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  • 1.
    Aurell, Erik
    et al.
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Fanelli, D.
    Gurbatov, S. N.
    Moshkov, A. Y.
    The inner structure of Zeldovich pancakes2003In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 186, no 04-mar, p. 171-184Article in journal (Refereed)
    Abstract [en]

    The evolution of a planar perturbation in a Einstein-de Sitter Universe is studied using a previously introduced Lagrangian scheme. An approximate discrete dynamical system is derived, which describes the mass agglomeration process. Quantitative predictions for the late-time mean density profile are obtained therefrom, and validated by numerical simulations. A simple but important result is that the characteristic scale of a mass agglomeration is an increasing function of cosmological time t. For one kind of initial conditions we further find a scaling regime for the density profile of a collapsing object. These results are compared with analogous investigations for the adhesion model (Burgers equation with positive viscosity). We further study the mutual motion of two mass agglomerations, and show that they oscillate around each other for long times, like two heavy particles. Individual particles in the two agglomerations do not mix effectively on the time scale of the inter-agglomeration motion.

  • 2.
    Aurell, Erik
    et al.
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Fanelli, D.
    Muratore-Ginanneschi, P.
    On the dynamics of a self-gravitating medium with random and non-random initial conditions2001In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 148, no 04-mar, p. 272-288Article in journal (Refereed)
    Abstract [en]

    The dynamics of a 1D self-gravitating medium with initial density almost uniform is studied. Numerical experiments are performed with ordered and with Gaussian random initial conditions. The phase space portraits art shown to be qualitatively similar to shock waves, in particular with initial conditions of Brownian type. The PDF of the mass distribution is investigated.

  • 3. Dankowicz, H.
    et al.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    On the origin and bifurcations of stick-slip oscillations2000In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 136, no 04-mar, p. 280-302Article in journal (Refereed)
    Abstract [en]

    A recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis. Particular emphasis is put on the bifurcations associated with the appearance of stick-slip oscillations. In the model it is found that the existence of these oscillations is a result of a periodic orbit straddling a discontinuity in the first derivative of the vector field. A local analysis tool is developed to discuss the stability of such an orbit and its bifurcations due to changes in system parameters. The analysis tool is found to be highly efficient at quantitatively predicting the location and type of bifurcations. It is argued that the method and the general results are applicable to a large class of friction models containing similar discontinuities and thus, hopefully, to actual frictional dynamics. (C)2000 Elsevier Science B.V. All rights reserved.

  • 4. Delvenne, Jean-Charles
    et al.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Finite-time thermodynamics of port-Hamiltonian systems2014In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 267, p. 123-132Article in journal (Refereed)
    Abstract [en]

    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.

  • 5. di Bernardo, M.
    et al.
    Kowalczyk, P.
    Nordmark, Arne B.
    KTH, Superseded Departments, Mechanics.
    Bifurcations of dynamical systems with sliding: derivation of normal-form mappings2002In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 170, no 04-mar, p. 175-205Article in journal (Refereed)
    Abstract [en]

    This paper is concerned with the analysis of so-called sliding bifurcations in n-dimensional piecewise-smooth dynamical systems with discontinuous vector field. These novel bifurcations occur when the system trajectory interacts with regions on the discontinuity set where sliding is possible. The derivation of appropriate normal-form maps is detailed. It is shown that the leading-order term in the map depends on the particular bifurcation scenario considered. This is in turn related to the possible bifurcation scenarios exhibited by a periodic orbit undergoing one of the sliding bifurcations discussed in the paper. A third-order relay system serves as a numerical example.

  • 6. di Bernardo, M.
    et al.
    Nordmark, Arne B.
    KTH, School of Engineering Sciences (SCI), Mechanics, Biomechanics.
    Olivar, G.
    Discontinuity-induced bifurcations of equilibria in piecewise-smooth and impacting dynamical systems2008In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 237, no 1, p. 119-136Article in journal (Refereed)
    Abstract [en]

    A rich variety of dynamical scenarios has been shown to occur when a fixed point of a non-smooth map undergoes a border-collision. This paper concerns a closely related class of discontinuity-induced bifurcations, those involving equilibria of n-dimensional piecewise-smooth flows. Specifically, transitions are studied which occur when a boundary equilibrium, that is one lying within a discontinuity manifold, is perturbed. It is shown that such equilibria can either persist under parameter variations or can disappear giving rise to different bifurcation scenarios. Conditions to classify among the possible simplest scenarios are given for piecewise-smooth continuous, Filippov and impacting systems. Also, we investigate the possible birth of other attractors (e.g. limit cycles) at a boundary-equilibrium bifurcation.

  • 7.
    Djehiche, Boualem
    KTH, Superseded Departments, Mathematics.
    Global solution of the pressureless gas equation with viscosity2002In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 163, no 3-4, p. 184-190Article in journal (Refereed)
    Abstract [en]

    We construct a global weak solution to a d-dimensional system of zero-pressure gas dynamics modified by introducing a finite artificial viscosity. We use discrete approximations to the continuous gas and make particles move along trajectories of the normalized simple symmetric random walk with deterministic drift. The interaction of these particles is given by a sticky particle dynamics. We show that a subsequence of these approximations converges to a weak solution of the system of zero-pressure gas dynamics in the sense of distributions. This weak solution is interpreted in terms of a random process solution of a nonlinear stochastic differential equation. We get a weak solution of the inviscid system by tending the viscosity to zero.

  • 8.
    Eliasson, Veronica
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Henshaw, William
    Department of Mechanical Engineering, University of California, Berkeley.
    Appelö, Daniel
    Lawrence Livermore National Laboratory, Livermore.
    On cylindrically converging shock waves shaped by obstacles2008In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 237, no 14-17, p. 2203-2209Article in journal (Refereed)
    Abstract [en]

    Motivated by recent experiments, numerical simulations of cylindrically converging shock waves were performed. The converging shocks impinged upon a set of 0-16 regularly space obstacles. For more than two obstacles the resulting diffracted shock fronts formed polygonal shaped patterns near the point of focus. The maximum pressure and temperature as a function of the number of obstacles were studied. The self-similar behavior of cylindrical, triangular and square-shaped shocks was also investigated.

  • 9.
    Gustafsson, Björn
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Putinar, Mihai
    Selected topics on quadrature domains2007In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 235, no 02-jan, p. 90-100Article in journal (Refereed)
    Abstract [en]

    This is a selection of facts, old and recent, about quadrature domains. The text, written in the form of a survey, is addressed to non-experts and covers a variety of phenomena related to quadrature domains, such as: the difference between quadrature domains for subharmonic, harmonic and respectively complex analytic functions, geometric properties of the boundary, instability in the reverse Hele-Shaw flow, dependence and nonuniqueness on the quadrature data, interpretation in terms of function theory on Riemann surfaces, a matrix model and a reconstruction algorithm. Also there are some low degree/order examples where computations can be carried out in detail.

  • 10.
    Lenells, Jonatan
    Baylor University, United States.
    Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs2012In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 241, no 8, p. 857-875Article in journal (Refereed)
    Abstract [en]

    We present an approach for analyzing initial-boundary value problems for integrable equations whose Lax pairs involve 3×3 matrices. Whereas initial value problems for integrable equations can be analyzed by means of the classical Inverse Scattering Transform (IST), the presence of a boundary presents new challenges. Over the last fifteen years, an extension of the IST formalism developed by Fokas and his collaborators has been successful in analyzing boundary value problems for several of the most important integrable equations with 2×2 Lax pairs, such as the Kortewegde Vries, the nonlinear Schrdinger, and the sine-Gordon equations. In this paper, we extend these ideas to the case of equations with Lax pairs involving 3×3 matrices.

  • 11.
    Lenells, Jonatan
    University of Cambridge, United Kingdom .
    The derivative nonlinear Schrödinger equation on the half-line2008In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 237, no 23, p. 3008-3019Article in journal (Refereed)
    Abstract [en]

    We analyze the derivative nonlinear Schrödinger equation i qt + qx x = i (| q |2 q)x on the half-line using the Fokas method. Assuming that the solution q (x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x, t dependence and is given in terms of the spectral functions a (ζ), b (ζ) (obtained from the initial data q0 (x) = q (x, 0)) as well as A (ζ), B (ζ) (obtained from the boundary values g0 (t) = q (0, t) and g1 (t) = qx (0, t)). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values {q0 (x), g0 (t), g1 (t)} such that there exist spectral functions satisfying the global relation, we show that the function q (x, t) defined by the above Riemann-Hilbert problem exists globally and solves the derivative nonlinear Schrödinger equation with the prescribed initial and boundary values.

  • 12.
    Lenells, Jonatan
    Baylor University, United States .
    The solution of the global relation for the derivative nonlinear Schrodinger equation on the half-line2011In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 240, no 6, p. 512-525Article in journal (Refereed)
    Abstract [en]

    We consider initial-boundary value problems for the derivative nonlinear Schrdinger (DNLS) equation on the half-line x>0. In a previous work, we showed that the solution q(x,t) can be expressed in terms of the solution of a RiemannHilbert problem with jump condition specified by the initial and boundary values of q(x,t). However, for a well-posed problem, only part of the boundary values can be prescribed; the remaining boundary data cannot be independently specified, but are determined by the so-called global relation. In general, an effective solution of the problem therefore requires solving the global relation. Here, we present the solution of the global relation in terms of the solution of a system of nonlinear integral equations. This also provides a construction of the Dirichlet-to-Neumann map for the DNLS equation on the half-line.

  • 13.
    Shi, Guodong
    et al.
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Sou, Kin Cheong
    Chalmers University of Technology.
    Sandberg, Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Johansson, Karl Henrik
    KTH, School of Electrical Engineering (EES), Automatic Control. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    A graph-theoretic approach on optimizing informed-node selection in multi-agent tracking control2014In: Physica D: Non-linear phenomena, ISSN 0167-2789, E-ISSN 1872-8022, Vol. 267, p. 104-111Article in journal (Refereed)
    Abstract [en]

    A graph optimization problem for a multi-agent leader follower problem is considered. In a multi-agent system with n followers and one leader, each agent's goal is to track the leader using the information obtained from its neighbors. The neighborhood relationship is defined by a directed communication graph where k agents, designated as informed agents, can become neighbors of the leader. This paper establishes that, for any given strongly connected communication graph with k informed agents, all agents will converge to the leader. In addition, an upper bound and a lower bound of the convergence rate are obtained. These bounds are shown to explicitly depend on the maximal distance from the leader to the followers. The dependence between this distance and the exact convergence rate is verified by empirical studies. Then we show that minimizing the maximal distance problem is a metric k-center problem in classical combinatorial optimization studies, which can be approximately solved. Numerical examples are given to illustrate the properties of the approximate solutions.

1 - 13 of 13
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