Related papers: A duality principle for a semi-linear model in mic…
We present manifestly duality invariant, non-linear, equations of motion for maximal depth, partially massless higher spins. These are based on a first order, Maxwell-like formulation of the known partially massless systems. Our models…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…
We formulate a notion of modular form on the double half-plane for half-integral weights and explain its relationship to the usual notion of modular form. The construction we provide is compatible with certain physical considerations due to…
A mixed type dual to a nondifferentiable variational problem involving higher order derivative is formulated and duality results are proved under generalized invexity conditions. Special cases are generated from our results.
We find the dual equivalent (gauge invariant) version of the Maxwell theory in D=4 with a Proca-like mass term by using the symplectic embedding method. The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative term and…
We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to…
Solid state theory, density functional theory and its generalizations for correlated systems together with numerical simulations on supercomputers allow nowadays to model magnetic systems realistically and in detail and can be even used to…
A theoretical model of quasi-stationary, two-dimensional magnetic reconnection is presented in the framework of incompressible two-fluid magnetohydrodynamics (MHD). The results are compared with recent numerical simulations and experiment.
We approximate the homogenization of fully nonlinear, convex, uniformly elliptic Partial Differential Equations in the periodic setting, using a variational formula for the optimal invariant measure, which may be derived via…
We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard's theorem for moment functionals is proven. The notion of semi-classical bilinear functionals is introduced as a generalization…
We develop a systematic method of obtaining duality symmetric actions in different dimensions. This technique is applied for the quantum mechanical harmonic oscillator, the scalar field theory in two dimensions and the Maxwell theory in…
Canonical duality-triality is a breakthrough methodological theory, which can be used not only for modeling complex systems within a unified framework, but also for solving a wide class of challenging problems from real-world applications.…
The study of convex functions - in particular, of their optimization (really minimization) is one of the most important fields of applied mathematics. Convexity seems to be one of those incredibly well-chosen hypotheses which is just…
Magnetoresistance as a tool of basic parameters determination of minority charge carriers and the ratio of minority charge carriers conductivity to majority ones in solid matter has been considered within the framework of the…
In four dimensions, partially massless fields of all spins and depths possess a duality invariance akin to electric-magnetic duality. We construct metric-like gauge invariant curvature tensors for partially massless fields of all integer…
Gauge functions significantly generalize the notion of a norm, and gauge optimization, as defined by Freund (1987}, seeks the element of a convex set that is minimal with respect to a gauge function. This conceptually simple problem can be…
We discuss the recent proposal of implementing Doubly Special Relativity in configuration space by means of Finsler geometry. Although this formalism leads to a consistent description of the dynamics of a particle, it does not seem to give…
It is shown how to break the symmetry of a Lagrangian with duality symmetry between electric and magnetic monopoles, so that at low energy, electric monopole interactions continue to be observed but magnetic monopole interactions become…
The partial Legendre transform of a non-linear elliptic differential equation is shown to be another non-linear elliptic differential equation. In particular, the partial Legendre transform of the Monge-Amp\`ere equation is another equation…
We present new theoretical results on the spectrum of the quantum field theory of the Double Sine Gordon model. This non-integrable model displays different varieties of kink excitations and bound states thereof. Their mass can be obtained…