Related papers: Truncations driven by constraints: consistency and…
The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [12,13], but, in…
We propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…
This paper is concerned with second-order optimality conditions for Tikhonov regularized optimal control problems governed by the obstacle problem. Using a simple observation that allows to characterize the structure of optimal controls on…
We study the N=4 gauged supergravity theory which arises from the consistent truncation of IIB supergravity on the coset T^{1,1}. We analyze three N=2 subsectors and in particular we clarify the relationship between true superpotentials for…
For a theory with first and second class constraints, we propose a procedure for conversion of second class constraints based on deformation the structure of local symmetries of the Lagrangian formulation. It does not require extension or…
We consider a dc-driven damped sine-Gordon model with a small nonlinear spatial-disorder term, onto which a sinusoidal modulation is superimposed. It describes, e.g., a weakly disordered system with a regular grain structure. We demonstrate…
Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…
The normal forms of different one- and two- parametric solutions of Thirring model are connected with each other by making use of generalized conformal shift transformations. A new alternative sources of superselection rules are shown and…
We consider quantum mechanics on constrained surfaces which have non-Euclidean metrics and variable Gaussian curvature. The old controversy about the ambiguities involving terms in the Hamiltonian of order hbar^2 multiplying the Gaussian…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Many mechanical systems exhibit changes in their kinematic topology altering the mobility. Ideal contact is the best known cause, but also stiction and controlled locking of parts of a mechanism lead to topology changes. The latter is…
Discrete time evolution of one-dimensional maps is embedded in continuous time by truncating the Taylor series expansion of the time evolution operator to a finite order N. Truncations with N > 4 leads to unconditional instability.…
The low-energy effective action of type-I superstring theory in ten dimensions is obtained performing a truncation of type-IIB supergravity in a background where D9-branes are present. The open sector corresponds to the first order in the…
Maximal supergravity in four dimensions admits two inequivalent dyonic gaugings of the group $\mathrm{SO}(4) \times \mathrm{SO}(2,2) \ltimes T^{16}$. Both admit a Minkowski vacuum with residual $\mathrm{SO}(4) \times \mathrm{SO}(2)^2$…
The scalar normal modes of higher dimensional gravitating kink solutions are derived. By perturbing to second order the gravity and matter parts of the action in the background of a five-dimensional kink, the effective Lagrangian of the…
We discuss the supersymmetry and fermionic sector of the recently obtained consistent truncations of IIB supergravity containing massive modes. In particular, we present the general form of the five-dimensional N = 4 supersymmetry…
Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
We construct consistent Kaluza-Klein truncations of type IIA supergravity on (i) $\Sigma_2\times S^3$ and (ii) $\Sigma_3\times S^3$, where $\Sigma_2 = S^2/\Gamma$, $\mathbb{R}^2/\Gamma$, or $\mathbb{H}^2/\Gamma$, and $\Sigma_3 =…
In this dissertation, we study the generalized symmetries in supergravities and superconformal field theories from the string theory perspective. Part one is devoted to the study of string universality in high spacetime dimensions.…