ambient thermal plasma. While a great deal of work has been done modeling SNRs, most work has concentrated on either the continuum emission from relativistic electrons or ions, or the thermal emission from the shock heated plasma. Ou...
Andreasen, J; Kolesik, M
2012-09-01
Unidirectional pulse propagation equations [UPPE, Phys. Rev. E 70, 036604 (2004)] have provided a theoretical underpinning for computer-aided investigations into dynamics of high-power ultrashort laser pulses and have been successfully utilized for almost a decade. Unfortunately, they are restricted to applications in bulk media or, with additional approximations, to simple waveguide geometries in which only a few guided modes can approximate the propagating waveform. The purpose of this work is to generalize the directional pulse propagation equations to structures characterized by strong refractive index differences and material interfaces. We also outline a numerical solution framework that draws on the combination of the bulk-media UPPE method with single-frequency beam-propagation techniques.
Generalized geometry lectures on type II backgrounds
Tsimpis, Dimitrios
2016-01-01
The first part of these notes is a self-contained introduction to generalized complex geometry. It is intended as a `user manual' for tools used in the study of supersymmetric backgrounds of supergravity. In the second part we review some past and recent results on the generalized complex structure of supersymmetric type II vacua in various dimensions.
一般非线性渗流方程正性的扩展%EXPANSION OF POSITIVITY FOR GENERAL NONLINEAR FILTRATION EQUATIONS
Institute of Scientific and Technical Information of China (English)
李海峰; 霍振宏; 曹贤通
2007-01-01
In this paper,we investigate a behavior of solution of general nonlinear filtration equations.Combining De Giorgi technique with Benilan,Cradall and Pirre(BCP) estimates,we obtain the expansion of positivity for general nonlinear filtration equation.%本文研究一般非线性渗流方程解的一种性态.利用De Giorgi方法与BCP估计相结合,得到了一般非线性渗流方程正性的扩展性质,推广了非线性渗流方程的结果.
Holographic description of non-supersymmetric orbifolded D1-D5-P solutions
Chakrabarty, Bidisha; Virmani, Amitabh
2015-01-01
Non-supersymmetric black hole microstates are of great interest in the context of the black hole information paradox. We identify the holographic description of the general class of non-supersymmetric orbifolded D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. This class includes both completely smooth solutions and solutions with conical defects, and in the near-decoupling limit these solutions describe degrees of freedom in the cap region. The CFT description involves a general class of states obtained by fractional spectral flow in both left-moving and right-moving sectors, generalizing previous work which studied special cases in this class. We compute the massless scalar emission spectrum and emission rates in both gravity and CFT and find perfect agreement, thereby providing strong evidence for our proposed identification. We also investigate the physics of ergoregion emission as pair creation for these orbifolded solutions. Our results represent the largest class of non-supe...
The unified minimal supersymmetric model with large Yukawa couplings
Rattazzi, Riccardo
1996-01-01
The consequences of assuming the third-generation Yukawa couplings are all large and comparable are studied in the context of the minimal supersymmetric extension of the standard model. General aspects of the RG evolution of the parameters, theoretical constraints needed to ensure proper electroweak symmetry breaking, and experimental and cosmological bounds on low-energy parameters are presented. We also present complete and exact semi-analytic solutions to the 1-loop RG equations. Focusing on SU(5) or SO(10) unification, we analyze the relationship between the top and bottom masses and the superspectrum, and the phenomenological implications of the GUT conditions on scalar masses. Future experimental measurements of the superspectrum and of the strong coupling will distinguish between various GUT-scale scenarios. And if present experimental knowledge is to be accounted for most naturally, a particular set of predictions is singled out.
Anatomy of Higgs mass in supersymmetric inverse seesaw models
Energy Technology Data Exchange (ETDEWEB)
Chun, Eung Jin, E-mail: ejchun@kias.re.kr [Korea Institute for Advanced Study, Seoul 130-722 (Korea, Republic of); Mummidi, V. Suryanarayana, E-mail: soori9@cts.iisc.ernet.in [Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012 (India); Vempati, Sudhir K., E-mail: vempati@cts.iisc.ernet.in [Centre for High Energy Physics, Indian Institute of Science, Bangalore 560012 (India)
2014-09-07
We compute the one loop corrections to the CP-even Higgs mass matrix in the supersymmetric inverse seesaw model to single out the different cases where the radiative corrections from the neutrino sector could become important. It is found that there could be a significant enhancement in the Higgs mass even for Dirac neutrino masses of O(30) GeV if the left-handed sneutrino soft mass is comparable or larger than the right-handed neutrino mass. In the case where right-handed neutrino masses are significantly larger than the supersymmetry breaking scale, the corrections can utmost account to an upward shift of 3 GeV. For very heavy multi TeV sneutrinos, the corrections replicate the stop corrections at 1-loop. We further show that general gauge mediation with inverse seesaw model naturally accommodates a 125 GeV Higgs with TeV scale stops.
Integrable structure in supersymmetric gauge theories with massive hypermultiplets
Ahn, C; Ahn, Changhyun; Nam, Soonkeon
1996-01-01
We study the quantum moduli space of vacua of N=2 supersymmetric SU(N_c) gauge theories coupled to N_f flavors of quarks in the fundamental representation. We identify the moduli space of the N_c = 3 and N_f=2 massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with {\\it massive} quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of N_{c}=3 with N_{f}=0, 1, 2. We discuss possible generalizations of the integrable systems relevant to gauge theories with N_c \
Local gauge coupling running in supersymmetric gauge theories on orbifolds
Energy Technology Data Exchange (ETDEWEB)
Hillenbach, M.
2007-11-21
By extending Feynman's path integral calculus to fields which respect orbifold boundary conditions we provide a straightforward and convenient framework for loop calculations on orbifolds. We take advantage of this general method to investigate supersymmetric Abelian and non-Abelian gauge theories in five, six and ten dimensions where the extra dimensions are compactified on an orbifold. We consider hyper and gauge multiplets in the bulk and calculate the renormalization of the gauge kinetic term which in particular allows us to determine the gauge coupling running. The renormalization of the higher dimensional theories in orbifold spacetimes exhibits a rich structure with three principal effects: Besides the ordinary renormalization of the bulk gauge kinetic term the loop effects may require the introduction of both localized gauge kinetic terms at the fixed points/planes of the orbifold and higher dimensional operators. (orig.)
An Interacting N = 2 Supersymmetric Quantum Mechanical Model: Novel Symmetries
Krishna, S; Malik, R P
2015-01-01
We demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting N = 2 supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realization of the de Rham cohomological operators of differential geometry. We derive the nilpotent N = 2 SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a (1, 2)-dimensional supermanifold on which our N = 2 SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables, obtained after the imposition of the SUSY invariant restrictions, and...
Supersymmetric quantum mechanics with Levy disorder in one dimension
Comtet, Alain; Tourigny, Yves
2011-01-01
We consider the Schroedinger equation with a supersymmetric random potential, where the superpotential is a Levy noise. We focus on the problem of computing the so-called complex Lyapunov exponent, whose real and imaginary parts are, respectively, the Lyapunov exponent and the integrated density of states of the system. In the case where the Levy process is non-decreasing, we show that the calculation of the complex Lyapunov exponent reduces to a Stieltjes moment problem, we ascertain the low-energy behaviour of the density of states in some generality, and relate it to the distributional properties of the Levy process. We review the known solvable cases, where the complex Lyapunov exponent can be expressed in terms of special functions, and discover a new one.