Application of fractional order theory of magneto-thermoelasticity to an infinite perfect conducting body with a cylindrical cavity

A fractional model of the equations of generalized magneto-thermoelasticity for a perfect conducting isotropic thermoelastic media is given. This model is applied to solve a problem of an infinite body with a cylindrical cavity in the presence of an axial uniform magnetic field. The boundary of the cavity is subjected to a combination of thermal and mechanical shock acting for a finite period of time. The solution is obtained by a direct approach by using the thermoelastic potential function. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Numerical computations for the temperature, the displacement and the stress distributions as well as for the induced magnetic and electric fields are carried out and represented graphically. Comparisons are made with the results predicted by the generalizations, Lord–Shulman theory, and Green–Lindsay theory as well as to the coupled theory.

     

The Equivalence of the Taut String Algorithm and BV-Regularization

It is known that discrete BV-regularization and the taut string algorithm are equivalent. In this paper we extend this result to the continuous case. First we derive necessary equations for the solution of both BV-regularization and the taut string algorithm by computing suitable Gateaux derivatives. The equivalence then follows from a uniqueness result. Markus Grasmair received his MSc degree in Mathematics in 2003 and is now writing his PhD-thesis at the University of Innsbruck under supervision of Prof. Otmar Scherzer. His main research interests lie in the field of variational calculus, in particular with applications to image processing.     

Meadows and the equational specification of division

The rational, real and complex numbers with their standard operations, including division, are partial algebras specified by the axiomatic concept of a field. Since the class of fields cannot be defined by equations, the theory of equational specifications of data types cannot use field theory in applications to number systems based upon rational, real and complex numbers. We study a new axiomatic concept for number systems with division that uses only equations: a meadow is a commutative ring with a total inverse operator satisfying two equations which imply 0^?1=0. All fields and products of fields can be viewed as meadows. After reviewing alternate axioms for inverse, we start the development of a theory of meadows. We give a general representation theorem for meadows and find, as a corollary, that the conditional equational theory of meadows coincides with the conditional equational theory of zero totalized fields. We also prove representation results for meadows of finite characteristic.     

Twistor structures and boost-invariant solutions to field equations

We start with a brief overview of a non-Lagrangian approach to field theory based on a generalization of the Kerr-Penrose theorem and algebraic twistor equations. Explicit algorithms for obtaining the set of fundamental (Maxwell, SL(2,?)-Yang-Mills, spinor Weyl and curvature) fields associated with every solution of the basic system of algebraic equations are presented. The notion of a boost-invariant solution is introduced, and the unique axially-symmetric and boost-invariant solution which can be generated by twistor functions is obtained, together with the associated fields. It is found that this solution possesses a wide variety of point-, string- and membrane-like singularities exhibiting nontrivial dynamics and transmutations.     

Motion in bimetric type theories of gravity

The problem of motion of different test particles, charged and spinning objects with a constant spin tensor in different versions of the bimetric theory of gravity is considered by deriving their corresponding path and path deviation equations using a modified Bazanski Lagrangian. Such a Lagrangian, as in the framework of Riemannian geometry, has a capability to obtain path and path deviations of any object simultaneously. This method enables us to derive the path and path deviation equations of different objects orbiting in very strong gravitational fields.     

Singularity-free dynamic equations of vehicle–manipulator systems

In this paper we derive the singularity-free dynamic equations of vehicle–manipulator systems using a minimal representation. These systems are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of the vehicle in general is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of vehicle–manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. We also show how to calculate the inertia and Coriolis matrices and present these for several different vehicle–manipulator systems in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and should reach a wider audience, including engineers and programmers.     

Solving Index Form Equations in Fields of Degree 9 with Cubic Subfields

We describe an efficient algorithm for solving index form equations in number fields of degree 9 which are composites of cubic fields with coprime discriminants. We develop the algorithm in detail for the case of complex cubic fields, but the main steps of the procedure are also applicable for other cases. Our most important tool is the main theorem of a recent paper of Gaál (1998a). In view of this result the index form equation in the ninth degree field implies relative index form equations over the subfields. In our case these equations are cubic relative Thue equations over cubic fields. The main purpose of the paper is to show that this approach is much more efficient than the direct method, which consists of reducing the index form equation to unit equations over the normal closure of the original field. At the end of the paper we describe our computational experience. Many ideas of the paper can be applied to develop fast algorithms for solving index form equations in other types of higher degree fields which are composites of subfields.     

Gravitational fields as generalized string models

We show that Einstein’s main equations for stationary axisymmetric fields in vacuum are equivalent to the equations of motion for bosonic strings moving in a special nonflat background. This new representation is based on the analysis of generalized harmonic maps in which the metric of the target space explicitly depends on the parametrization of the base space. It is shown that this representation is valid for any gravitational field which possesses two commuting Killing vector fields. We introduce the concept of dimensional extension which allows us to consider this type of gravitational fields as strings embedded in D-dimensional nonflat backgrounds, even in the limiting case where the Killing vector fields are hypersurface-orthogonal.     

Helicoseir as Shape of a Rotating String (II): 3D Theory and Simulation Using ANCF

This paper is the second one devoted to studying the dynamical behavior of a rotating uniform string with one fixed top point. Two-dimensional shapes of relative equilibrium for a string were analyzed in our paper [3] both analytically and numerically and found to be instable. This fact disagrees with the experimental appearance of this so-called helicoseir problem because one can easily demonstrate that its stable motion is possible. In this paper, spatial nonlinear equations of motion are derived and shown that a 2D equilibrium equation is one of their partial cases. The equations are, however, very complicated that is why we decided at first to analyze the motion numerically by a finite element approach called the absolute nodal coordinate formulation (ANCF). We developed a new 12-dof element of a thin string based on the Euler-Bernoulli theory. The simulation shows that the undamped spatial motion of the helicoseir is stable and looks like self-excited oscillations near the flat instable configurations that were obtained previously. This stability is destroyed when external damping is added to the system. Some examples of bifurcation instability fore spatial motion are presented; they satisfy the bifurcation diagram obtained in the previous work. Unfortunately, numerical simulation cannot give answers to some interesting questions, e.g. dependence of parameters of the self-excited oscillations on the angular velocity of rotation. Thus, further analytical research of this problem is desirable.     

Image Synthesis for Inverse Obstacle Scattering Using the Eigenfunction Expansion Theorem

In recent years several new inverse scattering techniques have been developed that determine the boundary of an unknown obstacle by reconstructing the surrounding scattered field. In the case of sound soft obstacles, the boundary is usually found as the minimum contour of the total field. In this note we derive a different approach for imaging the boundary from the reconstructed fields based on a generalization of the eigenfunction expansion theorem. The aim of this alternative approach is the construction of higher contrast images than is currently obtained with the minimum contour approach.     

Derivation of a parallel string matching algorithm

We derive an efficient parallel algorithm to find all occurrences of a pattern string in a subject string in O(logn) time, where n is the length of the subject string. The number of processors employed is of the order of the product of the two string lengths. The theory of powerlists [J. Kornerup, PhD Thesis, 1997; J. Misra, ACM Trans. Programming Languages Systems 16 (6) (1994) 1737-1740] is central to the development of the algorithm and its algebraic manipulations.     

Emergent universe supported by chiral cosmological fields in 5D Einstein-Gauss-Bonnet gravity

We propose application of the chiral cosmological model (CCM) for the Einstein-Gauss-Bonnet (EGB) 5D theory of gravitation with the aim of finding new models of the Emergent Universe (EmU) scenario. We analyze an EmU supported by two chiral cosmological fields for a spatially flat universe, and with three chiral fields when investigating open and closed universes. To prove the validity of the spatially flat EmU scenario, we fix the scale factor and find an exact solution by decomposing the 5D EGB equations and solving the chiral field dynamics equation. The EGB equations are decomposed in such a way that the first chiral field is responsible for the Einstein part of the model while the second field, together with kinetic interaction term, is connected with the Gauss-Bonnet part of the theory. We proved that both fields are phantom in this decomposition and that the model has a solution if the kinetic interaction factor between the fields is constant. The solution is presented in terms of cosmic time. In the case of open and closed universes, we introduce the third chiral field (a canonical one for a closed universe and a phantom one for an open universe) which is responsible for the EGB and curvature parts. The solution of the third field equation is obtained in quadratures. Thus we have prove that the CCM is able to support the EmU scenario in 5D EGB gravity for spatially flat, open and closed universes.     

A new multiscale formulation for the electromechanical behavior of nanomaterials

We present a new multiscale, finite deformation, electromechanical formulation to capture the response of surface-dominated nanomaterials to externally applied electric fields. To do so, we develop and discretize a total energy that combines both mechanical and electrostatic terms, where the mechanical potential energy is derived from any standard interatomic atomistic potential, and where the electrostatic potential energy is derived using a Gaussian-dipole approach. By utilizing Cauchy–Born kinematics, we derive both the bulk and surface electrostatic Piola–Kirchhoff stresses that are required to evaluate the resulting electromechanical finite element equilibrium equations, where the surface Piola–Kirchhoff stress enables us to capture the non-bulk electric field-driven polarization of atoms near the surfaces of nanomaterials. Because we minimize a total energy, the present formulation has distinct advantages as compared to previous approaches, where in particular, only one governing equation is required to be solved. This is in contrast to previous approaches which require either the staggered or monolithic solution of both the mechanical and electrostatic equations, along with coupling terms that link the two domains. The present approach thus leads to a significant reduction in computational expense both in terms of fewer equations to solve and also in eliminating the need to remesh either the mechanical or electrostatic domains due to being based on a total Lagrangian formulation. Though the approach can apply to three-dimensional cases, we concentrate in this paper on the one-dimensional case. We first derive the necessary formulas, then give numerical examples to validate the proposed approach in comparison to fully atomistic electromechanical calculations.     

Einstein equations with fluctuating volume

We develop a simple model for a study of classical fields in the background of a fluctuating spacetime volume. It is applied for a formulation of the Einstein equations with a perfect-fluid source. We investigate the particular case of a Friedmann-Lemaître-Robertson-Walker cosmology and show that the resulting field equations can lead to solutions which avoid the initial Big Bang singularity. By interpreting the fluctuations as a result of the presence of quantum spacetime, we conclude that classical singularities can be avoided even within a semiclassical model that includes quantum effects in a very simple manner.     

Dynamic analysis of neural encoding by point process adaptive filtering

Neural receptive fields are dynamic in that with experience, neurons change their spiking responses to relevant stimuli. To understand how neural systems adapt their representations of biological information, analyses of receptive field plasticity from experimental measurements are crucial. Adaptive signal processing, the well-established engineering discipline for characterizing the temporal evolution of system parameters, suggests a framework for studying the plasticity of receptive fields. We use the Bayes' rule Chapman-Kolmogorov paradigm with a linear state equation and point process observation models to derive adaptive filters appropriate for estimation from neural spike trains. We derive point process filter analogues of the Kalman filter, recursive least squares, and steepest-descent algorithms and describe the properties of these new filters. We illustrate our algorithms in two simulated data examples. The first is a study of slow and rapid evolution of spatial receptive fields in hippocampal neurons. The second is an adaptive decoding study in which a signal is decoded from ensemble neural spiking activity as the receptive fields of the neurons in the ensemble evolve. Our results provide a paradigm for adaptive estimation for point process observations and suggest a practical approach for constructing filtering algorithms to track neural receptive field dynamics on a millisecond timescale.     

Variational Multi-Valued Velocity Field Estimation for Transparent Sequences

Motion estimation in sequences with transparencies is an important problem in robotics and medical imaging applications. In this work we propose a variational approach for estimating multi-valued velocity fields in transparent sequences. Starting from existing local motion estimators, we derive a variational model for integrating in space and time such a local information in order to obtain a robust estimation of the multi-valued velocity field. With this approach, we can indeed estimate multi-valued velocity fields which are not necessarily piecewise constant on a layer—each layer can evolve according to a non-parametric optical flow. We show how our approach outperforms existing methods; and we illustrate its capabilities on challenging experiments on both synthetic and real sequences.     

An approach to automatic generation of dynamic equations of elastic joint manipulators in symbolic language

This paper describes an approach for automatic generation of the equations of motion of elastic joint manipulators in symbolic language. It is based on a vector-parametrization of the Lie groupSO(3) and uses the Lagrange's formalism to derive the dynamical equations, the final forms of which are like the equations generated by a recursive Newton-Eulerian algorithm. These characteristics together increase the computational efficiency of the algorithm and give a very good insight into the dynamical structure of the system. In addition to this, the inertia matrix is explicitly given in the final equations, which is very important for the applicability of a mathematical model in different fields of control and simulation. The suggested algorithm is therefore quite appropriate for the purposes of robot modeling, identification as well as for the applications in real time simulations and control.     

String stability of infinite-dimension stochastic interconnected large-scale systems with time-varying delay

The exponential string stability for a class of nonlinear interconnected large-scale systems with time-varying delay is analysed by using the box theory and constructing a vector Lyapunov function. Under the assumption that the time delay is bounded and continuous, a criterion for exponential string stability of the systems is obtained by analysing the stability of differential inequalities with time-varying delay. The large-scale system is exponential string stable when the conditions associating with the coefficient matrices of the system and the solutions of the Lyapunov equations, interconnected with the system, are satisfied. Since it is independent of the delays and simplifies the calculation, the criterion is easy to apply.