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Stress-based ensembles incorporating temperature-like variables have been proposed as a route to an equation of state for granular materials. To test the efficacy of this approach, we perform experiments on a two-dimensional photoelastic…
Dynamic state estimation, as opposed to kinematic state estimation, seeks to estimate not only the orientation of a rigid body but also its angular velocity, through Euler's equations of rotational motion. This paper demonstrates that the…
In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement.…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
In the mechanics of inviscid conservative fluids, it is classical to generate the equations of dynamics by formulating with adequate variables, that the pressure integral calculated in the time-space domain corresponding to the motion of…
The dynamics of a system, consisting of a particle initially in a Gaussian state interacting with a field mode, under the action of repeated measurements performed on the particle, is examined. It is shown that regardless of its initial…
This paper develops a general mathematical framework for pseudo-parabolic gradient systems with state-dependent dynamics. The state dependence is induced by variable coefficient fields in the governing energy functional. Such coefficients…
Equations of State model relations between thermodynamic variables and are ubiquitous in scientific modelling, appearing in modern day applications ranging from Astrophysics to Climate Science. The three desired properties of a general…
When an entangled state evolves under local unitaries, the entanglement in the state remains fixed. Here we show the dynamical phase acquired by an entangled state in such a scenario can always be understood as the sum of the dynamical…
The method to design exponentially stable adaptive observers is proposed for linear time-invariant systems parameterized by unknown physical parameters. Unlike existing adaptive solutions, the system state-space matrices A, B are not…
We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement…
A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
In quantum physics, multiparticle systems are described by quantum states acting on tensor products of Hilbert spaces. This product structure leads to the distinction between product states and entangled states; moreover, one can quantify…
We study entanglement concentration of continuous variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…
The nudged elastic band (NEB) and Dimer methods are standard tools for computing minimum-energy paths and index-one saddle points in atomistic transition problems. They are increasingly driven by surrogate or learned force models, whose…
We analyze the popular ``state-space'' class of algorithms for detecting casual interaction in coupled dynamical systems. These algorithms are often justified by Takens' embedding theorem, which provides conditions under which relationships…
In this article, we investigate the convergence behavior of two classes of gathering protocols with fixed circulant topologies using tools from dynamical systems. Given a fixed number of mobile entities moving in the Euclidean plane, we…
A serious problem in learning probabilistic models is the presence of hidden variables. These variables are not observed, yet interact with several of the observed variables. Detecting hidden variables poses two problems: determining the…