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The theory of controlled mechanical systems of Bloch et al (2001 IEEE Trans. Control Syst. Technol. 45 2253–70; Bloch et al 2001 Int. J. Robust Nonlinear Control 11 191–214; Bloch et al 1992 Automatica 28 745–56; Bloch et al 1997 Current and Future Directions in Applied Mathematics) and Krishnaprasad P S (1985 Nonlinear Anal. Theor. Methods Appl. 9 1011–35) is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and depends on the Eulerian state of the controlled system. Moreover, the control is set up so that the corresponding closed loop equations are Lie–Poisson. This implies that the energy–momentum method of Arnold V (1966 Ann. Inst. Fourier 16 319–61) and Holm et al (1985 Phys. Rep. 123 1–116) can be used to find a stabilizing control. As an example the case of planar parallel shear flow with an inflection point is treated. A state dependent feedback control is constructed which stabilizes the system for an arbitrarily long channel. [ABSTRACT FROM AUTHOR]

In the integrated circuit manufacturing process, the critical area extraction is a bottleneck to the layout optimization and the integrated circuit yield estimation. In this paper, we study the problem that the missing material defects may result in the open circuit fault. Combining the mathematical morphology theory, we present a new computation model and a novel extraction algorithm for the open critical area based on the net flow-axis. Firstly, we find the net flow-axis for different nets. Then, the net flow-edges based on the net flow-axis are obtained. Finally, we can extract the open critical area by the mathematical morphology. Compared with the existing methods, the nets need not to divide into the horizontal nets and the vertical nets, and the experimental results show that our model and algorithm can accurately extract the size of the open critical area and obtain the location information of the open circuit critical area. [ABSTRACT FROM AUTHOR]

TheHilbert space of three-qubit pure statesmay be identified with a Freudenthal triple system. Every state has an unique Freudenthal rank ranging from 1 to 4, which is determined by a set of automorphism group covariants. It is shown here that the optimal success rates for winning a three-player non-local game, varying over all local strategies, are strictly ordered by the Freudenthal rank of the shared three-qubit resource. [ABSTRACT FROM AUTHOR]

Bogomolny and Schmit proposed that the critical edge percolation on the square lattice is a good model for the nodal domains of a random plane wave. Based on this they made a conjecture about the number of nodal domains. Recent computer experiments showed that the mean number of clusters per vertex and the mean number of nodal domains per unit area are very close but different. Since the original argument was mostly supported by numerics, it was believed that the percolation model is wrong. In this paper we give some numerical evidence in favour of the percolation model. [ABSTRACT FROM AUTHOR]

The Weyl correspondence and the related Wigner formalism lie at the core of traditional quantum mechanics. We discuss here an alternative quantization scheme, the idea of which goes back to Born and Jordan, and which has recently been revived in another context, namely time-frequency analysis. We show in particular that the uncertainty principle does not enjoy full symplectic covariance properties in the Born and Jordan scheme, as opposed to what happens in the Weyl quantization. [ABSTRACT FROM AUTHOR]

Focusing on the problems in the process of simulation and experiment on a parafoil nonlinear dynamic system, such as limited methods, high cost and low efficiency we present a semi-physical simulation platform. It is designed by connecting parts of physical objects to a computer, and remedies the defect that a computer simulation is divorced from a real environment absolutely. The main components of the platform and its functions, as well as simulation flows, are introduced. The feasibility and validity are verified through a simulation experiment. The experimental results show that the platform has significance for improving the quality of the parafoil fixed-point airdrop system, shortening the development cycle and saving cost. [ABSTRACT FROM AUTHOR]

In this paper, we study homogeneous backgrounds of type IIB supergravity where the underlying geometry is that of a symmetric space. We determine which ten-dimensional Lorentzian symmetric spaces (up to local isometry) admit such backgrounds, and in about two-thirds of the cases we determine fully their moduli space. [ABSTRACT FROM AUTHOR]

Clouds in the tropics can organize the circulation on planetary scales and profoundly impact long range seasonal forecasting and climate on the entire globe, yet contemporary operational computer models are often deficient in representing these phenomena. On the other hand, contemporary observations reveal remarkably complex coherent waves and vortices in the tropics interacting across a bewildering range of scales from kilometers to ten thousand kilometers. This paper reviews the interdisciplinary contributions over the last decade through the modus operandi of applied mathematics to these important scientific problems. Novel physical phenomena, new multiscale equations, novel PDEs, and numerical algorithms are presented here with the goal of attracting mathematicians and physicists to this exciting research area. [ABSTRACT FROM AUTHOR]

This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 < q < 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a variable-coefficient modified Korteweg-de Vries (vc-mKdV) equation is considered. Bilinear forms are presented to explicitly construct periodic wave solutions based on a multidimensional Riemann theta function, then the one and two periodic wave solutions are presented, and it is also shown that the soliton solutions can be reduced from the periodic wave solutions. [ABSTRACT FROM AUTHOR]

In this paper, we give sufficient conditions for the existence of C² robust heterodimensional tangency, and present a non-empty open set in Diff²(M) with dimM ≥ 3 each element of which has a non-degenerate heterodimensional tangency on a C² robust heterodimensional cycle. [ABSTRACT FROM AUTHOR]

In this article, we use the fractional complex transformation to convert nonlinear partial fractional differential equations to nonlinear ordinary differential equations. We use the improved (G'=G)-expansion function method to calculate the exact solutions to the time- and space-fractional derivative foam drainage equation and the time- and space-fractional derivative nonlinear KdV equation. This method is efficient and powerful for solving wide classes of nonlinear evolution fractional order equations. [ABSTRACT FROM AUTHOR]

We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws (CLs) for the nonlinear integrable coupling of the lattice hierarchy. As an explicit application of the method proposed in the paper, the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented. [ABSTRACT FROM AUTHOR]

Observing the way a watering hose is wrapped on a rotating cylinder, a catenary shape is detected for the suspended portion of the hose. We calculate the angle a the tangent to the curve at the highest point of the suspended portion makes with the horizontal. By means of this quantity, the length of the suspended and dragged portions of the hose and the work done to retrieve the hose can be found. The problem may be solved by means of Newtonian mechanics, adopting elementary notions of calculus and trigonometry. [ABSTRACT FROM AUTHOR]

We specify for a general correlation scenario a particular type of local quasi hidden variable (LqHV) model (Loubenets 2012 J. Math. Phys. 53 022201)--a deterministic LqHV model, where all joint probability distributions of a correlation scenario are simulated via a single measure space with a normalized bounded real-valued measure not being necessarily positive and random variables, each depending only on a setting of the corresponding measurement at the corresponding site. We prove that an arbitrary multipartite correlation scenario admits a deterministic LqHV model if and only if all its joint probability distributions satisfy the consistency condition, constituting the general nonsignaling condition formulated in Loubenets (2008 J. Phys. A: Math. Theor. 41 445303). This mathematical result specifies a new probability model that has a measure-theoretic structure resembling the structure of the classical probability model but incorporates the latter only as a particular case. The local version of this quasi-classical probability model covers the probabilistic description of each nonsignaling correlation scenario, in particular, each correlation scenario on a multipartite quantum state. [ABSTRACT FROM AUTHOR]

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain--when the region within the heterojunctions is described by a non-Hermitian PT -symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated and plotted as a function of the energy. It is observed that at least two of the characteristic features of non-Hermitian PT - symmetric systems--namely left/right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed. [ABSTRACT FROM AUTHOR]

The numerical analytic continuation of a function f (z) = f (x + iy) on a strip is discussed in this paper. Data are only given approximately on the real axis. A mollification method based on expanded Hermite functions has been introduced to deal with the ill-posedness of the problem. We have shown that the mollification parameter can be chosen by a discrepancy principle and a corresponding error estimate has also been obtained. Numerical tests are given to show the effectiveness of the method. (Some figures may appear in colour only in the online journal) [ABSTRACT FROM AUTHOR]

We present a scheme for playing quantum repeated 2 &CROSS; 2 games based on Marinatto andWeber's approach to quantum games. As a potential application, we study the twice repeated Prisoner's Dilemma game. We show that results not available in the classical game can be obtained when the game is played in the quantum way. Before we present our idea, we comment on the previous scheme of playing quantum repeated games proposed by Iqbal and Toor. We point out the drawbacks that make their results unacceptable [ABSTRACT FROM AUTHOR]

We extend the results obtained in Sarlet and Prince (2010 J. Phys. A: Math. Theor. 43 445204) about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system [ABSTRACT FROM AUTHOR]

The problem of building coherent states from non-normalizable fiducial states is considered. We propose a way of constructing such coherent states by regularizing the divergence of the fiducial state norm. Then we successfully apply the formalism to particular cases involving systems with a continuous spectrum: coherent states for the free particle and for the inverted oscillator (p2 - x2) are explicitly provided. Similar ideas can be used for other systems having non-normalizable fiducial states [ABSTRACT FROM AUTHOR]

A connection between the finite ultradiscrete Toda lattice and the box-ball system is extended to the case where each box has its own capacity and a carrier has a capacity parameter depending on time. In order to consider this connection, new carrier rules 'size limit for solitons' and 'recovery of balls', and a concept 'expansion map' are introduced. A particular solution to the extended system of a special case is also presented. [ABSTRACT FROM AUTHOR]

The series solution of the cold emission tunneling problem is shown to be absolutely convergent for all distances between the emitter and the electron. The tunneling probability is expressed in terms of coefficients of this series, and its behavior is established in an important case. [ABSTRACT FROM AUTHOR]

A spherical Radon transform that averages a function over all spheres centered on a given sphere is related to not only pure but also applied mathematics topics. Especially, the problem of inverting this spherical Radon transform arising in photoacoustic tomography and sonar has been studied in many articles. We provide two series formulas for inversion: one does not require the compact support of the source function unlike most inversion formulas and the other is singular value decomposition type, i.e., the series formula is based on the complete orthogonal system. Last, we discuss its continuity. [ABSTRACT FROM AUTHOR]

The two-dimensional wake produced by a time-periodic pitching foil with the asymmetric geometry is investigated in the present work. Through numerically solving nonlinear Navier–Stokes equations, we discuss the relationship among the kinematics of the prescribed motion, the asymmetric parameter K ranged as 1 ≤ K ≤ 1, and the types of the wakes including the mP+nS wake, the Bénard–von Kármán wake, the reverse Bénard–von Kármán wake, and the deviated wake. Compared with previous studies, we reveal that the asymmetric geometry of a pitching foil directly affects the foil’s wake structures. The numerical results show that the reverse Bénard–von Kármán wake is easily deviated at K < 0, while the symmetry-breaking of the reverse Bénard–von Kármán wake is delayed at K > 0. Through the vortex dynamic method, we understand that the initial velocity of the vortex affected by the foil’s asymmetry plays a key role in the deviation of the reverse Bénard–von Kármán wake. Moreover, we provide a theoretical model to predict the wake deviation of the asymmetric foil. [ABSTRACT FROM AUTHOR]

In this paper we derive and compare numerical sequences obtained by adapted polynomials such as HOMFLYPT, Jones and Alexander-Conway for the topological cascade of vortex torus knots and links that progressively untie by a single reconnection event at a time. Two cases are considered: the alternate sequence of knots and co-oriented links (with positive crossings) and the sequence of two-component links with oppositely oriented components (negative crossings). New recurrence equations are derived and sequences of numerical values are computed. In all cases the adapted HOMFLYPT polynomial proves to be the best quantifier for the topological cascade of torus knots and links. [ABSTRACT FROM AUTHOR]

In this paper, we treat quantum walks in a two-dimensional lattice with cutting edges along a straight boundary introduced by Asboth and Edge (2015 Phys. Rev. A 91 022324) in order to study one-dimensional edge states originating from topological phases of matter and to obtain collateral evidence of how a quantum walker reacts to the boundary. Firstly, we connect this model to the CMV matrix, which provides a 5-term recursion relation of the Laurent polynomial associated with spectral measure on the unit circle. Secondly, we explicitly derive the spectra of bulk and edge states of the quantum walk with the boundary using spectral analysis of the CMV matrix. Thirdly, while topological numbers of the model studied so far are well-defined only when gaps in the bulk spectrum exist, we find a new topological number defined only when there are no gaps in the bulk spectrum. We confirm that the existence of the spectrum for edge states derived from the CMV matrix is consistent with the prediction from a bulk-edge correspondence using topological numbers calculated in the cases where gaps in the bulk spectrum do or do not exist. Finally, we show how the edge states contribute to the asymptotic behavior of the quantum walk through limit theorems of the finding probability. Conversely, we also propose a differential equation using this limit distribution whose solution is the underlying edge state. [ABSTRACT FROM AUTHOR]

The paper is concerned with the number of open gaps in spectra of periodic quantum graphs. The well-known conjecture by Bethe and Sommerfeld (1933) says that the number of open spectral gaps for a system periodic in more than one direction is finite. To date, its validity is established for numerous systems, however, it is known that quantum graphs do not comply with this law as their spectra have typically infinitely many gaps, or no gaps at all. These facts gave rise to the question about the existence of quantum graphs with the ‘Bethe–Sommerfeld property’, that is, featuring a nonzero finite number of gaps in the spectrum. In this paper we prove that the said property is impossible for graphs with vertex couplings which are either scale-invariant or associated to scale-invariant ones in a particular way. On the other hand, we demonstrate that quantum graphs with a finite number of open gaps do indeed exist. We illustrate this phenomenon on an example of a rectangular lattice with a δ coupling at the vertices and a suitable irrational ratio of the edges. Our result allows one to find explicitly a quantum graph with any prescribed exact number of gaps, which is the first such example to date. [ABSTRACT FROM AUTHOR]

We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a nonautonomous forcing. We prove the existence of a unique global attracting random periodic orbit and a stationary periodic measure. We use the stationary periodic measure to define an indicator for the stochastic resonance. [ABSTRACT FROM AUTHOR]

We consider implications of dynamical Borel–Cantelli lemmas for rates of growth of Birkhoff sums of non-integrable observables , k  >  0, on ergodic dynamical systems where . Some general results are given as well as some more concrete examples involving non-uniformly expanding maps, intermittent type maps as well as uniformly hyperbolic systems. [ABSTRACT FROM AUTHOR]

The availability of big data in materials science offers new routes for analyzing materials properties and functions and achieving scientific understanding. Finding structure in these data that is not directly visible by standard tools and exploitation of the scientific information requires new and dedicated methodology based on approaches from statistical learning, compressed sensing, and other recent methods from applied mathematics, computer science, statistics, signal processing, and information science. In this paper, we explain and demonstrate a compressed-sensing based methodology for feature selection, specifically for discovering physical descriptors, i.e., physical parameters that describe the material and its properties of interest, and associated equations that explicitly and quantitatively describe those relevant properties. As showcase application and proof of concept, we describe how to build a physical model for the quantitative prediction of the crystal structure of binary compound semiconductors. [ABSTRACT FROM AUTHOR]

Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase–space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

We consider a family of Pomeau–Manneville type interval maps , parametrized by , with the unique absolutely continuous invariant probability measures , and rate of correlations decay . We show that despite the absence of a spectral gap for all and despite nonsummable correlations for , the map is continuously differentiable for for q sufficiently large. [ABSTRACT FROM AUTHOR]

Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales, there is often need to resort to effective mathematical models such as stochastic differential equations (SDEs). In particular, here we consider effective SDEs describing the behavior of systems in the limits when natural time scales become very small. In the presence of multiplicative noise (i.e. noise whose intensity depends upon the system’s state), an additional drift term, called noise-induced drift or effective drift, appears. The nature of this noise-induced drift has been recently the subject of a growing number of theoretical and experimental studies. Here, we provide an extensive review of the state of the art in this field. After an introduction, we discuss a minimal model of how multiplicative noise affects the evolution of a system. Next, we consider several case studies with a focus on recent experiments: the Brownian motion of a microscopic particle in thermal equilibrium with a heat bath in the presence of a diffusion gradient; the limiting behavior of a system driven by a colored noise modulated by a multiplicative feedback; and the behavior of an autonomous agent subject to sensorial delay in a noisy environment. This allows us to present the experimental results, as well as mathematical methods and numerical techniques, that can be employed to study a wide range of systems. At the end we give an application-oriented overview of future projects involving noise-induced drifts, including both theory and experiment. [ABSTRACT FROM AUTHOR]

The scattering of electrons off nuclei is one of the best methods of probing nuclear structure. In this paper we focus on electron scattering off nuclei with spin and isospin zero within the Skyrme model. We consider two distinct methods and simplify our calculations by use of the Born approximation. The first method is to calculate the form factor of the spherically averaged Skyrmion charge density; the second uses the Patterson function to calculate the scattering intensity off randomly oriented Skyrmions, and spherically averages at the end. We compare our findings with experimental scattering data. We also find approximate analytical formulae for the first zero and first stationary point of a form factor. [ABSTRACT FROM AUTHOR]

Random matrix theory (RMT) has found applications throughout physics and applied mathematics, in subject areas as diverse as communications networks, population dynamics, neuroscience, and models of the banking system. Many of these analyses exploit elegant analytical results, particularly the circular law and its extensions. In order to apply these results, assumptions must be made about the distribution of matrix elements. Here we demonstrate that the choice of matrix distribution is crucial. In particular, adopting an unrealistic matrix distribution for the sake of analytical tractability is liable to lead to misleading conclusions. We focus on the application of RMT to the long-standing, and at times fractious, ‘diversity-stability debate’, which is concerned with establishing whether large complex systems are likely to be stable. Early work (and subsequent elaborations) brought RMT to bear on the debate by modelling the entries of a system’s Jacobian matrix as independent and identically distributed (i.i.d.) random variables. These analyses were successful in yielding general results that were not tied to any specific system, but relied upon a restrictive i.i.d. assumption. Other studies took an opposing approach, seeking to elucidate general principles of stability through the analysis of specific systems. Here we develop a statistical framework that reconciles these two contrasting approaches. We use a range of illustrative dynamical systems examples to demonstrate that: (i) stability probability cannot be summarily deduced from any single property of the system (e.g. its diversity); and (ii) our assessment of stability depends on adequately capturing the details of the systems analysed. Failing to condition on the structure of dynamical systems will skew our analysis and can, even for very small systems, result in an unnecessarily pessimistic diagnosis of their stability. [ABSTRACT FROM AUTHOR]

We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomization approach, which consists in treating the free parameters in the mapping as functions of the independent variable, applied to a mapping complemented with terms that are absent in the original mapping but which do not change the singularity structure. We shall show, on a host of examples including the well-known mapping of Hietarinta–Viallet, that our approach offers a way to compute the algebraic entropy for these mappings exactly, thereby allowing one to distinguish between the integrable and non-integrable cases even when both have confined singularities. [ABSTRACT FROM AUTHOR]

A method of the formal diagonalization of the discrete linear operator with a parameter is studied. In the case when the operator provides a Lax operator for a nonlinear quad system the formal diagonalization method allows one to describe effectively conservation laws and generalized symmetries for this system. Asymptotic representation of the Lax operators eigenfunctions are constructed and infinite series of conservation laws are described for the quad system connected with affine Lie algebra, for the modified discrete Boussinesq system and for the discrete Tzitzeica equation. For a newly found multiquadratic discrete model conservation laws and several generalized symmetries are presented. [ABSTRACT FROM AUTHOR]

We demonstrate the occurrence of permanent spikes using the Lemaître–Tolman–Bondi models, chosen because the solutions are exact and can be analyzed by qualitative dynamical systems methods. Three examples are given and illustrated numerically. The third example demonstrates that spikes can form directly in the matter density, as opposed to indirectly in previous studies of spikes in the Kasner regime. Spikes provide an alternative general relativistic mechanism for generating exceptionally large structures observed in the Universe. [ABSTRACT FROM AUTHOR]

Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within a special class of differential dynamical systems. The general properties of connecting curves are derived and selection rules stated. Examples are presented to illustrate these properties for dynamical systems of dimension n = 3, 4, 5. [ABSTRACT FROM AUTHOR]