764,487 research outputs found
Advances in surface EMG signal simulation with analytical and numerical descriptions of the volume conductor
Surface electromyographic (EMG) signal modeling is important for signal interpretation, testing of processing algorithms, detection system design, and didactic purposes. Various surface EMG signal models have been proposed in the literature. In this study we focus on 1) the proposal of a method for modeling surface EMG signals by either analytical or numerical descriptions of the volume conductor for space-invariant systems, and 2) the development of advanced models of the volume conductor by numerical approaches, accurately describing not only the volume conductor geometry, as mainly done in the past, but also the conductivity tensor of the muscle tissue. For volume conductors that are space-invariant in the direction of source propagation, the surface potentials generated by any source can be computed by one-dimensional convolutions, once the volume conductor transfer function is derived (analytically or numerically). Conversely, more complex volume conductors require a complete numerical approach. In a numerical approach, the conductivity tensor of the muscle tissue should be matched with the fiber orientation. In some cases (e.g., multi-pinnate muscles) accurate description of the conductivity tensor may be very complex. A method for relating the conductivity tensor of the muscle tissue, to be used in a numerical approach, to the curve describing the muscle fibers is presented and applied to representatively investigate a bi-pinnate muscle with rectilinear and curvilinear fibers. The study thus propose an approach for surface EMG signal simulation in space invariant systems as well as new models of the volume conductor using numerical methods
Evolutionary Algorithms for Community Detection in Continental-Scale High-Voltage Transmission Grids
Symmetry is a key concept in the study of power systems, not only because the admittance and Jacobian matrices used in power flow analysis are symmetrical, but because some previous studies have shown that in some real-world power grids there are complex symmetries. In order to investigate the topological characteristics of power grids, this paper proposes the use of evolutionary algorithms for community detection using modularity density measures on networks representing supergrids in order to discover densely connected structures. Two evolutionary approaches (generational genetic algorithm, GGA+, and modularity and improved genetic algorithm, MIGA) were applied. The results obtained in two large networks representing supergrids (European grid and North American grid) provide insights on both the structure of the supergrid and the topological differences between different regions. Numerical and graphical results show how these evolutionary approaches clearly outperform to the well-known Louvain modularity method. In particular, the average value of modularity obtained by GGA+ in the European grid was 0.815, while an average of 0.827 was reached in the North American grid. These results outperform those obtained by MIGA and Louvain methods (0.801 and 0.766 in the European grid and 0.813 and 0.798 in the North American grid, respectively)
Non-Equilibrium Quantum Dissipation
Dissipative processes in non-equilibrium many-body systems are fundamentally
different than their equilibrium counterparts. Such processes are of great
importance for the understanding of relaxation in single molecule devices. As a
detailed case study, we investigate here a generic spin-fermion model, where a
two-level system couples to two metallic leads with different chemical
potentials. We present results for the spin relaxation rate in the nonadiabatic
limit for an arbitrary coupling to the leads, using both analytical and exact
numerical methods. The non-equilibrium dynamics is reflected by an exponential
relaxation at long times and via complex phase shifts, leading in some cases to
an "anti-orthogonality" effect. In the limit of strong system-lead coupling at
zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with
{\it voltage difference} activation. This is analogous to the equilibrium
spin-boson model, where at strong coupling and high temperatures the spin
excitation rate manifests temperature activated Gaussian behavior. We find that
there is no simple linear relationship between the role of the temperature in
the bosonic system and a voltage drop in a non-equilibrium electronic case. The
two models also differ by the orthogonality-catastrophe factor existing in a
fermionic system, which modifies the resulting lineshapes. Implications for
current characteristics are discussed. We demonstrate the violation of
pair-wise Coulomb gas behavior for strong coupling to the leads. The results
presented in this paper form the basis of an exact, non-perturbative
description of steady-state quantum dissipative systems
A numerical approach for the bifurcation analysis of nonsmooth delay equations
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record .Mathematical models based on nonsmooth dynamical systems with delay are widely used to understand
complex phenomena, specially in biology, mechanics and control. Due to the infinite-dimensional nature
of dynamical systems with delay, analytical studies of such models are difficult and can provide in general only limited results, in particular when some kind of nonsmooth phenomenon is involved, such as
impacts, switches, impulses, etc. Consequently, numerical approximations are fundamental to gain both
a quantitative and qualitative insight into the model dynamics, for instance via numerical continuation
techniques. Due to the complex analytical framework and numerical challenges related to delayed nonsmooth systems, there exists so far no dedicated software package to carry out numerical continuation for
such type of models. In the present work, we propose an approximation scheme for nonsmooth dynamical
systems with delay that allows a numerical bifurcation analysis via continuation (path-following) methods, using existing numerical packages, such as COCO (Dankowicz and Schilder). The approximation
scheme is based on the well-known fact that delay differential equations can be approximated via large
systems of ODEs. The effectiveness of the proposed numerical scheme is tested on a case study given by
a periodically forced impact oscillator driven by a time-delayed feedback controller.Engineering and Physical Sciences Research Council (EPSRC
Computational Elements for High-fidelity Aerodynamic Analysis and Design Optimisation
The study reviews the role of computational fluid dynamics (CFD) in aerodynamic shape optimisation, and discusses some of the efficient design methodologies. The article in the first part, numerical schemes required for high-fidelity aerodynamic flow analysis are discussed. To accurately resolve high-speed flow physics, high-fidelity shock-stable schemes as well as intelligent limiting strategy mimicking multi-dimensional flow physics are essential. Exploiting these numerical schemes, some applications for 3-D internal/external flow analyses were carried out with various grid systems which enable the treatment of complex geometries. In the second part, depending on the number of design variables and the way to obtain sensitivities or design points, several global and local optimisation methods for aerodynamic shape optimisation are discussed. To avoid the problem that solutions of gradient-based optimisation method (GBOM), are often trapped in local optimum, remedy by combining GBOM with global optimum strategy, such as surrogate models and genetic algorithm (GA) has been examined. As an efficient grid deformation tool, grid deformation technique using NURBS function is discussed. Lastly, some 3-D examples for aerodynamic shape optimisation works based on the proposed design methodology are presented.Defence Science Journal, 2010, 60(6), pp.628-638, DOI:http://dx.doi.org/10.14429/dsj.60.58
Optimal subsets in the stability regions of multistep methods
In this work we study the stability regions of linear multistep or
multiderivative multistep methods for initial-value problems by using
techniques that are straightforward to implement in modern computer algebra
systems. In many applications, one is interested in (i) checking whether a
given subset of the complex plane (e.g. a sector, disk, or parabola) is
included in the stability region of the numerical method, (ii) finding the
largest subset of a certain shape contained in the stability region of a given
method, or (iii) finding the numerical method in a parametric family of
multistep methods whose stability region contains the largest subset of a given
shape. First we describe a simple procedure to exactly calculate the stability
angle in the definition of -stability. As an illustration,
we consider two finite families of implicit multistep methods: we exactly
compute the stability angles for the -step BDF methods () and
for the -step second-derivative multistep methods of Enright (). Next we determine the exact value of the stability radius in the BDF
family for each , that is, the radius of the largest disk in the
left half of the complex plane, symmetric with respect to the real axis,
touching the imaginary axis and lying in the stability region of the
corresponding method. Finally, we demonstrate how some Schur--Cohn-type
theorems of recursive nature and not relying on the RLC method can be used to
exactly solve some optimization problems within infinite parametric families of
multistep methods. As an example, we choose a two-parameter family of
implicit-explicit (IMEX) methods: we identify the unique method having the
largest stability angle in the family, then we find the unique method in the
same family whose stability region contains the largest parabola.Comment: 38 pages, 20 figure
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PATTERN FORMATION AND PHASE TRANSITION OF CONNECTIVITY IN TWO DIMENSIONS
This dissertation is devoted to the study and analysis of different types of emergent behavior in physical systems. Emergence is a phenomenon that has fascinated researchers from various fields of science and engineering. From the emergence of global pandemics to the formation of reaction-diffusion patterns, the main feature that connects all these diverse systems is the appearance of a complex global structure as a result of collective interactions of simple underlying components. This dissertation will focus on two types of emergence in physical systems: emergence of long-range connectivity in networks and emergence and analysis of complex patterns.
The most prominent theory which deals with the emergence of long-range connectivity is the percolation theory. This dissertation employs many concepts from the percolation theory to study connectivity transitions in various systems. Ordinary percolation theory is founded upon two main assumptions, namely locality and independence of the underlying components. In Chapters 2 and 3, we relax these assumptions in different manners and show that relaxing these assumptions leads to irregular behaviors such as appearance of different universality classes and, in some instances, violation of universality. Chapter 2 deals with relaxing the assumption of locality of interactions. In this Chapter, we define a hierarchy of various measures of robust connectivity. We study the phase transition of these robustness metrics as a function of site/bond occupation/removal probability on the square lattice. Furthermore, we perform extensive numerical analysis and extract these robustness metrics\u27 critical thresholds and critical behaviors. We show that some of these robustness metrics do not fall under the regular percolation universality class. The extensive numerical results in this work can serve as a foundation for any researcher who aims to design/study various degrees of connectivity in networks.
In Chapter 3, we study the non-equilibrium phase transition of long-range connectivity in a multi-particle interacting system on the square lattice. The interactions between different particles translate to relaxing the assumption of independence in the percolation theory. Using extensive numerical simulations, we show that the phase transition observed in this system violates the regular concept of universality. However, it conforms well with the concept of weak-universality recently introduced in the literature. We observe that by varying inter-particle interaction strength in our model, one can control the critical behavior of this phase transition. These observations could be pivotal in studying phase transitions and universality classes.
Chapter 4 focuses on the analysis of reaction-diffusion patterns. We utilize a multitude of machine learning algorithms to analyze reaction-diffusion patterns. In particular, we address two main problems using these techniques, namely, pattern regression and pattern classification. Given an observed instance of a pattern with a known generative function, in the pattern regression task, we aim to predict the specific set of reaction-diffusion parameters (i.e. diffusion constant) which can reproduce the observed pattern. We employ supervised learning techniques to successfully solve this problem and show the performance of our model in some real-world instances. We also address the task of pattern classification. In this task, we are interested in grouping different instances of similar patterns together. This task is usually performed visually by the researcher studying certain natural phenomena. However, this method is tedious and can be inconsistent among different researchers. We utilize supervised and unsupervised machine learning algorithms to classify patterns of the Gray-Scott model. We show that our methods show outstanding performance both in supervised and unsupervised settings. The methods introduced in this Chapter could bridge the gaps between researchers studying patterns in different fields of science and engineering
Differential equations of classical physics. Interpretation and solution through systems dynamics
Linear and nonlinear differential equations are mathematical instruments to study physical systems. In general, these equations can be analyzed and solved analytically by classical methods. In the case of complex nonlinear systems, numerical methods must be used for analysis and solution. Using Systems Dynamics (SD) methodology it is possible to represent, analyze and simulate the behavior of both linear and nonlinear physical systems. In this paper we consider some physical models using SD. Las ecuaciones diferenciales lineales y no lineales constituyen los medios matemĂĄticos para estudiar la dinĂĄmica de los sistemas fĂsicos. En general esas ecuaciones pueden ser analizadas y resueltas analĂticamente por mĂ©todos clĂĄsicos. En el caso de sistemas complejos no lineales hay que recurrir a mĂ©todos numĂ©ricos para su anĂĄlisis y soluciĂłn. Utilizando la metodologĂa de DinĂĄmica de Sistemas (DS) es posible representar, analizar y simular el comportamiento de sistemas fĂsicos tanto lineales como no lineales. En este trabajo se estudian algunos modelos fĂsicos mediante DS. 
Holomorphic Embedded Load-flow Method\u27s Application on Three-phase Distribution System With Unbalanced Wyeconnected Loads
With increasing load and aging grid infrastructure, an accurate study of power flow is very important for operation and planning studies. The study involves a numerical calculation of unknown parameters, such as voltage magnitude, angle, net complex power injection at buses and power flow on branches. The performance of traditional iterative power flow methods, such as Newton-Raphson, depends on initial starting point, does not guarantee solution for heavily loaded, and poor convergence for unbalanced radial power system. Holomorphic load embedding is a non-iterative and deterministic method for finding steady-state solutions of any power system network. The method involves converting voltage parameter at every bus into an embedded parameter (a) where analytic continuation is applied using Pade\u27 approximants. The embedded parameter (a) acts as a well-defined reference for the complex analysis and solution obtained when setting a simple value a is known as Germ Solution, by some texts. Using the values of coefficient of Maclaurin Series, the Holomorphic method can find solutions in the whole complex plane using analytic continuation as it extends the nature offunction beyond the radius of convergence. The holomorphic embedding method has been applied in the past to solve power flow problems in balanced power system models. There are several advantages ofthe iv said method over traditional iterative techniques, such as guaranteed convergence, the existence of solution, and faster calculation for certain cases. The method dives into complex analysis, algebraic curves, Taylor series expansion, Pade\u27 approximants, and solving a linear set of equations. . For simplicity purpose, the networks are often assumed to be balanced with constant power loads. Power flow analysis and its derivatives are performed on a single-phase equivalent of the same system. For bulk systems, the assumption is acceptable as load aggregation balances the loads in each phase to an acceptable level. However, in low-voltage distribution systems, ignoring such parameter could lead to an incorrect solution. In this work, a class of Holomorphic load-flow method is proposed to solve the power flow problem in three-phase distribution systems with unbalanced wye-connected loads
Effective algorithm of analysis of integrability via the Ziglin's method
In this paper we continue the description of the possibilities to use
numerical simulations for mathematically rigorous computer assisted analysis of
integrability of dynamical systems. We sketch some of the algebraic methods of
studying the integrability and present a constructive algorithm issued from the
Ziglin's approach. We provide some examples of successful applications of the
constructed algorithm to physical systems.Comment: a figure added, version accepted to JDC
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