Finite-Time Singularity Signature of Hyperinflation
Sornette, D; Zhou, W X
2003-01-01
We present a novel analysis extending the recent work of Mizuno et al. [2002] on the hyperinflations of Germany (1920/1/1-1923/11/1), Hungary (1945/4/30-1946/7/15), Brazil (1969-1994), Israel (1969-1985), Nicaragua (1969-1991), Peru (1969-1990) and Bolivia (1969-1985). On the basis of a generalization of Cagan's model of inflation based on the mechanism of ``inflationary expectation'' or positive feedbacks between realized growth rate and people's expected growth rate, we find that hyperinflations can be characterized by a power law singularity culminating at a critical time $t_c$. Mizuno et al.'s double-exponential function can be seen as a discrete time-step approximation of our more general nonlinear ODE formulation of the price dynamics which exhibits a finite-time singular behavior. This extension of Cagan's model, which makes natural the appearance of a critical time $t_c$, has the advantage of providing a well-defined end of the clearly unsustainable hyperinflation regime. We find an excellent and reli...
Finite time singularities in a class of hydrodynamic models
DEFF Research Database (Denmark)
Ruban, V.P.; Podolsky, D.I.; Juul Rasmussen, J.
2001-01-01
), a finite value of alpha results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales. The linear analysis of small symmetrical deviations from a stationary...... analytically. They describe the formation of a finite time singularity, with all length scales decreasing like (t*-t)(1/(2-alpha)), where t* is the singularity time....
Effects of Finite-time Singularities on Gravitational Waves
Kleidis, K
2016-01-01
We analyze the impact of finite-time singularities on gravitational waves, in the context of $F(R)$ gravity. We investigate which singularities are allowed to occur during the inflationary era, when gravitational waves are considered, and we discuss the quantitative implications of each allowed singularity. As we show, only a pressure singularity, the so-called Type II and also a Type IV singularity are allowed to occur during the inflationary era. In the case of a Type II, the resulting amplitude of the gravitational wave is zero or almost zero, hence this pressure singularity has a significant impact on the primordial gravitational waves. The case of a Type IV singularity is more interesting since as we show, the singularity has no effect on the amplitude of the gravitational waves. Therefore, this result combined with the fact that the Type IV singularity affects only the dynamics of inflation, leads to the conclusion that the Universe passes smoothly through a Type IV singularity.
Finite-time singularity in the evolution of hyperinflation episodes
Szybisz, Martin A.; Leszek Szybisz
2008-01-01
A model proposed by Sornette, Takayasu, and Zhou for describing hyperinflation regimes based on adaptive expectations expressed in terms of a power law which leads to a finite-time singularity is revisited. It is suggested to express the price index evolution explicitly in terms of the parameters introduced along the theoretical formulation avoiding any combination of them used in the original work. This procedure allows to study unambiguously the uncertainties of such parameters when an erro...
Finite-Time Singularities in $k=0$ FLRW Cosmologies
Kohli, Ikjyot Singh
2015-01-01
In this paper, we consider a spatially flat FLRW cosmological model with matter obeying a barotropic equation of state $p = w \\mu$, $-1
Finite time singularities in a class of hydrodynamic models
Ruban, V P; Rasmussen, J J
2001-01-01
Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form ${\\cal L}\\sim\\int k^\\alpha|{\\bf v_k}|^2d^3{\\bf k}$ in 3D Fourier representation, where $\\alpha$ is a constant, $0<\\alpha< 1$. Unlike the case $\\alpha=0$ (the usual Eulerian hydrodynamics), a finite value of $\\alpha$ results in a finite energy for a singular frozen-in vortex filament. This property allows us to study the dynamics of such filaments without necessity in some regularization procedure. The linear analysis of small symmetrical deviations from a stationary solution is performed for a pair of anti-parallel vortex filaments and an analog of the Crow instability is found at small wave-numbers. A local approximate Hamiltonian is obtained for nonlinear long-scale dynamics of this system. Self-similar solutions of the corresponding equations are found analytically, which describe finite time singularity formation with all length scales decreasing like $(t^*-t)^{1/(2-\\alph...
Energy identity of the heat flow of H-systems at finite singular time
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
It is well known that there exists a global solution to the heat flow of H-systems.If the solution satisfies a certain energy inequality,it is global regular with at most finitely many singularities.Under the same energy inequality,we can show the energy identity of the heat flow of H-systems at finite singular time.The most interesting thing in our proof is that we find the singular points can only occur in the interior of the set in some sense.
Finite-time singularities in f(R, T) gravity and the effect of conformal anomaly
Houndjo, M J S; Campos, J P; Piattella, O F
2012-01-01
We investigate $f(R,T)$ gravity models ($R$ is the curvature scalar and $T$ is the trace of the stress-energy tensor of ordinary matter) that are able to reproduce the four known types of future finite-time singularities. We choose a suitable expression for the Hubble parameter in order to realise the cosmic acceleration and we introduce two parameters, $\\alpha$ and $H_s$, which characterise each type of singularity. We address conformal anomaly and we observe that it cannot remove the sudden singularity or the type IV one, but, for some values of $\\alpha$, the big rip and the type III singularity may be avoided. We also find that, even without taking into account conformal anomaly, the big rip and the type III singularity may be removed thanks to the presence of the $T$ contribution of the $f(R,T)$ theory.
Finite-time singularities in the dynamical evolution of contact lines
Pelinovsky, D E
2013-01-01
We study finite-time singularities in the linear advection-diffusion equation with a variable speed on a semi-infinite line. The variable speed is determined by an additional condition at the boundary, which models the dynamics of a contact line of a hydrodynamic flow at a 180 contact angle. Using apriori energy estimates, we derive conditions on variable speed that guarantee that a sufficiently smooth solution of the linear advection--diffusion equation blows up in a finite time. Using the class of self-similar solutions to the linear advection-diffusion equation, we find the blow-up rate of singularity formation. This blow-up rate does not agree with previous numerical simulations of the model problem.
Shocks and finite-time singularities in Hele-Shaw flow
Energy Technology Data Exchange (ETDEWEB)
Teodorescu, Razvan [Los Alamos National Laboratory; Wiegmann, P [UNIV OF MONTREAL; Lee, S-y [UNIV OF CHICAGO
2008-01-01
Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusplike singularities. We show that the ill-defined problem admits a weak dispersive solution when singularities give rise to a graph of shock waves propagating in the viscous fluid. The graph of shocks grows and branches. Velocity and pressure jump across the shock. We formulate a few simple physical principles which single out the dispersive solution and interpret shocks as lines of decompressed fluid. We also formulate the dispersive solution in algebro-geometrical terms as an evolution of Krichever-Boutroux complex curve. We study in details the most generic (2,3) cusp singularity which gives rise to an elementary branching event. This solution is self-similar and expressed in terms of elliptic functions.
Finite-time singularity in the dynamics of the world population, economic and financial indices
Johansen, Anders; Sornette, Didier
2001-05-01
Contrary to common belief, both the Earth's human population and its economic output have grown faster than exponential, i.e., in a super-Malthusian mode, for most of the known history. These growth rates are compatible with a spontaneous singularity occurring at the same critical time 2052±10 signaling an abrupt transition to a new regime. The degree of abruptness can be infered from the fact that the maximum of the world population growth rate was reached in 1970, i.e., about 80 years before the predicted singular time, corresponding to approximately 4% of the studied time interval over which the acceleration is documented. This rounding-off of the finite-time singularity is probably due to a combination of well-known finite-size effects and friction and suggests that we have already entered the transition region to a new regime. As theoretical support, a multivariate analysis coupling population, capital, R&D and technology shows that a dramatic acceleration in the population growth during most of the timespan can occur even though the isolated dynamics do not exhibit it. Possible scenarios for the cross-over and the new regime are discussed.
Finite-time singularities in the dynamics of hyperinflation in an economy.
Szybisz, Martín A; Szybisz, Leszek
2009-08-01
The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective "adaptive inflation expectations" with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r(t), changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time t(c). By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p(t) . One is given by the already reported form p(t) approximately (t(c)-t)(-alpha) (with alpha>0 ) and the other exhibits a logarithmic divergence, p(t) approximately ln[1/(t(c)-t)] . The singularity is a signature for an economic crash. In the present work we express p(t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r(t) and p(t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.
Finite-time singularities in the dynamics of hyperinflation in an economy
Szybisz, Martín A.; Szybisz, Leszek
2009-08-01
The dynamics of hyperinflation episodes is studied by applying a theoretical approach based on collective “adaptive inflation expectations” with a positive nonlinear feedback proposed in the literature. In such a description it is assumed that the growth rate of the logarithmic price, r(t) , changes with a velocity obeying a power law which leads to a finite-time singularity at a critical time tc . By revising that model we found that, indeed, there are two types of singular solutions for the logarithmic price, p(t) . One is given by the already reported form p(t)≈(tc-t)-α (with α>0 ) and the other exhibits a logarithmic divergence, p(t)≈ln[1/(tc-t)] . The singularity is a signature for an economic crash. In the present work we express p(t) explicitly in terms of the parameters introduced throughout the formulation avoiding the use of any combination of them defined in the original paper. This procedure allows to examine simultaneously the time series of r(t) and p(t) performing a linked error analysis of the determined parameters. For the first time this approach is applied for analyzing the very extreme historical hyperinflations occurred in Greece (1941-1944) and Yugoslavia (1991-1994). The case of Greece is compatible with a logarithmic singularity. The study is completed with an analysis of the hyperinflation spiral currently experienced in Zimbabwe. According to our results, an economic crash in this country is predicted for these days. The robustness of the results to changes of the initial time of the series and the differences with a linear feedback are discussed.
Numerical investigations on the finite time singularity in two-dimensional Boussinesq equations
Yin, Z
2006-01-01
To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system describes a cap-like hot zone of fluid rising from the bottom, while the edges of the cap lag behind, forming eye-like vortices. The hot liquid is driven by the buoyancy and meanwhile attracted by the vortices, which leads to the singularity-forming mechanism in our simulation. In the previous 2D Boussinesq simulations, the symmetricial initial data is used. However, it is observed that the adoption of symmetry leads to coordinate singularity. Moreover, as demonstrated in this work that the locations of peak values for the vorticity and the temperature gradient becomes far apart as $t$ approaches the predicted blow-up time. This suggests that the symmetry assumption may be unreasonable for searching solution blow-ups. One of the main contributions of this work is to propose a...
Big-Bounce with Finite-time Singularity: The $F(R)$ Gravity Description
Odintsov, S D
2015-01-01
An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point, in the context of $F(R)$ modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce, do not produce a scale invariant spectrum and also the short wavelength modes, after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result, indicating the singular ...
Zhai, Ding; Lu, Anyang; Li, Jinghao; Zhang, Qingling
2016-10-01
This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman-Yakubovic-Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H- and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.
Ma, Yuechao; Fu, Lei
2016-10-01
This study employs the multiple Lyapunov-like function method and the average dwell-time concept of switching signal to investigate the finite-time H∞ static output-feedback (SOF) control problem for a class of discrete-time switched singular time-delay systems subject to actuator saturation. First, sufficient conditions are presented to guarantee the discrete-time switched singular time-delay system regular, causal and finite-time boundedness. Meanwhile, sufficient conditions are presented to ensure the H∞ disturbance attenuation level, and the design method of H∞ SOF controller is developed by solving matrix inequalities optimisation problem without any decompositions of system matrices and equivalent transformation. Finally, the effectiveness and merit of the theoretical results are shown through some numerical examples and several vivid illustrations.
Finite-time singularities in the dynamics of Mexican financial crises
Alvarez-Ramirez, Jose; Ibarra-Valdez, Carlos
2004-01-01
Historically, symptoms of Mexican financial crises have been strongly reflected in the dynamics of the Mexican peso to the dollar exchange currency market. Specifically, in the Mexican financial crises during 1990's, the peso suffered significant depreciation processes, which has important impacts in the macro- and micro-economical environment. In this paper, it is shown that the peso depreciation growth was greater than an exponential and that these growth rates are compatible with a spontaneous singularity occurring at a critical time, which signals an abrupt transition to new dynamical conditions. As in the major 1990's financial crisis in 1994-1995, some control actions (e.g., increasing the USA dollar supply) are commonly taken to decelerate the degree of abruptness of peso depreciation. Implications of these control actions on the crisis dynamics are discussed. Interestingly, by means of a simple model, it is demonstrated that the time at which the control actions begin to apply is critical to moderate the adverse effects of the financial crisis.
Inflation in exponential scalar model and finite-time singularity induced instability
Odintsov, S D
2015-01-01
We investigate how a Type IV future singularity can be included in the cosmological evolution of a well-known exponential model of inflation. In order to achieve this we use a two scalar field model, in the context of which the incorporation of the Type IV singularity can be consistently done. In the context of the exponential model we study, when a Type IV singularity is included in the evolution, an instability occurs in the slow-roll parameters, and in particular on the second slow-roll parameter. Particularly, if we abandon the slow-roll condition for both the scalars we shall use, then the most consistent description of the dynamics of the inflationary era is provided by the Hubble slow-roll parameters $\\epsilon_H$ and $\\eta_H$. Then, the second Hubble slow-roll parameter $\\eta_H$, which measures the duration of the inflationary era, becomes singular at the point where the Type IV singularity is chosen to occur, while the Hubble slow-roll parameter $\\epsilon_H$ is regular there. Therefore, this infinite ...
Carter subgroups of singular classical groups over finite fields
Institute of Scientific and Technical Information of China (English)
高有; 石新华
2004-01-01
Let Fq be a finite field with qelements whereq = pα. In the present paper, the authors study the existence and structure of Carter subgroups of singular symplectic group Sp (Fq), singular unitary group U ( Fq2 ) and singular orthogonal group O ( Fq ) ( n is even) over finite fields Fq.
Institute of Scientific and Technical Information of China (English)
冯俊娥; 吴臻; 孙甲冰
2005-01-01
The concept of finite-time stability for linear singular system is induced in this paper. Finite-time control problem is considered for linear singular systems with time-varying parametric uncertainties and exogenous disturbances. The disturbance satisfies a dynamical system with para- metric uncertainties. A sufficient condition is presented for robust finite-time stabilization via state feedback. The condition is translated to a feasibility problem involving restricted linear matrix in- equalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, an example is given to show the validity of the results.
Dallaston, M. C.; Tseluiko, D.; Zheng, Z.; Fontelos, M. A.; Kalliadasis, S.
2017-07-01
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilising the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent n = 3 has been used, namely, \\Pi(h)\\propto -1/h3 , where h is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent n (not necessarily equal to 3), which has not been previously performed. We focus on axisymmetric point-rupture solutions and show for the first time that pairs of solution branches merge as n decreases, starting at nc ≈ 1.485 . We verify that this observation also holds true for plane-symmetric line-rupture solutions for which the critical value turns out to be slightly larger than for the axisymmetric case, n_cplane≈ 1.499 . Computation of the full time-dependent problem also demonstrates the loss of stable similarity solutions and the subsequent onset of cascading, increasingly small structures.
Dallaston, Michael C; Zheng, Zhong; Fontelos, Marco A; Kalliadasis, Serafim
2016-01-01
A thin liquid film coating a planar horizontal substrate may be unstable to perturbations in the film thickness due to unfavourable intermolecular interactions between the liquid and the substrate, which may lead to finite-time rupture. The self-similar nature of the rupture has been studied before by utilizing the standard lubrication approximation along with the Derjaguin (or disjoining) pressure formalism used to account for the intermolecular interactions, and a particular form of the disjoining pressure with exponent $n=3$ has been used, namely, $\\Pi(h)\\propto -1/h^{3}$, where $h$ is the film thickness. In the present study, we use a numerical continuation method to compute discrete solutions to self-similar rupture for a general disjoining pressure exponent $n$. We focus on axisymmetric point-rupture solutions and show that pairs of solution branches merge as $n$ decreases, leading to a critical value $n_c \\approx 1.485$ below which stable similarity solutions do not appear to exist. We verify that this...
Curvature singularities and abstract boundary singularity theorems for space-time
Ashley, M J S L; Ashley, Michael J. S. L.; Scott, Susan M.
2003-01-01
The abstract boundary construction of Scott and Szekeres is a general and flexible way to define singularities in General Relativity. The abstract boundary construction also proves of great utility when applied to questions about more general boundary features of space-time. Within this construction an essential singularity is a non-regular boundary point which is accessible by a curve of interest (e.g. a geodesic) within finite (affine) parameter distance and is not removable. Ashley and Scott proved the first theorem linking abstract boundary essential singularities with the notion of causal geodesic incompleteness for strongly causal, maximally extended space-times. The relationship between this result and the classical singularity theorems of Penrose and Hawking has enabled us to obtain abstract boundary singularity theorems. This paper describes essential singularity results for maximally extended space-times and presents our recent efforts to establish a relationship between the strong curvature singula...
Finite-part singular integral approximations in Hilbert spaces
Directory of Open Access Journals (Sweden)
E. G. Ladopoulos
2004-01-01
Full Text Available Some new approximation methods are proposed for the numerical evaluation of the finite-part singular integral equations defined on Hilbert spaces when their singularity consists of a homeomorphism of the integration interval, which is a unit circle, on itself. Therefore, some existence theorems are proved for the solutions of the finite-part singular integral equations, approximated by several systems of linear algebraic equations. The method is further extended for the proof of the existence of solutions for systems of finite-part singular integral equations defined on Hilbert spaces, when their singularity consists of a system of diffeomorphisms of the integration interval, which is a unit circle, on itself.
Stability problem for singular Dirac equation system on finite interval
Ercan, Ahu; Panakhov, Etibar
2017-01-01
In this study, we show the stability problem for the singular Dirac equation system respect to two spectra on finite interval. The meaning of the stability problem of differential operators is to estimate difference of the spectral functions which considered problems when a finite number of eigenvalues of these problems coincide. The method is based on work by Ryabushko in [12]. The author in [12] studied to what extent only finitely many eigenvalues in one or both spectra determine the potential. We obtain a bound on variation of difference of the spectral functions for singular Dirac equation system.
High order finite volume methods for singular perturbation problems
Institute of Scientific and Technical Information of China (English)
CHEN ZhongYing; HE ChongNan; WU Bin
2008-01-01
In this paper we establish a high order finite volume method for the fourth order singular perturbation problems. In conjunction with the optimal meshes, the numerical solutions resulting from the method have optimal convergence order. Numerical experiments are presented to verify our theoretical estimates.
From Singularity Theory to Finiteness of Walrasian Equilibria
DEFF Research Database (Denmark)
Castro, Sofia B.S.D.; Dakhlia, Sami F.; Gothen, Peter
The paper establishes that for an open and dense subset of smooth exchange economies, the number of Walrasian equilibria is finite. In particular, our results extend to non-regular economies; it even holds when restricted to the subset of critical ones. The proof rests on concepts from singularity...
Eigenvalues of singular differential operators by finite difference methods. II.
Baxley, J. V.
1972-01-01
Note is made of an earlier paper which defined finite difference operators for the Hilbert space L2(m), and gave the eigenvalues for these operators. The present work examines eigenvalues for higher order singular differential operators by using finite difference methods. The two self-adjoint operators investigated are defined by a particular value in the same Hilbert space, L2(m), and are strictly positive with compact inverses. A class of finite difference operators is considered, with the idea of application to the theory of Toeplitz matrices. The approximating operators consist of a good approximation plus a perturbing operator.
hp-finite element methods for singular perturbations
Melenk, Jens M
2002-01-01
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Quantum cosmology and late-time singularities
Kamenshchik, A Yu
2013-01-01
The development of dark energy models has stimulated interest to cosmological singularities, which differ from the traditional Big Bang and Big Crunch singularities. We review a broad class of phenomena connected with soft cosmological singularities in classical and quantum cosmology. We discuss the classification of singularities from the geometrical point of view and from the point of view of the behaviour of finite size objects, crossing such singularities. We discuss in some detail quantum and classical cosmology of models based on perfect fluids (anti-Chaplygin gas and anti-Chaplygin gas plus dust), of models based on the Born-Infeld-type fields and of the model of a scalar field with a potential inversely proportional to the field itself. We dwell also on the phenomenon of the phantom divide line crossing in the scalar field models with cusped potentials. Then we discuss the Friedmann equations modified by quantum corrections to the effective action of the models under considerations and the influence o...
Instabilities of optical solitons and Hamiltonian singular solutions in a medium of finite extension
Energy Technology Data Exchange (ETDEWEB)
Assemat, E.; Picozzi, A.; Jauslin, H. R.; Sugny, D. [Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 5209 CNRS-Universite de Bourgogne, 9 Avenue A. Savary, Boite Postale 47 870, F-21078 Dijon Cedex (France)
2011-07-15
We analyze the role of soliton solutions and Hamiltonian singularities in the dynamics of counterpropagating waves in a medium of finite spatial extension. The soliton solution can become unstable due to the finite extension of the system. We show that the spatiotemporal dynamics then relaxes toward a Hamiltonian singular state of a nature different than that of the soliton state. This phenomenon can be explained through a geometrical analysis of the singularities of the stationary Hamiltonian system.
Space-time singularities in Weyl manifolds
Energy Technology Data Exchange (ETDEWEB)
Lobo, I.P. [CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Sapienza Universita di Roma, Dipartimento di Fisica, Rome (Italy); Barreto, A.B.; Romero, C. [Universidade Federal da Paraiba, Departamento de Fisica, C. Postal 5008, Joao Pessoa, PB (Brazil)
2015-09-15
We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time. We adopt an invariant formalism, so that the extended version of the theorem does not depend on a particular frame. (orig.)
Singular Finite-Gap Operators and Indefinite Metric. I
Grinevich, P
2009-01-01
Many "real" inverse spectral data for periodic finite-gap operators (consisting of Riemann Surface with marked "infinite point", local parameter and divisors of poles) lead to operators with real but singular coefficients. These operators cannot be considered as self-adjoint in the ordinary (positive) Hilbert spaces of functions of x. In particular, it is true for the special case of Lame operators with elliptic potential $n(n+1)\\wp(x)$ where eigenfunctions were found in XIX Century by Hermit. However, such Baker-Akhiezer (BA) functions present according to the ideas of works by Krichever-Novikov (1989), Grinevich-Novikov (2001) right analog of the Discrete and Continuous Fourier Bases on Riemann Surfaces. It turns out that these operators for the nonzero genus are symmetric in some indefinite inner product, described in this work. The analog of Continuous Fourier Transform is an isometry in this inner product. In the next work with number II we will present exposition of the similar theory for Discrete Fouri...
Singular finite-gap operators and indefinite metrics
Grinevich, Petr G.; Novikov, Sergei P.
2009-08-01
In many problems the 'real' spectral data for periodic finite-gap operators (consisting of a Riemann surface with a distingulished 'point at infinity', a local parameter near this point, and a divisor of poles) generate operators with singular real coefficients. These operators are not self-adjoint in an ordinary Hilbert space of functions of a variable x (with a positive metric). In particular, this happens for the Lamé operators with elliptic potential n(n+1)\\wp(x), whose wavefunctions were found by Hermite in the nineteenth century. However, ideas in [1]-[4] suggest that precisely such Baker-Akhiezer functions form a correct analogue of the discrete and continuous Fourier bases on Riemann surfaces. For genus g>0 these operators turn out to be symmetric with respect to an indefinite (not positive definite) inner product described in this paper. The analogue of the continuous Fourier transformation is an isometry in this inner product. A description is also given of the image of this Fourier transformation in the space of functions of x\\in R. Bibliography: 24 titles.
On Singular Problems in Linearized and Finite Elastostatics.
1980-08-01
of the singular solutions to which we have alluded. In view of the generalized uniqueness theorem [12], referred to earlier, no such limit process is...jump disconti- nuities in the first displacement gradients. Singular solutions of this kind are associated with localized shear failures and had been...considered earlier by Rudnicki and Rice [381 in a different constitutive setting. Mathematically, such singular solutions bear a more than casual
Quantum singularities in static and conformally static space-times
Konkowski, D A; 10.1142/S0217751X11054334
2011-01-01
The definition of quantum singularity is extended from static space-times to conformally static space-times. After the usual definitions of classical and quantum singularities are reviewed, examples of quantum singularities in static space-times are given. These include asymptotically power-law space-times, space-times with diverging higher-order differential invariants, and a space-time with a 2-sphere singularity. The theory behind quantum singularities in conformally static space-times is followed by an example, a Friedmann-Robertson-Walker space-time with cosmic string. The paper concludes by discussing areas of future research.
The wave equation on static singular space-times
Mayerhofer, Eberhard
2006-01-01
The first part of my thesis lays the foundations to generalized Lorentz geometry. The basic algebraic structure of finite-dimensional modules over the ring of generalized numbers is investigated. The motivation for this part of my thesis evolved from the main topic, the wave equation on singular space-times. The second and main part of my thesis is devoted to establishing a local existence and uniqueness theorem for the wave equation on singular space-times. The singular Lorentz metric subject to our discussion is modeled within the special algebra on manifolds in the sense of Colombeau. Inspired by an approach to generalized hyperbolicity of conical-space times due to Vickers and Wilson, we succeed in establishing certain energy estimates, which by a further elaborated equivalence of energy integrals and Sobolev norms allow us to prove existence and uniqueness of local generalized solutions of the wave equation with respect to a wide class of generalized metrics. The third part of my thesis treats three diff...
Time-periodic solutions of the Einstein’s field equations II:geometric singularities
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein’s field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,respectively.The singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.
Nonlinear singular vectors and nonlinear singular values
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
A novel concept of nonlinear singular vector and nonlinear singular value is introduced, which is a natural generalization of the classical linear singular vector and linear singular value to the nonlinear category. The optimization problem related to the determination of nonlinear singular vectors and singular values is formulated. The general idea of this approach is demonstrated by a simple two-dimensional quasigeostrophic model in the atmospheric and oceanic sciences. The advantage and its applications of the new method to the predictability, ensemble forecast and finite-time nonlinear instability are discussed. This paper makes a necessary preparation for further theoretical and numerical investigations.
Fast finite difference solvers for singular solutions of the elliptic Monge-Amp\\'ere equation
Froese, Brittany D
2010-01-01
The elliptic Monge-Amp\\`ere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Amp\\'ere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the nece...
Eigenvalues of singular differential operators by finite difference methods. I.
Baxley, J. V.
1972-01-01
Approximation of the eigenvalues of certain self-adjoint operators defined by a formal differential operator in a Hilbert space. In general, two problems are studied. The first is the problem of defining a suitable Hilbert space operator that has eigenvalues. The second problem concerns the finite difference operators to be used.
Analysis and synthesis of singular systems with time-delays
Wu, Zheng-Guang; Shi, Peng; Chu, Jian
2013-01-01
Singular time-delay systems are very suitable to describe a lot of practical systems such as manufacturing systems, networked control systems, power systems and electrical circuits. Thus, the past two decades have witnessed a significant progress on the theory of singular time-delay systems, and many fundamental and important topics have been successfully investigated including stability analysis, stabilization, guaranteed cost control, filtering, observer design, sliding mode control and so on. The main objective of this book is to present the latest developments and references in the analysis and synthesis of singular time-delay systems with or without Markov jumping parameters in a unified framework. The materials adopted in this book are mainly based on research results of the authors. This book will be of interest to academic researchers working in singular systems, time-delay systems and Markov jump systems and to graduate students interested in systems and control theory.
STABILITY OF TIME VARYING SINGULAR DIFFERENTIAL SYSTEMS WITH DELAY
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.
FINITE SINGULARITIES OF TOTAL MULTIPLICITY FOUR FOR A PARTICULAR SYSTEM WITH TWO PARAMETERS
Directory of Open Access Journals (Sweden)
Simona Cristina Nartea
2011-07-01
Full Text Available A particular Lotka-Volterra system with two parameters describingthe dynamics of two competing species is analyzed from the algebraicviewpoint. This study involves the invariants and the comitants of the system determinated by the application of the affine transformations group. First, the conditions for the existence of four (different or equal finite singularities for the general system are proofed, then is studied the particular case.
Sarwe, S B; Sarwe, Sanjay B.
2004-01-01
We study five dimensional(5D) spherically symmetric self-similar perfect fluid space-time with adiabatic equation of state, considering all the families of future directed non-spacelike geodesics. The space-time admits globally strong curvature naked singularities in the sense of Tipler and thus violates the cosmic censorship conjecture provided a certain algebraic equation has real positive roots. We further show that it is the weak energy condition (WEC) that is necessary for visibility of singularities for a finite period of time and for singularities to be gravitationally strong. We, also, match the solution to 5D Schwarzschild solution using the junction conditions.
Paszyński, Maciej R.
2013-04-01
This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.
Time-Dependent Warping and Non-Singular Bouncing Cosmologies
Balasubramanian, Koushik
2014-01-01
In this note, we construct a family of non-singular time-dependent solutions of a six-dimensional gravitational theory that are warped products of a four dimensional bouncing cosmological solution and a two dimensional internal manifold. The warp factor is time-dependent and breaks translation invariance along one of the internal directions. When the warp factor is periodic in time, the non-compact part of the geometry bounces periodically. The six dimensional geometry is supported by matter that does not violate the null energy condition. We show that this 6D geometry does not admit a closed trapped surface and hence the Hawking-Penrose singularity theorems do not apply to these solutions. We also present examples of singular solutions where the topology of the internal manifold changes dynamically.
Space-time singularities and the Kaehler cone
Energy Technology Data Exchange (ETDEWEB)
Jaerv, L.; Mayer, C.; Mohaupt, T.; Saueressig, F. [Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universitaet Jena, Max-Wien-Platz 1, 07743 Jena (Germany)
2004-06-01
We review recent results on the interplay between the five-dimensional space-time and the internal manifold in Calabi-Yau compactifications of M-theory. Black string, black hole and domain wall solutions as well as Kasner type cosmologies cannot develop a naked singularity as long as the moduli take values inside the Kaehler cone. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Brane-like singularities with no brane
Energy Technology Data Exchange (ETDEWEB)
Yurov, A.V., E-mail: artyom_yurov@mail.r [I. Kant Russian State University, Theoretical Physics Department, Al. Nevsky St. 14, Kaliningrad 236041 (Russian Federation)
2010-05-17
We use a method of linearization to study the emergence of the future cosmological singularity characterized by finite value of the cosmological radius. We uncover such singularities that keep Hubble parameter finite while making all higher derivatives of the scale factor (starting out from the a) diverge as the cosmological singularity is approached. Since such singularities has been obtained before in the brane world model we name them the 'brane-like' singularities. These singularities can occur during the expanding phase in usual Friedmann universe filled with both a self-acting, minimally coupled scalar field and a homogeneous tachyon field. We discover a new type of finite-time, future singularity which is different from type I-IV cosmological singularities in that it has the scale factor, pressure and density finite and nonzero. The generalization of w-singularity is obtained as well.
One-electron singular spectral features of the 1D Hubbard model at finite magnetic field
Carmelo, J. M. P.; Čadež, T.
2017-01-01
The momentum, electronic density, spin density, and interaction dependences of the exponents that control the (k , ω)-plane singular features of the σ = ↑ , ↓ one-electron spectral functions of the 1D Hubbard model at finite magnetic field are studied. The usual half-filling concepts of one-electron lower Hubbard band and upper Hubbard band are defined in terms of the rotated electrons associated with the model Bethe-ansatz solution for all electronic density and spin density values and the whole finite repulsion range. Such rotated electrons are the link of the non-perturbative relation between the electrons and the pseudofermions. Our results further clarify the microscopic processes through which the pseudofermion dynamical theory accounts for the one-electron matrix elements between the ground state and excited energy eigenstates.
Two-time-scale population evolution on a singular landscape
Xu, Song; Jiao, Shuyun; Jiang, Pengyao; Ao, Ping
2014-01-01
Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by singular peaks on a potential landscape. The genetic drift-induced noise gives rise to two-time-scale diffusion dynamics on the bipeaked landscape. We find that the logarithmically divergent (singular) peaks do not necessarily imply infinite escape times or biological fixations by iterating the Wright-Fisher model and approximating the average escape time. Our analytical results under weak mutation and weak selection extend Kramers's escape time formula to models with B (Beta) function-like equilibrium distributions and overcome constraints in previous methods. The constructed landscape provides a coherent description for the bistable system, supports the quantitative analysis of bipeaked dynamics, and generates mathematical insights for understanding the boundary behaviors of the diffusion model.
Finite-time control of DC-DC buck converters via integral terminal sliding modes
Chiu, Chian-Song; Shen, Chih-Teng
2012-05-01
This article presents novel terminal sliding modes for finite-time output tracking control of DC-DC buck converters. Instead of using traditional singular terminal sliding mode, two integral terminal sliding modes are introduced for robust output voltage tracking of uncertain buck converters. Different from traditional sliding mode control (SMC), the proposed controller assures finite convergence time for the tracking error and integral tracking error. Furthermore, the singular problem in traditional terminal SMC is removed from this article. When considering worse modelling, adaptive integral terminal SMC is derived to guarantee finite-time convergence under more relaxed stability conditions. In addition, several experiments show better start-up performance and robustness.
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-01-01
We study full QCD at finite density and low temperature with light quark mass using the complex Langevin method. Since the singular drift problem turns out to be mild on a $4^3 \\times 8$ lattice we use, the gauge cooling is performed only to control the unitarity norm in this exploratory study. We report on our preliminary data obtained from the complex Langevin simulation up to certain Langevin time. While the data are still noisy due to lack of statistics, the onset of the baryon number density seems to occur at larger $\\mu$ than half the pion mass, which is the value for the phase quenched QCD. The validity of our simulation is tested by the recently proposed criterion based on the probability distribution of the drift term.
Directory of Open Access Journals (Sweden)
Nicola Ponara
2012-11-01
Full Text Available Regularized Heaviside and Dirac delta function are used in several fields of computational physics and mechanics. Hence the issue of the quadrature of integrals of discontinuous and singular functions arises. In order to avoid ad-hoc quadrature procedures, regularization of the discontinuous and the singular fields is often carried out. In particular, weight functions of the signed distance with respect to the discontinuity interface are exploited. Tornberg and Engquist (Journal of Scientific Computing, 2003, 19: 527–552 proved that the use of compact support weight function is not suitable because it leads to errors that do not vanish for decreasing mesh size. They proposed the adoption of non-compact support weight functions. In the present contribution, the relationship between the Fourier transform of the weight functions and the accuracy of the regularization procedure is exploited. The proposed regularized approach was implemented in the eXtended Finite Element Method. As a three-dimensional example, we study a slender solid characterized by an inclined interface across which the displacement is discontinuous. The accuracy is evaluated for varying position of the discontinuity interfaces with respect to the underlying mesh. A procedure for the choice of the regularization parameters is proposed.
Finite escape fraction for ultrahigh energy collisions around Kerr naked singularity
Indian Academy of Sciences (India)
Mandar Patil; Pankaj S Joshi
2015-04-01
We investigate the issue of observability of high-energy collisions around Kerr naked singularity and show that results are in contrast with the Kerr black hole case. We had shown that it would be possible to have ultrahigh energy collisions between the particles close to the location = M around the Kerr naked singularity if the Kerr spin parameter transcends unity by an infinitesimally small amount → 1+. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing particle. We assume that two massless particles are produced in such a collision and their angular distribution is isotropic in the centre-of-mass frame. We calculated the escape fraction for the massless particles to reach infinity. We showed that the escape fraction is finite and approximately equal to half for the ultrahigh energy collisions. Therefore, the particles produced in high-energy collisions would escape to infinity providing the signature of the nature of basic interactions at those energies. This result is in contrast with the case of extremal Kerr black hole where almost all particles produced in high-energy collisions are absorbed by the black hole rendering collisions unobservable.
Singular perturbation methods for nonlinear dynamic systems with time delays
Energy Technology Data Exchange (ETDEWEB)
Hu, H.Y. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)], E-mail: hhyae@nuaa.edu.cn; Wang, Z.H. [MOE Key Laboratory of Structure Mechanics and Control for Aircraft, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing (China)
2009-04-15
This review article surveys the recent advances in the dynamics and control of time-delay systems, with emphasis on the singular perturbation methods, such as the method of multiple scales, the method of averaging, and two newly developed methods, the energy analysis and the pseudo-oscillator analysis. Some examples are given to demonstrate the advantages of the methods. The comparisons with other methods show that these methods lead to easier computations and higher accurate prediction on the local dynamics of time-delay systems near a Hopf bifurcation.
The Singular Universe and the Reality of Time
Mangabeira Unger, Roberto; Smolin, Lee
2015-01-01
Introduction; Part I. Roberto Mangabeira Unger: 1. The science of the one universe in time; 2. The context and consequences of the argument; 3. The singular existence of the universe; 4. The inclusive reality of time; 5. The mutability of the laws of nature; 6. The selective realism of mathematics; Part II. Lee Smolin: 1. Cosmology in crisis; 2. Principles for a cosmological theory; 3. The setting: the puzzles of contemporary cosmology; 4. Hypotheses for a new cosmology; 5. Mathematics; 6. Approaches to solving the metalaw dilemma; 7. Implications of temporal naturalism for philosophy of mind; 8. An agenda for science; 9. Concluding remarks; A note concerning disagreements between our views.
Directory of Open Access Journals (Sweden)
Baoqiang Yan
2006-07-01
Full Text Available In this paper, Krasnoselskii's theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.
Classical dynamics of the Bianchi IX model: space-like and time-like singularity cases
Parnovsky, S L
2016-01-01
We present the comparison of the dynamics of the vacuum Bianchi IX model near the space-like and time-like singularities. In both cases there exist oscillatory type solutions with diverging asymptotically curvature invariants. The dynamics of the time-like singularity case includes additionally the singular solutions with diverging volume density, but vanishing curvature invariants. Our numerical results are consistent with qualitative analytical considerations underlying finding the generic singular solutions to general relativity.
Quantum effects near future singularities
Barrow, John D; Dito, Giuseppe; Fabris, Julio C; Houndjo, Mahouton J S
2012-01-01
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a finite proper time and geometrical invariants of the space time will diverge. One question that naturally arises with respect to these cosmological scenarios is the following: can quantum effects lead to the avoidance of these future singularities? We analyze this problem considering massless and conformally coupled scalar fields in an isotropic and homogeneous background leading to future singularities. It is shown that near strong, big rip-type singularities, with violation of the energy conditions, the quantum effects are very important, while near some milder classes of singularity like the sudden singularity, which preserve the energy conditions, quantum effects are irrelevant.
Negative Time Delay in Strongly Naked Singularity Lensing
DeAndrea, Justin P
2014-01-01
We model the supermassive galactic center of the Milky Way galaxy as a strongly naked singularity lens described by the Janis-Newman-Winicour metric. This metric has an ordinary mass and a massless scalar charge parameters. For very accurate results, we use Virbhadra-Ellis lens equation for computations. The galactic center serving as gravitational lens gives rise to 4 images: 2 images on the same side as the source and 2 images on the opposite side of the source from the optic axis. We compute positions and time delays of these images for many values of the angular source position. The time delays of primary images decrease with increase in the angular source position and is always negative. The time delays of the other 3 images are negative for small angular source position; however, they increase with an increase in angular source position. Such observations would support strongly naked singularity interpretation of the galactic center and, if ever observed, would disprove the cosmic censorship hypothesis ...
The Universality of Penrose Limits near Space-Time Singularities
Blau, Matthias; O'Loughlin, M; Papadopoulos, G; Blau, Matthias; Borunda, Monica; Loughlin, Martin O'; Papadopoulos, George
2004-01-01
We prove that Penrose limits of metrics with arbitrary singularities of power-law type show a universal leading u^{-2}-behaviour near the singularity provided that the dominant energy condition is satisfied and not saturated. For generic power-law singularities of this type the oscillator frequencies of the resulting homogeneous singular plane wave turn out to lie in a range which is known to allow for an analytic extension of string modes through the singularity. The discussion is phrased in terms of the recently obtained covariant characterisation of the Penrose limit; the relation with null geodesic deviation is explained in detail.
Time Machines with Non-compactly Generated Cauchy Horizons and "Handy Singularities"
Krasnikov, S V
1997-01-01
The use of "handy singularities" (i.e. singularities similar to those arising in the Deutch-Politzer space) enables one to avoid (almost) all known difficulties inherent usually to creation of time machines. A simple method is discussed for constructing a variety of such singularities. A few 3-dimensional examples are cited.
Finite-time Thin Film Rupture Driven by Generalized Evaporative Loss
Ji, Hangjie
2016-01-01
Rupture is a nonlinear instability resulting in a finite-time singularity as a fluid layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term due to evaporation. Several different types of finite-time singularities are observed due to balances between evaporation and surface tension or intermolecular forces. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.
Finite-time thin film rupture driven by modified evaporative loss
Ji, Hangjie; Witelski, Thomas P.
2017-03-01
Rupture is a nonlinear instability resulting in a finite-time singularity as a film layer approaches zero thickness at a point. We study the dynamics of rupture in a generalized mathematical model of thin films of viscous fluids with modified evaporative effects. The governing lubrication model is a fourth-order nonlinear parabolic partial differential equation with a non-conservative loss term. Several different types of finite-time singularities are observed due to balances between conservative and non-conservative terms. Non-self-similar behavior and two classes of self-similar rupture solutions are analyzed and validated against high resolution PDE simulations.
Optimal initial condition of passive tracers for their maximal mixing in finite time
Farazmand, Mohammad
2016-01-01
The efficiency of a fluid mixing device is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here, we address the natural corollary question: Given the best available mixer, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Koopman operator. The truncation of the Koopman operator is made under the assumption that there is a small length-scale threshold $\\ell_\
Scalar Field Cosmologies and the Initial Space-Time Singularity
Foster, S
1998-01-01
The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical systems approach which may readily be generalised to more complicated space-times. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous 1-1 correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realised by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial value problem is briefly discussed.
Propagation of extended objects across singularity of time dependent orbifold
Malkiewicz, Przemyslaw
2010-01-01
In this paper we argue that the compactified Milne space is a promising model of the cosmological singularity. It is shown that extended objects like strings propagate in a well-defined manner across the singularity of the embedding space. Then a proposal for quantization of extended objects in the case of a membrane is given.
Delay-dependent state feedback robust stabilization for uncertain singular time-delay systems
Institute of Scientific and Technical Information of China (English)
Gao Huanli; Xu Bugong
2008-01-01
The problem of robust stabilization for uncertain singular time-delay systems is studied.First,a new delay-dependent asymptotic stability criteria for normal singular time-delay systems is given,which is less conservative.Using this result,the problem of state feedback robust stabilization for uncertain singular time-delay systems is discussed.Finally,two examples are given to illustrate the effectiveness of the results.
Free string evolution across plane wave singularities
Craps, Ben; Evnin, Oleg
2009-01-01
In these proceedings, we summarize our studies of free string propagation in (near-)singular scale-invariant plane wave geometries. We analyze the singular limit of the evolution for the center-of-mass motion and all excited string modes. The requirement that the entire excitation energy of the string should be finite excludes consistent propagation across the singularity, in case no dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).
Non-singular rotating black hole with a time delay in the center
De Lorenzo, Tommaso; Speziale, Simone
2015-01-01
As proposed by Bambi and Modesto, rotating non-singular black holes can be constructed via the Newman-Janis algorithm. Here we show that if one starts with a modified Hayward black hole with a time delay in the centre, the algorithm succeeds in producing a rotating metric, but curvature divergences reappear. To preserve finiteness, the time delay must be introduced directly at the level of the non-singular rotating metric. This is possible thanks to the deformation of the inner stationarity limit surface caused by the regularisation, and in more than one way. We outline three different possibilities, distinguished by the angular velocity of the event horizon. Along the way, we provide additional results on the Bambi-Modesto rotating Hayward metric, such as the structure of the regularisation occurring at the centre, the behaviour of the quantum gravity scale alike an electric charge in decreasing the angular momentum of the extremal black hole configuration, or details on the deformation of the ergosphere.
Shishkin, G. I.; Shishkina, L. P.
2009-05-01
The boundary value problem for the singularly perturbed reaction-diffusion parabolic equation in a ball in the case of spherical symmetry is considered. The derivatives with respect to the radial variable appearing in the equation are written in divergent form. The third kind boundary condition, which admits the Dirichlet and Neumann conditions, is specified on the boundary of the domain. The Laplace operator in the differential equation involves a perturbation parameter ɛ2, where ɛ takes arbitrary values in the half-open interval (0, 1]. When ɛ → 0, the solution of such a problem has a parabolic boundary layer in a neighborhood of the boundary. Using the integro-interpolational method and the condensing grid technique, conservative finite difference schemes on flux grids are constructed that converge ɛ-uniformly at a rate of O( N -2ln2 N + N {0/-1}), where N + 1 and N 0 + 1 are the numbers of the mesh points in the radial and time variables, respectively.
New Isotropic and Anisotropic Sudden Singularities
Barrow, J D; Barrow, John D.; Tsagas, Christos G.
2004-01-01
We show the existence of an infinite family of finite-time singularities in isotropically expanding universes which obey the weak, strong, and dominant energy conditions. We show what new type of energy condition is needed to exclude them ab initio. We also determine the conditions under which finite-time future singularities can arise in a wide class of anisotropic cosmological models. New types of finite-time singularity are possible which are characterised by divergences in the time-rate of change of the anisotropic-pressure tensor. We investigate the conditions for the formation of finite-time singularities in a Bianchi type $VII_{0}$ universe with anisotropic pressures and construct specific examples of anisotropic sudden singularities in these universes.
Robust admissibility and admissibilisation of uncertain discrete singular time-delay systems
Cui, Yukang; Lam, James; Feng, Zhiguang; Shen, Jun
2016-11-01
This paper is concerned with the characterisation of robust admissibility and admissibilisation for uncertain discrete-time singular system with interval time-varying delay. Considering the norm-bounded uncertainty and the interval time-varying delay, a new comparison model is introduced to transform the original singular system into two connected subsystems. After this transformation, a singular system without uncertainty and delay can be handled by the Lyapunov-Krasovskii functional method. By virtue of the scaled small gain theorem, an admissibility condition of the original singular system is proposed in terms of linear matrix inequalities. Moreover, the problem of robust admissibilisation of uncertain discrete singular time-varying system is also studied by iterative linear matrix inequality algorithm with initial condition optimisation. Several numerical examples are used to illustrate that the results are less conservative than existing ones.
Arbitrary Finite-time Tracking Control for Magnetic Levitation Systems
Directory of Open Access Journals (Sweden)
Xuan-Toa Tran
2014-10-01
Full Text Available In this paper, an arbitrary finite-time tracking control (AFTC method is developed for magnetic levitation systems with uncertain dynamics and external disturbances. By introducing a novel augmented sliding-mode manifold function, the proposed method can eliminate the singular problem in traditional terminal sliding-mode control, as well as the reaching-phase problem. Moreover, the tracking errors can reach the reference value with faster convergence and better tracking precision in arbitrarily determined finite time. In addition, a fuzzy-arbitrary finite-time tracking control (F-AFTC scheme that combines a fuzzy technique with AFTC to enhance the robustness and sliding performance is also proposed. A fuzzy logic system is used to replace the discontinuous control term. Thus, the chattering phenomenon is resolved without degrading the tracking performance. The stability of the closed-loop system is guaranteed by the Lyapunov theory. Finally, the effectiveness of the proposed methods is illustrated by simulation and experimental study in a real magnetic levitation system.
Arbitrary Finite-time Tracking Control for Magnetic Levitation Systems
Directory of Open Access Journals (Sweden)
Xuan-Toa Tran
2014-10-01
Full Text Available In this paper, an arbitrary finite-time tracking control (AFTC method is developed for magnetic levitation systems with uncertain dynamics and external disturbances. By introducing a novel augmented sliding- mode manifold function, the proposed method can eliminate the singular problem in traditional terminal sliding-mode control, as well as the reaching-phase problem. Moreover, the tracking errors can reach the reference value with faster convergence and better tracking precision in arbitrarily determined finite time. In addition, a fuzzy-arbitrary finite-time tracking control (F- AFTC scheme that combines a fuzzy technique with AFTC to enhance the robustness and sliding performance is also proposed. A fuzzy logic system is used to replace the discontinuous control term. Thus, the chattering phenomenon is resolved without degrading the tracking performance. The stability of the closed-loop system is guaranteed by the Lyapunov theory. Finally, the effectiveness of the proposed methods is illustrated by simulation and experimental study in a real magnetic levitation system.
Finite-time stability and control
Amato, Francesco; Ariola, Marco; Cosentino, Carlo; De Tommasi, Gianmaria
2014-01-01
Finite-time stability (FTS) is a more practical concept than classical Lyapunov stability, useful for checking whether the state trajectories of a system remain within pre-specified bounds over a finite time interval. In a linear systems framework, FTS problems can be cast as convex optimization problems and solved by the use of effective off-the-shelf computational tools such as LMI solvers. Finite-time Stability and Control exploits this benefit to present the practical applications of FTS and finite-time control-theoretical results to various engineering fields. The text is divided into two parts: · linear systems; and · hybrid systems. The building of practical motivating examples helps the reader to understand the methods presented. Finite-time Stability and Control is addressed to academic researchers and to engineers working in the field of robust process control. Instructors teaching graduate courses in advanced control will also find parts of this book useful for the...
Beljadid, Abdelaziz; Mohammadian, Abdolmajid; Qiblawey, Hazim
2016-10-01
The discretization of the shallow water system on unstructured grids can lead to spurious modes which usually can affect accuracy and/or cause stability problems. This paper introduces a new approach for stability analysis of unstructured linear finite volume schemes for linear shallow water equations with the Coriolis Effect using spectra, pseudospectra, and singular value decomposition. The discrete operator of the scheme is the principal parameter used in the analysis. It is shown that unstructured grids have a large influence on operator normality. In some cases the eigenvectors of the operator can be far from orthogonal, which leads to amplification of solutions and/or stability problems. Large amplifications of the solution can be observed, even for discrete operators which respect the condition of asymptotic stability, and in some cases even for Lax-Richtmyer stable methods. The pseudospectra are shown to be efficient for the verification of stability of finite volume methods for linear shallow water equations. In some cases, the singular value decomposition is employed for further analysis in order to provide more information about the existence of unstable modes. The results of the analysis can be helpful in choosing the type of mesh, the appropriate placements of the variables of the system on the grid, and the suitable discretization method which is stable for a wide range of modes.
Black hole thermodynamics in finite time
Gruber, Christine
2016-01-01
Finite-time thermodynamics provides the means to revisit ideal thermodynamic equilibrium processes in the light of reality and investigate the energetic "price of haste", i.e. the consequences of carrying out a process in finite time, when perfect equilibrium cannot be awaited due to economic reasons or the nature of the process. Employing the formalism of geometric thermodynamics, a lower bound on the energy dissipated during a process is derived from the thermodynamic length of that process. The notion of length is hereby defined via a metric structure on the space of equilibrium thermodynamics, spanned by a set of thermodynamic variables describing the system. Since the aim of finite-time thermodynamics is to obtain realistic limitations on idealized scenarios, it is a useful tool to reassess the efficiency of thermodynamic processes. We examine its implications for black hole thermodynamics, in particular scenarios inspired by the Penrose process, a thought experiment by which work can be extracted from a...
Ling, Eric
The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.
OUTPUT VARIABLE STRUCTURE CONTROL FOR TIME-INVARIANT LINEAR TIME-DELAY SINGULAR SYSTEM
Institute of Scientific and Technical Information of China (English)
Jifeng GUO; Cunchen GAO
2007-01-01
Synthesis and design of output variable structure controller for time-invariant linear time-delay singular system are studied. In the case that the system is regular and the system index is one, switching function with integral compensator and variable structure controller are designed, which guarantee that the sliding mode is asymptotically stable and the solution trajectory of the system arrives at the switching manifold in limited time. The design method is applicable to the systems which can be regularized. Finally, a numerical example is given to demonstrate effectiveness and simplicity of the design method.
Using clocks to determine the entropy of black holes and other space-time singularities
Ojo, A
2005-01-01
Space-time singularities, viz. Big bang, Big crunch and black holes have been shown to follow from the singularity theorems of General relativity. Whether the entropy at such infinite proper-time objects can be other than zero has also been a longstanding subject of research. Currently the property most commonly chosen to calculate their entropy is a multiple of the surface area of the event horizon and usually gives non-zero entropy values. Though popular, this choice still leaves some substantial questions unanswered hence the motivation for alternative methods for entropy derivation. Here, we use a different property, the proper-time at singularities based on the General relativity predicted behavior of clocks, to derive their entropy. We find, firstly within statistical and thermodynamic principles, secondly when this property is taken into account in the Bekenstein-Hawking formula and thirdly illustrating with a natural analogue, that the entropy of black holes and all other gravitational singularities c...
Extracting a Smooth Trend from a Time Series: A Modification of Singular Spectrum Analysis.
Solow, Andrew R.; Patwardhan, Anand
1996-09-01
Singular spectrum analysis is commonly used in climatology to extract a trend from a noisy time series. Implicit in this method is the association of trends with high variance. In many cases, it may be more natural to associate trends with smoothness. This paper describes how singular spectrum analysis can be modified to incorporate this idea. The modified approach is illustrated using the annual central England temperature series.
Institute of Scientific and Technical Information of China (English)
Grigory I. Shishkin
2008-01-01
A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on a priori (se-quentially) adapted meshes and study its convergence. The scheme on a priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find a priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in x, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for im-proving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical so-lution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N-1 = o(ev), where N denotes the number of nodes in the spatial mesh, and the value v=v(K) can be chosen arbitrarily small for suitable K.
Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field
Carmelo, J. M. P.; Sacramento, P. D.; Machado, J. D. P.; Campbell, D. K.
2015-10-01
We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents {{\\zeta}τ}(k) controlling the singularities for both the longitudinal ≤ft(τ =l\\right) and transverse ≤ft(τ =t\\right) dynamical structure factors for the whole momentum range k\\in ]0,π[ , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.
Time, Finite Statistics, and Bell's Fifth Position
Gill, R D
2003-01-01
I discuss three issues connected to Bell's theorem and Bell-CHSH-type experiments: time and the memory loophole, finite statistics (how wide are the error bars Under Local Realism), and the question of whether a loophole-free experiment is feasible, a surprising omission on Bell's list of four positions to hold in the light of his results. Levy's (1935) theory of martingales, and Fisher's (1935) theory of randomization in experimental design, take care of time and of finite statistics. I exploit a (classical) computer network metaphor for local realism to argue that Bell's conclusions are independent of how one likes to interpret probability, and give a critique of some recent anti-Bellist literature.
Input-output finite-time stabilization of linear systems with finite-time boundedness.
Guo, Yang; Yao, Yu; Wang, Shicheng; Ma, Kemao; Liu, Kai; Guo, Jian
2014-07-01
The paper presents linear system Input-Output Finite-Time Stabilization (IO-FTS) method under Finite-Time Boundedness (FTB) constraint. A state feedback controller is designed, via Linear Matrix Inequalities (LMIs), to guarantee the system both IO-FTS and FTB. The proposed methods are applied to the guidance design of a class of terminal guidance systems to suppress disturbances with IO-FTS method and FTB constraints simultaneously satisfied. The simulation results illustrate the effectiveness of the proposed methods.
Partial Hamiltonian formalism, multi-time dynamics and singular theories
Duplij, Steven
2013-01-01
We formulate singular classical theories without involving constraints. Applying the action principle for the action (27) we develop a partial (in the sense that not all velocities are transformed to momenta) Hamiltonian formalism in the initially reduced phase space (with the canonical coordinates $q_{i},p_{i}$, where the number $n_{p}$ of momenta $p_{i}$, $i=1,\\...,n_{p}$ (17) is arbitrary $n_{p}\\leq n$, where $n$ is the dimension of the configuration space), in terms of the partial Hamiltonian $H_{0}$ (18) and $(n-n_{p})$ additional Hamiltonians $H_{\\alpha}$, $\\alpha=n_{p}+1,\\...,n$ (20). We obtain $(n-n_{p}+1)$ Hamilton-Jacobi equations (25)-(26). The equations of motion are first order differential equations (33)-(34) with respect to $q_{i},p_{i}$ and second order differential equations (35) for $q_{\\alpha}$. If $H_{0}$, $H_{\\alpha}$ do not depend on $\\dot{q}_{\\alpha}$ (42), then the second order differential equations (35) become algebraic equations (43) with respect to $\\dot{q}_{\\alpha}$. We interpret ...
Zhang, Shangbin; Lu, Siliang; He, Qingbo; Kong, Fanrang
2016-09-01
For rotating machines, the defective faults of bearings generally are represented as periodic transient impulses in acquired signals. The extraction of transient features from signals has been a key issue for fault diagnosis. However, the background noise reduces identification performance of periodic faults in practice. This paper proposes a time-varying singular value decomposition (TSVD) method to enhance the identification of periodic faults. The proposed method is inspired by the sliding window method. By applying singular value decomposition (SVD) to the signal under a sliding window, we can obtain a time-varying singular value matrix (TSVM). Each column in the TSVM is occupied by the singular values of the corresponding sliding window, and each row represents the intrinsic structure of the raw signal, namely time-singular-value-sequence (TSVS). Theoretical and experimental analyses show that the frequency of TSVS is exactly twice that of the corresponding intrinsic structure. Moreover, the signal-to-noise ratio (SNR) of TSVS is improved significantly in comparison with the raw signal. The proposed method takes advantages of the TSVS in noise suppression and feature extraction to enhance fault frequency for diagnosis. The effectiveness of the TSVD is verified by means of simulation studies and applications to diagnosis of bearing faults. Results indicate that the proposed method is superior to traditional methods for bearing fault diagnosis.
An LMI approach to robust H-infinity control for uncertain singular time-delay systems
Institute of Scientific and Technical Information of China (English)
Xiaofu JI; Hongye SU; Jian CHU
2006-01-01
The problem of robust H-infinity control for a class of uncertain singular time-delay systems is studied in this paper. A new approach is proposed to describe the relationship between slow and fast subsystems of singular time-delay systems, based on which, a sufficient condition is presented for a singular time-delay system to be regular, impulse free and stable with an H-infinity performance. The robust H-infinity control problem is solved and an explicit expression of the desired state-feedback control law is also given. The obtained results are formulated in terms of strict linear matrix inequalities (LMIs) involving no decomposition of system matrices. A numerical example is given to show the effectiveness of the proposed method,
Thompson Sampling: An Optimal Finite Time Analysis
Kaufmann, Emilie; Munos, Rémi
2012-01-01
The question of the optimality of Thompson Sampling for solving the stochastic multi-armed bandit problem had been open since 1933. In this paper we answer it positively for the case of Bernoulli rewards by providing the first finite-time analysis that matches the asymptotic rate given in the Lai and Robbins lower bound for the cumulative regret. The proof is accompanied by a numerical comparison with other optimal policies, experiments that have been lacking in the literature until now for the Bernoulli case.
Liu, Zhou-Yang; Lin, Chong; Chen, Bing
2016-03-01
This paper studies the admissibility problem for a class of linear singular systems with time-varying delays. In order to highlight the relations between the delay and the state, the singular system is transformed into a neutral form. Then, an appropriate type of Lyapunov-Krasovskii functionals is proposed to develop a delay-derivative-dependent admissibility condition in terms of linear matrix inequalities. The derivation combines the Wirtinger-based inequality and reciprocally convex combination method. The present criterion is also for the stability test of retarded and neutral systems with time-varying delays. Some examples are provided to illustrate the effectiveness and the benefits of the proposed method.
On Type I Singularities in Ricci flow
Enders, Joerg; Topping, Peter M
2010-01-01
We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow.
Compositional Finite-Time Stability analysis of nonlinear systems
DEFF Research Database (Denmark)
Tabatabaeipour, Mojtaba; Blanke, Mogens
2014-01-01
for the system but with bounded disturbance. Sufficient conditions for finite-time stability and finite-time boundedness of nonlinear systems as well as a computational method based on sum of squares programming to check the conditions are given. The problem of finite-time stability for a system that consists......This paper, investigates finite-time stability and finite-time boundedness for nonlinear systems with polynomial vector fields. Finite-time stability requires the states of the system to remain a given bounded set in a finite-time interval and finite-time boundedness considers the same problem...... of an interconnection of subsystems is also considered and we show how to decompose the problem into subproblems for each subsystem with coupling constraints. A solution to the problem using sum of squares programming and dual decomposition is presented. The method is demonstrated through some examples....
Li, Chuang; Huang, Jian-Ping; Li, Zhen-Chun; Wang, Rong-Rong
2017-03-01
Least squares migration can eliminate the artifacts introduced by the direct imaging of irregular seismic data but is computationally costly and of slow convergence. In order to suppress the migration noise, we propose the preconditioned prestack plane-wave least squares reverse time migration (PLSRTM) method with singular spectrum constraint. Singular spectrum analysis (SSA) is used in the preconditioning of the take-offangle-domain common-image gathers (TADCIGs). In addition, we adopt randomized singular value decomposition (RSVD) to calculate the singular values. RSVD reduces the computational cost of SSA by replacing the singular value decomposition (SVD) of one large matrix with the SVD of two small matrices. We incorporate a regularization term into the preconditioned PLSRTM method that penalizes misfits between the migration images from the plane waves with adjacent angles to reduce the migration noise because the stacking of the migration results cannot effectively suppress the migration noise when the migration velocity contains errors. The regularization imposes smoothness constraints on the TADCIGs that favor differential semblance optimization constraints. Numerical analysis of synthetic data using the Marmousi model suggests that the proposed method can efficiently suppress the artifacts introduced by plane-wave gathers or irregular seismic data and improve the imaging quality of PLSRTM. Furthermore, it produces better images with less noise and more continuous structures even for inaccurate migration velocities.
Strings in Singular Space-Times and their Universal Gauge Theory
Chatzistavrakidis, Athanasios; Jonke, Larisa; Strobl, Thomas
2016-01-01
We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold $M$ by a singular foliation ${\\cal F}$ on it. Using the technical tool of a gauge theory, we propose a smooth functional for this scenario, such that the propagation is assured to lie in the singular target on-shell, i.e. only after taking into account the gauge invariant content of the theory. One of the main new aspects of our approach is that we do not limit ${\\cal F}$ to be generated by a group action. We will show that, whenever it exists, the above gauging is effectuated by a single geometrical and universal gauge theory, whose target space is the generalized tangent bundle $TM\\oplus T^*M$.
Strings in Singular Space-Times and Their Universal Gauge Theory
Chatzistavrakidis, Athanasios; Deser, Andreas; Jonke, Larisa; Strobl, Thomas
2017-08-01
We study the propagation of bosonic strings in singular target space-times. For describing this, we assume this target space to be the quotient of a smooth manifold $M$ by a singular foliation ${\\cal F}$ on it. Using the technical tool of a gauge theory, we propose a smooth functional for this scenario, such that the propagation is assured to lie in the singular target on-shell, i.e. only after taking into account the gauge invariant content of the theory. One of the main new aspects of our approach is that we do not limit ${\\cal F}$ to be generated by a group action. We will show that, whenever it exists, the above gauging is effectuated by a single geometrical and universal gauge theory, whose target space is the generalized tangent bundle $TM\\oplus T^*M$.
A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory
Energy Technology Data Exchange (ETDEWEB)
Berkooz, Micha [Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: micha.berkooz@weizmann.ac.il; Reichmann, Dori [Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)], E-mail: dor.reichmann@weizmann.ac.il
2007-09-15
These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such backgrounds. We review some of the various attempts to understand these singularities via generalizations of the BKL dynamics, using worldsheet methods and using non-perturbative tools such as the AdS/CFT correspondence and M(atrix) theory. These lecture notes are based on talks given at Cargese 06 and the dead-sea conference 06.
A Short Review of Time Dependent Solutions and Space-like Singularities in String Theory
Berkooz, Micha
2007-01-01
These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling picture of such backgrounds. We review some of the various attempts to understand these singularities via generalizations of the BKL dynamics, using worldsheet methods and using non-perturbative tools such as the AdS/CFT correspondence and M(atrix) theory. These lecture notes are based on talks given at Cargese 06 and the dead-sea conference 06.
Bifurcations of a singular prey-predator economic model with time delay and stage structure
Energy Technology Data Exchange (ETDEWEB)
Zhang Xue [Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110004 (China); Key Laboratory of Integrated Automation of Process Industry (Northeastern Univ.), Ministry of Education, Shenyang, Liaoning 110004 (China)], E-mail: zhangxueer@gmail.com; Zhang Qingling [Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110004 (China); Key Laboratory of Integrated Automation of Process Industry (Northeastern Univ.), Ministry of Education, Shenyang, Liaoning 110004 (China)], E-mail: qlzhang@mail.neu.edu.cn; Liu Chao [Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110004 (China); Key Laboratory of Integrated Automation of Process Industry (Northeastern Univ.), Ministry of Education, Shenyang, Liaoning 110004 (China); Xiang Zhongyi [Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei 445000 (China)
2009-11-15
This paper studies a singular prey-predator economic model with time delay and stage structure. Compared with other researches on dynamics of prey-predator population, this model is described by differential-algebraic equations due to economic factor. For zero economic profit, this model exhibits three bifurcational phenomena: transcritical bifurcation, Hopf bifurcation and singular induced bifurcation. For positive economic profit, the model undergoes a saddle-node bifurcation at critical value of positive economic profit, and the increase of delay destabilizes the positive equilibrium point of the system and bifurcates into small amplitude periodic solution. Finally, by using Matlab software, numerical simulations illustrate the effectiveness of the results.
String spectra near some null cosmological singularities
Madhu, Kallingalthodi
2009-01-01
We construct cosmological spacetimes with null Kasner-like singularities as purely gravitational solutions with no other background fields turned on. These can be recast as anisotropic plane-wave spacetimes by coordinate transformations. We analyse string quantization to find the spectrum of string modes in these backgrounds. The classical string modes can be solved for exactly in these time-dependent backgrounds, which enables a detailed study of the near singularity string spectrum, (time-dependent) oscillator masses and wavefunctions. We find that for low lying string modes(finite oscillation number), the classical near-singularity string mode functions are non-divergent for various families of singularities. Furthermore, for any infinitesimal regularization of the vicinity of the singularity, we find a tower of string modes of ultra-high oscillation number which propagate essentially freely in the background. The resulting picture suggests that string interactions are non-negligible near the singularity.
Periodic Solutions for a Class of Singular Hamiltonian Systems on Time Scales
Directory of Open Access Journals (Sweden)
Xiaofang Meng
2014-01-01
Full Text Available We are concerned with a class of singular Hamiltonian systems on time scales. Some results on the existence of periodic solutions are obtained for the system under consideration by means of the variational methods and the critical point theory.
Finite Time and Exact Time Controllability on Compact Manifolds
Jouan, Philippe
2010-01-01
It is first shown that a smooth controllable system on a compact manifold is finite time controllable. The technique of proof is close to the one of Sussmann's orbit theorem, and no rank condition is required. This technique is also used to give a new and elementary proof of the equivalence between controllability for essentially bounded inputs and for piecewise constant ones. Two sufficient conditions for controllability at exact time on a compact manifold are then stated. Some applications,...
Investigation of Finite Sources through Time Reversal
Kremers, Simon; Brietzke, Gilbert; Igel, Heiner; Larmat, Carene; Fichtner, Andreas; Johnson, Paul A.; Huang, Lianjie
2010-05-01
Under certain conditions time reversal is a promising method to determine earthquake source characteristics without any a-priori information (except the earth model and the data). It consists of injecting flipped-in-time records from seismic stations within the model to create an approximate reverse movie of wave propagation from which the location of the hypocenter and other information might be inferred. In this study, the backward propagation is performed numerically using a parallel cartesian spectral element code. Initial tests using point source moment tensors serve as control for the adaptability of the used wave propagation algorithm. After that we investigated the potential of time reversal to recover finite source characteristics (e.g., size of ruptured area, rupture velocity etc.). We used synthetic data from the SPICE kinematic source inversion blind test initiated to investigate the performance of current kinematic source inversion approaches (http://www.spice-rtn.org/library/valid). The synthetic data set attempts to reproduce the 2000 Tottori earthquake with 33 records close to the fault. We discuss the influence of various assumptions made on the source (e.g., origin time, hypocenter, fault location, etc.), adjoint source weighting (e.g., correct for epicentral distance) and structure (uncertainty in the velocity model) on the results of the time reversal process. We give an overview about the quality of focussing of the different wavefield properties (i.e., displacements, strains, rotations, energies). Additionally, the potential to recover source properties of multiple point sources at the same time is discussed.
Zamani, Iman; Shafiee, Masoud; Ibeas, Asier
2014-05-01
The issue of exponential stability of a class of continuous-time switched nonlinear singular systems consisting of a family of stable and unstable subsystems with time-varying delay is considered in this paper. Based on the free-weighting matrix approach, the average dwell-time approach and by constructing a Lyapunov-like Krasovskii functional, delay-dependent sufficient conditions are derived and formulated to check the exponential stability of such systems in terms of linear matrix inequalities (LMIs). By checking the corresponding LMI conditions, the average dwell-time and switching signal conditions are obtained. This paper also highlights the relationship between the average dwell-time of the switched nonlinear singular time-delay system, its stability and the exponential convergence rate of differential and algebraic states. A numerical example shows the effectiveness of the proposed method.
DEFF Research Database (Denmark)
Haldrup, Kristoffer
2014-01-01
The development of new X-ray light sources, XFELs, with unprecedented time and brilliance characteristics has led to the availability of very large datasets with high time resolution and superior signal strength. The chaotic nature of the emission processes in such sources as well as entirely novel...... on singular-value decomposition of no-signal subsets of acquired datasets in combination with model inputs and appears generally applicable to time-resolved X-ray diffuse scattering experiments....
Optimal disturbances rejection control for singularly perturbed systems with time-delay
Institute of Scientific and Technical Information of China (English)
Zhang Baolin; Tang Gongyou; Zhao Yandong
2008-01-01
The optimal control design for singularly perturbed time-delay systems affected by external disturbances is considered. Based on the decomposition theory of singular perturbation, the system is decomposed into a fast subsystem without time-delay and a slow time-delay subsystem with disturbances. The optimal disturbances rejection control law of the slow subsystem is obtained by using the successive approximation approach (SAA) and feedforward compensation method. Further, the feedforward and feedback composite control (FFCC) law for the original problem is developed. The FFCC law consists of linear analytic terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint vector equations. A disturbance observer is introduced to make the FFCC law physically realizable. Numerical examples show that the proposed algorithm is effective.
Majorosi, Szilárd; Czirják, Attila
2016-11-01
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schrödinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the symmetry axis. Our propagation algorithm is based on merging the method of the split-operator approximation of the exponential operator with the implicit equations of second order cylindrical 2D Crank-Nicolson scheme. We call this method hybrid splitting scheme because it inherits both the speed of the split step finite difference schemes and the robustness of the full Crank-Nicolson scheme. Based on a thorough error analysis, we verified both the fourth order accuracy of the spatial discretization in the optimal spatial step size range, and the fourth order scaling with the time step in the case of proper high order expressions of the split-operator. We demonstrate the performance and high accuracy of our hybrid splitting scheme by simulating optical tunneling from a hydrogen atom due to a few-cycle laser pulse with linear polarization.
Majorosi, Szilárd
2016-01-01
We present a novel numerical method and algorithm for the solution of the 3D axially symmetric time-dependent Schr\\"odinger equation in cylindrical coordinates, involving singular Coulomb potential terms besides a smooth time-dependent potential. We use fourth order finite difference real space discretization, with special formulae for the arising Neumann and Robin boundary conditions along the symmetry axis. Our propagation algorithm is based on merging the method of the split-operator approximation of the exponential operator with the implicit equations of second order cylindrical 2D Crank-Nicolson scheme. We call this method hybrid splitting scheme because it inherits both the speed of the split step finite difference schemes and the robustness of the full Crank-Nicolson scheme. Based on a thorough error analysis, we verified both the fourth order accuracy of the spatial discretization in the optimal spatial step size range, and the fourth order scaling with the time step in the case of proper high order e...
Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2012-01-01
A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... by using the concept and properties of the reciprocal systems. The results are further illustrated by two practical numerical examples: a model of CD player and a model of the atmospheric storm track....
Finite-Time Robust Stabilization for Stochastic Neural Networks
Directory of Open Access Journals (Sweden)
Weixiong Jin
2012-01-01
Full Text Available This paper is concerned with the finite-time stabilization for a class of stochastic neural networks (SNNs with noise perturbations. The purpose of the addressed problem is to design a nonlinear stabilizator which can stabilize the states of neural networks in finite time. Compared with the previous references, a continuous stabilizator is designed to realize such stabilization objective. Based on the recent finite-time stability theorem of stochastic nonlinear systems, sufficient conditions are established for ensuring the finite-time stability of the dynamics of SNNs in probability. Then, the gain parameters of the finite-time controller could be obtained by solving a linear matrix inequality and the robust finite-time stabilization could also be guaranteed for SNNs with uncertain parameters. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design method.
Institute of Scientific and Technical Information of China (English)
Peng CUI; Chenghui ZHANG
2008-01-01
The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed.The sufficient conditions of the existence of observers,which are normal linear time-delay systems,and the corresponding design steps are presented via linear matrix inequality(LMI).Moreover,the observer-based feedback stabilizing controller is obtained.Three examples are given to show the effectiveness of the proposed methods.
Dissipativity analysis for discrete singular systems with time-varying delay.
Feng, Zhiguang; Li, Wenxing; Lam, James
2016-09-01
In this paper, the issue of dissipativity analysis for discrete singular systems with time-varying delay is investigated. By using a recently developed inequality, which is less conservative than the Jensen inequality, and the improved reciprocally convex combination approach, sufficient criteria are established to guarantee the admissibility and dissipativity of the considered system. Moreover, H∞ performance characterization and passivity analysis are carried out. Numerical examples are presented to illustrate the effectiveness of the proposed method.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The guaranteed cost control problem for a continuous-time uncertain singular system with state and control delays, and a given quadratic cost function is studied in this paper. Sufficient conditions for the existence of the guaranteed cost controller are derived based on the linear inequality (LMI) approach. A parameterized characterization of the guaranteed cost laws is given in terms of the feasible solutions to a certain LMI, and the cost function of guaranteed cost controller exists an upper bound.
Finite-time disturbance attenuation of nonlinear systems
Institute of Scientific and Technical Information of China (English)
MO LiPo; JIA YingMin; ZHENG ZhiMing
2009-01-01
This paper is devoted to the finite-time disturbance attenuation problem of affine nonlinear systems.Based on the finite time Lyapunov stability theory,some finite-time H_∞ performance criterions are derived.Then the state-feedback control law is designed and the structure of such a controller is investigated.Furthermore,it is shown that the H_∞ controller can also make the closed-loop system satisfy finite-time H_∞ performance for nonlinear homogeneous systems.An example is provided to demonstrate the effectiveness of the presented results.
Singular boundary method using time-dependent fundamental solution for scalar wave equations
Chen, Wen; Li, Junpu; Fu, Zhuojia
2016-11-01
This study makes the first attempt to extend the meshless boundary-discretization singular boundary method (SBM) with time-dependent fundamental solution to two-dimensional and three-dimensional scalar wave equation upon Dirichlet boundary condition. The two empirical formulas are also proposed to determine the source intensity factors. In 2D problems, the fundamental solution integrating along with time is applied. In 3D problems, a time-successive evaluation approach without complicated mathematical transform is proposed. Numerical investigations show that the present SBM methodology produces the accurate results for 2D and 3D time-dependent wave problems with varied velocities c and wave numbers k.
Darboux transformations of coherent states of the time-dependent singular oscillator
Samsonov, B F
2004-01-01
Darboux transformation of both Barut-Girardello and Perelomov coherent states for the time-dependent singular oscillator is studied. In both cases the measure that realizes the resolution of the identity operator in terms of coherent states is found and corresponding holomorphic representation is constructed. For the particular case of a free particle moving with a fixed value of the angular momentum equal to two it is shown that Barut-Giriardello coherent states are more localized at the initial time moment while the Perelomov coherent states are more stable with respect to time evolution. It is also illustrated that Darboux transformation may keep unchanged this different time behavior.
Relative Error Model Reduction via Time-Weighted Balanced Stochastic Singular Perturbation
DEFF Research Database (Denmark)
Tahavori, Maryamsadat; Shaker, Hamid Reza
2012-01-01
A new mixed method for relative error model reduction of linear time invariant (LTI) systems is proposed in this paper. This order reduction technique is mainly based upon time-weighted balanced stochastic model reduction method and singular perturbation model reduction technique. Compared...... to the other analogous counterparts, the proposed method shows to provide more accurate results in terms of time weighted norms when applied to the practical examples. It is shown that important properties of the time-weighted stochastic balanced reduction technique are extended to the mixed reduction method...
Nonexistence of self-similar singularities in ideal viscoelastic flows
Directory of Open Access Journals (Sweden)
Anthony Suen
2012-06-01
Full Text Available We prove the nonexistence of finite time self-similar singularities in an ideal viscoelastic flow in R^3. We exclude the occurrence of Leray-type self-similar singularities under suitable integrability conditions on velocity and deformation tensor. We also prove the nonexistence of asymptotically self-similar singularities in our system. The present work extends the results obtained by Chae in the case of magnetohydrodynamics (MHD.
Robust reliable guaranteed cost control for nonlinear singular stochastic systems with time delay
Institute of Scientific and Technical Information of China (English)
Zhang Aiqing; Fang Huajing
2008-01-01
To study the design problem of robust reliable guaranteed cost controller for nonlinear singular stochastic systems,the Takagi-Sugeno(T-S)fuzzy model is used to represent a nonlinear singular stochastic system with norm-bounded parameter uncertainties and time delay.Based on the linear matrix inequality(LMI)techniques and stability theory of stochastic differential equations,a stochastic Lyapunov function method is adopted to design a state feedback fuzzy controller.The resulting closed-loop fuzzy system is robustly reliable stochastically stable,and the corresponding quadratic cost function is guarauteed to be no more than a certain upper bound for all admissible uncertainties,as well as different actuator fault cases.A sufficient condition of existence and design method of robust reliable guaranteed cost controller is presented.Finally,a numerical simulation is given to illustrate the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Koivistoinen Teemu
2007-01-01
Full Text Available As we know, singular value decomposition (SVD is designed for computing singular values (SVs of a matrix. Then, if it is used for finding SVs of an -by-1 or 1-by- array with elements representing samples of a signal, it will return only one singular value that is not enough to express the whole signal. To overcome this problem, we designed a new kind of the feature extraction method which we call ''time-frequency moments singular value decomposition (TFM-SVD.'' In this new method, we use statistical features of time series as well as frequency series (Fourier transform of the signal. This information is then extracted into a certain matrix with a fixed structure and the SVs of that matrix are sought. This transform can be used as a preprocessing stage in pattern clustering methods. The results in using it indicate that the performance of a combined system including this transform and classifiers is comparable with the performance of using other feature extraction methods such as wavelet transforms. To evaluate TFM-SVD, we applied this new method and artificial neural networks (ANNs for ballistocardiogram (BCG data clustering to look for probable heart disease of six test subjects. BCG from the test subjects was recorded using a chair-like ballistocardiograph, developed in our project. This kind of device combined with automated recording and analysis would be suitable for use in many places, such as home, office, and so forth. The results show that the method has high performance and it is almost insensitive to BCG waveform latency or nonlinear disturbance.
Akhbardeh, Alireza; Junnila, Sakari; Koivuluoma, Mikko; Koivistoinen, Teemu; Värri, Alpo
2006-12-01
As we know, singular value decomposition (SVD) is designed for computing singular values (SVs) of a matrix. Then, if it is used for finding SVs of an [InlineEquation not available: see fulltext.]-by-1 or 1-by- [InlineEquation not available: see fulltext.] array with elements representing samples of a signal, it will return only one singular value that is not enough to express the whole signal. To overcome this problem, we designed a new kind of the feature extraction method which we call ''time-frequency moments singular value decomposition (TFM-SVD).'' In this new method, we use statistical features of time series as well as frequency series (Fourier transform of the signal). This information is then extracted into a certain matrix with a fixed structure and the SVs of that matrix are sought. This transform can be used as a preprocessing stage in pattern clustering methods. The results in using it indicate that the performance of a combined system including this transform and classifiers is comparable with the performance of using other feature extraction methods such as wavelet transforms. To evaluate TFM-SVD, we applied this new method and artificial neural networks (ANNs) for ballistocardiogram (BCG) data clustering to look for probable heart disease of six test subjects. BCG from the test subjects was recorded using a chair-like ballistocardiograph, developed in our project. This kind of device combined with automated recording and analysis would be suitable for use in many places, such as home, office, and so forth. The results show that the method has high performance and it is almost insensitive to BCG waveform latency or nonlinear disturbance.
Directory of Open Access Journals (Sweden)
Alpo Värri
2007-01-01
Full Text Available As we know, singular value decomposition (SVD is designed for computing singular values (SVs of a matrix. Then, if it is used for finding SVs of an m-by-1 or 1-by-m array with elements representing samples of a signal, it will return only one singular value that is not enough to express the whole signal. To overcome this problem, we designed a new kind of the feature extraction method which we call ‘‘time-frequency moments singular value decomposition (TFM-SVD.’’ In this new method, we use statistical features of time series as well as frequency series (Fourier transform of the signal. This information is then extracted into a certain matrix with a fixed structure and the SVs of that matrix are sought. This transform can be used as a preprocessing stage in pattern clustering methods. The results in using it indicate that the performance of a combined system including this transform and classifiers is comparable with the performance of using other feature extraction methods such as wavelet transforms. To evaluate TFM-SVD, we applied this new method and artificial neural networks (ANNs for ballistocardiogram (BCG data clustering to look for probable heart disease of six test subjects. BCG from the test subjects was recorded using a chair-like ballistocardiograph, developed in our project. This kind of device combined with automated recording and analysis would be suitable for use in many places, such as home, office, and so forth. The results show that the method has high performance and it is almost insensitive to BCG waveform latency or nonlinear disturbance.
A unified approach to finite-time hyperbolicity which extends finite-time Lyapunov exponents
Doan, T. S.; Karrasch, D.; Nguyen, T. Y.; Siegmund, S.
A hyperbolicity notion for linear differential equations x˙=A(t)x, t∈[t-,t+], is defined which unifies different existing notions like finite-time Lyapunov exponents (Haller, 2001, [13], Shadden et al., 2005, [24]), uniform or M-hyperbolicity (Haller, 2001, [13], Berger et al., 2009, [6]) and (t-,(t+-t-))-dichotomy (Rasmussen, 2010, [21]). Its relation to the dichotomy spectrum (Sacker and Sell, 1978, [23], Siegmund, 2002, [26]), D-hyperbolicity (Berger et al., 2009, [6]) and real parts of the eigenvalues (in case A is constant) is described. We prove a spectral theorem and provide an approximation result for the spectral intervals.
Stinis, Panagiotis
2010-01-01
We present numerical results for the solution of the 1D critical nonlinear Schrodinger with periodic boundary conditions and initial data that give rise to a finite time singularity. We construct, through the Mori-Zwanzig formalism, a reduced model which allows us to follow the solution after the formation of the singularity. The computed post-singularity solution exhibits the same characteristics as the post-singularity solutions constructed recently by Terence Tao.
Optimal initial condition of passive tracers for their maximal mixing in finite time
Farazmand, Mohammad
2017-05-01
The efficiency of fluid flow for mixing passive tracers is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here we address the natural corollary question: Given a fluid flow, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The truncation of the PF operator is made under the assumption that there is a small length-scale threshold ℓν under which the tracer blobs are considered, for all practical purposes, completely mixed. We demonstrate our results on two examples: a prototypical model known as the sine flow and a direct numerical simulation of two-dimensional turbulence. Evaluating the optimal initial condition through this framework requires only the position of a dense grid of fluid particles at the final instance and their preimages at the initial instance of the prescribed time interval. As such, our framework can be readily applied to flows where such data are available through numerical simulations or experimental measurements.
Blow Up in Finite Time for the Zakharov System
Institute of Scientific and Technical Information of China (English)
甘在会; 郭柏灵
2009-01-01
@@ In [1],Merle guessed that the solution of Zakharov system always blows up in finite time.In accordance with the guess,in this paper we study the finite time blow-up results for the solution to the Cauchy problem of the generalized Zakharov system with combined power-type nonlinearities in R3:
Mariwalla, K H
2002-01-01
Basis and limitations of singularity theorems for Gravity are examined. As singularity is a critical situation in course of time, study of time paths, in full generality of Equivalence principle, provides two mechanisms to prevent singularity. Resolution of singular Time translation generators into space of its orbits, and essential higher dimensions for Relativistic particle interactions has facets to resolve any real singularity problem. Conceptually, these varied viewpoints have a common denominator: arbitrariness in the definition of `energy' intrinsic to the space of operation in each case, so as to render absence of singularity a tautology for self-consistency of the systems.
The structure of the classical cosmological singularity
Tipler, Frank J.
The existence of an all-encompassing initial classical cosmological singularity is established: it is shown that if: (1) global hyperbolicity, (2) the timelike convergence condition, and (3) all past-directed nonspacelike geodesics start to reconverge within a compact region in the causal past of the present-day earth, then all timelike curves in the past have a finite proper time length less than a universal constant L. It is argued that an analogue of this predicted cosmological singularity should exist even when quantum effects are taken into account. In particular, in a closed Friedmann radiation-filled universe quantized via the ADM method, the R = 0 singularity still exists and influences wave packet evolution at all times. Furthermore, quantum effects can in most cases eliminate curvature singularities only by introducing singularities in the universal action; most classical closed universes have finite action if and only if they begin and end in curvature singularities. Finally, the two basic ways of studying the structure of cosmological singularities are reviewed: completion methods (e.g., the c-boundary construction), and approach methods (e.g., analyzing metric behavior in a synchronous coordinate system).
Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.
Kanno, Kazutaka; Uchida, Atsushi
2014-03-01
We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent ∼0.5 as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.
Problems on Finite Automata and the Exponential Time Hypothesis
Directory of Open Access Journals (Sweden)
Henning Fernau
2017-02-01
Full Text Available We study several classical decision problems on finite automata under the (Strong Exponential Time Hypothesis. We focus on three types of problems: universality, equivalence, and emptiness of intersection. All these problems are known to be CoNP-hard for nondeterministic finite automata, even when restricted to unary input alphabets. A different type of problems on finite automata relates to aperiodicity and to synchronizing words. We also consider finite automata that work on commutative alphabets and those working on two-dimensional words.
Robust H∞ control for singular systems with time-varying uncertainties
Institute of Scientific and Technical Information of China (English)
DONG Xinzhuang; ZHANG Qingling
2006-01-01
In this paper,we investigate the problem of robust H∞ control for singular systems with polytopic time-varying parameter uncertainties.By introducing the notion of generalized quadratic H∞ performance,the relationship between the existence of a robust H∞ dynamic state feedback controller and that of a robust H∞ static state feedback controller is given.By using matrix inequalities,the existence conditions of robust H∞ static state feedback and dynamic output feedback controllers are derived.Moreover,the design methods for such controllers are provided in terms of the solutions of matrix inequalities.An example is also presented to demonstrate the validity of the proposed methods.
Delay-Dependent H∞ Filtering for Singular Time-Delay Systems
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Zhenbo Li
2011-01-01
Full Text Available This paper deals with the problem of delay-dependent H∞ filtering for singular time-delay systems. First, a new delay-dependent condition which guarantees that the filter error system has a prescribed H∞ performance γ is given in terms of linear matrix inequalities (LMIs. Then, the sufficient condition is obtained for the existence of the H∞ filter, and the explicit expression for the desired H∞ filter is presented by using LMIs and the cone complementarity linearization iterative algorithm. A numerical example is provided to illustrate the effectiveness of the proposed method.
Analysis of local ionospheric time varying characteristics with singular value decomposition
DEFF Research Database (Denmark)
Jakobsen, Jakob Anders; Knudsen, Per; Jensen, Anna B. O.
2010-01-01
In this paper, a time series from 1999 to 2007 of absolute total electron content (TEC) values has been computed and analyzed using singular value decomposition (SVD). The data set has been computed using a Kalman Filter and is based on dual frequency GPS data from three reference stations...... filter processing making it more robust, but can also be used as starting values in the initialization phase in case of gaps in the data stream. Furthermore, the models can be used to detect variations from the normal local ionospheric activity....
Finite-time performance analysis for genetic algorithms
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Finite-time performance of genetic algorithm with elitist operator in finite solution space is studied, and the relationship between evolution generation and the quality of the solution found best so far is analyzed. The estimating formulations of the expectation value as well as upper bound and lower bound for the evolution generation earliest achieving specific performance are provided.
Duplij, Steven
2013-01-01
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number of velocities) is proposed. The equations of motion become first-order differential equations, and they coincide with those of multi-time dynamics, if a certain condition is imposed. In a singular theory, this condition is fulfilled in the case of the coincidence of the number of generalized momenta with the rank of the Hessian matrix. The noncanonical generalized velocities satisfy a system of linear algebraic equations, which allows an appropriate classification of singular theories (gauge and nongauge). A new antisymmetric bracket (similar to the Poisson bracket) is introduced, which describes the time evolution of physical quantities in a singular theory. The origin of constraints is shown to be a consequence of the (unneeded in our formulation) extension...
Analysis of local ionospheric time varying characteristics with singular value decomposition
DEFF Research Database (Denmark)
Jakobsen, Jakob Anders; Knudsen, Per; Jensen, Anna B. O.
2010-01-01
In this paper, a time series from 1999 to 2007 of absolute total electron content (TEC) values has been computed and analyzed using singular value decomposition (SVD). The data set has been computed using a Kalman Filter and is based on dual frequency GPS data from three reference stations...... in Denmark located in the midlatitude region. The station separation between the three stations is 132–208 km (the time series of the TEC can be freely downloaded at http://www.heisesgade.dk). For each year, a SVD has been performed on the TEC time series in order to identify the three time varying (daily...... characteristics of the ionosphere very clearly. By prediction of the yearly mean sunspot number, future yearly models can also be predicted. These can serve as a priori information for a real time space weather service providing information of the current status of the ionosphere. They will improve the Kalman...
Finite-time consensus of heterogeneous multi-agent systems
Institute of Scientific and Technical Information of China (English)
Zhu Ya-Kun; Guan Xin-Ping; Luo Xiao-Yuan
2013-01-01
We investigate the finite-time consensus problem for heterogeneous multi-agent systems composed of first-order and second-order agents.A novel continuous nonlinear distributed consensus protocol is constructed,and finite-time consensus criteria are obtained for the heterogeneous multi-agent systems.Compared with the existing results,the stationary and kinetic consensuses of the heterogeneous multi-agent systems can be achieved in a finite time respectively.Moreover,the leader can be a first-order or a second-order integrator agent.Finally,some simulation examples are employed to verify the efficiency of the theoretical results.
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
Singular solutions of a singular differential equation
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Naito Manabu
2000-01-01
Full Text Available An attempt is made to study the problem of existence of singular solutions to singular differential equations of the type which have never been touched in the literature. Here and are positive constants and is a positive continuous function on . A solution with initial conditions given at is called singular if it ceases to exist at some finite point . Remarkably enough, it is observed that the equation may admit, in addition to a usual blowing-up singular solution, a completely new type of singular solution with the property that Such a solution is named a black hole solution in view of its specific behavior at . It is shown in particular that there does exist a situation in which all solutions of are black hole solutions.
Nagata, Keitaro; Shimasaki, Shinji
2016-01-01
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a gene...
Nagata, Keitaro; Nishimura, Jun; Shimasaki, Shinji
2016-07-01
Recently, the complex Langevin method has been applied successfully to finite density QCD either in the deconfinement phase or in the heavy dense limit with the aid of a new technique called the gauge cooling. In the confinement phase with light quarks, however, convergence to wrong limits occurs due to the singularity in the drift term caused by small eigenvalues of the Dirac operator including the mass term. We propose that this singular-drift problem should also be overcome by the gauge cooling with different criteria for choosing the complexified gauge transformation. The idea is tested in chiral Random Matrix Theory for finite density QCD, where exact results are reproduced at zero temperature with light quarks. It is shown that the gauge cooling indeed changes drastically the eigenvalue distribution of the Dirac operator measured during the Langevin process. Despite its non-holomorphic nature, this eigenvalue distribution has a universal diverging behavior at the origin in the chiral limit due to a generalized Banks-Casher relation as we confirm explicitly.
Singularities in fully developed turbulence
Energy Technology Data Exchange (ETDEWEB)
Shivamoggi, Bhimsen K., E-mail: bhimsen.shivamoggi@ucf.edu
2015-09-18
Phenomenological arguments are used to explore finite-time singularity (FTS) development in different physical fully-developed turbulence (FDT) situations. Effects of spatial intermittency and fluid compressibility in three-dimensional (3D) FDT and the role of the divorticity amplification mechanism in two-dimensional (2D) FDT and quasi-geostrophic FDT and the advection–diffusion mechanism in magnetohydrodynamic turbulence are considered to provide physical insights into the FTS development in variant cascade physics situations. The quasi-geostrophic FDT results connect with the 2D FDT results in the barotropic limit while they connect with 3D FDT results in the baroclinic limit and hence apparently provide a bridge between 2D and 3D. - Highlights: • Finite-time singularity development in turbulence situations is phenomenologically explored. • Spatial intermittency and compressibility effects are investigated. • Quasi-geostrophic turbulence is shown to provide a bridge between two-dimensional and three-dimensional cases.
Van, Mien; Ge, Shuzhi Sam; Ren, Hongliang
2016-04-28
In this paper, a novel finite time fault tolerant control (FTC) is proposed for uncertain robot manipulators with actuator faults. First, a finite time passive FTC (PFTC) based on a robust nonsingular fast terminal sliding mode control (NFTSMC) is investigated. Be analyzed for addressing the disadvantages of the PFTC, an AFTC are then investigated by combining NFTSMC with a simple fault diagnosis scheme. In this scheme, an online fault estimation algorithm based on time delay estimation (TDE) is proposed to approximate actuator faults. The estimated fault information is used to detect, isolate, and accommodate the effect of the faults in the system. Then, a robust AFTC law is established by combining the obtained fault information and a robust NFTSMC. Finally, a high-order sliding mode (HOSM) control based on super-twisting algorithm is employed to eliminate the chattering. In comparison to the PFTC and other state-of-the-art approaches, the proposed AFTC scheme possess several advantages such as high precision, strong robustness, no singularity, less chattering, and fast finite-time convergence due to the combined NFTSMC and HOSM control, and requires no prior knowledge of the fault due to TDE-based fault estimation. Finally, simulation results are obtained to verify the effectiveness of the proposed strategy.
Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems
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Nawel Khelil
2016-09-01
Full Text Available This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder, non-Lipschitz state feedback, which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system finite-time stable. The proof is based on a recursive design algorithm developed recently to construct the virtual Hölder continuous, finite-time stabilizer as well as a C1 positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz nonlinear systems.
Design of variable structure controller for uncertain time-delay singular system
Institute of Scientific and Technical Information of China (English)
GUO Ji-feng; GAO Cun-chen
2009-01-01
To study the approximation theory of real sliding mode and the design of variable structure controller for time.invariant linear uncertain time-delay singular system,the approximation theory of real sliding mode was developed to provide foundation for obtaining sliding mode by equivalent control,and switching functions with integral dynamic compensators and variable structure controllers were designed respectively under two circum-stances that the system without uncertain part was stabilized by delay-dependent and delay-independent linear stale feedback.The design guarantees the asymptotical stablity of switching manifolds,and the variable struc-ture controllers can.force solution trajectory of the system to arrive at the switching manifolds in limited time.A numerical example is given to demonstrate the feasibility and simplicity of the design method.
Singular perturbations and time scales in the design of digital flight control systems
Naidu, Desineni S.; Price, Douglas B.
1988-01-01
The results are presented of application of the methodology of Singular Perturbations and Time Scales (SPATS) to the control of digital flight systems. A block diagonalization method is described to decouple a full order, two time (slow and fast) scale, discrete control system into reduced order slow and fast subsystems. Basic properties and numerical aspects of the method are discussed. A composite, closed-loop, suboptimal control system is constructed as the sum of the slow and fast optimal feedback controls. The application of this technique to an aircraft model shows close agreement between the exact solutions and the decoupled (or composite) solutions. The main advantage of the method is the considerable reduction in the overall computational requirements for the evaluation of optimal guidance and control laws. The significance of the results is that it can be used for real time, onboard simulation. A brief survey is also presented of digital flight systems.
Can we see naked singularities?
Deshingkar, Shrirang S.
2007-01-01
We study singularities which can form in a spherically symmetric gravitational collapse of a general matter field obeying weak energy condition. We show that no energy can reach an outside observer from a null naked singularity. That means they will not be a serious threat to the Cosmic Censorship Conjecture (CCC). For the timelike naked singularities, where only the central shell gets singular, the redshift is always finite and they can in principle, carry energy to a faraway observer. Hence...
On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout
Directory of Open Access Journals (Sweden)
Yingqi Zhang
2012-01-01
Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.
2009-08-01
setting in Duc & Siegmund [28]: Definition A.10 (Dynamic partition of IR2). Consider the extended phase space, IR2 × I, associated with the flow...Fluid Dynamics, Cambridge University Press, Cam- bridge, 1967. [8] A. Berger, D. T. Son, and S. Siegmund , Nonautonomous finite-time dynamics, Discrete...28] L. H. Duc and S. Siegmund , Hyperbolicity and invariant manifolds for planar nonau- tonomous systems on finite time intervals, Int. J. Bif. Chaos
A note on singularities of the 3-D Euler equation
Tanveer, S.
1994-01-01
In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.
Directory of Open Access Journals (Sweden)
M. Branicki
2010-01-01
Full Text Available We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of transport barriers in the flow, i.e. material curves and surfaces. We argue that a general theory of Lagrangian transport has to account for the effects of transient flow phenomena which are not captured by the infinite-time notions of hyperbolicity even for flows defined for all time. Notions of finite-time hyperbolic trajectories, their finite time stable and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE fields and associated Lagrangian coherent structures have been the main tools for characterising transport barriers in the time-aperiodic situation. In this paper we consider a variety of examples, some with explicit solutions, that illustrate in a concrete manner the issues and phenomena that arise in the setting of finite-time dynamical systems. Of particular significance for geophysical applications is the notion of flow transition which occurs when finite-time hyperbolicity is lost or gained. The phenomena discovered and analysed in our examples point the way to a variety of directions for rigorous mathematical research in this rapidly developing and important area of dynamical systems theory.
Finite-time behavior of inner systems
Ludlage, Jobert H.A.; Weiland, Siep; Stoorvogel, Anton A.; Backx, Ton A.C.P.M.
2003-01-01
In this paper, we investigate how nonminimum phase characteristics of a dynamical system affect its controllability and tracking properties. For the class of linear time-invariant dynamical systems, these characteristics are determined by transmission zeros of the inner factor of the system transfer
Approximating the Finite-Time Ruin Probability under Interest Force
Brekelmans, R.C.M.; De Waegenaere, A.M.B.
2000-01-01
We present an algorithm to determine both a lower and an upper bound for the finite-time probability of ruin for a risk process with constant interest force. We split the time horizon into smaller intervals of equal length and consider the probability of ruin in case premium income for a time interv
Space-time discontinuous Galerkin finite element methods
Vegt, van der J.J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilizati
Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series
Vautard, R.; Ghil, M.
1989-01-01
Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.
Branicki, Michal
2009-01-01
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this problem arises from the desire to study transport and mixing problems in geophysical flows where the flow is obtained from a numerical solution, on a finite space-time grid, of an appropriate partial differential equation model for the velocity field. Of particular interest is the characterisation, location, and evolution of "transport barriers" in the flow, i.e. material curves and surfaces. We argue that a general theory of Lagrangian transport has to account for the effects of transient flow phenomena which are not captured by the infinite-time notions of hyperbolicity even for flows defined for all time. Notions of finite-time hyperbolic trajectories, their finite time stable and unstable manifolds, as well as finite-time Lyapunov exponent (FTLE) fields and associated Lagra...
Finite time control of a class of time-varying unified chaotic systems.
Ying, Yang; Guopei, Chen
2013-09-01
This paper considers the problem of finite time control for a class of time-varying unified chaotic system. First, based on the finite-time stability theory, a novel adaptive control technique is presented to achieve finite-time stabilization for time-varying unified chaotic system. Comparing with the existing methods, the proposed controller only need to be added on one state variable of systems and it is easy to be implemented. Then, a finite time control technique is provided to realize the tracking of any target function with second-order derivatives. Finally, Simulation results are provided to show the effectiveness of the proposed method.
Mixed time discontinuous space-time finite element method for convection diffusion equations
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
A mixed time discontinuous space-time finite element scheme for second-order convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method.
Akcay, A R
1999-01-01
This paper describes two new formulas: "formula A" and the Enhanced Einstein's Famous Formula (EEFF). The "formula A" has been experimentally proved and justified by using the High-Tc Superconductors, and provides the transmission of infinite (theoretically) frequencies. The EEFF has been mathematically derived from the Einstein's Famous Formula (EFF) by using the concept of the "formula A". The EEFF has been developed in place of EFF towards the prediction of the space-time singularities. The EEFF can predict and describe the space-time singularities without the distribution of mass and energy.
Directory of Open Access Journals (Sweden)
Yanbo Li
2014-01-01
Full Text Available This paper is devoted to the investigation of the design of robust guaranteed cost observer for a class of linear singular Markovian jump time-delay systems with generally incomplete transition probability. In this singular model, each transition rate can be completely unknown or only its estimate value is known. Based on stability theory of stochastic differential equations and linear matrix inequality (LMI technique, we design an observer to ensure that, for all uncertainties, the resulting augmented system is regular, impulse free, and robust stochastically stable with the proposed guaranteed cost performance. Finally, a convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters for linear singular Markovian jump time-delay systems with generally incomplete transition probability.
Singularities in the Boussinesq equation and in the generalized Korteweg-de Vries equation.
Lei, Y; Kongqing, Y
2001-03-01
In this paper, two kinds of analytic singular solutions (finite-time and infinite-time singular solutions) of two classical wave equations (the Boussinesq equation and a generalized Korteweg-de Vries equation) are obtained by means of the improved homogeneous balance method and a nonlinear transformation. The solutions show that special singular wave patterns exist in the classical models of shallow water wave problem.
A stringy cloak for a classical singularity
Energy Technology Data Exchange (ETDEWEB)
Dabholkar, Atish [Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005 (India); Kallosh, Renata [Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305 (United States); Maloney, Alexander [Institute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305 (United States) and Theory Group, Stanford Linear Accelerator Center, 2575 Sand Hill Rd, Menlo Park, CA 94025 (United States)]. E-mail: maloney@slac.stanford.edu
2004-12-01
We consider a class of 4D supersymmetric black hole solutions, arising from string theory compactifications, which classically have vanishing horizon area and singular space-time geometry. String theory motivates the inclusion of higher derivative terms, which convert these singular classical solutions into regular black holes with finite horizon area. In particular, the supersymmetric attractor equations imply that the central charge, which determines the radius of the AdS{sub 2} x S{sup 2} near horizon geometry, acquires a non-vanishing value due to quantum effects. In this case quantum corrections to the Bekenstein-Hawking relation between entropy and area are large. This is the first explicit example where stringy quantum gravity effects replace a classical null singularity by a black hole with finite horizon area. (author)
Institute of Scientific and Technical Information of China (English)
DAI Qian-wei; FENG De-shan; HE Ji-shan
2005-01-01
The ground penetrating radar(GPR) forward simulation all aims at the singular and regular models, such as sandwich model, round cavity, square cavity, and so on, which are comparably simple. But as to the forward of curl interface underground or "v" figure complex model, it is difficult to realize. So it is important to forward the complex geoelectricity model. This paper takes two Maxwell's vorticity equations as departure point, makes use of the principles of Yee's space grid model theory and the basic principle finite difference time domain method, and deduces a GPR forward system of equation of two dimensional spaces. The Mur super absorbed boundary condition is adopted to solve the super strong reflection on the interceptive boundary when there is the forward simulation. And a self-made program is used to process forward simulation to two typical geoelectricity model.
Finite-Time Stability of Neutral Fractional Time-Delay Systems via Generalized Gronwalls Inequality
Directory of Open Access Journals (Sweden)
Pang Denghao
2014-01-01
Full Text Available This paper studies the finite-time stability of neutral fractional time-delay systems. With the generalized Gronwall inequality, sufficient conditions of the finite-time stability are obtained for the particular class of neutral fractional time-delay systems.
Finite-Time Stability of Nonautonomous Delayed Systems
Institute of Scientific and Technical Information of China (English)
孙武军; 孔德兴
2003-01-01
The finite-time stability to linear discontinuous time-varying delayed system was investigated. By applying the method of upper and lower solutions, some sufficient conditions of this kind of stability were obtained.Furthermore, it also developed a monotone iterative technique for obtaining solutions which are obtained as limits of monotone sequences
Triangle Interception Scenario: A Finite-Time Guidance Approach
Directory of Open Access Journals (Sweden)
Yang Guo
2016-01-01
Full Text Available Considering an aircraft threatened by an interceptor, one of the effective penetration strategies is to release a Defender from the aircraft to confront the interceptor. In this case, the aircraft, the Defender, and the interceptor constitute the three-body guidance relationship, and the cooperation of the aircraft and its Defender to achieve the best tactical effects turns into a concerned problem. This paper studies the triangle interception guidance problem via the finite-time theory. The paper presents linear system Input-Output Finite-Time Stabilization (IO-FTS method. The sufficient conditions of the linear system, being IO-FTS, under Finite-Time Boundedness (FTB constraint are proposed, by which the state feedback controllers design method is obtained, via Linear Matrix Inequalities (LMIs. The triangle interception guidance problems are studied in three different cases, where the proposed methods are applied to the guidance design. The simulation results illustrate the effectiveness of the proposed methods.
Local dimension and finite time prediction in coupled map lattices
Indian Academy of Sciences (India)
P Muruganandam; G Francisco
2005-03-01
Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension.
Electrochemical etching of sharp tips for STM reveals singularity
DEFF Research Database (Denmark)
Quaade, Ulrich; Oddershede, Lene
2002-01-01
Electrochemical etching of metal wires is widely used to produce atomically sharp tips for use in scanning tunneling microscopy (STM). In this letter we uncover the existence of a finite-time singularity in the process: Several of the physical parameters describing the system exhibit scaling...... towards and away from a particular singular point in time, exactly the time at which the wire breaks. The obtained scaling exponents coincide with exponents reported from other singular dynamical systems. The results also provide knowledge of how to control STM tip properties on the nano-scale....
Directory of Open Access Journals (Sweden)
Juing-Shian Chiou
2013-01-01
Full Text Available This paper presents a novel and general approach, which is based on the composite control method, to synthesize the controller and observer-based state feedback to stabilize the singularly perturbed time-delay systems. First, the equivalent models of the original systems and the subsystems reduced via singular perturbation techniques are derived. Through these equivalent models, approximation of the stabilization and observer design for the original systems can be achieved through separate analyses for the slow and fast subsystems via a transformation of block diagonalization.
Institute of Scientific and Technical Information of China (English)
Jinxing Lin; Shumin Fei; Jiong Shen
2010-01-01
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities(LMIs).An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms(ignored in previous methods)when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.
Chruściel, Piotr T.; Delay, Erwann
2017-08-01
We construct infinite-dimensional families of non-singular static space-times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.
Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C
2017-08-01
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.
Minei, A. J.; Cooke, S. A.
2013-06-01
A singular value decomposition (SVD) signal processing method is newly applied to molecular free induction decays (FIDs) obtained using a time domain, broadband rotational spectrometer. It is demonstrated that for the strongest spectral transitions the SVD method can determine transition frequencies with a precision matching that of the fast Fourier transform method. Furthermore, the SVD-based analysis produces information concerning transition phase, amplitude, damping, and frequency for the strongest molecular signals. These parameters are shown as useful in regards to time-domain signal filtering. The computational expense of the SVD method is high and therefore this approach has the disadvantage that with our present computers the full molecular FID must be considerably truncated. The effects of FID truncation on the determined transition frequencies have been examined. Conversely, this truncation method illustrates that broadband spectra may be recovered from fragments as small as 1 % of the complete FID. The success of the SVD-based method is further examined in regards to weak signal detection, and frequency dependent detection. The pure rotational spectrum of 1H,1H,2H-perfluorocyclobutane is used for illustrative purposes in this study.
Axially Symmetric Null Dust Space-Time, Naked Singularity, and Cosmic Time Machine
National Research Council Canada - National Science Library
Faizuddin Ahmed
2017-01-01
... the cylinder which has closed orbits. The space-time admits closed timelike curves (CTCs) which develop at some particular moment in a causally well-behaved manner and may represent a Cosmic Time Machine...
Finite-time Control of One-link Mechanical System
Matoba, Shunsuke; Nakamura, Nami; Nakamura, Hisakazu; Akiba, Hideyuki
This paper considers finite-time position control of an one-link mechanical system. The system is modeled by discontinuous differential equations. In this paper, we prove that the Nakamura's local homogeneous controller based on a control Lyapunov function is valid to the position control of the robot manipulators, and show the effectiveness of the controller by experiments.
Generalised time functions and finiteness of the Lorentzian distance
Rennie, Adam
2014-01-01
We show that finiteness of the Lorentzian distance is equivalent to the existence of generalised time functions with gradient uniformly bounded away from light cones. To derive this result we introduce new techniques to construct and manipulate achronal sets. As a consequence of these techniques we obtain a functional description of the Lorentzian distance extending the work of Franco and Moretti.
Finiteness of the playing time in strategy free card games
Aleksenko, A
2011-01-01
It is proved that in card games similar to 'Beggar-my-neighbour' the mathematical expectation of the playing time is finite, provided that the player who starts the round is determined randomly and the deck is shuffled when the trick is added. The result holds for the generic setting of the game.
Consensus networks with time-delays over finite fields
Li, Xiuxian; Su, Housheng; Chen, Michael Z. Q.
2016-05-01
In this paper, we investigate the consensus problem in networks with time-delays over finite fields. The delays are categorised into three cases: single constant delay, multiple constant delays, and time-varying bounded delays. For all cases, some sufficient and necessary conditions for consensus are derived. Furthermore, assuming that the communication graph is strongly connected, some of the obtained necessary conditions reveal that the conditions for consensus with time-delays over finite fields depend not only on the diagonal entries but also on the off-diagonal entries, something that is intrinsically distinct from the case over real numbers (where having at least one nonzero diagonal entry is a sufficient and necessary condition to guarantee consensus). In addition, it is shown that delayed networks cannot achieve consensus when the interaction graph is a tree if the corresponding delay-free networks cannot reach consensus, which is consistent with the result over real numbers. As for average consensus, we show that it can never be achieved for delayed networks over finite fields, although it indeed can be reached under several conditions for delay-free networks over finite fields. Finally, networks with time-varying delays are discussed and one sufficient condition for consensus is presented by graph-theoretic method.
Singular Soliton Operators and Indefinite Metrics
Grinevich, P. G.; Novikov, S. P.
2011-01-01
The singular real second order 1D Schrodinger operators are considered here with such potentials that all local solutions near singularities to the eigenvalue problem are meromorphic for all values of the spectral parameter. All algebro-geometrical or "singular finite-gap" potentials satisfy to this condition. A Spectral Theory is constructed here for the periodic and rapidly decreasing cases in the special classes of functions with singularities and indefinite inner product. It has a finite ...
一类离散时间广义系统的迭代学习控制∗%Iterative learning control of a class of discrete-time singular system
Institute of Scientific and Technical Information of China (English)
曹伟; 郭媛; 孙明
2016-01-01
Singular systems are also called descriptor systems. Compared with normal systems, singular systems have become one of effective tools which can describe and characterize varieties of real systems, because they can better describe physical properties of the systems. Up to now, the analyses and syntheses of singular systems have been widespread applied to linear matrix inequality (LMI) method. The method requires known systems to have accurate mathematical model information, however, real systems have diﬃculties in obtaining their accurate mathematical models, owing to the fact that real systems are frequently subjected to all kinds of interferences, uncertainties, and nonlinear factors. Specially, in the case of singular systems, obtained LMI conditions often have a constraint equation or LMI is semi-definite, which makes it more diﬃcult to solve LMI. Therefore, in order to avoid the above two problems occurring in settling state tracking issue for singular systems, in the meantime, for convenience of computating control algorithm and information storage, in this paper we propose a discrete-time iterative learning control algorithm for a class of discrete-time singular system with repetitive running characteristics in finite time interval. The specific process is divided into two steps. First, the class of discrete-time singular system is decomposed into normal discrete-time state equation and algebraic equation form by nonsingular transformation. Accordingly, the singular system state is also decomposed into two parts. Among them, the dimension of the first part state is equal to singular matrix rank and another is equal to system dimension minus singular matrix rank. In addition, the control law of last iterative learning is modified by using two tracking errors at two different times: one error is real-time tracking error generated from the comparison between the first part state and its desired state and another is tracking error at a previous time
Directory of Open Access Journals (Sweden)
Abhishek Khanna
2012-01-01
Full Text Available We revisit the problem of optimal power extraction in four-step cycles (two adiabatic and two heat-transfer branches when the finite-rate heat transfer obeys a linear law and the heat reservoirs have finite heat capacities. The heat-transfer branch follows a polytropic process in which the heat capacity of the working fluid stays constant. For the case of ideal gas as working fluid and a given switching time, it is shown that maximum work is obtained at Curzon-Ahlborn efficiency. Our expressions clearly show the dependence on the relative magnitudes of heat capacities of the fluid and the reservoirs. Many previous formulae, including infinite reservoirs, infinite-time cycles, and Carnot-like and non-Carnot-like cycles, are recovered as special cases of our model.
Singularity formation for one dimensional full Euler equations
Pan, Ronghua; Zhu, Yi
2016-12-01
We investigate the basic open question on the global existence v.s. finite time blow-up phenomena of classical solutions for the one-dimensional compressible Euler equations of adiabatic flow. For isentropic flows, it is well-known that the solutions develop singularity if and only if initial data contain any compression (the Riemann variables have negative spatial derivative). The situation for non-isentropic flow is not quite clear so far, due to the presence of non-constant entropy. In [4], it is shown that initial weak compressions do not necessarily develop singularity in finite time, unless the compression is strong enough for general data. In this paper, we identify a class of solutions of the full (non-isentropic) Euler equations, developing singularity in finite time even though their initial data do not contain any compression. This is in sharp contrast to the isentropic flow.
Harada, T; Iguchi, H; Harada, Tomohiro; Nakao, Ken-ichi; Iguchi, Hideo
1999-01-01
It was recently shown that the metric functions which describe a spherically symmetric space-time with vanishing radial pressure can be explicitly integrated. We investigate the nakedness and curvature strength of the shell-focusing singularity in that space-time. If the singularity is naked, the relation between the circumferential radius and the Misner-Sharp mass is given by $R\\approx 2y_{0} m^{\\beta}$ with $ 1/3<\\beta\\le 1$ along the first radial null geodesic from the singularity. The $\\beta$ is closely related to the curvature strength of the naked singularity. For example, for the outgoing or ingoing null geodesic, if the strong curvature condition (SCC) by Tipler holds, then $\\beta$ must be equal to 1. We define the ``gravity dominance condition'' (GDC) for a geodesic. If GDC is satisfied for the null geodesic, both SCC and the limiting focusing condition (LFC) by Królak hold for $\\beta=1$ and $y_{0}\
Duplij, Steven
2015-09-01
A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number of velocities) is proposed. The equations of motion become first-order differential equations, and they coincide with those of multi-time dynamics, if a certain condition is imposed. In a singular theory, this condition is fulfilled in the case of the coincidence of the number of generalized momenta with the rank of the Hessian matrix. The noncanonical generalized velocities satisfy a system of linear algebraic equations, which allows an appropriate classification of singular theories (gauge and nongauge). A new antisymmetric bracket (similar to the Poisson bracket) is introduced, which describes the time evolution of physical quantities in a singular theory. The origin of constraints is shown to be a consequence of the (unneeded in our formulation) extension of the phase space, when the new bracket transforms into the Dirac bracket. Quantization is briefly discussed.
Resonant cyclotron acceleration of particles by a time periodic singular flux tube
Asch, Joachim; Stovicek, Pavel
2010-01-01
We study the dynamics of a classical nonrelativistic charged particle moving on a punctured plane under the influence of a homogeneous magnetic field and driven by a periodically time-dependent singular flux tube through the hole. We observe an effect of resonance of the flux and cyclotron frequencies. The particle is accelerated to arbitrarily high energies even by a flux of small field strength which is not necessarily encircled by the cyclotron orbit; the cyclotron orbits blow up and the particle oscillates between the hole and infinity. We support this observation by an analytic study of an approximation for small amplitudes of the flux which is obtained with the aid of averaging methods. This way we derive asymptotic formulas that are afterwards shown to represent a good description of the accelerated motion even for fluxes which are not necessarily small. More precisely, we argue that the leading asymptotic terms may be regarded as approximate solutions of the original system in the asymptotic domain as...
Finite-frequency model reduction of continuous-time switched linear systems with average dwell time
Ding, Da-Wei; Du, Xin
2016-11-01
This paper deals with the model reduction problem of continuous-time switched linear systems with finite-frequency input signals. The objective of the paper is to propose a finite-frequency model reduction method for such systems. A finite-frequency ? performance index is first defined in frequency domain, and then a finite-frequency performance analysis condition is derived by Parseval's theorem. Combined with the average dwell time approach, sufficient conditions for the existence of exponentially stable reduced-order models are derived. An algorithm is proposed to construct the desired reduced-order models. The effectiveness of the proposed method is illustrated by a numerical example.
Finite Block-Length Achievable Rates for Queuing Timing Channels
2011-01-01
The exponential server timing channel is known to be the simplest, and in some sense canonical, queuing timing channel. The capacity of this infinite-memory channel is known. Here, we discuss practical finite-length restrictions on the codewords and attempt to understand the amount of maximal rate that can be achieved for a target error probability. By using Markov chain analysis, we prove a lower bound on the maximal channel coding rate achievable at blocklength $n$ and error probability $...
Wu, Yuanyuan; Cao, Jinde; Alofi, Abdulaziz; Al-Mazrooei, Abdullah; Elaiw, Ahmed
2015-09-01
This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results.
Directory of Open Access Journals (Sweden)
Jinxing Lin
2010-01-01
Full Text Available This paper is concerned with the problems of exponential admissibility and dynamic output feedback (DOF control for a class of continuous-time switched singular systems with interval time-varying delay. A full-order, dynamic, synchronously switched DOF controller is considered. First, by using the average dwell time approach, a delay-range-dependent exponential admissibility criterion for the unforced switched singular time-delay system is established in terms of linear matrix inequalities (LMIs. Then, based on this criterion, a sufficient condition on the existence of a desired DOF controller, which guarantees that the closed-loop system is regular, impulse free and exponentially stable, is proposed by employing the LMI technique. Finally, some illustrative examples are given to show the effectiveness of the proposed approach.
Finite Time Blowup in a Realistic Food-Chain Model
Parshad, Rana
2013-05-19
We investigate a realistic three-species food-chain model, with generalist top predator. The model based on a modified version of the Leslie-Gower scheme incorporates mutual interference in all the three populations and generalizes several other known models in the ecological literature. We show that the model exhibits finite time blowup in certain parameter range and for large enough initial data. This result implies that finite time blowup is possible in a large class of such three-species food-chain models. We propose a modification to the model and prove that the modified model has globally existing classical solutions, as well as a global attractor. We reconstruct the attractor using nonlinear time series analysis and show that it pssesses rich dynamics, including chaos in certain parameter regime, whilst avoiding blowup in any parameter regime. We also provide estimates on its fractal dimension as well as provide numerical simulations to visualise the spatiotemporal chaos.
Phantom cosmology without Big Rip singularity
Energy Technology Data Exchange (ETDEWEB)
Astashenok, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation); Nojiri, Shin' ichi, E-mail: nojiri@phys.nagoya-u.ac.jp [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602 (Japan); Odintsov, Sergei D. [Department of Physics, Nagoya University, Nagoya 464-8602 (Japan); Institucio Catalana de Recerca i Estudis Avancats - ICREA and Institut de Ciencies de l' Espai (IEEC-CSIC), Campus UAB, Facultat de Ciencies, Torre C5-Par-2a pl, E-08193 Bellaterra (Barcelona) (Spain); Tomsk State Pedagogical University, Tomsk (Russian Federation); Yurov, Artyom V. [Baltic Federal University of I. Kant, Department of Theoretical Physics, 236041, 14, Nevsky st., Kaliningrad (Russian Federation)
2012-03-23
We construct phantom energy models with the equation of state parameter w which is less than -1, w<-1, but finite-time future singularity does not occur. Such models can be divided into two classes: (i) energy density increases with time ('phantom energy' without 'Big Rip' singularity) and (ii) energy density tends to constant value with time ('cosmological constant' with asymptotically de Sitter evolution). The disintegration of bound structure is confirmed in Little Rip cosmology. Surprisingly, we find that such disintegration (on example of Sun-Earth system) may occur even in asymptotically de Sitter phantom universe consistent with observational data. We also demonstrate that non-singular phantom models admit wormhole solutions as well as possibility of Big Trip via wormholes.
Improving time-frequency domain sleep EEG classification via singular spectrum analysis.
Mahvash Mohammadi, Sara; Kouchaki, Samaneh; Ghavami, Mohammad; Sanei, Saeid
2016-11-01
Manual sleep scoring is deemed to be tedious and time consuming. Even among automatic methods such as time-frequency (T-F) representations, there is still room for more improvement. To optimise the efficiency of T-F domain analysis of sleep electroencephalography (EEG) a novel approach for automatically identifying the brain waves, sleep spindles, and K-complexes from the sleep EEG signals is proposed. The proposed method is based on singular spectrum analysis (SSA). The single-channel EEG signal (C3-A2) is initially decomposed and then the desired components are automatically separated. In addition, the noise is removed to enhance the discrimination ability of features. The obtained T-F features after preprocessing stage are classified using a multi-class support vector machines (SVMs) and used for the identification of four sleep stages over three sleep types. Furthermore, to emphasise on the usefulness of the proposed method the automatically-determined spindles are parameterised to discriminate three sleep types. The four sleep stages are classified through SVM twice: with and without preprocessing stage. The mean accuracy, sensitivity, and specificity for before the preprocessing stage are: 71.5±0.11%, 56.1±0.09% and 86.8±0.04% respectively. However, these values increase significantly to 83.6±0.07%, 70.6±0.14% and 90.8±0.03% after applying SSA. The new T-F representation has been compared with the existing benchmarks. Our results prove that, the proposed method well outperforms the previous methods in terms of identification and representation of sleep stages. Experimental results confirm the performance improvement in terms of classification rate and also representative T-F domain. Copyright © 2016 Elsevier B.V. All rights reserved.
Reciprocal space-time and momentum-space singularities in the narrow resonance approximation
Green, M B
1976-01-01
A general scheme is proposed which makes explicit the relationship between the singularities of off-shell amplitudes in position-space and momentum-space in the narrow resonance approximation. In some ways this may be viewed as a duality scheme for amplitudes involving external quarks, in which narrow resonances in certain channels build the Fourier transform of power singularities in x/sup 2/(x/sup mu / being a position vector). This scheme is made precise by dual string off-shell amplitudes. (11 refs).
Discrete Time Mean-variance Analysis with Singular Second Moment Matrixes and an Exogenous Liability
Institute of Scientific and Technical Information of China (English)
Wen Cai CHEN; Zhong Xing YE
2008-01-01
We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem a.ected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonal transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the e.cient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.
Robust finite time observer design for multicellular converters
Defoort, Michael; Djemai, Mohamed; Floquet, Thierry; Perruquetti, Wilfrid
2011-11-01
In this article, a nonlinear finite time observer is designed for multicellular converters. The aim is to estimate the capacitor voltages by taking into account the hybrid behaviour of the converter. This article extends the validity of the strong Lyapunov function, proposed in Moreno and Osorio (Moreno, J., and Osorio, M. (2008), 'A Lyapunov Approach to Second Order Sliding Mode Controllers and Observers', in Proceedings of the IEEE Conference on Decision and Control, New Orleans, USA, pp. 2856-2861), in order to deeply study the reaching time estimation and robustness of the homogeneous finite time observer given in Perruquetti et al. (Perruquetti, W., Floquet, T., and Moulay, E. (2008), 'Finite Time Observers: Application to Secure Communication', IEEE Transactions on Automatic Control, 53, 356-360). The proposed approach enables the stabilisation of the observation errors in spite of the presence of perturbations and uncertainties. Some simulations and comparisons with the super-twisting sliding mode observer highlight the efficiency of the proposed strategy.
Composite control of a class of nonlinear singularly perturbed discrete-time systems via D-SDRE
Zhang, Yan; Subbaram Naidu, D.; Cai, Chenxiao; Zou, Yun
2016-08-01
In this paper, the regulation problem of a class of nonlinear singularly perturbed discrete-time systems is investigated. Using the theory of singular perturbations and time scales, the nonlinear system is decoupled into reduced-order slow and fast (boundary layer) subsystems. Then, a composite controller consisting of two sub-controllers for the slow and fast subsystems is developed using the discrete-time state-dependent Riccati equation (D-SDRE). It is proved that the equilibrium point of the original closed-loop system with a composite controller is locally asymptotically stable. Moreover, the region of attraction of the closed-loop system is estimated by using linear matrix inequality. One example is given to illustrate the effectiveness of the results obtained.
Institute of Scientific and Technical Information of China (English)
崔鹏; 张承慧
2007-01-01
The finite time horizon indefinite linear quadratic(LQ) optimal control problem for singular linear discrete time-varying systems is discussed. Indefinite LQ optimal control problem for singular systems can be transformed to that for standard state-space systems under a reasonable assumption. It is shown that the indefinite LQ optimal control problem is dual to that of projection for backward stochastic systems. Thus, the optimal LQ controller can be obtained by computing the gain matrices of Kalman filter.Necessary and sufficient conditions guaranteeing a unique solution for the indefinite LQ problem are given. An explicit solution for the problem is obtained in terms of the solution of Riccati difference equations.
Sliding mode control method having terminal convergence in finite time
Venkataraman, Subramanian T. (Inventor); Gulati, Sandeep (Inventor)
1994-01-01
An object of this invention is to provide robust nonlinear controllers for robotic operations in unstructured environments based upon a new class of closed loop sliding control methods, sometimes denoted terminal sliders, where the new class will enforce closed-loop control convergence to equilibrium in finite time. Improved performance results from the elimination of high frequency control switching previously employed for robustness to parametric uncertainties. Improved performance also results from the dependence of terminal slider stability upon the rate of change of uncertainties over the sliding surface rather than the magnitude of the uncertainty itself for robust control. Terminal sliding mode control also yields improved convergence where convergence time is finite and is to be controlled. A further object is to apply terminal sliders to robot manipulator control and benchmark performance with the traditional computed torque control method and provide for design of control parameters.
Finite time convergent control using terminal sliding mode
Institute of Scientific and Technical Information of China (English)
Yiguang HONG; Guowu YANG; Daizhan CHENG; Sarah SPURGEON
2004-01-01
A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control design methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples.
Finite-Time Approach to Microeconomic and Information Exchange Processes
Directory of Open Access Journals (Sweden)
Serghey A. Amelkin
2009-07-01
Full Text Available Finite-time approach allows one to optimize regimes of processes in macrosystems when duration of the processes is restricted. Driving force of the processes is difference of intensive variables: temperatures in thermodynamics, values in economics, etc. In microeconomic systems two counterflow fluxes appear due to the only driving force. They are goods and money fluxes. Another possible case is two fluxes with the same direction. The processes of information exchange can be described by this formalism.
A finite-time exponent for random Ehrenfest gas
Energy Technology Data Exchange (ETDEWEB)
Moudgalya, Sanjay; Chandra, Sarthak [Indian Institute of Technology, Kanpur 208016 (India); Jain, Sudhir R., E-mail: srjain@barc.gov.in [Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai 400085 (India)
2015-10-15
We consider the motion of a system of free particles moving on a plane with regular hard polygonal scatterers arranged in a random manner. Calling this the Ehrenfest gas, which is known to have a zero Lyapunov exponent, we propose a finite-time exponent to characterize its dynamics. As the number of sides of the polygon goes to infinity, when polygon tends to a circle, we recover the usual Lyapunov exponent for the Lorentz gas from the exponent proposed here. To obtain this result, we generalize the reflection law of a beam of rays incident on a polygonal scatterer in a way that the formula for the circular scatterer is recovered in the limit of infinite number of vertices. Thus, chaos emerges from pseudochaos in an appropriate limit. - Highlights: • We present a finite-time exponent for particles moving in a plane containing polygonal scatterers. • The exponent found recovers the Lyapunov exponent in the limit of the polygon becoming a circle. • Our findings unify pseudointegrable and chaotic scattering via a generalized collision rule. • Stretch and fold:shuffle and cut :: Lyapunov:finite-time exponent :: fluid:granular mixing.
Finite Horizon Decision Timing with Partially Observable Poisson Processes
Ludkovski, Michael
2011-01-01
We study decision timing problems on finite horizon with Poissonian information arrivals. In our model, a decision maker wishes to optimally time her action in order to maximize her expected reward. The reward depends on an unobservable Markovian environment, and information about the environment is collected through a (compound) Poisson observation process. Examples of such systems arise in investment timing, reliability theory, Bayesian regime detection and technology adoption models. We solve the problem by studying an optimal stopping problem for a piecewise-deterministic process which gives the posterior likelihoods of the unobservable environment. Our method lends itself to simple numerical implementation and we present several illustrative numerical examples.
Finite-time stabilization control for discontinuous time-delayed networks: New switching design.
Zhang, Ling-Ling; Huang, Li-Hong; Cai, Zuo-Wei
2016-03-01
This paper discusses the finite-time stabilization problem for time-varying delayed neural networks (DNNs) with discontinuous activation functions. By using fixed point theory and set-valued analysis, we establish the existence theorem of equilibrium point. In order to stabilize the states of this class of discontinuous DNNs in finite time, we design two different kinds of switching controllers which are described by discontinuous functions. Under the framework of Filippov solutions, several new and effective criteria are derived to realize finite-time stabilization of discontinuous DNNs based on the famous finite-time stability theory. Besides, the upper bounds of the settling time of stabilization are estimated. Numerical examples are finally provided to illustrate the correctness of the proposed design method and theoretical results.
Abelian Vortices with Singularities
Baptista, J M
2012-01-01
Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle has parabolic structure. These conditions appear naturally in the study of vortex configurations with constraints, or configurations invariant under the action of a finite group. We first show that the moduli space of singular vortex solutions is the same as in the regular case. Then we compute the total volume and total scalar curvature of the moduli space singular vortex solutions. These numbers differ from the case of regular vortices by a very natural term. Finally we exhibit explicit non-trivial vortex solutions over the thrice punctured hyperbolic sphere.
Vaz, C; Vaz, Cenalo; Witten, Louis
1995-01-01
A naked singularity is formed by the collapse of a Sine-Gordon soliton in 1+1 dimensional dilaton gravity with a negative cosmological constant. We examine the quantum stress tensor resulting from the formation of the singularity. Consistent boundary conditions require that the incoming soliton is accompanied by a flux of incoming radiation across past null infinity, but neglecting the back reaction of the spacetime leads to the absurd conclusion that the total energy entering the system by the time the observer is able to receive information from the singularity is infinite. We conclude that the back reaction must prevent the formation of the naked singularity.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This paper deals with the problem of H-infinity filter design for uncertain time-delay singular stochastic systems with Markovian jump.Based on the extended It(o) stochastic differential formula,sufficient conditions for the solvability of these problems are obtained.Furthermore,It is shown that a desired filter can be constructed by solving a set of linear matrix inequalities.Finally,a simulation example is given to demonstrate the effectiveness of the proposed method.
Singular value decomposition as a denoising tool for airborne time domain electromagnetic data
Reninger, P.-A.; Martelet, G.; Deparis, J.; Perrin, J.; Chen, Y.
2011-10-01
Airborne time domain electromagnetic (TDEM) surveys are increasingly carried out in anthropized areas as part of environmental studies. In such areas, noise arises mainly from either natural sources, such as spherics, or cultural sources, such as couplings with man-made installations. This results in various distortions on the measured decays, which make the EM noise spectrum complex and may lead to erroneous inversion and subsequent misinterpretations. Thresholding and stacking standard techniques, commonly used to filter TDEM data, are less efficient in such environment, requiring a time-consuming and subjective manual editing. The aim of this study was therefore to propose an alternative fast and efficient user-assisted filtering approach. This was achieved using the singular value decomposition (SVD). The SVD method uses the principal component analysis to extract into components the dominant shapes from a series of raw input curves. EM decays can then be reconstructed with particular components only. To do so, we had to adapt and implement the SVD, firstly, to separate clearly and so identify easily the components containing the geological signal, and then to denoise properly TDEM data. The reconstructed decays were used to detect noisy gates on their corresponding measured decays. This denoising step allowed rejecting efficiently mainly spikes and oscillations. Then, we focused on couplings with man-made installations, which may result in artifacts on the inverted models. An analysis of the map of weights of the selected "noisy components" highlighted high correlations with man-made installations localized by the flight video. We had therefore a tool to cull most likely decays biased by capacitive coupling noises. Finally, rejection of decays affected by galvanic coupling noises was also possible locating them through the analysis of specific SVD components. This SVD procedure was applied on airborne TDEM data surveyed by SkyTEM Aps. over an anthropized area
String theory and cosmological singularities
Indian Academy of Sciences (India)
Sumit R Das
2007-07-01
In general relativity space-like or null singularities are common: they imply that `time' can have a beginning or end. Well-known examples are singularities inside black holes and initial or final singularities in expanding or contracting universes. In recent times, string theory is providing new perspectives of such singularities which may lead to an understanding of these in the standard framework of time evolution in quantum mechanics. In this article, we describe some of these approaches.
Energy Technology Data Exchange (ETDEWEB)
Xing, Zhanqiang; Qu, Jianfeng; Chai, Yi; Tang, Qiu; Zhou, Yuming [Chongqing University, Chongqing (China)
2017-02-15
The gear vibration signal is nonlinear and non-stationary, gear fault diagnosis under variable conditions has always been unsatisfactory. To solve this problem, an intelligent fault diagnosis method based on Intrinsic time-scale decomposition (ITD)-Singular value decomposition (SVD) and Support vector machine (SVM) is proposed in this paper. The ITD method is adopted to decompose the vibration signal of gearbox into several Proper rotation components (PRCs). Subsequently, the singular value decomposition is proposed to obtain the singular value vectors of the proper rotation components and improve the robustness of feature extraction under variable conditions. Finally, the Support vector machine is applied to classify the fault type of gear. According to the experimental results, the performance of ITD-SVD exceeds those of the time-frequency analysis methods with EMD and WPT combined with SVD for feature extraction, and the classifier of SVM outperforms those for K-nearest neighbors (K-NN) and Back propagation (BP). Moreover, the proposed approach can accurately diagnose and identify different fault types of gear under variable conditions.
Finite-time thermodynamics of port-Hamiltonian systems
Delvenne, Jean-Charles; Sandberg, Henrik
2014-01-01
In this paper, we identify a class of time-varying port-Hamiltonian systems that is suitable for studying problems at the intersection of statistical mechanics and control of physical systems. Those port-Hamiltonian systems are able to modify their internal structure as well as their interconnection with the environment over time. The framework allows us to prove the First and Second Laws of thermodynamics, but also lets us apply results from optimal and stochastic control theory to physical systems. In particular, we show how to use linear control theory to optimally extract work from a single heat source over a finite time interval in the manner of Maxwell’s demon. Furthermore, the optimal controller is a time-varying port-Hamiltonian system, which can be physically implemented as a variable linear capacitor and transformer. We also use the theory to design a heat engine operating between two heat sources in finite-time Carnot-like cycles of maximum power, and we compare those two heat engines.
Hyperbolic neighborhoods as organizers of finite-time exponential stretching
Balasuriya, Sanjeeva; Ouellette, Nicholas
2016-11-01
Hyperbolic points and their unsteady generalization, hyperbolic trajectories, drive the exponential stretching that is the hallmark of nonlinear and chaotic flow. Typical experimental and observational velocity data is unsteady and available only over a finite time interval, and in such situations hyperbolic trajectories will move around in the flow, and may lose their hyperbolicity at times. Here we introduce a way to determine their region of influence, which we term a hyperbolic neighborhood, which marks fluid elements whose dynamics are instantaneously dominated by the hyperbolic trajectory. We establish, using both theoretical arguments and numerical verification from model and experimental data, that the hyperbolic neighborhoods profoundly impact Lagrangian stretching experienced by fluid elements. In particular, we show that fluid elements traversing a flow experience exponential boosts in stretching while within these time-varying regions, that greater residence time within hyperbolic neighborhoods is directly correlated to larger Finite-Time Lyapunov Exponent (FTLE) values, and that FTLE diagnostics are reliable only when the hyperbolic neighborhoods have a geometrical structure which is regular in a specific sense. Future Fellowship Grant FT130100484 from the Australian Research Council (SB), and a Terman Faculty Fellowship from Stanford University (NO).
Alternating-time temporal logic with finite-memory strategies
Directory of Open Access Journals (Sweden)
Steen Vester
2013-07-01
Full Text Available Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In this paper we consider two other types of semantics based on finite-memory strategies. One where the memory size allowed is bounded and one where the memory size is unbounded (but must be finite. This is motivated by the high complexity of model-checking with perfect recall semantics and the severe limitations of memoryless strategies. We show that both types of semantics introduced are different from perfect recall and memoryless semantics and next focus on the decidability and complexity of model-checking in both complete and incomplete information games for ATL/ATL*. In particular, we show that the complexity of model-checking with bounded-memory semantics is Delta_2p-complete for ATL and PSPACE-complete for ATL* in incomplete information games just as in the memoryless case. We also present a proof that ATL and ATL* model-checking is undecidable for n >= 3 players with finite-memory semantics in incomplete information games.
Fernández-Jambrina, L
2015-01-01
In this talk we would like to analyse the appearance of singularities in FLRW cosmological models which evolve close to w=-1, where w is the barotropic index of the universe. We relate small terms in cosmological time around w=-1 with the correspondent scale factor of the universe and check for the formation of singularities.
Robust H∞ Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach
Directory of Open Access Journals (Sweden)
Li-li Liu
2014-01-01
Full Text Available A new version of delay-dependent bounded real lemma for singular systems with state delay is established by parameterized Lyapunov-Krasovskii functional approach. In order to avoid generating nonconvex problem formulations in control design, a strategy that introduces slack matrices and decouples the system matrices from the Lyapunov-Krasovskii parameter matrices is used. Examples are provided to demonstrate that the results in this paper are less conservative than the existing corresponding ones in the literature.
A quantitative analysis of singular inflation with scalar-tensor and modified gravity
Nojiri, S; Oikonomou, V K
2015-01-01
We provide a detailed quantitative description of singular inflation. Its close analogy with finite-time future singularity which is associated to dark energy era is described. Calling and classifying the singularities of such inflation as finite-time cosmological singularities we investigate their occurrence, with special emphasis on the Type IV singularity. The study is performed in the context of a general non-canonical scalar-tensor theory. In addition, the impact of finite time singularities on the slow-roll parameters is also investigated. Particularly, we study three cases, in which the singularity occurs during the inflationary era, at the end, and also we study the case that the singularity occurs much more later than inflation ends. Using the obtained slow-roll parameters, for each case, we calculate explicitly the spectral index of primordial curvature perturbations $n_s$, the associated running of the spectral index $a_s$ and of the scalar-to-tensor ratio $r$ and compare the resulting values to th...
Transit light curves with finite integration time: Fisher information analysis
Energy Technology Data Exchange (ETDEWEB)
Price, Ellen M. [California Institute of Technology, 1200 East California Boulevard, Pasadena, CA 91125 (United States); Rogers, Leslie A. [California Institute of Technology, MC249-17, 1200 East California Boulevard, Pasadena, CA 91125 (United States)
2014-10-10
Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute integration times, and the upcoming Transiting Exoplanet Survey Satellite will record full frame images with a similar integration time. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal to noise. Using the Fisher information matrix technique, we derive analytic approximations for the variances and covariances on the transit parameters obtained from fitting light curve photometry collected with a finite integration time. We find that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters when comparing scenarios with constant total signal to noise (constant total integration time in the absence of read noise). Uncertainties on the transit ingress/egress time increase by a factor of 34 for Earth-size planets and 3.4 for Jupiter-size planets around Sun-like stars for integration times of 30 minutes compared to instantaneously sampled light curves. Similarly, uncertainties on the mid-transit time for Earth and Jupiter-size planets increase by factors of 3.9 and 1.4. Uncertainties on the transit depth are largely unaffected by finite integration times. While correlations among the transit depth, ingress duration, and transit duration all increase in magnitude with longer integration times, the mid-transit time remains uncorrelated with the other parameters. We provide code in Python and Mathematica for predicting the variances and covariances at www.its.caltech.edu/∼eprice.
Morphological Lightcurve Distortions due to Finite Integration Time
Kipping, David M
2010-01-01
We explore how finite integration times or equivalently temporal binning induces morphological distortions to the transit lightcurve. These distortions, if uncorrected for, lead to the retrieval of erroneous system parameters and may even lead to some planetary candidates being rejected as ostensibly unphysical. We provide analytic expressions for estimating the disturbance to the various lightcurve parameters as a function of the integration time. These effects are particularly crucial in light of the long-cadence photometry often used for discovering new exoplanets by for example CoRoT and the Kepler Mission (8.5 and 30 minutes). One of the dominant effects of long integration times is a systematic underestimation of the lightcurve derived stellar density, which has significant ramifications for transit surveys. We present a discussion of numerical integration techniques to compensate for the effects and produce expressions to quickly estimate the errors of such techniques, as a function of integration time...
Improving the Timing of Extended Finite State Machines Via Catalyst
Directory of Open Access Journals (Sweden)
Shi-Yu Huang
2002-01-01
Full Text Available We propose a timing optimization technique for a complex finite state machine that consists of not only random logic but also data operators. In such a design, the timing critical path often forms a cycle and thus cannot be cut down easily by popular techniques such as pipelining or retiming. The proposed technique, based on the concept of catalyst, adds a functionally redundant block—which includes a piece of combinational logic and several other registers—to the circuits under consideration so that the timing critical paths are divided into stages. During this transformation, the circuit's functionality is not affected, while the speed is improved significantly. This technique has been successfully applied to an industrial application—a Built-In Self-Test (BIST circuit for static random access memories (SRAMs. The synthesis result indicates a 47% clock cycle time reduction.
Transit Light Curves with Finite Integration Time: Fisher Information Analysis
Price, Ellen M
2014-01-01
Kepler has revolutionized the study of transiting planets with its unprecedented photometric precision on more than 150,000 target stars. Most of the transiting planet candidates detected by Kepler have been observed as long-cadence targets with 30 minute integration times, and the upcoming Transiting Exoplanet Survey Satellite (TESS) will record full frame images with a similar integration time. Integrations of 30 minutes affect the transit shape, particularly for small planets and in cases of low signal-to-noise. Using the Fisher information matrix technique, we derive analytic approximations for the variances and covariances on the transit parameters obtained from fitting light curve photometry collected with a finite integration time. We find that binning the light curve can significantly increase the uncertainties and covariances on the inferred parameters when comparing scenarios with constant total signal-to-noise (constant total integration time in the absence of read noise). Uncertainties on the tran...
Ardema, M. D.
1979-01-01
Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.
Acoustic radiation force analysis using finite difference time domain method.
Grinenko, A; Wilcox, P D; Courtney, C R P; Drinkwater, B W
2012-05-01
Acoustic radiation force exerted by standing waves on particles is analyzed using a finite difference time domain Lagrangian method. This method allows the acoustic radiation force to be obtained directly from the solution of nonlinear fluid equations, without any assumptions on size or geometry of the particles, boundary conditions, or acoustic field amplitude. The model converges to analytical results in the limit of small particle radii and low field amplitudes, where assumptions within the analytical models apply. Good agreement with analytical and numerical models based on solutions of linear scattering problems is observed for compressible particles, whereas some disagreement is detected when the compressibility of the particles decreases.
Directory of Open Access Journals (Sweden)
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Efficiency statistics at all times: Carnot limit at finite power.
Polettini, M; Verley, G; Esposito, M
2015-02-01
We derive the statistics of the efficiency under the assumption that thermodynamic fluxes fluctuate with normal law, parametrizing it in terms of time, macroscopic efficiency, and a coupling parameter ζ. It has a peculiar behavior: no moments, one sub-, and one super-Carnot maxima corresponding to reverse operating regimes (engine or pump), the most probable efficiency decreasing in time. The limit ζ→0 where the Carnot bound can be saturated gives rise to two extreme situations, one where the machine works at its macroscopic efficiency, with Carnot limit corresponding to no entropy production, and one where for a transient time scaling like 1/ζ microscopic fluctuations are enhanced in such a way that the most probable efficiency approaches the Carnot limit at finite entropy production.
Institute of Scientific and Technical Information of China (English)
Renji Han; Wei Jiang
2009-01-01
The problem of delay-dependent robust stability for uncertain linear singular neu-tral systems with time-varying and distributed delays is investigated. The uncertain-ties under consideration are norm bounded, and possibly time varying. Some new stability criteria, which are simpler and less conservative than existing results, are derived based on a new class of Lyapunov-Krasovskii functionals combined with the descriptor model transformation and the decomposition technique of coefficient matrix and formulated in the form of a linear matrix inequalitys (LMIs). Also, the criteria can be easily checked by the Matlab LMI toolbox.
Jarina Banu, L; Balasubramaniam, P
2015-11-01
This paper deals with the problem of admissibility analysis for discrete-time singular system with time-delays. The uncertainties occurring in the system parameters are assumed to be random. By constructing Lyapunov functional, sufficient delay-dependent stochastic admissibility conditions are established via delay divisioning approach in terms of linear matrix inequalities (LMIs), which can be easily checked by utilizing the numerically efficient Matlab LMI toolbox. Numerical examples and their simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Finite time exergoeconomic performance optimization of a thermoacoustic heat engine
Directory of Open Access Journals (Sweden)
Xuxian Kan, Lingen Chen, Fengrui Sun, Feng Wu
2011-01-01
Full Text Available Finite time exergoeconomic performance optimization of a generalized irreversible thermoacoustic heat engine with heat resistance, heat leakage, thermal relaxation, and internal dissipation is investigated in this paper. Both the real part and the imaginary part of the complex heat transfer exponent change the optimal profit rate versus efficiency relationship quantitatively. The operation of the generalized irreversible thermoacoustic engine is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimization of the generalized irreversible thermoacoustic engine is performed by taking profit rate as the objective. The analytical formulas about the profit rate and thermal efficiency of the thermoacoustic engine are derived. Furthermore, the comparative analysis of the influences of various factors on the relationship between optimal profit rate and the thermal efficiency of the generalized irreversible thermoacoustic engine is carried out by detailed numerical examples. The optimal zone on the performance of the thermoacoustic heat engine is obtained by numerical analysis. The results obtained herein may be useful for the selection of the operation parameters for real thermoacoustic heat engines.
Fluctuation dynamo at finite correlation times using renewing flows
Bhat, Pallavi
2014-01-01
Fluctuation dynamos are generic to turbulent astrophysical systems. The only analytical model of the fluctuation dynamo, due to Kazantsev, assumes the velocity to be delta-correlated in time. This assumption breaks down for any realistic turbulent flow. We generalize the analytic model of fluctuation dynamo to include the effects of a finite correlation time, $\\tau$, using renewing flows. The generalized evolution equation for the longitudinal correlation function $M_L$ leads to the standard Kazantsev equation in the $\\tau \\to 0$ limit, and extends it to the next order in $\\tau$. We find that this evolution equation involves also third and fourth spatial derivatives of $M_L$, indicating that the evolution for finite $\\tau$ will be non-local in general. In the perturbative case of small-$\\tau$ (or small Strouhl number), it can be recast using the Landau-Lifschitz approach, to one with at most second derivatives of $M_L$. Using both a scaling solution and the WKBJ approximation, we show that the dynamo growth r...
Finite-time Consensus for Nonlinear Multi-agent Systems with Fixed Topologies
Shang, Yilun
2009-01-01
In this paper, we study finite-time state consensus problems for continuous nonlinear multi-agent systems. Building on the theory of finite-time Lyapunov stability, we propose sufficient criteria which guarantee the system to reach a consensus in finite time, provided that the underlying directed network contains a spanning tree. Novel finite-time consensus protocols are introduced as examples for applying the criteria. Simulations are also presented to illustrate our theoretical results.
Finite-Time Adaptive Synchronization of a New Hyperchaotic System with Uncertain Parameters
Directory of Open Access Journals (Sweden)
Ma Yongguang
2014-01-01
Full Text Available This paper presents a finite-time adaptive synchronization strategy for a class of new hyperchaotic systems with unknown slave system’s parameters. Based on the finite-time stability theory, an adaptive control law is derived to make the states of the new hyperchaotic systems synchronized in finite-time. Numerical simulations are presented to show the effectiveness of the proposed finite time synchronization scheme.
Holographic complexity and spacetime singularities
Energy Technology Data Exchange (ETDEWEB)
Barbón, José L.F. [Instituto de Física Teórica IFT UAM/CSIC,C/ Nicolás Cabrera 13, Campus Universidad Autónoma de Madrid,Madrid 28049 (Spain); Rabinovici, Eliezer [Racah Institute of Physics, The Hebrew University,Jerusalem 91904 (Israel); Laboratoire de Physique Théorique et Hautes Energies, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
2016-01-15
We study the evolution of holographic complexity in various AdS/CFT models containing cosmological crunch singularities. We find that a notion of complexity measured by extremal bulk volumes tends to decrease as the singularity is approached in CFT time, suggesting that the corresponding quantum states have simpler entanglement structure at the singularity.
A Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Directory of Open Access Journals (Sweden)
Erdogan Fevzi
2010-01-01
Full Text Available Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect to the perturbation parameter. A numerical example is solved using the presented method, and the computed result is compared with exact solution of the problem.
Refining and classifying finite-time Lyapunov exponent ridges
Allshouse, Michael R
2015-01-01
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by complex, time-dependent two-dimensional flows. In light of its enduring appeal, and in support of good practice, we begin by investigating the effects of discretization and noise on two numerical approaches for calculating the FTLE field. A practical method to extract and refine FTLE ridges in two-dimensional flows, which builds on previous methods, is then presented. Seeking to better ascertain the role of an FTLE ridge in flow transport, we adapt an existing classification scheme and provide a thorough treatment of the challenges of classifying the types of deformation represented by an FTLE ridge. As a practical demonstration, the methods are applied to an ocean surface velocity field data set generated by a numerical model.
Computing Finite-Time Lyapunov Exponents with Optimally Time Dependent Reduction
Babaee, Hessam; Farazmand, Mohammad; Sapsis, Themis; Haller, George
2016-11-01
We present a method to compute Finite-Time Lyapunov Exponents (FTLE) of a dynamical system using Optimally Time-Dependent (OTD) reduction recently introduced by H. Babaee and T. P. Sapsis. The OTD modes are a set of finite-dimensional, time-dependent, orthonormal basis {ui (x , t) } |i=1N that capture the directions associated with transient instabilities. The evolution equation of the OTD modes is derived from a minimization principle that optimally approximates the most unstable directions over finite times. To compute the FTLE, we evolve a single OTD mode along with the nonlinear dynamics. We approximate the FTLE from the reduced system obtained from projecting the instantaneous linearized dynamics onto the OTD mode. This results in a significant reduction in the computational cost compared to conventional methods for computing FTLE. We demonstrate the efficiency of our method for double Gyre and ABC flows. ARO project 66710-EG-YIP.
Foam on troubled water: Capillary induced finite-time arrest of sloshing waves
Viola, Francesco; Brun, P.-T.; Dollet, Benjamin; Gallaire, François
2016-09-01
Interfacial forces exceed gravitational forces on a scale small relative to the capillary length—two millimeters in the case of an air-water interface—and therefore dominate the physics of sub-millimetric systems. They are of paramount importance for various biological taxa and engineering processes where the motion of a liquid meniscus induces a viscous frictional force that exhibits a sublinear dependence in the meniscus velocity, i.e., a power law with an exponent smaller than one. Interested in the fundamental implications of this dependence, we use a liquid-foam sloshing system as a prototype to exacerbate the effect of sublinear friction on the macroscopic mechanics of multi-phase flows. In contrast to classical theory, we uncover the existence of a finite-time singularity in our system yielding the arrest of the fluid's oscillations. We propose a minimal theoretical framework to capture this effect, thereby amending the paradigmatic damped harmonic oscillator model. Our results suggest that, although often not considered at the macroscale, sublinear capillary forces govern the friction at liquid-solid and liquid-liquid interfaces.
Finite-time synchronization of fractional-order memristor-based neural networks with time delays.
Velmurugan, G; Rakkiyappan, R; Cao, Jinde
2016-01-01
In this paper, we consider the problem of finite-time synchronization of a class of fractional-order memristor-based neural networks (FMNNs) with time delays and investigated it potentially. By using Laplace transform, the generalized Gronwall's inequality, Mittag-Leffler functions and linear feedback control technique, some new sufficient conditions are derived to ensure the finite-time synchronization of addressing FMNNs with fractional order α:1neural networks. Finally, three numerical examples are presented to show the effectiveness of our proposed theoretical results.
Finite-Time Consensus with a Time-Varying Reference State and Switching Topology
Directory of Open Access Journals (Sweden)
Jian-Yong Wang
2017-01-01
Full Text Available The finite-time consensus problem in the networks of multiple mobile agents is comprehensively investigated. In order to resolve this problem, a novel nonlinear information exchange protocol is proposed. The proposed protocol ensures that the states of the agents are converged to a weighted-average consensus in finite time if the communication topology is a weighted directed graph with a spanning tree and each strongly connected component is detail-balanced. Furthermore, the proposed protocol is also able to solve the finite-time consensus problem of networks with a switching topology. Finally, computer simulations are presented to demonstrate and validate the effectiveness of the theoretical analysis under the proposed protocol.
Finite-time master-slave synchronization and parameter identification for uncertain Lurie systems.
Wang, Tianbo; Zhao, Shouwei; Zhou, Wuneng; Yu, Weiqin
2014-07-01
This paper investigates the finite-time master-slave synchronization and parameter identification problem for uncertain Lurie systems based on the finite-time stability theory and the adaptive control method. The finite-time master-slave synchronization means that the state of a slave system follows with that of a master system in finite time, which is more reasonable than the asymptotical synchronization in applications. The uncertainties include the unknown parameters and noise disturbances. An adaptive controller and update laws which ensures the synchronization and parameter identification to be realized in finite time are constructed. Finally, two numerical examples are given to show the effectiveness of the proposed method.
Finite Time Analysis of a Tri-Generation Cycle
Directory of Open Access Journals (Sweden)
Brian Agnew
2015-06-01
Full Text Available A review of the literature indicates that current tri-generation cycles show low thermal performance, even when optimised for maximum useful output. This paper presents a Finite Time analysis of a tri-generation cycle that is based upon coupled power and refrigeration Carnot cycles. The analysis applies equally well to Stirling cycles or any cycle that exhibits isothermal heat transfer with the environment and is internally reversible. It is shown that it is possible to obtain a significantly higher energy utilisation factor with this type of cycle by considering the energy transferred during the isothermal compression and expansion processes as useful products thus making the energy utilisation larger than the enthalpy drop of the working fluid of the power cycle. The cycle is shown to have the highest energy utilisation factor when energy is supplied from a low temperature heat source and in this case the output is biased towards heating and cooling.
Computational electrodynamics the finite-difference time-domain method
Taflove, Allen
2005-01-01
This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers engineers the most up-to-date and definitive resource on this critical method for solving Maxwell's equations. The method helps practitioners design antennas, wireless communications devices, high-speed digital and microwave circuits, and integrated optical devices with unsurpassed efficiency. There has been considerable advancement in FDTD computational technology over the past few years, and the third edition brings professionals the very latest details with entirely new chapters on important techniques, major updates on key topics, and new discussions on emerging areas such as nanophotonics. What's more, to supplement the third edition, the authors have created a Web site with solutions to problems, downloadable graphics and videos, and updates, making this new edition the ideal textbook on the subject as well.
Accurate finite difference methods for time-harmonic wave propagation
Harari, Isaac; Turkel, Eli
1994-01-01
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
Parallel finite-difference time-domain method
Yu, Wenhua
2006-01-01
The finite-difference time-domain (FTDT) method has revolutionized antenna design and electromagnetics engineering. This book raises the FDTD method to the next level by empowering it with the vast capabilities of parallel computing. It shows engineers how to exploit the natural parallel properties of FDTD to improve the existing FDTD method and to efficiently solve more complex and large problem sets. Professionals learn how to apply open source software to develop parallel software and hardware to run FDTD in parallel for their projects. The book features hands-on examples that illustrate the power of parallel FDTD and presents practical strategies for carrying out parallel FDTD. This detailed resource provides instructions on downloading, installing, and setting up the required open source software on either Windows or Linux systems, and includes a handy tutorial on parallel programming.
GPU and APU computations of Finite Time Lyapunov Exponent fields
Conti, Christian; Rossinelli, Diego; Koumoutsakos, Petros
2012-03-01
We present GPU and APU accelerated computations of Finite-Time Lyapunov Exponent (FTLE) fields. The calculation of FTLEs is a computationally intensive process, as in order to obtain the sharp ridges associated with the Lagrangian Coherent Structures an extensive resampling of the flow field is required. The computational performance of this resampling is limited by the memory bandwidth of the underlying computer architecture. The present technique harnesses data-parallel execution of many-core architectures and relies on fast and accurate evaluations of moment conserving functions for the mesh to particle interpolations. We demonstrate how the computation of FTLEs can be efficiently performed on a GPU and on an APU through OpenCL and we report over one order of magnitude improvements over multi-threaded executions in FTLE computations of bluff body flows.
Onsager coefficients of a finite-time Carnot cycle.
Izumida, Yuki; Okuda, Koji
2009-08-01
We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of T(h)-T(c) --> 0 where T(h) and T(c) are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power eta(max) of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.
A Stochastic Investment Model on a Finite Time Horizon
Institute of Scientific and Technical Information of China (English)
Tao; Pang
2014-01-01
In this paper,we consider an investment optimization problem on a finite time horizon.One risky and one riskless asset are considered,and transaction costs are ignored.The risky asset prices obey a logarithmic Brownian motion,and interest rates vary according to a Vasicek interest rate model.The goal is to choose optimal investment policies to maximize the expected Hyperbolic Absolute Risk Aversion(HARA)utility of final payoff(wealth).The problem is then reduced to a 1-dimensional stochastic control problem by virtue of the Girsanov transformation.A dynamic programming principle is used to derive the dynamic programming equation(DPE).Explicit solutions are derived under certain conditions.The solutions are then used to derive the optimal investment strategy.
Singular Spectrum Analysis for astronomical time series: constructing a parsimonious hypothesis test
Greco, G; Kobayashi, S; Ghil, M; Branchesi, M; Guidorzi, C; Stratta, G; Ciszak, M; Marino, F; Ortolan, A
2015-01-01
We present a data-adaptive spectral method - Monte Carlo Singular Spectrum Analysis (MC-SSA) - and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with $1/f^{\\beta}$ power-law noise affected by photon counting statistics. Such noise process is simulated by a first-order autoregressive, AR(1) process corrupted by intrinsic Poisson noise. In doing so, we statistically estimate a basic stochastic variation of the source and the corresponding fluctuations due to the quantum nature of light. In addition, MC-SSA test retains its effectiveness even when a significant percentage of the signal falls below a certain level of detection, e.g., caused by the instrument sensitivity. The parsimonious approach presented here may be broadly applied, from the search for extrasolar planets to the extraction of low-intensity coherent phenomena probably hidden in high energy transients.
The structure of precipitation fronts for finite relaxation time
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Department of Mathematics and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York, NY (United States)
2006-11-15
When convection is parameterized in an atmospheric circulation model, what types of waves are supported by the parameterization? Several studies have addressed this question by finding the linear waves of simplified tropical climate models with convective parameterizations. In this paper's simplified tropical climate model, convection is parameterized by a nonlinear precipitation term, and the nonlinearity gives rise to precipitation front solutions. Precipitation fronts are solutions where the spatial domain is divided into two regions, and the precipitation (and other model variables) changes abruptly at the boundary of the two regions. In one region the water vapor is below saturation and there is no precipitation, and in the other region the water vapor is above saturation level and precipitation is nonzero. The boundary between the two regions is a free boundary that moves at a constant speed. It is shown that only certain front speeds are allowed. The three types of fronts that exist for this model are drying fronts, slow moistening fronts, and fast moistening fronts. Both types of moistening fronts violate Lax's stability criterion, but they are robustly realizable in numerical experiments that use finite relaxation times. Remarkably, here it is shown that all three types of fronts are robustly realizable analytically for finite relaxation time. All three types of fronts may be physically unreasonable if the front spans an unrealistically large physical distance; this depends on various model parameters, which are investigated below. From the viewpoint of applied mathematics, these model equations exhibit novel phenomena as well as features in common with the established applied mathematical theories of relaxation limits for conservation laws and waves in reacting gas flows. (orig.)
Dadić, I.
2001-01-01
We study out of equilibrium thermal field theories with switching on the interaction occurring at finite time using the Wigner transforms of two-point functions. For two-point functions we define the concept of a projected function: it is zero if any of the times refers to the time before switching on the interaction; otherwise it depends only on the relative coordinates. This definition includes bare propagators, one-loop self-energies, etc. For the infinite-average-time limit of the Wigner transforms of projected functions we define the analyticity assumptions: (1) The function of energy is analytic above (below) the real axis. (2) The function goes to zero as the absolute value of energy approaches infinity in the upper (lower) semiplane. Without use of the gradient expansion, we obtain the convolution product of projected functions. We sum the Schwinger-Dyson series in closed form. In the calculation of the Keldysh component (both resummed and single self-energy insertion approximation) contributions appear which are not the Fourier transforms of projected functions, signaling the limitations of the method. In the Feynman diagrams there is no explicit energy conservation at vertices; there is an overall energy-smearing factor taking care of the uncertainty relations. The relation between the theories with the Keldysh time path and with the finite time path enables one to rederive the results, such as the cancellation of pinching, collinear, and infrared singularities, hard thermal loop resummation, etc.
Elitzur, Shmuel; Rabinovici, Eliezer; Elitzur, Shmuel; Giveon, Amit; Rabinovici, Eliezer
2003-01-01
Big bang/crunch curvature singularities in exact CFT string backgrounds can be removed by turning on gauge fields. This is described within a family of {SL(2)xSU(2)xU(1)_x}/{U(1)xU(1)} quotient CFTs. Uncharged incoming wavefunctions from the ``whiskers'' of the extended universe can be fully reflected if and only if a big bang/crunch curvature singularity, from which they are scattered, exists. Extended BTZ-like singularities remain as long as U(1)_x is compact.
DEFF Research Database (Denmark)
Cappellin, Cecilia; Breinbjerg, Olav; Frandsen, Aksel
2008-01-01
An effective technique for extracting the singularity of plane wave spectra in the computation of antenna aperture fields is proposed. The singular spectrum is first factorized into a product of a finite function and a singular function. The finite function is inverse Fourier transformed...... numerically using the Inverse Fast Fourier Transform, while the singular function is inverse Fourier transformed analytically, using the Weyl-identity, and the two resulting spatial functions are then convolved to produce the antenna aperture field. This article formulates the theory of the singularity...
Backward Finite-Time Lyapunov Exponents in Inertial Flows.
Gunther, Tobias; Theisel, Holger
2017-01-01
Inertial particles are finite-sized objects that are carried by fluid flows and in contrast to massless tracer particles they are subject to inertia effects. In unsteady flows, the dynamics of tracer particles have been extensively studied by the extraction of Lagrangian coherent structures (LCS), such as hyperbolic LCS as ridges of the Finite-Time Lyapunov Exponent (FTLE). The extension of the rich LCS framework to inertial particles is currently a hot topic in the CFD literature and is actively under research. Recently, backward FTLE on tracer particles has been shown to correlate with the preferential particle settling of small inertial particles. For larger particles, inertial trajectories may deviate strongly from (massless) tracer trajectories, and thus for a better agreement, backward FTLE should be computed on inertial trajectories directly. Inertial backward integration, however, has not been possible until the recent introduction of the influence curve concept, which - given an observation and an initial velocity - allows to recover all sources of inertial particles as tangent curves of a derived vector field. In this paper, we show that FTLE on the influence curve vector field is in agreement with preferential particle settling and more importantly it is not only valid for small (near-tracer) particles. We further generalize the influence curve concept to general equations of motion in unsteady spatio-velocity phase spaces, which enables backward integration with more general equations of motion. Applying the influence curve concept to tracer particles in the spatio-velocity domain emits streaklines in massless flows as tangent curves of the influence curve vector field. We demonstrate the correlation between inertial backward FTLE and the preferential particle settling in a number of unsteady vector fields.
Joint Statistics of Finite Time Lyapunov Exponents in Isotropic Turbulence
Johnson, Perry; Meneveau, Charles
2014-11-01
Recently, the notion of Lagrangian Coherent Structures (LCS) has gained attention as a tool for qualitative visualization of flow features. LCS visualize repelling and attracting manifolds marked by local ridges in the field of maximal and minimal finite-time Lyapunov exponents (FTLE), respectively. To provide a quantitative characterization of FTLEs, the statistical theory of large deviations can be used based on the so-called Cramér function. To obtain the Cramér function from data, we use both the method based on measuring moments and measuring histograms (with finite-size correction). We generalize the formalism to characterize the joint distributions of the two independent FTLEs in 3D. The ``joint Cramér function of turbulence'' is measured from the Johns Hopkins Turbulence Databases (JHTDB) isotropic simulation at Reλ = 433 and results are compared with those computed using only the symmetric part of the velocity gradient tensor, as well as with those of instantaneous strain-rate eigenvalues. We also extend the large-deviation theory to study the statistics of the ratio of FTLEs. When using only the strain contribution of the velocity gradient, the maximal FTLE nearly doubles in magnitude and the most likely ratio of FTLEs changes from 4:1:-5 to 8:3:-11, highlighting the role of rotation in de-correlating the fluid deformations along particle paths. Supported by NSF Graduate Fellowship (DGE-1232825), a JHU graduate Fellowship, and NSF Grant CMMI-0941530. CM thanks Prof. Luca Biferale for useful discussions on the subject.
Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An
2012-12-01
This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.
Belinski, V
2009-01-01
The talk at international conference in honor of Ya. B. Zeldovich 95th Anniversary, Minsk, Belarus, April 2009. The talk represents a review of the old results and contemporary development on the problem of cosmological singularity.
Du, Kongchang; Zhao, Ying; Lei, Jiaqiang
2017-09-01
In hydrological time series prediction, singular spectrum analysis (SSA) and discrete wavelet transform (DWT) are widely used as preprocessing techniques for artificial neural network (ANN) and support vector machine (SVM) predictors. These hybrid or ensemble models seem to largely reduce the prediction error. In current literature researchers apply these techniques to the whole observed time series and then obtain a set of reconstructed or decomposed time series as inputs to ANN or SVM. However, through two comparative experiments and mathematical deduction we found the usage of SSA and DWT in building hybrid models is incorrect. Since SSA and DWT adopt 'future' values to perform the calculation, the series generated by SSA reconstruction or DWT decomposition contain information of 'future' values. These hybrid models caused incorrect 'high' prediction performance and may cause large errors in practice.
Non-linear shape functions over time in the space-time finite element method
Directory of Open Access Journals (Sweden)
Kacprzyk Zbigniew
2017-01-01
Full Text Available This work presents a generalisation of the space-time finite element method proposed by Kączkowski in his seminal of 1970’s and early 1980’s works. Kączkowski used linear shape functions in time. The recurrence formula obtained by Kączkowski was conditionally stable. In this paper, non-linear shape functions in time are proposed.
Big Bounce Singularity of a Simple Five-Dimensional Cosmological Model
Institute of Scientific and Technical Information of China (English)
徐立昕; 刘宏亚; 王贝利
2003-01-01
The big bounce singularity of a simple five-dimensional cosmological model is studied. Contrary to the standard big bang space-time singularity, this big bounce singularity is found to be an event horizon at which the scale factor and the mass density of the universe are finite, while the pressure undergoes a sudden transition from negative infinity to positive infinity. By using coordinate transformation it is also shown that before the bounce the universe contracts deflationary. According to the proper-time, the universe may have existed for an infinitely long time.
On singular and sincerely singular compact patterns
Rosenau, Philip; Zilburg, Alon
2016-08-01
A third order dispersive equation ut +(um)x +1/b[ua∇2ub]x = 0 is used to explore two very different classes of compact patterns. In the first, the prevailing singularity at the edge induces traveling compactons, solitary waves with a compact support. In the second, the singularity induced at the perimeter of the initial excitation, entraps the dynamics within the domain's interior (nonetheless, certain very singular excitations may escape it). Here, overlapping compactons undergo interaction which may result in an interchange of their positions, or form other structures, all confined within their initial support. We conjecture, and affirm it empirically, that whenever the system admits more than one type of compactons, only the least singular compactons may be evolutionary. The entrapment due to singularities is also unfolded and confirmed numerically in a class of diffusive equations ut =uk∇2un with k > 1 and n > 0 with excitations entrapped within their initial support observed to converge toward a space-time separable structure. A similar effect is also found in a class of nonlinear Klein-Gordon Equations.
Directory of Open Access Journals (Sweden)
Zhenhua Zhou
2015-01-01
Full Text Available This paper is concerned with the problem of designing robust H-infinity output feedback controller and resilient filtering for a class of discrete-time singular piecewise-affine systems with input saturation and state constraints. Based on a singular piecewise Lyapunov function combined with S-procedure and some matrix inequality convexifying techniques, the H-infinity stabilization condition is established and the resilient H-infinity filtering error dynamic system is investigated, and, meanwhile, the domain of attraction is well estimated. Under energy bounded disturbance, the input saturation disturbance tolerance condition is proposed; then, the resilient H-infinity filter is designed in some restricted region. It is shown that the controller gains and filter design parameters can be obtained by solving a family of LMIs parameterized by one or two scalar variables. Meanwhile, by using the corresponding optimization methods, the domain of attraction and the disturbance tolerance level is maximized, and the H-infinity performance γ is minimized. Numerical examples are given to illustrate the effectiveness of the proposed design methods.
Analysis of log-periodic power law singularity patterns in time series related to credit risk
Wosnitza, Jan Henrik; Sornette, Didier
2015-04-01
The log-periodic (super-exponential) power law singularity (LPPLS) has become a promising tool for predicting extreme behavior of self-organizing systems in natural sciences and finance. Some researchers have recently proposed to employ the LPPLS on credit risk markets. The review article at hand summarizes four papers in this field and shows how they are linked. After structuring the research questions, we collect the corresponding answers from the four articles. This eventually gives us an overall picture of the application of the LPPLS to credit risk data. Our literature review begins with grounding the view that credit default swap (CDS) spreads are hotbeds for LPPLS patterns and it ends up with drawing attention to the recently proposed alarm index for the prediction of institutional bank runs. By presenting a new field of application for the LPPLS, the reviewed strand of literature further substantiates the LPPLS hypothesis. Moreover, the results suggest that CDS spread trajectories belong to a different universality class than, for instance, stock prices.
Generic singularity studies revisited
Barrow, John D.; Tipler, Frank J.
1981-04-01
We comment on a reply by Belinskii, Khalatnikov and Lifshitz to our analysis of their conclusions regarding the general structure of space-time singularities. We support our contention that it is impossible to provide a reliable analysis of the evolution of a general (or stable) solution with local techniques in a synchronous coordinate system having a simultaneous physical singularity. Work supported in part by the National Science Foundation under grant number PHY 78-26592.
Finite-Time Reentry Attitude Control Using Time-Varying Sliding Mode and Disturbance Observer
Xuzhong Wu; Shengjing Tang; Jie Guo; Yao Zhang
2015-01-01
This paper presents the finite-time attitude control problem for reentry vehicle with redundant actuators in consideration of planet uncertainties and external disturbances. Firstly, feedback linearization technique is used to cancel the nonlinearities of equations of motion to construct a basic mode for attitude controller. Secondly, two kinds of time-varying sliding mode control methods with disturbance observer are integrated with the basic mode in order to enhance the control performance ...
Finite time convergent learning law for continuous neural networks.
Chairez, Isaac
2014-02-01
This paper addresses the design of a discontinuous finite time convergent learning law for neural networks with continuous dynamics. The neural network was used here to obtain a non-parametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties was the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on discontinuous algorithms was used to adjust the weights of the neural network. The adaptive algorithm was derived by means of a non-standard Lyapunov function that is lower semi-continuous and differentiable in almost the whole space. A compensator term was included in the identifier to reject some specific perturbations using a nonlinear robust algorithm. Two numerical examples demonstrated the improvements achieved by the learning algorithm introduced in this paper compared to classical schemes with continuous learning methods. The first one dealt with a benchmark problem used in the paper to explain how the discontinuous learning law works. The second one used the methane production model to show the benefits in engineering applications of the learning law proposed in this paper.
Finite-difference time-domain analysis of time-resolved terahertz spectroscopy experiments
DEFF Research Database (Denmark)
Larsen, Casper; Cooke, David G.; Jepsen, Peter Uhd
2011-01-01
In this paper we report on the numerical analysis of a time-resolved terahertz (THz) spectroscopy experiment using a modified finite-difference time-domain method. Using this method, we show that ultrafast carrier dynamics can be extracted with a time resolution smaller than the duration of the THz...... probe pulse and can be determined solely by the pump pulse duration. Our method is found to reproduce complicated two-dimensional transient conductivity maps exceedingly well, demonstrating the power of the time-domain numerical method for extracting ultrafast and dynamic transport parameters from time...
Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps
Directory of Open Access Journals (Sweden)
Minsong Zhang
2014-01-01
Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.
Auto-Regressive Models of Non-Stationary Time Series with Finite Length
Institute of Scientific and Technical Information of China (English)
FEI Wanchun; BAI Lun
2005-01-01
To analyze and simulate non-stationary time series with finite length, the statistical characteristics and auto-regressive (AR) models of non-stationary time series with finite length are discussed and studied. A new AR model called the time varying parameter AR model is proposed for solution of non-stationary time series with finite length. The auto-covariances of time series simulated by means of several AR models are analyzed. The result shows that the new AR model can be used to simulate and generate a new time series with the auto-covariance same as the original time series. The size curves of cocoon filaments regarded as non-stationary time series with finite length are experimentally simulated. The simulation results are significantly better than those obtained so far, and illustrate the availability of the time varying parameter AR model. The results are useful for analyzing and simulating non-stationary time series with finite length.
Directory of Open Access Journals (Sweden)
Jinxing Lin
2013-01-01
Full Text Available This paper is concerned with the problems of delay-dependent robust stability and stabilization for a class of continuous singular systems with time-varying delay in range and parametric uncertainties. The parametric uncertainties are assumed to be of a linear fractional form, which includes the norm bounded uncertainty as a special case and can describe a class of rational nonlinearities. In terms of strict linear matrix inequalities (LMIs, delay-range-dependent robust stability criteria for the unforced system are presented. Moreover, a strict LMI design approach is developed such that, when the LMI is feasible, a desired state feedback stabilizing controller can be constructed, which guarantees that, for all admissible uncertainties, the closed-loop dynamics will be regular, impulse free, and robustly asymptotically stable. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.
Ma, Yuechao; Yang, Pingjing; Yan, Yifang; Zhang, Qingling
2017-01-10
This paper investigates the problem of robust observer-based passive control for uncertain singular time-delay system subject to actuator saturation. A polytopic approach is used to describe the saturation behavior. First, by constructing Lyapunov-Krasovskii functional, a less conservative sufficient condition is obtained which guarantees that the closed-loop system is regular, impulse free, stable and robust strictly passive. Then, with this condition, the design method of state feedback controller and the observer are given by solving linear matrix inequalities. In addition, a domain of attraction in which the admissible initial states are ensured to converge asymptotically to the origin is solved as a convex optimization problem. Finally, some simulations are provided to demonstrate the effectiveness and superiority of the proposed method.
Finite-time consensus for leader-following second-order multi-agent system
Sun, Fenglan; Guan, Zhi-Hong
2013-04-01
The finite-time consensus problems of second-order multi-agent system under fixed and switching network topologies are studied in this article. Based on the graph theory, LaSalle's invariance principle and the homogeneity with dilation, the finite-time consensus protocol of each agent using local information is designed. The leader-following finite-time consensus is analysed in detail. Moreover, some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Fast and Robust Control of Excitation Systems:A Finite-time Method
Institute of Scientific and Technical Information of China (English)
WANG Yu-zhen; CHENG Dai-zhan; HONG Yi-guang; QIN Hua-shu
2001-01-01
Using finite-time control approach, this paper proposes a new design method for nonlinear robust excitation control of a widely used 5th-order model of synchronous generators. The finite-time excitation controller achieved here can improve the system's behaviors in some aspects such as quick convergence and robustness for uncertainties. Simulations demonstrate that the finite-time excitation controller is more effective than some other excitation controllers.
Finite-Time Chaos Control of a Complex Permanent Magnet Synchronous Motor System
Directory of Open Access Journals (Sweden)
Xiaobing Zhou
2014-01-01
Full Text Available This paper investigates the finite-time chaos control of a permanent magnet synchronous motor system with complex variables. Based on the finite-time stability theory, two control strategies are proposed to realize stabilization of the complex permanent magnet synchronous motor system in a finite time. Two numerical simulations have been conducted to demonstrate the validity and feasibility of the theoretical analysis.
Directory of Open Access Journals (Sweden)
Meng-Meng Jiang
2016-01-01
Full Text Available Under the weaker assumption on nonlinear functions, the adaptive finite-time stabilization of more general high-order nonlinear systems with dynamic and parametric uncertainties is solved in this paper. To solve this problem, finite-time input-to-state stability (FTISS is used to characterize the unmeasured dynamic uncertainty. By skillfully combining Lyapunov function, sign function, backstepping, and finite-time input-to-state stability approaches, an adaptive state feedback controller is designed to guarantee high-order nonlinear systems are globally finite-time stable.
Liu, Ping
2013-07-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lü and Chen systems are presented to validate the design and analysis.
Journey Beyond the Schwarzschild Black Hole Singularity
Araya, Ignacio J; James, Albin
2015-01-01
We present the geodesical completion of the Schwarzschild black hole in four dimensions which covers the entire space in (u,v) Kruskal-Szekeres coordinates, including the spacetime behind the black and white hole singularities. The gravitational constant switches sign abruptly at the singularity, thus we interpret the other side of the singularity as a region of antigravity. The presence of such sign flips is a prediction of local (Weyl) scale invariant geodesically complete spacetimes which improve classical general relativity and string theory. We compute the geodesics for our new black hole and show that all geodesics of a test particle are complete. Hence, an ideal observer, that starts its journey in the usual space of gravity, can reach the other side of the singularity in a finite amount of proper time. As usual, an observer outside of the horizon cannot verify that such phenomena exist. However, the fact that there exist proper observers that can see this, is of fundamental significance for the constr...
Gruszczynska, Marta; Rosat, Severine; Klos, Anna; Bogusz, Janusz
2017-04-01
Seasonal oscillations in the GPS position time series can arise from real geophysical effects and numerical artefacts. According to Dong et al. (2002) environmental loading effects can account for approximately 40% of the total variance of the annual signals in GPS time series, however using generally acknowledged methods (e.g. Least Squares Estimation, Wavelet Decomposition, Singular Spectrum Analysis) to model seasonal signals we are not able to separate real from spurious signals (effects of mismodelling aliased into annual period as well as draconitic). Therefore, we propose to use Multichannel Singular Spectrum Analysis (MSSA) to determine seasonal oscillations (with annual and semi-annual periods) from GPS position time series and environmental loading displacement models. The MSSA approach is an extension of the classical Karhunen-Loève method and it is a special case of SSA for multivariate time series. The main advantage of MSSA is the possibility to extract common seasonal signals for stations from selected area and to investigate the causality between a set of time series as well. In this research, we explored the ability of MSSA application to separate real geophysical effects from spurious effects in GPS time series. For this purpose, we used GPS position changes and environmental loading models. We analysed the topocentric time series from 250 selected stations located worldwide, delivered from Network Solution obtained by the International GNSS Service (IGS) as a contribution to the latest realization of the International Terrestrial Reference System (namely ITRF2014, Rebishung et al., 2016). We also researched atmospheric, hydrological and non-tidal oceanic loading models provided by the EOST/IPGS Loading Service in the Centre-of-Figure (CF) reference frame. The analysed displacements were estimated from ERA-Interim (surface pressure), MERRA-land (soil moisture and snow) as well as ECCO2 ocean bottom pressure. We used Multichannel Singular Spectrum
Non-smooth finite-time stabilization for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, global finite-time stabilization problem for a large class of nonlinear control systems is considered. An iterative design approach is given based on Lyapunov function. The finite time stabilizing control laws are constructed in the form of continuous but non-smooth time-invariant feedback.
Singularity-free Bianchi spaces with nonlinear electrodynamics
García-Salcedo, R; Garcia-Salcedo, Ricardo; Breton, Nora
2004-01-01
In this paper we present the analysis to determine the existence of singularities in spatially homogeneous anisotropic universes filled with nonlinear electromagnetic radiation. These spaces are conformal to Bianchi spaces admitting a three parameter group of motions G$_3$. We study analytical extensions as well as geodesic completeness. It is shown that with nonlinear electromagnetic field some of the Bianchi spaces are geodesically complete, like G$_3$II and G$_3$VIII; however Bianchi G$_3$IX presents the phenomenon of geodesics that are imprisoned. In contrast, diagonal Bianchi spaces like G$_3$I, G$_3$III and Kantowski-Sachs have a finite time existence ending in a scalar polynomial curvature singularity.
Big-Rip, Sudden Future, and other exotic singularities in the universe
Dabrowski, Mariusz P
2016-01-01
We discuss exotic singularities in the evolution of the universe motivated by the progress of observations in cosmology. Among them there are: Big-Rip (BR), Sudden Future Singularities (SFS), Generalized Sudden Future Singularities (GSFS), Finite Density Singularities (FD), type III, and type IV singularities. We relate some of these singularities with higher-order characteristics of expansion such as jerk and snap. We also discuss the behaviour of pointlike objects and classical strings on the approach to these singularities.
Institute of Scientific and Technical Information of China (English)
Li Long; Zhang Yu; Liang Changhong
2004-01-01
An Improved Locally Conformal Finite-Difference Time-Domain (ILC-FDTD) method is presented in this paper, which is used to analyze the edge inclined slots penetrating adjacent broadwalls of a finite wall thickness waveguide. ILC-FDTD not only removes the instability of the original locally conformal FDTD algorithm, but also improves the computational accuracy by locally modifying magnetic field update equations and the virtual iterative electric fields according to the complexity of the slot fringe fields. The mutual coupling between two edge inclined slots can also be analyzed by ILC-FDTD effectively.
SPACE-TIME FINITE ELEMENT METHOD FOR SCHR(O)DINGER EQUATION AND ITS CONSERVATION
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Energy conservation of nonlinear Schr(o)dinger ordinary differential equation was proved through using continuous finite element methods of ordinary differential equation; Energy integration conservation was proved through using space-time continuous fully discrete finite element methods and the electron nearly conservation with higher order error was obtained through using time discontinuous only space continuous finite element methods of nonlinear Schrodinger partial equation. The numerical results are in accordance with the theory.
Connections Between Singular Control and Optimal Switching
Guo, Xin; Tomecek, Pascal
2007-01-01
This paper builds a new theoretical connection between singular control of finite variation and optimal switching problems. This correspondence provides a novel method for solving high-dimensional singular control problems, and enables us to extend the theory of reversible investment: sufficient conditions are derived for the existence of optimal controls and for the regularity of value functions. Consequently, our regularity result links singular controls and Dynkin games through sequential ...
Quantum Singularity of Quasiregular Spacetimes
Konkowski, Deborah A.; Helliwell, Thomas M.
2001-04-01
A quasiregular spacetime is a spacetime with a classical quasiregular singularity, the mildest form of true singularity [G.F.R. Ellis and B.G. Schmidt, Gen. Rel. Grav. 8, 915 (1977)]. The definition of G.T. Horowitz and D. Marolf [Phys. Rev. D52, 5670 (1995)] for a quantum-mechanically singular spacetime is one in which the spatial-derivative operator in the Klein-Gordon equation for a massive scalar field is not essentially self-adjoint. In such a quantum-mechanically singular spacetime, the time evolution of a quantum test particle is not uniquely determined. Horowitz and Marolf showed that a two-dimensional spacetime with a classical conical singularity (i.e., a two-dimensional quasiregular singularity) is also quantum-mechanically singular. Here we show that a class of static quasiregular spacetimes possessing disclinations and dislocations [R.A.Puntigam and H.H. Soleng , Class. Quantum Grav. 14, 1129 (1997)] is quantum-mechanically singular, since the scalar wave operator is not essentially self-adjoint. These spacetimes include an idealized cosmic string spacetime, i.e., a four-dimensional spacetime with conical singularity, and a Galtsov/Letelier/Tod spacetime featuring a screw dislocation [K.P. Tod, Class. Quantum Grav. 11, 1331 (1994); D.V. Galtsov and P.S. Letelier, Phys. Rev. D47, 4273 (1993)]. In addition, we show that the definition of quantum-mechanically singular spacetimes can be extended to include Maxwell and Dirac fields.
How Does Naked Singularity Look?
Nakao, Ken-ichi; Kobayashi, Naoki; Ishihara, Hideki
2002-01-01
There are non-radial null geodesics emanating from the shell focusing singularity formed at the symmetric center in a spherically symmetric dust collapse. In this article, assuming the self-similarity in the region filled with the dust fluid, we study these singular null geodesics in detail. We see the time evolution of the angular diameter of the central naked singularity and show that it might be bounded above by the value corresponding to the circular null geodesic in the Schwarzschild spa...
Odintsov, S D
2016-01-01
We present some cosmological models which unify the late and early-time acceleration eras with the radiation and the matter domination era, and we realize the cosmological models by using the theoretical framework of $F(R)$ gravity. Particularly, the first model unifies the late and early-time acceleration with the matter domination era, and the second model unifies all the evolution eras of our Universe. The two models are described in the same way at early and late times, and only the intermediate stages of the evolution have some differences. Each cosmological model contains two Type IV singularities which are chosen to occur one at the end of the inflationary era and one at the end of the matter domination era. The cosmological models at early times are approximately identical to the $R^2$ inflation model, so these describe a slow-roll inflationary era which ends when the slow-roll parameters become of order one. The inflationary era is followed by the radiation era and after that the matter domination er...
Energy Technology Data Exchange (ETDEWEB)
Sevost' yanov, Evgenii A [Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences, Donetsk (Ukraine)
2010-02-28
We prove that sets of zero modulus with weight Q (in particular, isolated singularities) are removable for discrete open Q-maps f:D{yields}R-bar{sup n} if the function Q(x) has finite mean oscillation or a logarithmic singularity of order not exceeding n-1 on the corresponding set. We obtain analogues of the well-known Sokhotskii-Weierstrass theorem and also of Picard's theorem. In particular, we show that in the neighbourhood of an essential singularity, every discrete open Q-map takes any value infinitely many times, except possibly for a set of values of zero capacity.
Robust control of post-stall pitching maneuver based on finite-time observer.
Wu, Dawei; Chen, Mou; Gong, Huajun
2017-09-01
This article presents a robust finite-time maneuver control scheme for the longitudinal attitude dynamic of the aircraft with unsteady aerodynamic disturbances and input saturation. To efficiently eliminate the influence of unsteady aerodynamic disturbances, nonlinear finite-time observers are developed. Despite the existence of the nonlinearity and the coupling between aircraft states and unsteady aerodynamic disturbances, the proposed observers can still precisely estimate the unmeasurable unsteady aerodynamic disturbances in finite time. To attenuate the effect caused by input saturation, a finite-time auxiliary system is constructed. With the error between the desired control input and saturation input as the input of the auxiliary system, the additional signals are generated to compensate for the effect of input saturation. Combined with the finite-time observers and the finite-time auxiliary system, a robust finite-time backstepping attitude control design is developed. The finite-time convergence of all closed-loop system signals is rigorously proved via Lyapunov analysis method under the developed robust attitude control schemes. Finally, simulation results are presented to illustrate the effectiveness of the proposed attitude control approaches. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Finite-time synchronization of a class of autonomous chaotic systems
Indian Academy of Sciences (India)
Huini Lin; Jianping Cai
2014-03-01
Some criteria for achieving the finite-time synchronization of a class of autonomous chaotic systems are derived by the finite-time stability theory and Gerschgorin disc theorem. Numerical simulations are shown to illustrate the effectiveness of the proposed method.
Finite-Time Chaos Suppression of Permanent Magnet Synchronous Motor Systems
Directory of Open Access Journals (Sweden)
Yi-You Hou
2014-04-01
Full Text Available This paper considers the problem of the chaos suppression for the Permanent Magnet Synchronous Motor (PMSM system via the finite-time control. Based on Lyapunov stability theory and the finite-time controller are developed such that the chaos behaviors of PMSM system can be suppressed. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.
The Finite-time Ruin Probability for the Jump-Diffusion Model with Constant Interest Force
Institute of Scientific and Technical Information of China (English)
Tao Jiang; Hai-feng Yan
2006-01-01
In this paper, we consider the finite-time ruin probability for the jump-diffusion Poisson process.Under the assumptions that the claimsizes are subexponentially distributed and that the interest force is constant, we obtain an asymptotic formula for the finite-time ruin probability. The results we obtain extends the
Finite-time analysis of global projective synchronization on coloured networks
Indian Academy of Sciences (India)
Cai Guoliang; Jiang Shengqin; Cai Shuiming; Tian Lixin
2016-03-01
A novel finite-time analysis is given to investigate the global projective synchronization on coloured networks. Some less conservative conditions are derived by utilizing finite-time control techniques and Lyapunov stability theorem. In addition, two illustrative numerical simulations are provided to verify the effectiveness of the proposed theoretical results.
Directory of Open Access Journals (Sweden)
Zahra Hojjati Tavassoli
2016-07-01
Full Text Available During a construction project life cycle, project costs and time estimations contribute greatly to baseline scheduling. Besides, schedule risk analysis and project control are also influenced by the above factors. Although many papers have offered estimation techniques, little attempt has been made to generate project time series data as daily progressive estimations in different project environments that could help researchers in generating general and customized formulae in further studies. This paper, however, is an attempt to introduce a new simulation approach to reflect the data regarding time series progress of the project, considering the specifications and the complexity of the project and the environment where the project is performed. Moreover, this simulator can equip project managers with estimated information, which reassures them of the execution stages of the project although they lack historical data. A case study is presented to show the usefulness of the model and its applicability in practice. In this study, singular spectrum analysis has been employed to analyze the simulated outputs, and the results are separated based on their signal and noise trends. The signal trend is used as a point-of-reference to compare the outputs of a simulation employing S-curve technique results and the formulae corresponding to earned value management, as well as the life of a given project.
Chu, Chong-Sun
2008-01-01
We continue the studies of our earlier proposal for an AdS/CFT correspondence for time-dependent supergravity backgrounds. We note that by performing a suitable change of variables, the dual super Yang-Mills theory lives on a flat base space, and the time-dependence of the supergravity background is entirely encoded in the time-dependent couplings (gauge and axionic) and their supersymmetric completion. This form of the SYM allows a detailed perturbative analysis to be performed. In particular the one-loop Wilsonian effective action of the boundary SYM theory is computed. By using the holographic UV/IR relation, we propose a way to extract the bulk metric from the Wilsonian effective action; and we find that the bulk metric of our supergravity solutions can be reproduced precisely. While the bulk geometry can have various singularities such as geodesic incompleteness, gauge theory quantum effects can introduce higher derivative corrections in the effective action which can serve as a way to resolve the singul...
Time-dependent optimal heater control using finite difference method
Energy Technology Data Exchange (ETDEWEB)
Li, Zhen Zhe; Heo, Kwang Su; Choi, Jun Hoo; Seol, Seoung Yun [Chonnam National Univ., Gwangju (Korea, Republic of)
2008-07-01
Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying temperature of forming window.
Time dependent wave envelope finite difference analysis of sound propagation
Baumeister, K. J.
1984-01-01
A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.
Continuous composite finite-time convergent guidance laws with autopilot dynamics compensation.
He, Shaoming; Lin, Defu
2015-09-01
This paper has proposed two continuous composite finite-time convergent guidance laws to intercept maneuvering targets in the presence of autopilot lag: one is for hit-to-kill and the other is for zeroing the line-of-sight (LOS) angular rate. More specifically, the nonlinear disturbance observer (NDOB) is used to estimate the lumped uncertainty online while the finite-time control technique is used to fulfill the design goal in finite time. The key feature in derivation of the proposed guidance law is that two integral-type Lyapunov functions are used to avoid analytic differentiation of virtual control law encountered with traditional backstepping. The finite-time stability of the closed-loop nonlinear observer-controller system is established using finite-time bounded (FTB) function and Lyapunov function methods. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.
Directory of Open Access Journals (Sweden)
Xiaohui Mo
2017-01-01
Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.
Tamascelli, D; Plenio, M B
2015-01-01
When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in the system size. A class of algorithms, exemplified by the Time-Evolving Block-Decimation (TEBD) algorithm, make use of this observation by selecting the relevant subspace through a decimation technique relying on the Singular Value Decomposition (SVD). In these algorithms, the complexity of each time-evolution step is dominated by the SVD. Here we show that, by applying a randomized version of the SVD routine (RRSVD), the power law governing the computational complexity of TEBD is lowered by one degree, resulting in a considerable speed-up. We exemplify the potential gains in efficiency at the hand of some real world examples to which TEBD can be successfully applied to and demonstrate that for those system RRSVD delivers results as accurate as state-of-the-art deterministi...
Quantization of time-dependent singular potential systems: Non-central potential in three dimensions
Directory of Open Access Journals (Sweden)
Salah Menouar
2016-09-01
Full Text Available Quantum features of a dynamical system subjected to time-dependent non-central potentials are investigated. The entire potential of the system is composed of the inverse quadratic potential and the Coulomb potential. An invariant operator that enables us to treat the time-dependent Hamiltonian system in view of quantum mechanics is introduced in order to derive Schrödinger solutions (wave functions of the system. To simplify the problem, the invariant operator is transformed to a simple form by unitary transformation. Quantum solutions in the transformed system are easily obtained because the transformed invariant operator is a time-independent simple one. The Nikiforov-Uvarov method is used for solving eigenvalue equation of the transformed invariant operator. The double ring-shaped generalized non-central time-dependent potential is considered as a particular case for further study. From inverse transformation of quantum solutions obtained in the transformed system, the complete quantum solutions in the original system are identified. The quantum properties of the system are addressed on the basis of the wave functions.
Finite-Time Reentry Attitude Control Using Time-Varying Sliding Mode and Disturbance Observer
Directory of Open Access Journals (Sweden)
Xuzhong Wu
2015-01-01
Full Text Available This paper presents the finite-time attitude control problem for reentry vehicle with redundant actuators in consideration of planet uncertainties and external disturbances. Firstly, feedback linearization technique is used to cancel the nonlinearities of equations of motion to construct a basic mode for attitude controller. Secondly, two kinds of time-varying sliding mode control methods with disturbance observer are integrated with the basic mode in order to enhance the control performance and system robustness. One method is designed based on boundary layer technique and the other is a novel second-order sliding model control method. The finite-time stability analyses of both resultant closed-loop systems are carried out. Furthermore, after attitude controller produces the torque commands, an optimization control allocation approach is introduced to allocate them into aerodynamic surface deflections and on-off reaction control system thrusts. Finally, the numerical simulation results demonstrate that both of the time-varying sliding mode control methods are robust to uncertainties and disturbances without chattering phenomenon. Moreover, the proposed second-order sliding mode control method possesses better control accuracy.
Zanotti, Olindo; Dumbser, Michael; Hidalgo, Arturo
2015-01-01
In this paper we present a novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space-time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order \\aposteriori sub-cell ADER-WENO finite volume \\emph{limiter}. Notoriously, the original DG method produces strong oscillations in the presence of discontinuous solutions and several types of limiters have been introduced over the years to cope with this problem. Following the innovative idea recently proposed in \\cite{Dumbser2014}, the discrete solution within the troubled cells is \\textit{recomputed} by scattering the DG polynomial at the previous time step onto a suitable number of sub-cells along each direction. Relying on the robustness of classical finite volume WENO schemes, the sub-cell averages are recomputed and then gathered back into the DG polynomials over the main grid. In this paper this approach is implemented for the first time within a space-time adaptive ...
The singular universe and the reality of time a proposal in natural philosophy
Unger, Roberto Mangabeira
2015-01-01
Cosmology is in crisis. The more we discover, the more puzzling the universe appears to be. How and why are the laws of nature what they are? A philosopher and a physicist, world-renowned for their radical ideas in their fields, argue for a revolution. To keep cosmology scientific, we must replace the old view in which the universe is governed by immutable laws by a new one in which laws evolve. Then we can hope to explain them. The revolution that Roberto Mangabeira Unger and Lee Smolin propose relies on three central ideas. There is only one universe at a time. Time is real: everything in the structure and regularities of nature changes sooner or later. Mathematics, which has trouble with time, is not the oracle of nature and the prophet of science; it is simply a tool with great power and immense limitations. The argument is readily accessible to non-scientists as well as to the physicists and cosmologists whom it challenges.
Finite-Time Stabilization of Dynamic Nonholonomic Wheeled Mobile Robots with Parameter Uncertainties
Directory of Open Access Journals (Sweden)
Hua Chen
2013-01-01
settling time. The systematic strategy combines the theory of finite-time stability with a new switching control design method. Finally, the simulation result illustrates the effectiveness of the proposed controller.
Potentially Singular Solutions of the 3D Incompressible Euler Equations
Luo, Guo
2013-01-01
Whether the 3D incompressible Euler equations can develop a singularity in finite time from smooth initial data is one of the most challenging problems in mathematical fluid dynamics. This work attempts to provide an affirmative answer to this long-standing open question from a numerical point of view, by presenting a class of potentially singular solutions to the Euler equations computed in axisymmetric geometries. The solutions satisfy a periodic boundary condition along the axial direction and no-flow boundary condition on the solid wall. The equations are discretized in space using a hybrid 6th-order Galerkin and 6th-order finite difference method, on specially designed adaptive (moving) meshes that are dynamically adjusted to the evolving solutions. With a maximum effective resolution of over $(3 \\times 10^{12})^{2}$ near the point of the singularity, we are able to advance the solution up to $\\tau_{2} = 0.003505$ and predict a singularity time of $t_{s} \\approx 0.0035056$, while achieving a \\emph{pointw...
Finite time extinction for nonlinear fractional evolution equations and related properties.
Jesus Ildefonso Diaz; Teresa Pierantozzi; Luis Vazquez
2016-01-01
The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time) is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly,...
Self-modulation instability of ultra-relativistic particle bunches with finite rise times
Vieira, J; Fang, Y; Mori, W B; Muggli, P; Silva, L O
2014-01-01
We study the evolution of the self-modulation instability using bunches with finite rise times. Using particle-in-cell simulations we show that unlike long bunches with sharp rise times, there are large variations of the wake amplitudes and wake phase velocity when bunches with finite rise times are used. These results show that use of bunches with sharp rise times is important to seed the self-modulation instability and to ensure stable acceleration regimes.
Wu, Yuanyuan; Cao, Jinde; Li, Qingbo; Alsaedi, Ahmed; Alsaadi, Fuad E
2017-01-01
This paper deals with the finite-time synchronization problem for a class of uncertain coupled switched neural networks under asynchronous switching. By constructing appropriate Lyapunov-like functionals and using the average dwell time technique, some sufficient criteria are derived to guarantee the finite-time synchronization of considered uncertain coupled switched neural networks. Meanwhile, the asynchronous switching feedback controller is designed to finite-time synchronize the concerned networks. Finally, two numerical examples are introduced to show the validity of the main results. Copyright © 2016 Elsevier Ltd. All rights reserved.
Sun, Yongzheng; Li, Wang; Zhao, Donghua
2012-06-01
In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.
Gravastars with Dark Energy Evolving to Naked Singularity
Chan, R; Senna, P; da Rocha, J F Villas
2011-01-01
We consider a gravastar model made of anisotropic dark energy with an infinitely thin spherical shell of a perfect fluid with the equation of state $p = (1-\\gamma)\\sigma$ with an external de Sitter-Schwarzschild region. It is found that in some cases the models represent the "bounded excursion" stable gravastars, where the thin shell is oscillating between two finite radii, while in other cases they collapse until the formation of black holes or naked singularities. An interesting result is that we can have black hole and stable gravastar formation even with an interior and a shell constituted of dark and repulsive dark energy, as also shown in previous work. Besides, in three cases we have a dynamical evolution to a black hole (for $\\Lambda=0$) or to a naked singularity (for $\\Lambda > 0$). This is the first time in the literature that a naked singularity emerges from a gravastar model.
Global-in-time Uniform Convergence for Linear Hyperbolic-Parabolic Singular Perturbations
Institute of Scientific and Technical Information of China (English)
Marina GHISI; Massimo GOBBING
2006-01-01
We consider the Cauchy problem εuε" + δu'ε + Auε = 0, uε(0) = u0, u'ε(0) = u1, where ε＞0, δ＞ 0, H is a Hilbert space, and A is a self-adjoint linear non-negative operator on H with dense domain D(A). We study the convergence of {uε} to the solution of the limit problem δu' + Au = 0, u(0) = u0.For initial data (u0,u1) ∈D(A1/2)×H, we prove global-in-time convergence with respect to strong topologies.Moreover, we estimate the convergence rate in the case where (u0,u1)∈ D(A3/2)×D(A1/2), and we show that this regularity requirement is sharp for our estimates. We give also an upper bound for |u'ε(t)| which does not depend on ε.
Adaptive Control of the Chaotic System via Singular System Approach
Directory of Open Access Journals (Sweden)
Yudong Li
2014-01-01
Full Text Available This paper deals with the control problem of the chaotic system subject to disturbance. The sliding mode surface is designed by singular system approach, and sufficient condition for convergence is given. Then, the adaptive sliding mode controller is designed to make the state arrive at the sliding mode surface in finite time. Finally, Lorenz system is considered as an example to show the effectiveness of the proposed method.
Directory of Open Access Journals (Sweden)
Bin Wang
2016-01-01
Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.
Finite-time consensus for heterogeneous multi-agent systems with mixed-order agents
Sun, Fenglan; Zhu, Wei
2015-08-01
This paper studies the finite-time consensus for heterogeneous multi-agent systems composed of mixed-order agents over fixed and switching topologies. The control protocol of each agent using local information is designed and the detailed analysis of the finite-time consensus for fixed and switching interaction topologies is presented. The design of the finite-time consensus protocol is based on graph theory, matrix theory, and LaSalle's invariance principle. Both theoretical studies and simulation results show the effectiveness of the proposed method and the correctness of the obtained theoretical results.
Robust Finite-Time Control for Spacecraft with Coupled Translation and Attitude Dynamics
Directory of Open Access Journals (Sweden)
Guo-Qiang Wu
2013-01-01
Full Text Available Robust finite-time control for spacecraft with coupled translation and attitude dynamics is investigated in the paper. An error-based spacecraft motion model in six-degree-of-freedom is firstly developed. Then a finite-time controller based on nonsingular terminal sliding mode control technique is proposed to achieve translation and attitude maneuvers in the presence of model uncertainties and environmental perturbations. A finite-time observer is designed and a modified controller is then proposed to deal with uncertainties and perturbations and alleviate chattering. Numerical simulations are finally provided to illustrate the performance of the proposed controllers.
Finite-time stabilization for a class of stochastic nonlinear systems via output feedback.
Zha, Wenting; Zhai, Junyong; Fei, Shumin; Wang, Yunji
2014-05-01
This paper investigates the problem of global finite-time stabilization in probability for a class of stochastic nonlinear systems. The drift and diffusion terms satisfy lower-triangular or upper-triangular homogeneous growth conditions. By adding one power integrator technique, an output feedback controller is first designed for the nominal system without perturbing nonlinearities. Based on homogeneous domination approach and stochastic finite-time stability theorem, it is proved that the solution of the closed-loop system will converge to the origin in finite time and stay at the origin thereafter with probability one. Two simulation examples are presented to illustrate the effectiveness of the proposed design procedure.
Liu, Xiaoyang; Ho, Daniel W C; Cao, Jinde; Xu, Wenying
2016-08-24
This brief investigates the problem of finite-time robust consensus (FTRC) for second-order nonlinear multiagent systems with external disturbances. Based on the global finite-time stability theory of discontinuous homogeneous systems, a novel finite-time convergent discontinuous disturbed observer (DDO) is proposed for the leader-following multiagent systems. The states of the designed DDO are then used to design the control inputs to achieve the FTRC of nonlinear multiagent systems in the presence of bounded disturbances. The simulation results are provided to validate the effectiveness of these theoretical results.
Finite-Time Attractivity for Diagonally Dominant Systems with Off-Diagonal Delays
Directory of Open Access Journals (Sweden)
T. S. Doan
2012-01-01
Full Text Available We introduce a notion of attractivity for delay equations which are defined on bounded time intervals. Our main result shows that linear delay equations are finite-time attractive, provided that the delay is only in the coupling terms between different components, and the system is diagonally dominant. We apply this result to a nonlinear Lotka-Volterra system and show that the delay is harmless and does not destroy finite-time attractivity.
Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control
Basin, Michael; Bharath Panathula, Chandrasekhara; Shtessel, Yuri
2016-09-01
This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.
Directory of Open Access Journals (Sweden)
Guo Yong
2014-04-01
Full Text Available This paper investigates two finite-time controllers for attitude control of spacecraft based on rotation matrix by an adaptive backstepping method. Rotation matrix can overcome the drawbacks of unwinding which makes a spacecraft perform a large-angle maneuver when a small-angle maneuver in the opposite rotational direction is sufficient to achieve the objective. With the use of adaptive control, the first robust finite-time controller is continuous without a chattering phenomenon. The second robust finite-time controller can compensate external disturbances with unknown bounds. Theoretical analysis shows that both controllers can make a spacecraft following a time-varying reference attitude signal in finite time and guarantee the stability of the overall closed-loop system. Numerical simulations are presented to demonstrate the effectiveness of the proposed control schemes.
Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions.
Meng, Deyuan; Jia, Yingmin; Du, Junping
2016-04-01
This paper deals with finite-time consensus problems for multiagent systems that are subject to hybrid cooperative and antagonistic interactions. Two consensus protocols are constructed by employing the nearest neighbor rule. It is shown that under the presented protocols, the states of all agents can be guaranteed to reach an agreement in a finite time regarding consensus values that are the same in modulus but may not be the same in sign. In particular, the second protocol can enable all agents to reach a finite-time consensus with a settling time that is not dependent upon the initial states of agents. Simulation results are given to demonstrate the effectiveness and finite-time convergence of the proposed consensus protocols.
Finite-Time Control for Robust Tracking Consensus in MASs With an Uncertain Leader.
Lu, Xiaoqing; Wang, Yaonan; Yu, Xinghuo; Lai, Jingang
2016-03-31
This paper investigates the finite-time control for robust tracking consensus problems of multiagent systems with an uncertain leader for situations where the state of the considered active leader may not be measured and the directed network topology is time-varying. Based on the neighbor-based state-estimation rule and a new Lyapunov stability analysis method, a continuous and nonlinear distributed tracking protocol using only relative position information is designed, under which each agent can follow the leader in finite time if the input (acceleration) of the leader is known, and the tracking errors can converge to a bounded region in finite time if the input of the leader is unknown. In particular, a special continuous distributed tracking protocol with bounded control inputs is introduced to track the active leader in finite time. Numerical simulations are also given to illustrate the effectiveness of the theoretic results.
Ran, Dechao; Chen, Xiaoqian; Misra, Arun K.
2017-07-01
This paper investigates the finite time coordinated formation control problem for spacecraft formation flying (SFF) under the assumption of directed communication topology. By using the neighborhood state measurements, a robust finite time coordinated formation controller is firstly designed based on the nonsingular terminal sliding mode surface. To address the special case that the desired trajectory of the formation is only accessible to a subset of spacecraft in the formation, an adaptive finite time coordinated formation controller is also proposed by designing a novel sliding mode surface. In both cases, the external disturbances are explicitly taken into account. Rigorous theoretical analysis proves that the proposed control schemes ensure that the closed-loop system can track the desired time-varying trajectory in finite time. Numerical simulations are presented that not only highlights the closed-loop performance benefits from the proposed control algorithms, but also illustrates the effectiveness in the presence of external disturbances when compared with the existing coordinated formation control schemes.
线性奇异时滞系统的观测器设计%Observer Design for Linear Singular Time-delay Systems
Institute of Scientific and Technical Information of China (English)
冯俊娥; 张维海; 程兆林
2005-01-01
Two kinds of observers for linear singular time-delay systems, namely functional observers and full-order observers, are considered in this paper. For the former, observers with and without internal delay are considered. For the latter, observers without internal delay is given. The corresponding design steps for various observers, which are all normal linear time-delay systems, are presented. Numerical examples are given to illustrate the methods.
Finite time control for MIMO nonlinear system based on higher-order sliding mode.
Liu, Xiangjie; Han, Yaozhen
2014-11-01
Considering a class of MIMO uncertain nonlinear system, a novel finite time stable control algorithm is proposed based on higher-order sliding mode concept. The higher-order sliding mode control problem of MIMO nonlinear system is firstly transformed into finite time stability problem of multivariable system. Then continuous control law, which can guarantee finite time stabilization of nominal integral chain system, is employed. The second-order sliding mode is used to overcome the system uncertainties. High frequency chattering phenomenon of sliding mode is greatly weakened, and the arbitrarily fast convergence is reached. The finite time stability is proved based on the quadratic form Lyapunov function. Examples concerning the triple integral chain system with uncertainty and the hovercraft trajectory tracking are simulated respectively to verify the effectiveness and the robustness of the proposed algorithm.
Institute of Scientific and Technical Information of China (English)
Liu Ping
2013-01-01
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters.Based on the finite-time stability theory,nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems,respectively.The two controllers are simple,and one of the uncertain unified chaotic complex systems is robust.For the design of a finite-time controller on uncertain unified chaotic complex systems,only some of the unknown parameters need to be bounded.Simulation results for the chaotic complex Lorenz,Lü and Chen systems are presented to validate the design and analysis.
Robust finite-time tracking control for nonlinear suspension systems via disturbance compensation
Pan, Huihui; Jing, Xingjian; Sun, Weichao
2017-05-01
This paper focuses on the finite-time tracking control with external disturbance for active suspension systems. In order to compensate unknown disturbance efficiently, a disturbance compensator with finite-time convergence property is studied. By analyzing the discontinuous phenomenon of classical disturbance compensation techniques, this study presents a simple approach to construct a continuous compensator satisfying the finite-time disturbance rejection performance. According to the finite-time separation principle, the design procedures of the nominal controller for the suspension system without disturbance and the disturbance compensator can be implemented in a completely independent manner. Therefore, the overall control law for the closed-loop system is continuous, which offers some distinct advantages over the existing discontinuous ones. From the perspective of practical implementation, the continuous controller can avoid effectively the unexpected chattering in active suspension control. Comparative experimental results are presented and discussed to illustrate the advantage and effectiveness of the proposed control strategy.
Distributed finite-time containment control for double-integrator multiagent systems.
Wang, Xiangyu; Li, Shihua; Shi, Peng
2014-09-01
In this paper, the distributed finite-time containment control problem for double-integrator multiagent systems with multiple leaders and external disturbances is discussed. In the presence of multiple dynamic leaders, by utilizing the homogeneous control technique, a distributed finite-time observer is developed for the followers to estimate the weighted average of the leaders' velocities at first. Then, based on the estimates and the generalized adding a power integrator approach, distributed finite-time containment control algorithms are designed to guarantee that the states of the followers converge to the dynamic convex hull spanned by those of the leaders in finite time. Moreover, as a special case of multiple dynamic leaders with zero velocities, the proposed containment control algorithms also work for the case of multiple stationary leaders without using the distributed observer. Simulations demonstrate the effectiveness of the proposed control algorithms.
Neural Network Observer-Based Finite-Time Formation Control of Mobile Robots
Directory of Open Access Journals (Sweden)
Caihong Zhang
2014-01-01
Full Text Available This paper addresses the leader-following formation problem of nonholonomic mobile robots. In the formation, only the pose (i.e., the position and direction angle of the leader robot can be obtained by the follower. First, the leader-following formation is transformed into special trajectory tracking. And then, a neural network (NN finite-time observer of the follower robot is designed to estimate the dynamics of the leader robot. Finally, finite-time formation control laws are developed for the follower robot to track the leader robot in the desired separation and bearing in finite time. The effectiveness of the proposed NN finite-time observer and the formation control laws are illustrated by both qualitative analysis and simulation results.
Mutually singular functions and computation of the lengths of curves
Energy Technology Data Exchange (ETDEWEB)
Dovgoshei, A A [Institute of Applied Mathematics and Mechanics of the National Academy of Sciences of Ukraine, Donetsk (Ukraine); Martio, O [Department of Mathematics, University of Helsinki (Finland)
2006-08-31
We study rectifiable curves given by mutually singular coordinate functions in finite-dimensional normed spaces. We describe these curves in terms of the behaviour of approximative tangents and find a simple formula for their lengths. We deduce from these results new necessary and sufficient conditions for the mutual singularity of finitely many functions of bounded variation.
Finite-time consensus for leader-following multi-agent systems over switching network topologies
Sun, Feng-Lan; Zhu, Wei
2013-11-01
Finite-time consensus problem of the leader-following multi-agent system under switching network topologies is studied in this paper. Based on the graph theory, matrix theory, homogeneity with dilation, and LaSalle's invariance principle, the control protocol of each agent using local information is designed, and the detailed analysis of the leader-following finite-time consensus is provided. Some examples and simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Formation of Root Singularities on the Free Surface of a Conducting Fluid in an Electric Field
Zubarev, N M
1998-01-01
The formation of singularities on a free surface of a conducting ideal fluid in a strong electric field is considered. It is found that the nonlinear equations of two-dimensional fluid motion can be solved in the small-angle approximation. This enables us to show that for almost arbitrary initial conditions the surface curvature becomes infinite in a finite time.
Diamagnetism of quantum gases with singular potentials
DEFF Research Database (Denmark)
Briet, Philippe; Cornean, Horia; Savoie, Baptiste
2010-01-01
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is analytic with respect to the chemical potential and the intensity of the external magnetic...
How the universe got its spots diary of a finite time in a finite space
Levin, Janna
2002-01-01
Is the universe infinite, or is it just really big? Does nature abhor infinity? In startling and beautiful prose, Janna Levin's diary of unsent letters to her mother describes what we know about the shape and extent of the universe, about its beginning and its end. She grants the uninitiated access to the astounding findings of contemporary theoretical physics and makes tangible the contours of space and time--those very real curves along which apples fall and planets orbit. Levin guides the reader through the observations and thought-experiments that have enabled physicists to begin charting the universe. She introduces the cosmic archaeology that makes sense of the pattern of hot spots left over from the big bang, a pursuit on the verge of discovering the shape of space itself. And she explains the topology and the geometry of the universe now coming into focus--a strange map of space full of black holes, chaotic flows, time warps, and invisible strings. Levin advances the controversial idea that this map ...
Potentially singular solutions of the 3D axisymmetric Euler equations.
Luo, Guo; Hou, Thomas Y
2014-09-09
The question of finite-time blowup of the 3D incompressible Euler equations is numerically investigated in a periodic cylinder with solid boundaries. Using rotational symmetry, the equations are discretized in the (2D) meridian plane on an adaptive (moving) mesh and is integrated in time with adaptively chosen time steps. The vorticity is observed to develop a ring-singularity on the solid boundary with a growth proportional to ∼(ts - t)(-2.46), where ts ∼ 0.0035056 is the estimated singularity time. A local analysis also suggests the existence of a self-similar blowup. The simulations stop at τ(2) = 0.003505 at which time the vorticity amplifies by more than (3 × 10(8))-fold and the maximum mesh resolution exceeds (3 × 10(12))(2). The vorticity vector is observed to maintain four significant digits throughout the computations.
Chemical relaxation times in a hadron gas at finite temperature
Goity, J L
1993-01-01
The relaxation times of particle numbers in hot hadronic matter with vanishing baryon number are estimated using the ideal gas approximation and taking into account resonance decays and annihilation processes as the only sources of particle number fluctuations. Near the QCD critical temperature the longest relaxation times turn out to be of the order of 10 fm and grow roughly exponentially to become of the order of $10^{3}$ fm at temperatures around 100 MeV. As a consequence of such long relaxation times, a clear departure from chemical equilibrium must be observed in the momentum distribution of secondary particles produced in high energy nuclear collisions.
Finite correlation time effects in kinematic dynamo problem
Energy Technology Data Exchange (ETDEWEB)
Schekochihin, A.A.; Kulsrud, R.M.
2000-02-11
One-point statistics of the magnetic fluctuations in kinematic regime with large Prandtl number and non delta-correlated in time advecting velocity field are studied. A perturbation expansion in the ratio of the velocity correlation time to the dynamo growth time is constructed in the spirit of the Kliatskin-Tatarskii functional method and carried out to first order. The convergence properties are improved compared to the commonly used van Kampen-Terwiel method. The zeroth-order growth rate of the magnetic energy is estimated to be reduced (in three dimensions) by approximately 40%. This reduction is quite close to existing numerical results.
Korayem, M H; Nekoo, S R
2015-01-01
This article investigates finite-time optimal and suboptimal controls for time-varying systems with state and control nonlinearities. The state-dependent Riccati equation (SDRE) controller was the main framework. A finite-time constraint imposed on the equation changes it to a differential equation, known as the state-dependent differential Riccati equation (SDDRE) and this equation was applied to the problem reported in this study that provides general formulation and stability analysis. The following four solution methods were developed for solving the SDDRE; backward integration, state transition matrix (STM) and the Lyapunov based method. In the Lyapunov approach, both positive and negative definite solutions to related SDRE were used to provide suboptimal gain for the SDDRE. Finite-time suboptimal control is applied for robotic manipulator, as finite-time constraint strongly decreases state error and operation time. General state-dependent coefficient (SDC) parameterizations for rigid and flexible joint arms (prismatic or revolute joints) are introduced. By including nonlinear control inputs in the formulation, the actuator׳s limits can be inserted directly to the state-space equation of a manipulator. A finite-time SDRE was implemented on a 6R manipulator both in theory and experimentally. And a reduced 3R arm was modeled and tested as a flexible joint robot (FJR). Evaluations of load carrying capacity and operation time were investigated to assess the capability of this approach, both of which showed significant improvement.
Babaee, Hessam; Farazmand, Mohamad; Haller, George; Sapsis, Themistoklis P.
2017-06-01
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.
Babaee, Hessam; Farazmand, Mohamad; Haller, George; Sapsis, Themistoklis P
2017-06-01
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have a finite-time duration. Because of the finite-time character of these transient events, their detection through infinite-time methods, e.g., long term averages, Lyapunov exponents or information about the statistical steady-state, is not possible. Here, we utilize a recently developed framework, the Optimally Time-Dependent (OTD) modes, to extract a time-dependent subspace that spans the modes associated with transient features associated with finite-time instabilities. As the main result, we prove that the OTD modes, under appropriate conditions, converge exponentially fast to the eigendirections of the Cauchy-Green tensor associated with the most intense finite-time instabilities. Based on this observation, we develop a reduced-order method for the computation of finite-time Lyapunov exponents (FTLE) and vectors. In high-dimensional systems, the computational cost of the reduced-order method is orders of magnitude lower than the full FTLE computation. We demonstrate the validity of the theoretical findings on two numerical examples.
Robust L2-L∞ Filtering of Time-Delay Jump Systems with Respect to the Finite-Time Interval
Directory of Open Access Journals (Sweden)
Shuping He
2011-01-01
Full Text Available This paper studied the problem of stochastic finite-time boundedness and disturbance attenuation for a class of linear time-delayed systems with Markov jumping parameters. Sufficient conditions are provided to solve this problem. The L2-L∞ filters are, respectively, designed for time-delayed Markov jump linear systems with/without uncertain parameters such that the resulting filtering error dynamic system is stochastically finite-time bounded and has the finite-time interval disturbance attenuation γ for all admissible uncertainties, time delays, and unknown disturbances. By using stochastic Lyapunov-Krasovskii functional approach, it is shown that the filter designing problem is in terms of the solutions of a set of coupled linear matrix inequalities. Simulation examples are included to demonstrate the potential of the proposed results.
Finite time extinction for nonlinear fractional evolution equations and related properties
Directory of Open Access Journals (Sweden)
Jesus Ildefonso Diaz
2016-08-01
Full Text Available The finite time extinction phenomenon (the solution reaches an equilibrium after a finite time is peculiar to certain nonlinear problems whose solutions exhibit an asymptotic behavior entirely different from the typical behavior of solutions associated to linear problems. The main goal of this work is twofold. Firstly, we extend some of the results known in the literature to the case in which the ordinary time derivative is considered jointly with a fractional time differentiation. Secondly, we consider the limit case when only the fractional derivative remains. The latter is the most extraordinary case, since we prove that the finite time extinction phenomenon still appears, even with a non-smooth profile near the extinction time.
Optimal Selling Time in Stock Market over a Finite Time Horizon
Institute of Scientific and Technical Information of China (English)
S.C.P. YAM; S.P. YUNG; W. ZHOU
2012-01-01
In this paper,we examine the best time to sell a stock at a price being as close as possible to its highest price over a finite time horizon [0,T],where the stock price is modelled by a geometric Brownian motion and the 'closeness' is measured by the relative error of the stock price to its highest price over [0,T]. More precisely,we want to optimize the expression:V*=sup0≤τ≤T IE[Vτ/MT],where (Vt)t≥0 is a geometric Brownish motion with constant drift α and constant volatility σ ＞ 0,Mt =max0≤s≤t Vs is the running maximum of the stock price,and the supremum is taken over all possible stopping times 0 ＜ τ ＜ Tadapted to the natural filtration (Ft)t≥0 of the stock price.The above problem has been considered by Shiryaev,Xu and Zhou (2008) and Du Toit and Peskir (2009).In this paper we provide an independent proof that when α =1/2σ2,a selling strategy is optimal if and only if it sells the stock either at the terminal time T or at the moment when the stock price hits its maximum price so far.Besides,when α ＞ 1/2σ2,selling the stock at the terminal time T is the unique optimal selling strategy.Our approach to the problem is purely probabilistic and has been inspired by relating the notion of dominant stopping pτ of a stopping time τ to the optimal stopping strategy arisen in the classical "Secretary Problem".
Fractal Two-Level Finite Element Method For Free Vibration of Cracked Beams
Directory of Open Access Journals (Sweden)
A.Y.T. Leung
1998-01-01
Full Text Available The fractal two-level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial program.
Institute of Scientific and Technical Information of China (English)
Fa-yong Zhang; Shu-juan Lu
2001-01-01
A weakly demped Schrodinger equation possessing a global attractor are considered.The dynamical properties of a class of finite difference scheme are analysed. The exsitence of global attractor is proved for the discrete system. The stability of the difference scheme and the error estimate of the difference solution are obtained in the autonomous system case. Finally, long-time stability and convergence of the class of finite difference scheme also are analysed in the nonautonomous system case.
Alternating-time temporal logic with finite-memory strategies
DEFF Research Database (Denmark)
Vester, Steen
2013-01-01
Model-checking the alternating-time temporal logics ATL and ATL* with incomplete information is undecidable for perfect recall semantics. However, when restricting to memoryless strategies the model-checking problem becomes decidable. In this paper we consider two other types of semantics based...
An approach to design semi-global finite-time observers for a class of nonlinear systems
Institute of Scientific and Technical Information of China (English)
DENG XiuCheng; SHEN YanJun
2009-01-01
In this paper, the problem of designing semi-global finite-time observers for a class of nonlinear systems is investigated. Based on the theories of finite-time stability, an approach to designing semi-global finite-time observers for the nonlinear systems is presented. It has been shown that, after the finite time, the designed finite-time observer realizes the accurate reconstruction of the states of the nonlinear system. A numerical example is given to illustrate the effectiveness and validity of the method.
Spacetime Singularities in Quantum Gravity
Minassian, Eric A.
2000-04-01
Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.
Saini, Sahil; Singh, Parampreet
2016-12-01
Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.
Contrast structure for singular singularly perturbed boundary value problem
Institute of Scientific and Technical Information of China (English)
王爱峰; 倪明康
2014-01-01
The step-type contrast structure for a singular singularly perturbed problem is shown. By use of the method of boundary function, the formal asymptotic expansion is constructed. At the same time, based on sewing orbit smooth, the existence of the step-type solution and the uniform validity of the asymptotic expansion are proved. Finally, an example is given to demonstrate the effectiveness of the present results.
Sliding Mode Cooperative Control for Multirobot Systems: A Finite-Time Approach
Directory of Open Access Journals (Sweden)
Masood Ghasemi
2013-01-01
Full Text Available Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. We consider a group of agents described by Euler-Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. We further extend these results to multiagent systems involving underactuated dynamical agents such as mobile wheeled robots. For this case, we show that while the position variables can be coordinated in finite time, the orientation variables converge to the steady states asymptotically. Finally, we validate our results experimentally using a wheeled mobile robot platform.
Controlling chaos in power system based on finite-time stability theory
Institute of Scientific and Technical Information of China (English)
Zhao Hui; Ma Ya-Jun; Liu Si-Jia; Gao Shi-Gen; Zhong Dan
2011-01-01
Recent investigations show that a power system is a highly nonlinear system and can exhibit chaotic behaviour leading to a voltage collapse,which severely threatens the secure and stable operation of the power system.Based on the finite-time stability theory,two control strategies are presented to achieve finite-time chaos control.In addition,the problem of how to stabilize an unstable nonzero equilibrium point in a finite time is solved by coordinate transformation for the first time.Numerical simulations are presented to demonstrate the effectiveness and the robustness of the proposed scheme.The research in this paper may help to maintain the secure operation of power systems.
Finite-Time Consensus of Multiagent Systems With a Switching Protocol.
Liu, Xiaoyang; Lam, James; Yu, Wenwu; Chen, Guanrong
2016-04-01
In this paper, we study the problem of finite-time consensus of multiagent systems on a fixed directed interaction graph with a new protocol. Existing finite-time consensus protocols can be divided into two types: 1) continuous and 2) discontinuous, which were studied separately in the past. In this paper, we deal with both continuous and discontinuous protocols simultaneously, and design a centralized switching consensus protocol such that the finite-time consensus can be realized in a fast speed. The switching protocol depends on the range of the initial disagreement of the agents, for which we derive an exact bound to indicate at what time a continuous or a discontinuous protocol should be selected to use. Finally, we provide two numerical examples to illustrate the superiority of the proposed protocol and design method.
Distributed robust finite-time nonlinear consensus protocols for multi-agent systems
Zuo, Zongyu; Tie, Lin
2016-04-01
This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.
Institute of Scientific and Technical Information of China (English)
LI Xikui; YAO Dongmei
2004-01-01
A time-discontinuous Galerkin finite element method for dynamic analyses in saturated poro-elasto-plastic medium is proposed. As compared with the existing discontinuous Galerkin finite element methods, the distinct feature of the proposed method is that the continuity of the displacement vector at each discrete time instant is automatically ensured, whereas the discontinuity of the velocity vector at the discrete time levels still remains. The computational cost is then obviously reduced,particularly, for material non-linear problems. Both the implicit and explicit algorithms to solve the derived formulations for material non-linear problems are developed. Numerical results show a good performance of the present method in eliminating spurious numerical oscillations and providing with much more accurate solutions over the traditional Galerkin finite element method using the Newmark algorithm in the time domain.
Zhong, Qishui; Cheng, Jun; Zhao, Yuqing
2015-07-01
In this paper, a novel method is developed for delay-dependent finite-time boundedness of a class of Markovian switching neural networks with time-varying delays. New sufficient condition for stochastic boundness of Markovian jumping neural networks is presented and proved by an newly augmented stochastic Lyapunov-Krasovskii functional and novel activation function conditions, the state trajectory remains in a bounded region of the state space over a given finite-time interval. Finally, a numerical example is given to illustrate the efficiency and less conservative of the proposed method.
Guaranteed Cost Finite-Time Control of Fractional-Order Positive Switched Systems
Directory of Open Access Journals (Sweden)
Leipo Liu
2017-01-01
Full Text Available The problem of guaranteed cost finite-time control of fractional-order positive switched systems (FOPSS is considered in this paper. Firstly, a new cost function is defined. Then, by constructing linear copositive Lyapunov functions and using the average dwell time (ADT approach, a state feedback controller and a static output feedback controller are constructed, respectively, and sufficient conditions are derived to guarantee that the corresponding closed-loop systems are guaranteed cost finite-time stable (GCFTS. Such conditions can be easily solved by linear programming. Finally, two examples are given to illustrate the effectiveness of the proposed method.
Finite-time H∞ filtering for non-linear stochastic systems
Hou, Mingzhe; Deng, Zongquan; Duan, Guangren
2016-09-01
This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.
Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements
Shi, Shang; Yu, Xin; Khoo, Suiyang
2016-02-01
The problem of robust finite-time trajectory tracking of nonholonomic mobile robots with unmeasurable velocities is studied. The contributions of the paper are that: first, in the case that the angular velocity of the mobile robot is unmeasurable, a composite controller including the observer-based partial state feedback control and the disturbance feed-forward compensation is designed, which guarantees that the tracking errors converge to zero in finite time. Second, if the linear velocity as well as the angular velocity of mobile robot is unmeasurable, with a stronger constraint, the finite-time trajectory tracking control of nonholonomic mobile robot is also addressed. Finally, the effectiveness of the proposed control laws is demonstrated by simulation.
Finite-Time Control for Attitude Tracking Maneuver of Rigid Satellite
Directory of Open Access Journals (Sweden)
Mingyi Huo
2014-01-01
Full Text Available The problem of finite-time control for attitude tracking maneuver of a rigid spacecraft is investigated. External disturbance, unknown inertia parameters are addressed. As stepping stone, a sliding mode controller is designed. It requires the upper bound of the lumped uncertainty including disturbance and inertia matrix. However, this upper bound may not be easily obtained. Therefore, an adaptive sliding mode control law is then proposed to release that drawback. Adaptive technique is applied to estimate that bound. It is proved that the closed-loop attitude tracking system is finite-time stable. The tracking errors of the attitude and the angular velocity are asymptotically stabilized. Moreover, the upper bound on the lumped uncertainty can be exactly estimated in finite time. The attitude tracking performance with application of the control scheme is evaluated through a numerical example.
Estimates for the Finite-time Ruin Probability with Insurance and Financial Risks
Institute of Scientific and Technical Information of China (English)
Min ZHOU; Kai-yong WANG; Yue-bao WANG
2012-01-01
The paper gives estimates for the finite-time ruin probability with insurance and financial risks.When the distribution of the insurance risk belongs to the class (L)(γ) for some γ ＞ 0 or the subexponential distribution class,we abtain some asymptotic equivalent relationships for the finite-time ruin probability,respectively. When the distribution of the insurance risk belongs to the dominated varying-tailed distribution class,we obtain asymptotic upper bound and lower bound for the finite-time ruin probability,where for the asymptotic upper bound,we completely get rid of the restriction of mutual independence on insurance risks,and for the lower bound,we only need the insurance risks to have a weak positive association structure.The obtained results extend and improve some existing results.
Passivity control with practically finite-time convergence for large space structures
Hu, Quan; Li, Jinyue; Zhang, Jingrui
2017-02-01
A nonlinear output feedback control law based on passivity is proposed to reduce the vibration of large space structures. The considered system is assumed to be equipped with collocated actuators and sensors. The concept of practically finite-time stability is first developed to describe the finite-time convergence of a passive system. Then, an output feedback is introduced to drive the trajectories of a passive system into a small set around the origin in finite time. Finally, the proposed control strategy is applied to the vibration suppression of large space structures with distributed thrusters and velocity sensors or torque outputting devices and angular rate sensors. Numerical simulations are conducted to validate the effectiveness of the proposed controller.
Infinitesimal Structure of Singularities
Directory of Open Access Journals (Sweden)
Michael Heller
2017-02-01
Full Text Available Some important problems of general relativity, such as the quantisation of gravity or classical singularity problems, crucially depend on geometry on very small scales. The so-called synthetic differential geometry—a categorical counterpart of the standard differential geometry—provides a tool to penetrate infinitesimally small portions of space-time. We use this tool to show that on any “infinitesimal neighbourhood” the components of the curvature tensor are themselves infinitesimal, and construct a simplified model in which the curvature singularity disappears, owing to this effect. However, one pays a price for this result. Using topoi as a generalisation of spaces requires a weakening of arithmetic (the existence of infinitesimals and of logic (to the intuitionistic logic. Is this too high a price to pay for acquiring a new method of solving unsolved problems in physics? Without trying, we shall never know the answer.
Fan, Xiaofei; Zhang, Xian; Wu, Ligang; Shi, Michael
2017-01-01
This paper is concerned with the finite-time stability problem of the delayed genetic regulatory networks (GRNs) with reaction-diffusion terms under Dirichlet boundary conditions. By constructing a Lyapunov-Krasovskii functional including quad-slope integrations, we establish delay-dependent finite-time stability criteria by employing the Wirtinger-type integral inequality, Gronwall inequality, convex technique, and reciprocally convex technique. In addition, the obtained criteria are also reaction-diffusion-dependent. Finally, a numerical example is provided to illustrate the effectiveness of the theoretical results.
Adaptive Fuzzy Sliding Mode Control of MEMS Gyroscope with Finite Time Convergence
Directory of Open Access Journals (Sweden)
Jianxin Ren
2016-01-01
Full Text Available This paper presents adaptive fuzzy finite time sliding mode control of microelectromechanical system gyroscope with uncertainty and external disturbance. Firstly, fuzzy system is employed to approximate the uncertainty nonlinear dynamics. Secondly, nonlinear sliding mode hypersurface and double exponential reaching law are selected to design the finite time convergent sliding mode controller. Thirdly, based on Lyapunov methods, adaptive laws are presented to adjust the fuzzy weights and the system can be guaranteed to be stable. Finally, the effectiveness of the proposed method is verified with simulation.
The Galerkin finite element method for a multi-term time-fractional diffusion equation
Jin, Bangti
2015-01-01
© 2014 The Authors. We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space semidiscrete scheme based on the standard Galerkin finite element method using continuous piecewise linear functions. Nearly optimal error estimates for both cases of initial data and inhomogeneous term are derived, which cover both smooth and nonsmooth data. Further we develop a fully discrete scheme based on a finite difference discretization of the time-fractional derivatives, and discuss its stability and error estimate. Extensive numerical experiments for one- and two-dimensional problems confirm the theoretical convergence rates.
Directory of Open Access Journals (Sweden)
P. Siricharuanun
2016-01-01
Full Text Available A second-order sliding mode control for chaotic synchronization with bounded disturbance is studied. A robust finite-time controller is designed based on super twisting algorithm which is a popular second-order sliding mode control technique. The proposed controller is designed by combining an adaptive law with super twisting algorithm. New results based on adaptive super twisting control for the synchronization of identical Qi three-dimensional four-wing chaotic system are presented. The finite-time convergence of synchronization is ensured by using Lyapunov stability theory. The simulations results show the usefulness of the developed control method.
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics
Gedney, Stephen
2011-01-01
Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to p
Finite-time Consensus of Heterogeneous Multi-agent Systems with Linear and Nonlinear Dynamics
Institute of Scientific and Technical Information of China (English)
ZHU Ya-Kun; GUAN Xin-Ping; LUO Xiao-Yuan
2014-01-01
In this paper, the finite-time consensus problems of heterogeneous multi-agent systems composed of both linear and nonlinear dynamics agents are investigated. Nonlinear consensus protocols are proposed for the heterogeneous multi-agent systems. Some suﬃcient conditions for the finite-time consensus are established in the leaderless and leader-following cases. The results are also extended to the case where the communication topology is directed and satisfies a detailed balance condition on coupling weights. At last, some simulation results are given to illustrate the effectiveness of the obtained theoretical results.
Energy Technology Data Exchange (ETDEWEB)
Fleischer, M.; Jacobson, S.
1994-12-31
This paper presents a new empirical approach designed to illustrate the theory developed in Fleischer and Jacobson regarding entropy measures and the finite-time performance of the simulated annealing (SA) algorithm. The theory is tested using several experimental methodologies based on a new structure, generic configuration spaces, and polynomial transformations between NP-hard problems. Both approaches provide several ways to alter the configuration space and its associated entropy measure while preserving the value of the globally optimal solution. This makes it possible to illuminate the extent to which entropy measures impact the finite-time performance of the SA algorithm.
Controlling Chaos in permanent magnet synchronous motor based on finite-time stability theory
Institute of Scientific and Technical Information of China (English)
Wei Du-Qu; Zhang So
2009-01-01
This paper reports that the performance of permanent magnet synchronous motor(PMSM)degrades due to chaos when its systemic parameters fall into a certain area.To control the undesirable chaos in PMSM,a nonlinear controller,which is simple and easy to be constructed,is presented to achieve finite-time chaos control based on the finite-time stability theory.Computer simulation results show that the proposed controller is very effective.The obtained results may help to maintain the industrial servo driven system's security operation.
A novel recurrent neural network with finite-time convergence for linear programming.
Liu, Qingshan; Cao, Jinde; Chen, Guanrong
2010-11-01
In this letter, a novel recurrent neural network based on the gradient method is proposed for solving linear programming problems. Finite-time convergence of the proposed neural network is proved by using the Lyapunov method. Compared with the existing neural networks for linear programming, the proposed neural network is globally convergent to exact optimal solutions in finite time, which is remarkable and rare in the literature of neural networks for optimization. Some numerical examples are given to show the effectiveness and excellent performance of the new recurrent neural network.
Finite-time synchronization control of a class of memristor-based recurrent neural networks.
Jiang, Minghui; Wang, Shuangtao; Mei, Jun; Shen, Yanjun
2015-03-01
This paper presents a global and local finite-time synchronization control law for memristor neural networks. By utilizing the drive-response concept, differential inclusions theory, and Lyapunov functional method, we establish several sufficient conditions for finite-time synchronization between the master and corresponding slave memristor-based neural network with the designed controller. In comparison with the existing results, the proposed stability conditions are new, and the obtained results extend some previous works on conventional recurrent neural networks. Two numerical examples are provided to illustrate the effective of the design method.
Enveloping branes and brane-world singularities
Energy Technology Data Exchange (ETDEWEB)
Antoniadis, Ignatios; Cotsakis, Spiros [CERN-Theory Division, Department of Physics, Geneva 23 (Switzerland); Klaoudatou, Ifigeneia [University of the Aegean, Research Group of Geometry, Dynamical Systems and Cosmology, Department of Information and Communication Systems Engineering, Samos (Greece)
2014-12-01
The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Deupree, R.G.
1977-01-01
Finite difference techniques were used to examine the coupling of radial pulsation and convection in stellar models having comparable time scales. Numerical procedures are emphasized, including diagnostics to help determine the range of free parameters.
Gravitational collapse and naked singularities
Indian Academy of Sciences (India)
Tomohiro Harada
2004-10-01
Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of `effective naked singularities', which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.
Geometrical constraints on finite-time Lyapunov exponents in two and three dimensions.
Thiffeault, Jean-Luc; Boozer, Allen H.
2001-03-01
Constraints are found on the spatial variation of finite-time Lyapunov exponents of two- and three-dimensional systems of ordinary differential equations. In a chaotic system, finite-time Lyapunov exponents describe the average rate of separation, along characteristic directions, of neighboring trajectories. The solution of the equations is a coordinate transformation that takes initial conditions (the Lagrangian coordinates) to the state of the system at a later time (the Eulerian coordinates). This coordinate transformation naturally defines a metric tensor, from which the Lyapunov exponents and characteristic directions are obtained. By requiring that the Riemann curvature tensor vanish for the metric tensor (a basic result of differential geometry in a flat space), differential constraints relating the finite-time Lyapunov exponents to the characteristic directions are derived. These constraints are realized with exponential accuracy in time. A consequence of the relations is that the finite-time Lyapunov exponents are locally small in regions where the curvature of the stable manifold is large, which has implications for the efficiency of chaotic mixing in the advection-diffusion equation. The constraints also modify previous estimates of the asymptotic growth rates of quantities in the dynamo problem, such as the magnitude of the induced current. (c) 2001 American Institute of Physics.
Fluctuations in a Cosmology with a Space-Like Singularity and their Gauge Theory Dual Description
Brandenberger, Robert H; Das, Sumit R; Ferreira, Elisa G M; Morrison, Ian A; Wang, Yi
2016-01-01
We consider a time-dependent deformation of anti-de-Sitter (AdS) space-time which contains a cosmological "singularity" - a space-like region of high curvature. Making use of the AdS/CFT correspondence we can map the bulk dynamics onto the boundary. The boundary theory has a time dependent coupling constant which becomes small at times when the bulk space-time is highly curved. We investigate the propagation of small fluctuations of a test scalar field from early times before the bulk singularity to late times after the singularity. Under the assumption that the AdS/CFT correspondence extends to deformed AdS space-times, we can map the bulk evolution of the scalar field onto the evolution of the boundary gauge field. The time evolution of linearized fluctuations is well defined in the boundary theory as long as the coupling remains finite, so that we can extend the boundary perturbations to late times after the singularity. Assuming that the spacetime in the future of the singularity has a weakly coupled regi...
Local Stable and Unstable Manifolds and Their Control in Nonautonomous Finite-Time Flows
Balasuriya, Sanjeeva
2016-08-01
It is well known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite- and finite-time intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained.
Finite-Time Thermoeconomic Optimization of a Solar-Driven Heat Engine Model
Directory of Open Access Journals (Sweden)
Fernando Angulo-Brown
2011-01-01
Full Text Available In the present paper, the thermoeconomic optimization of an irreversible solar-driven heat engine model has been carried out by using finite-time/finite-size thermodynamic theory. In our study we take into account losses due to heat transfer across finite time temperature differences, heat leakage between thermal reservoirs and internal irreversibilities in terms of a parameter which comes from the Clausius inequality. In the considered heat engine model, the heat transfer from the hot reservoir to the working fluid is assumed to be Dulong-Petit type and the heat transfer to the cold reservoir is assumed of the Newtonian type. In this work, the optimum performance and two design parameters have been investigated under two objective functions: the power output per unit total cost and the ecological function per unit total cost. The effects of the technical and economical parameters on the thermoeconomic performance have been also discussed under the aforementioned two criteria of performance.
Explicit finite-difference time domain for nonlinear analysis of waveguide modes
Barakat, N. M.; Shabat, M. M.; El-Azab, S.; Jaeger, Dieter
2003-07-01
The Finite Difference Time Domain Technique is at present the most widely used tool employed in the study of light propagation in various photonic waveguide structure. In this paper we derived an explicit finite-difference time-domain (FDTD) method for solving the wave equation in a four optical waveguiding rectangular structure. We derive the stability condition to achieve the stability in nonlinear media region, we also check that the wave equation used is consistence and convergent with the approximate finite difference equation. Our method is tested against some previous problems and we find a high degree of accuracy, moreover it is easy for programming. Numerical results are illustrated for a rectangular waveguide with four layers, where one of these layers is a nonlinear medium.
Finite time thermodynamic analysis of endoreversible Stirling heat engine with regenerative losses
Energy Technology Data Exchange (ETDEWEB)
Kaushik, S.C.; Kumar, S. [Indian Inst. of Technology, Centre for Energy Studies, New Delhi (India)
2000-10-01
This communication presents an investigation of a finite time thermodynamic analysis of an endoreversible Stirling heat engine. Finite time thermodynamics has been applied to maximise the power output and the corresponding thermal efficiency of an endoreversible Stirling heat engine with internal heat loss in the regenerator and for the finite heat capacity of the external reservoirs. The effect of the effectiveness of the various heat exchangers, the inlet temperatures of external heat reservoirs on the power output and the corresponding thermal efficiency have been studied. It is seen that an endoreversible Stirling heat engine with an ideal regenerator ({epsilon}{sub R}=1.00) is as efficient as an endoreversible Carnot heat engine. It is also found that the maximum power output increases with the heat capacitance rates and effectiveness of the source/sink side heat exchangers while thermal efficiency increases with the effectiveness of the regenerator. (Author)
Ghost and singularity free theories of gravity
Buoninfante, L; Mazumdar, A
2016-01-01
Albert Einstein's General Relativity (GR) from 1916 has become the widely accepted theory of gravity and been tested observationally to a very high precision at different scales of energy and distance. At the same time, there still remain important questions to resolve. The presence of cosmological and black hole singularities are examples of problems at the classical level which strongly suggest the incompleteness of GR at short distances (high energy). Furthermore, at the quantum level GR is not UV complete, namely it is not perturbatively renormalizable. These two kind of questions, classical and quantum, could be closely related as both concern short-distance (high energy) physics. Most of the work try to solve these problems modifying GR by considering finite higher order derivative terms. Fourth Order Gravity, for example, turns out to be renormalizable, but at the same time it introduces ghost. To avoid both UV divergence and presence of ghost one could consider an infinite set of higher derivative ter...
Exact stabilization of entangled states in finite time by dissipative quantum circuits
Johnson, Peter D.; Ticozzi, Francesco; Viola, Lorenza
2017-07-01
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly noncanonical) commuting parent Hamiltonian may be found. Aside from graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi [Quantum Inf. Comput. 5, 187 (2005)]. Extensions to representative classes of mixed graph-product and thermal states are also discussed.
The Geometry of Black Hole Singularities
Directory of Open Access Journals (Sweden)
Ovidiu Cristinel Stoica
2014-01-01
Full Text Available Recent results show that important singularities in General Relativity can be naturally described in terms of finite and invariant canonical geometric objects. Consequently, one can write field equations which are equivalent to Einstein's at nonsingular points but, in addition remain well-defined and smooth at singularities. The black hole singularities appear to be less undesirable than it was thought, especially after we remove the part of the singularity due to the coordinate system. Black hole singularities are then compatible with global hyperbolicity and do not make the evolution equations break down, when these are expressed in terms of the appropriate variables. The charged black holes turn out to have smooth potential and electromagnetic fields in the new atlas. Classical charged particles can be modeled, in General Relativity, as charged black hole solutions. Since black hole singularities are accompanied by dimensional reduction, this should affect Feynman's path integrals. Therefore, it is expected that singularities induce dimensional reduction effects in Quantum Gravity. These dimensional reduction effects are very similar to those postulated in some approaches to make Quantum Gravity perturbatively renormalizable. This may provide a way to test indirectly the effects of singularities, otherwise inaccessible.
Quantum dress for a naked singularity
Casals, Marc; Fabbri, Alessandro; Martínez, Cristián; Zanelli, Jorge
2016-09-01
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2 + 1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing (weak) cosmic censorship.
Quantum dress for a naked singularity
Casals, Marc; Martínez, Cristián; Zanelli, Jorge
2016-01-01
We investigate semiclassical backreaction on a conical naked singularity space-time with a negative cosmological constant in (2+1)-dimensions. In particular, we calculate the renormalized quantum stress-energy tensor for a conformally coupled scalar field on such naked singularity space-time. We then obtain the backreacted metric via the semiclassical Einstein equations. We show that, in the regime where the semiclassical approximation can be trusted, backreaction dresses the naked singularity with an event horizon, thus enforcing cosmic censorship.
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
The Finite Time Ruin Probability with the Same Heavy-tailed Insurance and Financial Risks
Institute of Scientific and Technical Information of China (English)
Yi-qing Chen; Xiang-sheng Xie
2005-01-01
This note complements a recent study in ruin theory with risky investment by establishing the same asymptotic estimate for the finite time ruin probability under a weaker restriction on the financial risks.In particular, our result applies to a critical case that the insurance and financial risks have Pareto-type tails with the same regular index.
The finite difference time domain method on a massively parallel computer
Ewijk, L.J. van
1996-01-01
At the Physics and Electronics Laboratory TNO much research is done in the field of computational electromagnetics (CEM). One of the tools in this field is the Finite Difference Time Domain method (FDTD), a method that has been implemented in a program in order to be able to compute electromagnetic
DEFF Research Database (Denmark)
Tanev, Stoyan; Sun, Wenbo
2012-01-01
This chapter reviews the fundamental methods and some of the applications of the three-dimensional (3D) finite-difference time-domain (FDTD) technique for the modeling of light scattering by arbitrarily shaped dielectric particles and surfaces. The emphasis is on the details of the FDTD algorithms...
Finite-difference, spectral and Galerkin methods for time-dependent problems
Tadmor, E.
1983-01-01
Finite difference, spectral and Galerkin methods for the approximate solution of time dependent problems are surveyed. A unified discussion on their accuracy, stability and convergence is given. In particular, the dilemma of high accuracy versus stability is studied in some detail.
Generalized Nehari functionals and finite time blow up of the solutions to Boussinesq equation
Kolkovska, N.; Dimova, M.; Kutev, N.
2015-10-01
We study the Cauchy problem to generalized Boussinesq equation with linear restoring force and combined power type nonlinearities. Generalized Nehari functionals are introduced and their monotonicity and sign preserving properties are established. By means of an extension of the concavity method of Levine and generalized Nehari functionals finite time blow up of the solutions with arbitrary high positive initial energy is proved.
Finite difference time domain modeling of light matter interaction in light-propelled microtools
DEFF Research Database (Denmark)
Bañas, Andrew Rafael; Palima, Darwin; Aabo, Thomas
2013-01-01
may trigger highly localized non linear processes in the surface of a cell. Since these functionalities are strongly dependent on design, it is important to use models that can handle complexities and take in little simplifying assumptions about the system. Hence, we use the finite difference time...
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2011-01-01
The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic...
DEFF Research Database (Denmark)
Tanev, Stoyan; Sun, Wenbo
2012-01-01
This chapter reviews the fundamental methods and some of the applications of the three-dimensional (3D) finite-difference time-domain (FDTD) technique for the modeling of light scattering by arbitrarily shaped dielectric particles and surfaces. The emphasis is on the details of the FDTD algorithms...
Staircase-free finite-difference time-domain formulation for general materials in complex geometries
DEFF Research Database (Denmark)
Dridi, Kim; Hesthaven, J.S.; Ditkowski, A.
2001-01-01
A stable Cartesian grid staircase-free finite-difference time-domain formulation for arbitrary material distributions in general geometries is introduced. It is shown that the method exhibits higher accuracy than the classical Yee scheme for complex geometries since the computational representation...
Time-integration methods for finite element discretisations of the second-order Maxwell equation
Sármány, D.; Botchev, M.A.; Vegt, van der J.J.W.
2012-01-01
This article deals with time integration for the second-order Maxwell equations with possibly non-zero conductivity in the context of the discontinuous Galerkin finite element method DG-FEM) and the $H(\\mathrm{curl})$-conforming FEM. For the spatial discretisation, hierarchic $H(\\mathrm{curl})$-conf
Energy Technology Data Exchange (ETDEWEB)
Sato, K.; Koide, Tomoi; Maruyama, Masahiro [Tohoku Univ., Faculty of Science, Sendai, Miyagi (Japan)
1999-08-01
There are various approaches to nonequilibrium system. We use the projection operator method investigated by F. Shibata and N. Hashitsume on the linear sigma model at finite temperature and density. We derive a differential equation of the time evolution for the order parameter and pion number density in chiral phase transition. (author)
Finite Time Ruin Probabilities and Large Deviations for Generalized Compound Binomial Risk Models
Institute of Scientific and Technical Information of China (English)
Yi Jun HU
2005-01-01
In this paper, we extend the classical compound binomial risk model to the case where the premium income process is based on a Poisson process, and is no longer a linear function. For this more realistic risk model, Lundberg type limiting results for the finite time ruin probabilities are derived. Asymptotic behavior of the tail probabilities of the claim surplus process is also investigated.
Real-time volumetric deformable models for surgery simulation using finite elements and condensation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten; Cotin, S.
1996-01-01
This paper discusses the application of SD solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real-time performance for these models. The simulation system we have developed is described and we demonstrate...
Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2010-01-25
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.
GLOBAL SOLUTIONS AND FINITE TIME BLOW UP FOR DAMPED KLEIN-GORDON EQUATION
Institute of Scientific and Technical Information of China (English)
Runzhang XU; Yunhua DING
2013-01-01
We study the Cauchy problem of strongly damped Klein-Gordon equation.Global existence and asymptotic behavior of solutions with initial data in the potential well are derived.Moreover,not only does finite time blow up with initial data in the unstable set is proved,but also blow up results with arbitrary positive initial energy are obtained.
Space-time discontinuous Galerkin finite element method for inviscid gas dynamics
van der Ven, H.; van der Vegt, Jacobus J.W.; Bouwman, E.G.; Bathe, K.J.
2003-01-01
In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated
Real-time volumetric deformable models for surgery simulation using finite elements and condensation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten; Cotin, S.
1996-01-01
This paper discusses the application of SD solid volumetric Finite Element models to surgery simulation. In particular it introduces three new ideas for solving the problem of achieving real-time performance for these models. The simulation system we have developed is described and we demonstrate...
Finite-time tracking control for multiple non-holonomic mobile robots based on visual servoing
Ou, Meiying; Li, Shihua; Wang, Chaoli
2013-12-01
This paper investigates finite-time tracking control problem of multiple non-holonomic mobile robots via visual servoing. It is assumed that the pinhole camera is fixed to the ceiling, and camera parameters are unknown. The desired reference trajectory is represented by a virtual leader whose states are available to only a subset of the followers, and the followers have only interaction. First, the camera-objective visual kinematic model is introduced by utilising the pinhole camera model for each mobile robot. Second, a unified tracking error system between camera-objective visual servoing model and desired reference trajectory is introduced. Third, based on the neighbour rule and by using finite-time control method, continuous distributed cooperative finite-time tracking control laws are designed for each mobile robot with unknown camera parameters, where the communication topology among the multiple mobile robots is assumed to be a directed graph. Rigorous proof shows that the group of mobile robots converges to the desired reference trajectory in finite time. Simulation example illustrates the effectiveness of our method.
The finite-difference time-domain method for electromagnetics with Matlab simulations
Elsherbeni, Atef Z
2016-01-01
This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices.
A, Savelyev D.; N, Khonina S.
2014-03-01
We analyze the diffraction of the laser beam with a vortex phase singularity on the basis of the finite-difference time-domain method (FDTD). It is shown that, when incident beam has phase singularity, increase of the micro-axicon radius leads to extension of the light needle consisting of longitudinal electric field component. The numerical investigations held of the near-field diffraction for the most common and easily implemented types of polarization of the incident beam - linear and circular.
Resolution of quantum singularities
Konkowski, Deborah; Helliwell, Thomas
2017-01-01
A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.
Robust Fusion Filtering for Multisensor Time-Varying Uncertain Systems: The Finite Horizon Case
Directory of Open Access Journals (Sweden)
Xiaoliang Feng
2016-01-01
Full Text Available The robust H∞ fusion filtering problem is considered for linear time-varying uncertain systems observed by multiple sensors. A performance index function for this problem is defined as an indefinite quadratic inequality which is solved by the projection method in Krein space. On this basis, a robust centralized finite horizon H∞ fusion filtering algorithm is proposed. However, this centralized fusion method is with poor real time property, as the number of sensors increases. To resolve this difficulty, within the sequential fusion framework, the performance index function is described as a set of quadratic inequalities including an indefinite quadratic inequality. And a sequential robust finite horizon H∞ fusion filtering algorithm is given by solving this quadratic inequality group. Finally, two simulation examples for time-varying/time-invariant multisensor systems are exploited to demonstrate the effectiveness of the proposed methods in the respect of the real time property and filtering accuracy.
Finite frequency H_∞ filtering for uncertain discrete-time switched linear systems
Institute of Scientific and Technical Information of China (English)
Dawei Ding; Guanghong Yang
2009-01-01
This paper is concerned with the problem of robust H_∞ filtering for discrete-time switched linear systems with polytopic uncertainties in the finite frequency domain. Based on the generalized Kalman-Yakubovich-Popov (GKYP) iemma and switched parameter-depen-dent Lyapunov functions, a switched full-order filter is designed such that the corresponding filtering error system is asymptotically sta-ble and satisfies a prescribed finite frequency H_∞ performance index. Compared with the existing full frequency approaches, the proposed finite frequency one receives better results for the cases in which the frequency ranges of noises are known. A numerical exam-ple is given to illustrate the effectiveness of the proposed method.
Yulmetyev, R M; Hänggi, P; Khusaenova, E V; Shimojo, S; Yulmetyeva, D G
2006-01-01
To analyze the crucial role of the fluctuation and relaxational effects in the human brain functioning we have studied a some statistical quantifiers that support the informational characteristics of neuromagnetic responses of magnetoencephalographic (MEG) signals. The signals to a flickering stimulus of different color combinations has been obtained from a group of control subjects which is contrasted with those for a patient with photosensitive epilepsy (PSE). We have revealed that the existence of the specific stratification of the phase clouds and the concomitant relaxation singularities of the corresponding nonequilibrium processes of chaotic behavior of the signals in the separate areas for a patient most likely shows the pronounced zones responsible the appearance of PSE.
Wang, Ronghao; Xing, Jianchun; Li, Juelong; Xiang, Zhengrong
2016-10-01
This paper studies the problem of stabilising a sampled-data switched linear system by quantised feedback asynchronously switched controllers. The idea of a quantised feedback asynchronously switched control strategy originates in earlier work reflecting actual system characteristic of switching and quantising, respectively. A quantised scheme is designed depending on switching time using dynamic quantiser. When sampling time, system switching time and controller switching time are all not uniform, the proposed switching controllers guarantee the system to be finite-time stable by a piecewise Lyapunov function and the average dwell-time method. Simulation examples are provided to show the effectiveness of the developed results.
Large dimension forecasting models and random singular value spectra
Bouchaud, J P; Miceli, M A; Potters, M; Bouchaud, Jean-Philippe; Laloux, Laurent; Potters, Marc
2005-01-01
We present a general method to detect and extract from a finite time sample statistically meaningful correlations between input and output variables of large dimensionality. Our central result is derived from the theory of free random matrices, and gives an explicit expression for the interval where singular values are expected in the absence of any true correlations between the variables under study. Our result can be seen as the natural generalization of the Marcenko-Pastur distribution for the case of rectangular correlation matrices. We illustrate the interest of our method on a set of macroeconomic time series.
Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study
Energy Technology Data Exchange (ETDEWEB)
Christov, Ivan P., E-mail: ivan.christov@phys.uni-sofia.bg
2016-08-15
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.
Finite-time Partitions for Lagrangian Structure Identification in Gulf Stream Eddy Transport
Fabregat, Alexandre; Poje, Andrew C
2016-01-01
We develop a methodology to identify finite-time Lagrangian structures from data and models using an extension of the Koopman operator-theoretic methods developed for velocity fields with simple (periodic, quasi-periodic) time-dependence. To achieve this, the notion of the Finite Time Ergodic (FiTER) partition is developed and rigorously justified. In combination with a clustering-based approach, the methodology enables identification of the temporal evolution of Lagrangian structures in a classic, benchmark, oceanographic transport problem, namely the cross-stream flux induced by the interaction of a meso- scale Gulf Stream Ring eddy with the main jet. We focus on a single mixing event driven by the interaction between an energetic cold core ring (a cyclone), the strong jet, and a number of smaller scale cyclones and anticyclones. The new methodology enab les reconstruction of Lagrangian structures in three dimensions and analysis of their time-evolution.
Gao, Lijun; Jiang, Xiaoxiao; Wang, Dandan
2016-03-01
This paper investigates the problem of robust finite time H∞ sliding mode control for a class of Markovian switching systems. The system is subjected to the mode-dependent time-varying delay, partly unknown transition rate and unmeasurable state. The main difficulty is that, a sliding mode surface cannot be designed based on the unknown transition rate and unmeasurable state directly. To overcome this obstacle, the set of modes is firstly divided into two subsets standing for known transition rate subset and unknown one, based on which a state observer is established. A component robust finite-time sliding mode controller is also designed to cope with the effect of partially unknown transition rate. It is illustrated that the reachability, finite-time stability, finite-time boundedness, finite-time H∞ state feedback stabilization of sliding mode dynamics can be ensured despite the unknown transition rate. Finally, the simulation results verify the effectiveness of robust finite time control problem.
Phantom evolving wormholes with big rip singularities
Cataldo, Mauricio
2013-01-01
We investigate a family of inhomogeneous and anisotropic gravitational fields exhibiting a future singularity at a finite value of the proper time. The studied spherically symmetric spacetimes are asymptotically Friedmann-Robertson-Walker at spatial infinity and describe wormhole configurations filled with two matter components: one inhomogeneous and anisotropic fluid and another isotropic and homogeneously distributed fluid, characterized by the supernegative equation of state \\omega=p/\\rho < -1. In previously constructed wormholes, the notion of the phantom energy was used in a more extended sense than in cosmology, where the phantom energy is considered a homogeneously distributed fluid. Specifically, for some static wormhole geometries the phantom matter was considered as an inhomogeneous and anisotropic fluid, with radial and lateral pressures satisfying the relations $p_{r}/\\rho<-1$ and $p_{_l} \
On exceptional quotient singularities
Cheltsov, Ivan; Shramov, Constantin
2011-01-01
We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.
The finite-time ruin probability in the presence of Sarmanov dependent financial and insurance risks
Institute of Scientific and Technical Information of China (English)
YANG Yang; LIN Jin-guan; TAN Zhong-quan
2014-01-01
Consider a discrete-time insurance risk model. Within period i, i ≥ 1, Xi and Yi denote the net insurance loss and the stochastic discount factor of an insurer, respectively. Assume that{(Xi, Yi), i≥1}form a sequence of independent and identically distributed random vectors following a common bivariate Sarmanov distribution. In the presence of heavy-tailed net insurance losses, an asymptotic formula is derived for the finite-time ruin probability.
Institute of Scientific and Technical Information of China (English)
ZHANG JIA-SHU; XIAO XIAN-CI
2001-01-01
A multistage adaptive higher-order nonlinear finite impulse response (MAHONFIR) filter is proposed to predict chaotic time series. Using this approach, we may readily derive the decoupled parallel algorithm for the adaptation of the coefficients of the MAHONFIR filter, to guarantee a more rapid convergence of the adaptive weights to their optimal values. Numerical simulation results show that the MAHONFIR filters proposed here illustrate a very good performance for making an adaptive prediction of chaotic time series.
Heterogeneous ice nucleation: bridging stochastic and singular freezing behavior
Directory of Open Access Journals (Sweden)
D. Niedermeier
2011-01-01
Full Text Available Heterogeneous ice nucleation, a primary pathway for ice formation in the atmosphere, has been described alternately as being stochastic, in direct analogy with homogeneous nucleation, or singular, with ice nuclei initiating freezing at deterministic temperatures. We present an idealized model that bridges these stochastic and singular descriptions of heterogeneous ice nucleation. This "soccer ball" model treats statistically similar particles as being covered with surface sites (patches of finite area characterized by different nucleation barriers, but with each surface site following the stochastic nature of ice embryo formation. The model provides a phenomenological explanation for seemingly contradictory experimental results obtained in our research groups. We suggest that ice nucleation is fundamentally a stochastic process but that for realistic atmospheric particle populations this process can be masked by the heterogeneity of surface properties. Full evaluation of the model will require experiments with well characterized ice nucleating particles and the ability to vary both temperature and waiting time for freezing.
Gorenstein quotient singularities of monomial type in dimension three
Ito, Y
1994-01-01
The purpose of this paper is to construct a crepant resolution of quotient singularities by finite subgroups of SL(3,C) of monomial type, and prove that the Eular number of the resolution is equal to the number of conjugacy classes. This result is a part of conjecture II in previous paper "crepant resolution of trihedral singularities" ( alg-geom 9404008). These singularities are different from trihedral, but main idea for the proof is based on the method of trihedral case.
STRUCTURAL DECOMPOSITION AND ITS PROPERTIES OF LINEAR MULTIVARIABLE SINGULAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Minghua HE; Ben M. CHEN; Zongli LIN
2007-01-01
We present in this paper a structural decomposition for linear multivariable singular systems.Such a decomposition has a distinct feature of capturing and displaying all the structural properties,such as the finite and infinite zero structures, invertibility structures, and redundant dynamics of the given system. As its counterpart for non-singular systems, we believe that the technique is a powerful tool in solving control problems for singular systems.
Quantum control of finite-time disentanglement in qubit-qubit and qubit-qutrit systems
Energy Technology Data Exchange (ETDEWEB)
Ali, Mazhar
2009-07-13
This thesis is a theoretical study of entanglement dynamics and its control of qubit-qubit and qubit-qutrit systems. In particular, we focus on the decay of entanglement of quantum states interacting with dissipative environments. Qubit-qubit entanglement may vanish suddenly while interacting with statistically independent vacuum reservoirs. Such finite- time disentanglement is called sudden death of entanglement (ESD). We investigate entanglement sudden death of qubit-qubit and qubit-qutrit systems interacting with statistically independent reservoirs at zero- and finite-temperature. It is shown that for zero-temperature reservoirs, some entangled states exhibit sudden death while others lose their entanglement only after infinite time. Thus, there are two possible routes of entanglement decay, namely sudden death and asymptotic decay. We demonstrate that starting with an initial condition which leads to finite-time disentanglement, we can alter the future course of entanglement by local unitary actions. In other words, it is possible to put the quantum states on other track of decay once they are on a particular route of decay. We show that one can accelerate or delay sudden death. However, there is a critical time such that if local actions are taken before that critical time then sudden death can be delayed to infinity. Any local unitary action taken after that critical time can only accelerate or delay sudden death. In finite-temperature reservoirs, we demonstrate that a whole class of entangled states exhibit sudden death. This conclusion is valid if at least one of the reservoirs is at finite-temperature. However, we show that we can still hasten or delay sudden death by local unitary transformations up to some finite time. We also study sudden death for qubit-qutrit systems. Similar to qubit-qubit systems, some states exhibit sudden death while others do not. However, the process of disentanglement can be effected due to existence of quantum interference
Pascual-Marqui, Roberto D
2010-01-01
Understanding of normal and pathological brain function requires the identification and localization of functional connections between specialized regions. The availability of high time resolution signals of electric neuronal activity at several regions offers information for quantifying the connections in terms of information flow. When the signals cover the whole cortex, the number of connections is very large, making visualization and interpretation very difficult. We introduce here the singular value decomposition of time-lagged multiple signals, which localizes the senders, hubs, and receivers (SHR) of information transmission. Unlike methods that operate on large connectivity matrices, such as correlation thresholding and graph-theoretic analyses, this method operates on the multiple time series directly, providing 3D brain images that assign a score to each location in terms of its sending, relaying, and receiving capacity. The scope of the method is general and encompasses other applications outside t...
Geometric and material modeling environment for the finite-difference time-domain method
Lee, Yong-Gu; Muhammad, Waleed
2012-02-01
The simulation of electromagnetic problems using the Finite-Difference Time-Domain method starts with the geometric design of the devices and their surroundings with appropriate materials and boundary conditions. This design stage is one of the most time consuming part in the Finite-Difference Time-Domain (FDTD) simulation of photonics devices. Many FDTD solvers have their own way of providing the design environment which can be burdensome for a new user to learn. In this work, geometric and material modeling features are developed on the freely available Google SketchUp, allowing users who are fond of its environment to easily model photonics simulations. The design and implementation of the modeling environment are discussed.
Quantification of the degree of mixing in chaotic micromixers using finite time Lyapunov exponents
Sarkar, Aniruddha; Harting, Jens
2010-01-01
Chaotic micromixers such as the staggered herringbone mixer developed by Stroock et al. allow efficient mixing of fluids even at low Reynolds number by repeated stretching and folding of the fluid interfaces. The ability of the fluid to mix well depends on the rate at which "chaotic advection" occurs in the mixer. An optimization of mixer geometries based on the quantification of chaotic advection is a non trivial task which is often performed by time consuming and expensive trial and error experiments. In this paper it is shown that the concept of finite-time Lyapunov exponents is a suitable tool to provide a quantitative measure of the chaotic advection of the flow. By performing lattice Boltzmann simulations of the flow inside a mixer geometry, introducing massless and non-interacting tracer particles and following their trajectories the finite time Lyapunov exponents can be calculated. The applicability of the method is demonstrated by optimizing the geometrical structure of the staggered herringbone mixe...
Xu, Xiaole; Chen, Shengyong; Gao, Lixin
2014-01-01
This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach.
Directory of Open Access Journals (Sweden)
Xiaole Xu
2014-01-01
Full Text Available This paper investigates the finite-time consensus problem of leader-following multiagent systems. The dynamical models for all following agents and the leader are assumed the same general form of linear system, and the interconnection topology among the agents is assumed to be switching and undirected. We mostly consider the continuous-time case. By assuming that the states of neighbouring agents are known to each agent, a sufficient condition is established for finite-time consensus via a neighbor-based state feedback protocol. While the states of neighbouring agents cannot be available and only the outputs of neighbouring agents can be accessed, the distributed observer-based consensus protocol is proposed for each following agent. A sufficient condition is provided in terms of linear matrix inequalities to design the observer-based consensus protocol, which makes the multiagent systems achieve finite-time consensus under switching topologies. Then, we discuss the counterparts for discrete-time case. Finally, we provide an illustrative example to show the effectiveness of the design approach.
Directory of Open Access Journals (Sweden)
Chao Sun
2016-01-01
Full Text Available The problem of delay-dependent robust fault estimation for a class of Takagi-Sugeno (T-S fuzzy singular systems is investigated. By decomposing the delay interval into two unequal subintervals and with a new and tighter integral inequality transformation, an improved delay-dependent stability criterion is given in terms of linear matrix inequalities (LMIs to guarantee that the fuzzy singular system with time-varying delay is regular, impulse-free, and stable firstly. Then, based on this criterion, by considering the system fault as an auxiliary disturbance vector and constructing an appropriate fuzzy augmented system, a fault estimation observer is designed to ensure that the error dynamic system is regular, impulse-free, and robustly stable with a prescribed H∞ performance satisfied for all actuator and sensor faults simultaneously, and the obtained fault estimates can practically better depict the size and shape of the faults. Finally, numerical examples are given to show the effectiveness of the proposed approach.
Classically stable non-singular cosmological bounces
Ijjas, Anna
2016-01-01
One of the fundamental questions of theoretical cosmology is whether the universe can undergo a non-singular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a non-singular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this letter, we examine cubic Galileon theories and present a procedure for explicitly constructing examples of a non-singular cosmological bounce without encountering any pathologies and maintaining a sub-luminal sound speed for co-moving curvature modes throughout the NEC violating phase. We also discuss the relation between our procedure and earlier work.
Fully stable cosmological solutions with a non-singular classical bounce
Ijjas, Anna
2016-01-01
We recently showed how it is possible to use a cubic Galileon action to construct classical cosmological solutions that enter a contracting null energy condition (NEC) violating phase, bounce at finite values of the scale factor and exit into an expanding NEC-satisfying phase without encountering any singularities or pathologies. A drawback of these examples is that singular behavior is encountered at some time either just before or just after the NEC-violating phase. In this Letter, we show that it is possible to circumvent this problem by extending our method to actions that include the next order ${\\cal L}_4$ Galileon interaction. Using this approach, we construct non-singular classical bouncing cosmological solutions that are non-pathological for all times.
FINITE-TIME RUIN PROBABILITY WITH NQD DOMINATED VARYING-TAILED CLAIMS AND NLOD INTER-ARRIVAL TIMES
Institute of Scientific and Technical Information of China (English)
Jingzhi LI; Kaiyong WANG; Yuebao WANG
2009-01-01
In 2007, Chen and Ng investigated infinite-time ruin probability with constant interest force and negatively quadrant dependent and extended regularly varying-tailed claims. Following this work, the authors obtain a weakly asymptotic equivalent formula for the finite-time and infinite-time ruin probability with constant interest force, negatively quadrant dependent, and dominated varying-tailed claims and negatively lower orthant dependent inter-arrival times. In particular, when the claims are consistently varying-tailed, an asymptotic equivalent formula is presented.
Weyl Anomaly and Initial Singularity Crossing
Awad, Adel
2015-01-01
We consider the role of quantum effects, mainly, Weyl anomaly in modifying FLRW model singular behavior at early times. Weyl anomaly corrections to FLRW models have been considered in the past, here we reconsider this model and show the following: The singularity of this model is weak according to Tipler and Krolak, therefore, the spacetime might admit a geodesic extension. Weyl anomaly corrections changes the nature of the initial singularity from a big bang singularity to a sudden singularity. The two branches of solutions consistent with the semiclassical treatment form a disconnected manifold. Joining these two parts at the singularity provides us with a $C^1$ extension to nonspacelike geodesics and leaves the spacetime geodesically complete. Using Gauss-Codazzi equations one can derive generalized junction conditions for this higher-derivative gravity. The extended spacetime obeys Friedmann and Raychaudhuri equations and the junction conditions. The junction does not generate Dirac delta functions in mat...
Homogeneous spacelike singularities inside spherical black holes
Burko, L M
1997-01-01
Recent numerical simulations have found that the Cauchy horizon inside spherical charged black holes, when perturbed nonlinearly by a self-gravitating, minimally-coupled, massless, spherically-symmetric scalar field, turns into a null weak singularity which focuses monotonically to $r=0$ at late times, where the singularity becomes spacelike. Our main objective is to study this spacelike singularity. We study analytically the spherically-symmetric Einstein-Maxwell-scalar equations asymptotically near the singularity. We obtain a series-expansion solution for the metric functions and for the scalar field near $r=0$ under the simplifying assumption of homogeneity. Namely, we neglect spatial derivatives and keep only temporal derivatives. We find that there indeed exists a generic spacelike singularity solution for these equations (in the sense that the solution depends on enough free parameters), with similar properties to those found in the numerical simulations. This singularity is strong in the Tipler sense,...
Panayappan, Kadappan
With the advent of sub-micron technologies and increasing awareness of Electromagnetic Interference and Compatibility (EMI/EMC) issues, designers are often interested in full- wave solutions of complete systems, taking to account a variety of environments in which the system operates. However, attempts to do this substantially increase the complexities involved in computing full-wave solutions, especially when the problems involve multi- scale geometries with very fine features. For such problems, even the well-established numerical methods, such as the time domain technique FDTD and the frequency domain methods FEM and MoM, are often challenged to the limits of their capabilities. In an attempt to address such challenges, three novel techniques have been introduced in this work, namely Dipole Moment (DM) Approach, Recursive Update in Frequency Domain (RUFD) and New Finite Difference Time Domain ( vFDTD). Furthermore, the efficacy of the above techniques has been illustrated, via several examples, and the results obtained by proposed techniques have been compared with other existing numerical methods for the purpose of validation. The DM method is a new physics-based approach for formulating MoM problems, which is based on the use of dipole moments (DMs), as opposed to the conventional Green's functions. The absence of the Green's functions, as well as those of the vector and scalar potentials, helps to eliminate two of the key sources of difficulties in the conventional MoM formulation, namely the singularity and low-frequency problems. Specifically, we show that there are no singularities that we need to be concerned with in the DM formulation; hence, this obviates the need for special techniques for integrating these singularities. Yet another salutary feature of the DM approach is its ability to handle thin and lossy structures, or whether they are metallic, dielectric-type, or even combinations thereof. We have found that the DM formulation can handle these
Institute of Scientific and Technical Information of China (English)
ZHANG Hua-rong; QU Guo-qing; REN Ting
2012-01-01
There are various influencing factors that affect the deformation observation,and deformation signals show different characteristics under different scales.Wavelet analysis possesses multi-scale property,and the information entropy has great representational capability to the complexity of information.By hamming window to the wavelet coefficients and windowed wavelet energy obtained by multi-resolution analysis (MRA),it can be achieved to measure the wavelet time entropy (WTE) and wavelet energy entropy (WEE).The paper established deformation signals,selected the parameters,and compared the singularity detection ability and anti-noise ability of two kinds of wavelet entropy and applied them to the singularity detection at the GPS continuously operating reference stations.It is shown that the WTE performs well in weak singularity information detection in finite frequency components signals and the WEE is more suitable for detecting the singularity in the signals with complex,strong background noise.
Exploring the potentials and limitations of the time-reversal imaging of finite seismic sources
Directory of Open Access Journals (Sweden)
S. Kremers
2011-06-01
Full Text Available The characterisation of seismic sources with time-reversed wave fields is developing into a standard technique that has already been successful in numerous applications. While the time-reversal imaging of effective point sources is now well-understood, little work has been done to extend this technique to the study of finite rupture processes. This is despite the pronounced non-uniqueness in classic finite source inversions.
The need to better constrain the details of finite rupture processes motivates the series of synthetic and real-data time reversal experiments described in this paper. We address questions concerning the quality of focussing in the source area, the localisation of the fault plane, the estimation of the slip distribution and the source complexity up to which time-reversal imaging can be applied successfully. The frequency band for the synthetic experiments is chosen such that it is comparable to the band usually employed for finite source inversion.
Contrary to our expectations, we find that time-reversal imaging is useful only for effective point sources, where it yields good estimates of both the source location and the origin time. In the case of finite sources, however, the time-reversed field does not provide meaningful characterisations of the fault location and the rupture process. This result cannot be improved sufficiently with the help of different imaging fields, realistic modifications of the receiver geometry or weights applied to the time-reversed sources.
The reasons for this failure are manifold. They include the choice of the frequency band, the incomplete recording of wave field information at the surface, the excitation of large-amplitude surface waves that deteriorate the depth resolution, the absence of a sink that should absorb energy radiated during the later stages of the rupture process, the invisibility of small slip and the neglect of prior information concerning the fault
2005-01-01
This self-paced narrated tutorial covers the following about Finite Automata: Uses, Examples, Alphabet, strings, concatenation, powers of an alphabet, Languages (automata and formal languages), Deterministic finite automata (DFA) SW4600 Automata, Formal Specification and Run-time Verification
Spectral analysis of finite-time correlation matrices near equilibrium phase transitions
Vinayak; Prosen, T.; Buča, B.; Seligman, T. H.
2014-10-01
We study spectral densities for systems on lattices, which, at a phase transition display, power-law spatial correlations. Constructing the spatial correlation matrix we prove that its eigenvalue density shows a power law that can be derived from the spatial correlations. In practice time series are short in the sense that they are either not stationary over long time intervals or not available over long time intervals. Also we usually do not have time series for all variables available. We shall make numerical simulations on a two-dimensional Ising model with the usual Metropolis algorithm as time evolution. Using all spins on a grid with periodic boundary conditions we find a power law, that is, for large grids, compatible with the analytic result. We still find a power law even if we choose a fairly small subset of grid points at random. The exponents of the power laws will be smaller under such circumstances. For very short time series leading to singular correlation matrices we use a recently developed technique to lift the degeneracy at zero in the spectrum and find a significant signature of critical behavior even in this case as compared to high temperature results which tend to those of random matrix models.
Yang, Yana; Hua, Changchun; Guan, Xinping
2016-03-01
Due to the cognitive limitations of the human operator and lack of complete information about the remote environment, the work performance of such teleoperation systems cannot be guaranteed in most cases. However, some practical tasks conducted by the teleoperation system require high performances, such as tele-surgery needs satisfactory high speed and more precision control results to guarantee patient' health status. To obtain some satisfactory performances, the error constrained control is employed by applying the barrier Lyapunov function (BLF). With the constrained synchronization errors, some high performances, such as, high convergence speed, small overshoot, and an arbitrarily predefined small residual constrained synchronization error can be achieved simultaneously. Nevertheless, like many classical control schemes only the asymptotic/exponential convergence, i.e., the synchronization errors converge to zero as time goes infinity can be achieved with the error constrained control. It is clear that finite time convergence is more desirable. To obtain a finite-time synchronization performance, the terminal sliding mode (TSM)-based finite time control method is developed for teleoperation system with position error constrained in this paper. First, a new nonsingular fast terminal sliding mode (NFTSM) surface with new transformed synchronization errors is proposed. Second, adaptive neural network system is applied for dealing with the system uncertainties and the external disturbances. Third, the BLF is applied to prove the stability and the nonviolation of the synchronization errors constraints. Finally, some comparisons are conducted in simulation and experiment results are also presented to show the effectiveness of the proposed method.
Real-time finite-temperature correlators from AdS/CFT
Barnes, Edwin; Wu, Chaolun; Arnold, Peter
2010-01-01
In this paper we use AdS/CFT ideas in conjunction with insights from finite temperature real-time field theory formalism to compute 3-point correlators of ${\\cal N}{=}4$ super Yang-Mills operators, in real time and at finite temperature. To this end, we propose that the gravity field action is integrated only over the right and left quadrants of the Penrose diagram of the Anti de Sitter-Schwarzschild background, with a relative sign between the two terms. For concreteness we consider the case of a scalar field in the black hole background. Using the scalar field Schwinger-Keldysh bulk-to-boundary propagators, we give the general expression of a 3-point real-time Green's correlator. We then note that this particular prescription amounts to adapting the finite-temperature analog of Veltman's circling rules to tree-level Witten diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary propagators. We subject our prescription to several checks: KMS identities, the largest time equation and the zer...
Lansing, Faiza S.; Rascoe, Daniel L.
1993-01-01
This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.
Directory of Open Access Journals (Sweden)
Cheng Gong
2014-01-01
Full Text Available This paper investigates the H∞ filtering problem of discrete singular Markov jump systems (SMJSs with mode-dependent time delay based on T-S fuzzy model. First, by Lyapunov-Krasovskii functional approach, a delay-dependent sufficient condition on H∞-disturbance attenuation is presented, in which both stability and prescribed H∞ performance are required to be achieved for the filtering-error systems. Then, based on the condition, the delay-dependent H∞ filter design scheme for SMJSs with mode-dependent time delay based on T-S fuzzy model is developed in term of linear matrix inequality (LMI. Finally, an example is given to illustrate the effectiveness of the result.
Institute of Scientific and Technical Information of China (English)
Wo Songlin; Shi Guodong; Zou Yun
2007-01-01
The decentralized robust guaranteed cost control problem is studied for a class ofinterconnected singular large-scale systems with time-delay and norm-bounded time-invariant parameter uncertainty under a given quadratic cost performance function. The problem that is addressed in this study is to design a decentralized robust guaranteed cost state feedback controller such that the closed-loop system is not only regular, impulse-free and stable, but also guarantees an adequate level of performance for all admissible uncertainties. A sufficient condition for the existence of the decentralized robust guaranteed cost state feedback controllers is proposed in terms of a linear matrix inequality (LMI) via LMI approach. When this condition is feasible, the desired state feedback decentralized robust guaranteed cost controller gain matrices can be obtained. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed approach.
Adaptive Finite-Time Control for a Flexible Hypersonic Vehicle with Actuator Fault
Directory of Open Access Journals (Sweden)
Jie Wang
2013-01-01
Full Text Available The problem of robust fault-tolerant tracking control is investigated. Simulation on the longitudinal model of a flexible air-breathing hypersonic vehicle (FAHV with actuator faults and uncertainties is conducted. In order to guarantee that the velocity and altitude track their desired commands in finite time with the partial loss of actuator effectiveness, an adaptive fault-tolerant control strategy is presented based on practical finite-time sliding mode method. The adaptive update laws are used to estimate the upper bound of uncertainties and the minimum value of actuator efficiency factor. Finally, simulation results show that the proposed control strategy is effective in rejecting uncertainties even in the presence of actuator faults.
Directory of Open Access Journals (Sweden)
Aihua Zhang
2013-01-01
Full Text Available A novel attitude tracking control scheme is presented for overactuated spacecraft to address the attitude stabilization problem in presence of reaction wheel installation deviation, external disturbance and uncertain mass of moment inertia. An adaptive sliding mode control technique is proposed to track the uncertainty. A Lyapunov-based analysis shows that the compensation control law can guarantee that the desired attitude trajectories are followed in finite-time. The key feature of the proposed control strategy is that it globally asymptotically stabilizes the system, even in the presence of reaction wheel installation deviation, external disturbances, and uncertain mass of moment inertia. The attitude track performance using the proposed finite-time compensation control is evaluated through a numerical example.
Finite-time control for nonlinear spacecraft attitude based on terminal sliding mode technique.
Song, Zhankui; Li, Hongxing; Sun, Kaibiao
2014-01-01
In this paper, a fast terminal sliding mode control (FTSMC) scheme with double closed loops is proposed for the spacecraft attitude control. The FTSMC laws are included both in an inner control loop and an outer control loop. Firstly, a fast terminal sliding surface (FTSS) is constructed, which can drive the inner loop tracking-error and the outer loop tracking-error on the FTSS to converge to zero in finite time. Secondly, FTSMC strategy is designed by using Lyaponov's method for ensuring the occurrence of the sliding motion in finite time, which can hold the character of fast transient response and improve the tracking accuracy. It is proved that FTSMC can guarantee the convergence of tracking-error in both approaching and sliding mode surface. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.
Smy, Tom J
2016-01-01
An explicit time-domain finite-difference technique for modelling zero-thickness Huygens' metasurfaces based on Generalized Sheet Transition Conditions (GSTCs), is proposed and demonstrated using full-wave simulations. The Huygens' metasurface is modelled using electric and magnetic surface susceptibilities, which are found to follow a double-Lorentz dispersion profile. To solve zero-thickness Huygens' metasurface problems for general broadband excitations, the double-Lorentz dispersion profile is combined with GSTCs, leading to a set of first-order differential fields equations in time-domain. Identifying the exact equivalence between Huygens' metasurfaces and coupled RLC oscillator circuits, the field equations are then subsequently solved using standard circuit modelling techniques based on a finite-difference formulation. Several examples including generalized refraction are shown to illustrate the temporal evolution of scattered fields from the Huygens' metasurface under plane-wave normal incidence, in b...
Finite-time synchronization of tunnel-diode-based chaotic oscillators.
Louodop, Patrick; Fotsin, Hilaire; Kountchou, Michaux; Ngouonkadi, Elie B Megam; Cerdeira, Hilda A; Bowong, Samuel
2014-03-01
This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel-diode-based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulations followed by pspice experiment are presented to show the feasibility of the proposed method.
Input-output finite-time stabilisation of nonlinear stochastic system with missing measurements
Song, Jun; Niu, Yugang; Jia, Tinggang
2016-09-01
This paper considers the problem of the input-output finite-time stabilisation for a class of nonlinear stochastic system with state-dependent noise. The phenomenon of the missing measurements may occur when state signals are transmitted via communication networks. An estimating method is proposed to compensate the lost state information. And then, a compensator-based controller is designed to ensure the input-output finite-time stochastic stability (IO-FTSS) of the closed-loop system. Some parameters-dependent sufficient conditions are derived and the corresponding solving approach is given. Finally, numerical simulations are provided to demonstrate the feasibility and effectiveness of the developed IO-FTSS scheme.
Finite-Time Anti-Disturbance Inverse Optimal Attitude Tracking Control of Flexible Spacecraft
Directory of Open Access Journals (Sweden)
Chutiphon Pukdeboon
2013-01-01
Full Text Available We propose a new robust optimal control strategy for flexible spacecraft attitude tracking maneuvers in the presence of external disturbances. An inverse optimal control law is designed based on a Sontag-type formula and a control Lyapunov function. An adapted extended state observer is used to compensate for the total disturbances. The proposed controller can be expressed as the sum of an inverse optimal control and an adapted extended state observer. It is shown that the developed controller can minimize a cost functional and ensure the finite-time stability of a closed-loop system without solving the associated Hamilton-Jacobi-Bellman equation directly. For an adapted extended state observer, the finite-time convergence of estimation error dynamics is proven using a strict Lyapunov function. An example of multiaxial attitude tracking maneuvers is presented and simulation results are included to show the performance of the developed controller.
Estimating inter-event time distributions from finite observation periods in communication networks
Kivelä, Mikko
2014-01-01
A diverse variety of processes --- including recurrent disease episodes, neuron firing, and communication patterns among humans --- can be described using inter-event time (IET) distributions. Many such processes are ongoing, although event sequences are only available during a finite observation window. Because the observation time window is more likely to begin or end during long IETs than during short ones, the analysis of such data is susceptible to a bias induced by the finite observation period. In this paper, we illustrate how this length bias is born and how it can be corrected. To do this, we model event sequences using stationary renewal processes, and we formulate simple heuristics for determining the severity of the bias. To illustrate our results, we focus on the example of empirical communication networks, which are temporal networks that are constructed from communication events. The IET distributions of such systems guide efforts to build models of human behavior, and the variance of IETs is v...
Lee, Daero; Vukovich, George; Gui, Haichao
2017-05-01
This paper presents an adaptive variable-structure finite-time control for spacecraft proximity maneuvers under parameter uncertainties, external disturbances and actuator saturation. The coupled six degrees-of-freedom dynamics are modeled for spacecraft relative motion, where the exponential coordinates on the Lie group SE(3) are employed to describe relative configuration. No prior knowledge of inertia matrix and mass of the spacecraft is required for the proposed control law, which implies that the proposed control scheme can be applied in spacecraft systems with large parametric uncertainties in inertia matrix and mass. Finite-time convergence of the feedback system with the proposed control law is established. Numerical simulation results are presented to illustrate the effectiveness of the proposed control law for spacecraft proximity operations with actuator saturation.
Dyja, Robert; van der Zee, Kristoffer G
2016-01-01
We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns instead of marching sequentially in time. The methodology is a combination of a computationally efficient implementation of a parallel-in-space-time finite element solver coupled with a posteriori space-time error estimates and a parallel mesh generator. This methodology enables, in principle, simultaneous adaptivity in both space and time (within the block) domains. We explore this basic concept in the context of a variety of time-steppers including $\\Theta$-schemes and Backward Differentiate Formulas. We specifically illustrate this framework with applications involving time dependent linear, quasi-linear and semi-linear diffusion equations. We focus on investigating how the coupled space-time refinement indicators for this class of problems affect spatial adaptivity. Final...
The stability of polarisation singularities in disordered photonic crystal waveguides
Lang, Ben; Young, Andrew B; Rarity, John G; Oulton, Ruth
2015-01-01
The effects of short range disorder on the polarisation characteristics of light in photonic crystal waveguides were investigated using finite difference time domain simulations with a view to investigating the stability of polarisation singularities. It was found that points of local circular polarisation (C-points) and contours of linear polarisation (L-lines) continued to appear even in the presence of high levels of disorder, and that they remained close to their positions in the ordered crystal. These results are a promising indication that devices exploiting polarisation in these structures are viable given current fabrication standards.
Simulation of acoustic streaming by means of the finite-difference time-domain method
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2012-01-01
the finite-difference time-domain method. To simplify the problem, thermal effects are not considered. The motivation of the described investigation has been the possibility of using the numerical method to study acoustic streaming, particularly under non-steady conditions. Results are discussed for channels...... of different width, which illustrate the applicability of the method. The obtained numerical simulations agree quite will with analytical solutions available in the literature....
A Novel Absorbing Boundary Condition for the Frequency-DependentFinite-Difference Time-Domain Method
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
A new absorbing boundary condition (ABC) for frequency-dependent finite-difference time-domain algorithm for the arbitrary dispersive media is presented. The concepts of the digital systems are introduced to the (FD)2TD method. On the basis of digital filter designing and vector algebra, the absorbing boundary condition under arbitrary angle of incidence are derived. The transient electromagnetic problems in two-dimensions and three-dimensions are calculated and the validity of the ABC is verified.
Accurate finite-difference time-domain simulation of anisotropic media by subpixel smoothing.
Oskooi, Ardavan F; Kottke, Chris; Johnson, Steven G
2009-09-15
Finite-difference time-domain methods suffer from reduced accuracy when discretizing discontinuous materials. We previously showed that accuracy can be significantly improved by using subpixel smoothing of the isotropic dielectric function, but only if the smoothing scheme is properly designed. Using recent developments in perturbation theory that were applied to spectral methods, we extend this idea to anisotropic media and demonstrate that the generalized smoothing consistently reduces the errors and even attains second-order convergence with resolution.
Some properties of asymmetric Hopfield neural networks with finite time of transition between states
Suleimenov, Ibragim; Mun, Grigoriy; Panchenko, Sergey; Pak, Ivan
2016-11-01
There were implemented samples of asymmetric Hopfield neural networks which have finite time of transition from one state to another. It was shown that in such systems, various oscillation modes could occur. It was revealed that the oscillation of the output signal of certain neuron could be treated as extra logical variable, which describes the state of the neuron. Asymmetric Hopfield neural networks are described in terms of ternary logic. Such logic may be employed in image recognition procedure.
Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking
Institute of Scientific and Technical Information of China (English)
Chutiphon Pukdeboon
2015-01-01
This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid-ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con-trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se-cond control law is also designed by combining the second or-der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya-punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed control ers.
Directory of Open Access Journals (Sweden)
Sharma Arjun
2011-01-01
Full Text Available The present study investigates the performance of the solar-driven Stirling engine system to maximize the power output and thermal efficiency using the non-linearized heat loss model of the solar dish collector and the irreversible cycle model of the Stirling engine. Finite time thermodynamic analysis has been done for combined system to calculate the finite-rate heat transfer, internal heat losses in the regenerator, conductive thermal bridging losses and finite regeneration process time. The results indicate that exergy efficiency of dish system increases as the effectiveness of regenerator increases but decreases with increase in regenerative time coefficient. It is also found that optimal range of collector temperature and corresponding concentrating ratio are 1000 K~1400 K and 1100~1400, respectively in order to get maximum value of exergy efficiency. It is reported that the exergy efficiency of this dish system can reach the maximum value when operating temperature and concentrating ratio are 1150 K and 1300, respectively.
Yan, Zhiguo; Song, Yunxia; Park, Ju H
2017-05-01
This paper is concerned with the problems of finite-time stability and stabilization for stochastic Markov systems with mode-dependent time-delays. In order to reduce conservatism, a mode-dependent approach is utilized. Based on the derived stability conditions, state-feedback controller and observer-based controller are designed, respectively. A new N-mode algorithm is given to obtain the maximum value of time-delay. Finally, an example is used to show the merit of the proposed results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Occurrence of discontinuities in the performance of finite-time quantum Otto cycles
Zheng, Yuanjian; Hänggi, Peter; Poletti, Dario
2016-07-01
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.
The Time Discontinuous H1-Galerkin Mixed Finite Element Method for Linear Sobolev Equations
Directory of Open Access Journals (Sweden)
Hong Yu
2015-01-01
Full Text Available We combine the H1-Galerkin mixed finite element method with the time discontinuous Galerkin method to approximate linear Sobolev equations. The advantages of these two methods are fully utilized. The approximate schemes are established to get the approximate solutions by a piecewise polynomial of degree at most q-1 with the time variable. The existence and uniqueness of the solutions are proved, and the optimal H1-norm error estimates are derived. We get high accuracy for both the space and time variables.
Institute of Scientific and Technical Information of China (English)
SHA Wei; HUANG Zhi-Xiang; WU Xian-Liang; CHEN Ming-Sheng
2006-01-01
Using symplectic integrator propagator, a three-dimensional fourth-order symplectic finite difference time domain (SFDTD) method is studied, which is of the fourth order in both the time and space domains. The method is nondissipative and can save more memory compared with the traditional FDTD method. The total field and scattered field (TF-SF) technique is derived for the SFDTD method to provide the incident wave source conditions. The bistatic radar cross section (RCS) of a dielectric sphere is computed by using the SFDTD method for the first time. Numerical results suggest that the SFDTD algorithm acquires better stability and accuracy compared with the traditional FDTD method.
CSIR Research Space (South Africa)
Loveday, PW
2007-03-01
Full Text Available conventional finite element methods available in commercial software, these models tend to be very large. An alternative method is to use specially formulated waveguide finite elements (sometimes called Semi-Analytical Finite Elements). Models using...
Singularity analysis: theory and further developments
Cheng, Qiuming
2015-04-01
Since the concept of singularity and local singularity analysis method (LSA) were originally proposed by the author for characterizing the nonlinear property of hydrothermal mineralization processes, the local singularity analysis technique has been successfully applied for identification of geochemical and geophysical anomalies related to various types of mineral deposits. It has also been shown that the singularity is the generic property of singular geo-processes which result in anomalous amounts of energy release or material accumulation within a narrow spatial-temporal interval. In the current paper we introduce several new developments about singularity analysis. First is a new concept of 'fractal density' which describes the singularity of complex phenomena of fractal nature. While the ordinary density possesses a unit of ratio of mass and volume (e.g. g/cm3, kg/m3) or ratio of energy over volume or time (e.g. J/cm3, w/L3, w/s), the fractal density has a unit of ratio of mass over fractal set or energy over fractal set (e.g. g/cmα, kg/mα, J/ mα, w/Lα, where α can be a non-integer). For the matter with fractal density (a non-integer α), the ordinary density of the phenomena (mass or energy) no longer exists and depicts singularity. We demonstrate that most of extreme geo-processes occurred in the earth crust originated from cascade earth dynamics (mental convection, plate tectonics, orogeny and weathering etc) may cause fractal density of mass accumulation or energy release. The examples to be used to demonstrate the concepts of fractal density and singularity are earthquakes, floods, volcanos, hurricanes, heat flow over oceanic ridge, hydrothermal mineralization in orogenic belt, and anomalies in regolith over mine caused by ore and toxic elements vertical migration. Other developments of singularity theory and methodologies including singular Kriging and singularity weights of evidence model for information integration will also be introduced.
Evidence for a singularity in ideal magnetohydrodynamics implications for fast reconnection
Kerr, R M; Kerr, Robert M.; Brandenburg, Axel
1998-01-01
Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\\infty \\sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.
Time-domain finite element models of electrochemistry in intracochlear electrodes.
Sue, Andrian; Tran, Phillip; Wong, Paul; Li, Qing; Carter, Paul
2013-01-01
Most neural prostheses feature metallic electrodes to act as an interface between the device and the physiological tissue. When charge is injected through these electrodes, potentially harmful reactions may result. Others have developed finite element models to evaluate the performance of stimulating electrodes in vivo. Few however, model an electrode-electrolyte interface, and many do not address electrode corrosion and safety concerns with respect to irreversible reactions. In this work, we successfully develop a time domain finite element model of cochlear implant electrodes that incorporate oxygen reduction and platinum oxidation reactions. We find that when electrodes are stimulated with current pulses (0.5 mA, 25 µs), faradaic reactions may cause an increase in the peripheral enhancement of the current density.
Czarnik, Piotr; Rams, Marek M.; Dziarmaga, Jacek
2016-12-01
A Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a 3D tensor network, with the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension. The coarse graining is performed by a tree tensor network of isometries. They are optimized variationally to maximize the accuracy of the PEPO as a representation of the 2D thermal state e-β H. The algorithm is applied to the two-dimensional Hubbard model on an infinite square lattice. Benchmark results at finite temperature are obtained that are consistent with the best cluster dynamical mean-field theory and power-series expansion in the regime of parameters where they yield mutually consistent results.
Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2010-12-15
Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.
Optimization of solar-powered Stirling heat engine with finite-time thermodynamics
Energy Technology Data Exchange (ETDEWEB)
Yaqi, Li [School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China); Xi' an Research Institute of Hi-Tech, Xi' an, Shaanxi 710025 (China); Yaling, He; Weiwei, Wang [School of Energy and Power Engineering, Xi' an Jiaotong University, Xi' an, Shaanxi 710049 (China)
2011-01-15
A mathematical model for the overall thermal efficiency of the solar-powered high temperature differential dish-Stirling engine with finite-rate heat transfer, regenerative heat losses, conductive thermal bridging losses and finite regeneration processes time is developed. The model takes into consideration the effect of the absorber temperature and the concentrating ratio on the thermal efficiency; radiation and convection heat transfer between the absorber and the working fluid as well as convection heat transfer between the heat sink and the working fluid. The results show that the optimized absorber temperature and concentrating ratio are at about 1100 K and 1300, respectively. The thermal efficiency at optimized condition is about 34%, which is not far away from the corresponding Carnot efficiency at about 50%. Hence, the present analysis provides a new theoretical guidance for designing dish collectors and operating the Stirling heat engine system. (author)
Stability of stationary states of non-local equations with singular interaction potentials
Fellner, Klemens
2011-04-01
We study the large-time behaviour of a non-local evolution equation for the density of particles or individuals subject to an external and an interaction potential. In particular, we consider interaction potentials which are singular in the sense that their first derivative is discontinuous at the origin.For locally attractive singular interaction potentials we prove under a linear stability condition local non-linear stability of stationary states consisting of a finite sum of Dirac masses. For singular repulsive interaction potentials we show the stability of stationary states of uniformly bounded solutions under a convexity condition.Finally, we present numerical simulations to illustrate our results. © 2010 Elsevier Ltd.
Spontaneous generation of singularities in paraxial optical fields
Aiello, Andrea
2015-01-01
In nonrelativistic quantum mechanics the spontaneous generation of singularities in continue and finite wave functions, is a well understood phenomenon also occurring for free particles. We use the familiar analogy between the two-dimensional Schroedinger equation and the optical paraxial wave equation to show that even weakly-focused collimated light beams may develop a spatial singularity during free-space propagation. We find that according to the shape of the field, its amplitude may be either finite or infinite at the singular point.
Effective optical response of silicon to sunlight in the finite-difference time-domain method.
Deinega, Alexei; John, Sajeev
2012-01-01
The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. Numerical precision of our model is demonstrated for Mie scattering from a silicon sphere and solar absorption in a silicon nanowire photonic crystal.
DEFF Research Database (Denmark)
Santillan, Arturo Orozco
2011-01-01
The aim of the work described in this paper has been to investigate the use of the finite-difference time-domain method to describe the interactions between a moving object and a sound field. The main objective was to simulate oscillational instabilities that appear in single-axis acoustic...... levitation devices and to describe their evolution in time to further understand the physical mechanism involved. The study shows that the method gives accurate results for steady state conditions, and that it is a promising tool for simulations with a moving object....
Institute of Scientific and Technical Information of China (English)
韩帮军; 潘军; 范秀敏; 马登哲
2004-01-01
The recursion relation of preventive maintenance (PM) cycle is built up concerning the concept of effective age and age setback factor proposed in this paper, which illustrates the dynamic relationship between failure rate and preventive maintenance activity. And the nonlinear optimal PM policy model satisfying the reliability constraints in finite time horizon following Weibull distribution is proposed. The model built in this paper avoids the shortcoming of steady analytical PM model in infinite time horizon and can be used to aid scheduling the maintenance plan and providing decision supporting for job shop scheduling.
Automotive brake squeal analysis with rotating finite elements of asymmetric disc in time
Kang, Jaeyoung
2017-04-01
The new finite element brake squeal model is proposed where the finite elements of a real brake disc rotate in time. Contact nodal forces between the rotating disc and stationary pads are allocated to the moving contact area at every time step. When the proposed model is applied to an asymmetric automotive brake disc, it becomes the periodic time-varying brake system. The stability boundary of the discrete time-varying system is numerically calculated by the Floquet theory. Also, the quasi-static linearized eigenvalue analysis is conducted to show that the unstable modes repeatedly appear at the short interval of the disc rotation angle. The results are consistent with the angle-dependent local phenomenon of squeal termed squeal periodicity in the squeal experiment. In the nonlinear time-domain analysis, the squeal vibration increases and then decays in time for the rotating mode shape functions. It demonstrates that the rotation of an asymmetric disc can change the nonlinear squeal behavior as well as the linear stability character drastically.
A semi-analytical finite element method for a class of time-fractional diffusion equations
Sun, HongGuang; Sze, K Y
2011-01-01
As fractional diffusion equations can describe the early breakthrough and the heavy-tail decay features observed in anomalous transport of contaminants in groundwater and porous soil, they have been commonly employed in the related mathematical descriptions. These models usually involve long-time range computation, which is a critical obstacle for its application, improvement of the computational efficiency is of great significance. In this paper, a semi-analytical method is presented for solving a class of time-fractional diffusion equations which overcomes the critical long-time range computation problem of time fractional differential equations. In the procedure, the spatial domain is discretized by the finite element method which reduces the fractional diffusion equations into approximate fractional relaxation equations. As analytical solutions exist for the latter equations, the burden arising from long-time range computation can effectively be minimized. To illustrate its efficiency and simplicity, four...
Halyo, Edi
2009-01-01
We describe solitons that live on the world--volumes of D5 branes wrapped on deformed $A_2$ singularities fibered over $C(x)$. We show that monopoles are D3 branes wrapped on a node of the deformed singularity and stretched along $C(x)$. F and D--term strings are D3 branes wrapped on a node of a singularity that is deformed and resolved respectively. Domain walls require deformed $A_3$ singularities and correspond to D5 branes wrapped on a node and stretched along $C(x)$.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Energy Technology Data Exchange (ETDEWEB)
2016-04-12
Singularity is a container solution designed to facilitate mobility of compute across systems and HPC infrastructures. It does this by creating minimal containers that are defined by a specfile and files from the host system are used to build the container. The resulting container can then be launched by any Linux computer with Singularity installed regardless if the programs inside the container are present on the target system, or if they are a different version, or even incompatible versions. Singularity achieves extreme portability without sacrificing usability thus solving the need of mobility of compute. Singularity containers can be executed within a normal/standard command line process flow.
Huang, Kuan-Ju; Shih, Wei-Yeh; Chang, Jui Chung; Feng, Chih Wei; Fang, Wai-Chi
2013-01-01
This paper presents a pipeline VLSI design of fast singular value decomposition (SVD) processor for real-time electroencephalography (EEG) system based on on-line recursive independent component analysis (ORICA). Since SVD is used frequently in computations of the real-time EEG system, a low-latency and high-accuracy SVD processor is essential. During the EEG system process, the proposed SVD processor aims to solve the diagonal, inverse and inverse square root matrices of the target matrices in real time. Generally, SVD requires a huge amount of computation in hardware implementation. Therefore, this work proposes a novel design concept for data flow updating to assist the pipeline VLSI implementation. The SVD processor can greatly improve the feasibility of real-time EEG system applications such as brain computer interfaces (BCIs). The proposed architecture is implemented using TSMC 90 nm CMOS technology. The sample rate of EEG raw data adopts 128 Hz. The core size of the SVD processor is 580×580 um(2), and the speed of operation frequency is 20MHz. It consumes 0.774mW of power during the 8-channel EEG system per execution time.
Ju, Jinyong; Li, Wei; Wang, Yuqiao; Fan, Mengbao; Yang, Xuefeng
2016-01-01
Effective feedback control requires all state variable information of the system. However, in the translational flexible-link manipulator (TFM) system, it is unrealistic to measure the vibration signals and their time derivative of any points of the TFM by infinite sensors. With the rigid-flexible coupling between the global motion of the rigid base and the elastic vibration of the flexible-link manipulator considered, a two-time scale virtual sensor, which includes the speed observer and the vibration observer, is designed to achieve the estimation for the vibration signals and their time derivative of the TFM, as well as the speed observer and the vibration observer are separately designed for the slow and fast subsystems, which are decomposed from the dynamic model of the TFM by the singular perturbation. Additionally, based on the linear-quadratic differential games, the observer gains of the two-time scale virtual sensor are optimized, which aims to minimize the estimation error while keeping the observer stable. Finally, the numerical calculation and experiment verify the efficiency of the designed two-time scale virtual sensor. PMID:27801840
Ju, Jinyong; Li, Wei; Wang, Yuqiao; Fan, Mengbao; Yang, Xuefeng
2016-10-28
Effective feedback control requires all state variable information of the system. However, in the translational flexible-link manipulator (TFM) system, it is unrealistic to measure the vibration signals and their time derivative of any points of the TFM by infinite sensors. With the rigid-flexible coupling between the global motion of the rigid base and the elastic vibration of the flexible-link manipulator considered, a two-time scale virtual sensor, which includes the speed observer and the vibration observer, is designed to achieve the estimation for the vibration signals and their time derivative of the TFM, as well as the speed observer and the vibration observer are separately designed for the slow and fast subsystems, which are decomposed from the dynamic model of the TFM by the singular perturbation. Additionally, based on the linear-quadratic differential games, the observer gains of the two-time scale virtual sensor are optimized, which aims to minimize the estimation error while keeping the observer stable. Finally, the numerical calculation and experiment verify the efficiency of the designed two-time scale virtual sensor.
Wang, Leimin; Shen, Yi; Sheng, Yin
2016-04-01
This paper is concerned with the finite-time robust stabilization of delayed neural networks (DNNs) in the presence of discontinuous activations and parameter uncertainties. By using the nonsmooth analysis and control theory, a delayed controller is designed to realize the finite-time robust stabilization of DNNs with discontinuous activations and parameter uncertainties, and the upper bound of the settling time functional for stabilization is estimated. Finally, two examples are provided to demonstrate the effectiveness of the theoretical results.
The Singularity Problem in Brane Cosmology
Directory of Open Access Journals (Sweden)
Ignatios Antoniadis
2017-02-01
Full Text Available We review results about the development and asymptotic nature of singularities in “brane–bulk” systems. These arise for warped metrics obeying the five-dimensional Einstein equations with fluid-like sources, and including a brane four-metric that is either Minkowski, de Sitter, or Anti-de Sitter. We characterize all singular Minkowski brane solutions, and look for regular solutions with nonzero curvature. We briefly comment on matching solutions, energy conditions, and finite Planck mass criteria for admissibility, and we briefly discuss the connection of these results to ambient theory.
Finite-key analysis for time-energy high-dimensional quantum key distribution
Niu, Murphy Yuezhen; Xu, Feihu; Shapiro, Jeffrey H.; Furrer, Fabian
2016-11-01
Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.
Efficiency at maximum power output of quantum heat engines under finite-time operation
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, ηm, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ηm becomes identical to the Carnot efficiency ηC=1-Tc/Th. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ηm at maximum power output is bounded from above by ηC/(2-ηC) and from below by ηC/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ηCA=1-Tc/Th is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Finite-time barriers to front propagation in two-dimensional fluid flows
Mahoney, John R
2015-01-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear", introduced by Farazmand, Blazevski, and Haller [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our techniqu...
An efficient inplementation of boolean functions and finite state machines as self-timed circuits
Energy Technology Data Exchange (ETDEWEB)
David, I.; Ginosar, R.; Yoeli, M. (Technion-Israel Institute of Technology, Haifa (IL))
1989-12-01
Self-timed logic provides a method for designing logic circuits such that their correct behavior depends neither on the speed of their components nor on the delay along the communication wires. General synthesis methods for efficiently implementing self-timed combinational logic (CL) and finite state machines (FSM) are presented. The resulting CL is shown to require less gates than other proposed methods. The FSM is implemented by interconnectng a CL module with a self-timed master-slave register. The FSM synthesis method is also compared with other approaches. A formal system of behavioral sequential constraints is presented for each of the systems, and their behavior is proven correct. Thus, the synthesized CLs and FSMs can serve as correct-by-construction building blocks for self-timed silicon system compilation.
Efficiency at maximum power output of quantum heat engines under finite-time operation.
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1-T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2-η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency η(CA)=1-√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Pattern Recognition of Non-Stationary Time Series with Finite Length
Institute of Scientific and Technical Information of China (English)
FEI Wanchun; BAI Lun
2006-01-01
Statistical learning and recognition methods were used to extract the characteristics of size series measurements of cocoon filaments that are non-stationary in terms of mean and auto-covariance, by using the time varying parameter auto-regressive (TVPAR) model. After the system was taught to recognize the size data, the system correctly recognized the size of series of cocoon filaments as much as 96.95% of the time for a single series and 98.72% of the time for the mean of two series. The correct recognition rate was higher after suitable filtering. The theory and method can be used to analyze other types of non-stationary finite length time series.
Positive role of glassy dynamics in finite-time optimization by threshold algorithms
Hasegawa, M.
2011-01-01
The optimization mechanism of threshold algorithms is investigated in the solving process of a random Euclidean traveling salesman problem. A series of computer experiments previously designed for simulated annealing is conducted with algorithms such as generalized simulated annealing. The results show that if the threshold function decays fast enough, a previous positive view of slow relaxation dynamics in finite-time optimization by simulated annealing is still applicable regardless of the algorithm. These dynamics work effectively as an optimizer at around an intermediate temperature, which can be identified by using the Deborah number.
Finite Time Ruin Probability with Variable Interest Rate and Extended Regular Variation
Institute of Scientific and Technical Information of China (English)
WEI Xiao; HU Yi-jun
2004-01-01
Consider an insurance risk model, in which the surplus process satisfies a recursive equation Un=Un-1(1+rn)-Xn for n≥ 1, where U0=x≥0 is the initial surplus, {rn;n≥1} the interest rate sequence, {Xn;n≥1} the sequence of i.i.d. real-valued random variables with common distribution function F, which denotes the gross loss during the nth year. We investigate the ruin probability within a finite time horizon and give the asymptotic result as x→∞.
Fast Evaluation of Time-Domain Green Function for Finite Water Depth
Institute of Scientific and Technical Information of China (English)
滕斌; 韩凌; 勾莹
2003-01-01
For computation of large amplitude motions of ships fastened to a dock, a fast evaluation scheme is implemented for computation of the time-domain Green function for finite water depth. Based on accurate evaluation of the Green function directly, a fast approximation method for the Green function is developed by use of Chebyshev polynomials. Examinations are carried out of the accuracy of the Green function and its derivatives from the scheme. It is shown that when an appropriate number of polynomial terms are used, very accurate approximation can be obtained.
Finite-time control for asteroid hovering and landing via terminal sliding-mode guidance
Yang, Hongwei; Bai, Xiaoli; Baoyin, Hexi
2017-03-01
This paper proposes a new nonlinear guidance algorithm applicable for asteroid both hovering and landing. With the new guidance, a spacecraft achieves its target position and velocity in finite-time without the requirement of reference trajectories. The global stability is proven for the controlled system. A parametric analysis is conducted to illustrate the parameters' effects on the guidance algorithm. Simulations of straight landing, hovering to hovering and landing with a prior hovering phase of the highly irregular asteroid 2063 Bacchus are presented and the effectiveness of the proposed method is demonstrated.
Yamamoto, Kaho; Iwai, Yosuke; Uchida, Yoshiaki; Nishiyama, Norikazu
2016-08-01
We numerically analyzed the light propagation in cholesteric liquid crystalline (CLC) droplet array by the finite-difference time-domain (FDTD) method. The FDTD method successfully reproduced the experimental light path observed in the complicated photonic structure of the CLC droplet array more accurately than the analysis of CLC droplets by geometric optics with Bragg condition, and this method help us understand the polarization of the propagating light waves. The FDTD method holds great promise for the design of various photonic devices composed of curved photonic materials like CLC droplets and microcapsules.
Scattering analysis of periodic structures using finite-difference time-domain
ElMahgoub, Khaled; Elsherbeni, Atef Z
2012-01-01
Periodic structures are of great importance in electromagnetics due to their wide range of applications such as frequency selective surfaces (FSS), electromagnetic band gap (EBG) structures, periodic absorbers, meta-materials, and many others. The aim of this book is to develop efficient computational algorithms to analyze the scattering properties of various electromagnetic periodic structures using the finite-difference time-domain periodic boundary condition (FDTD/PBC) method. A new FDTD/PBC-based algorithm is introduced to analyze general skewed grid periodic structures while another algor