Showing papers on "Degrees of freedom published in 2017"

Stability analysis for the virtual element method

Abstract: We analyze the virtual element methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to the parent element diameter) can be dealt with. Our general approach applies to different choices of the stability form, including, for example, the “classical” one introduced in Ref. 4, and a recent one presented in Ref. 34. Finally, we show that the stabilization term can be simplified by dropping the contribution of the internal-to-the-element degrees of freedom. The resulting stabilization form, involving only the boundary degrees of freedom, can be used in the VEM scheme without affecting the stability and convergence properties. The numerical tests are in accordance with the theoretical predictions.

Divergence free virtual elements for the stokes problem on polygonal meshes

Abstract: In the present paper we develop a new family of Virtual Elements for the Stokes problem on polygonal meshes. By a proper choice of the Virtual space of velocities and the associated degrees of freedom, we can guarantee that the final discrete velocity is pointwise divergence-free, and not only in a relaxed (projected) sense, as it happens for more standard elements. Moreover, we show that the discrete problem is immediately equivalent to a reduced problem with fewer degrees of freedom, thus yielding a very efficient scheme. We provide a rigorous error analysis of the method and several numerical tests, including a comparison with a different Virtual Element choice.

New frontiers for quantum gases of polar molecules

Abstract: Compared to atoms, molecules possess additional degrees of freedom that can be exploited in fundamental tests, ultracold chemistry, and engineering new quantum phases in many-body systems Here, we review the recent progress in creating and manipulating ultracold bialkali molecules to study quantum gases of polar molecules Recent progress in engineering quantum gases of polar molecules brings closer their application in fundamental tests, ultracold chemistry and the study of new quantum phases of matter

Anisotropic elastoplasticity for cloth, knit and hair frictional contact

Abstract: The typical elastic surface or curve simulation method takes a Lagrangian approach and consists of three components: time integration, collision detection and collision response. The Lagrangian view is beneficial because it naturally allows for tracking of the codimensional manifold, however collision must then be detected and resolved separately. Eulerian methods are promising alternatives because collision processing is automatic and while this is effective for volumetric objects, advection of a codimensional manifold is too inaccurate in practice. We propose a novel hybrid Lagrangian/Eulerian approach that preserves the best aspects of both views. Similar to the Drucker-Prager and Mohr-Coulomb models for granular materials, we define our collision response with a novel elastoplastic constitutive model. To achieve this, we design an anisotropic hyperelastic constitutive model that separately characterizes the response to manifold strain as well as shearing and compression in the directions orthogonal to the manifold. We discretize the model with the Material Point Method and a novel codimensional Lagrangian/Eulerian update of the deformation gradient. Collision intensive scenarios with millions of degrees of freedom require only a few minutes per frame and examples with up to one million degrees of freedom run in less than thirty seconds per frame.

Loop gravity string

Abstract: In this work we study canonical gravity in finite regions for which we introduce a generalisation of the Gibbons-Hawking boundary term including the Immirzi parameter. We study the canonical formulation on a spacelike hypersuface with a boundary sphere and show how the presence of this term leads to an unprecedented type of degrees of freedom coming from the restoration of the gauge and diffeomorphism symmetry at the boundary. In the presence of a loop quantum gravity state, these boundary degrees of freedom localize along a set of punctures on the boundary sphere. We demonstrate that these degrees of freedom are effectively described by auxiliary strings with a 3-dimensional internal target space attached to each puncture. We show that the string currents represent the local frame field, that the string angular momenta represent the area flux and that the string stress tensor represents the two dimensional metric on the boundary of the region of interest. Finally, we show that the commutators of these broken diffeomorphisms charges of quantum geometry satisfy at each puncture a Virasoro algebra with central charge $c=3$. This leads to a description of the boundary degrees of freedom in terms of a CFT structure with central charge proportional to the number of loop punctures. The boundary $SU(2)$ gauge symmetry is recovered via the action of the $U(1)^3$ Kac-Moody generators (associated with the string current) in a way that is the exact analog of an infinite dimensional generalization of the Schwinger spin-representation. We finally show that this symmetry is broken by the presence of background curvature.

Gravity Degrees of Freedom on a Null Surface

Abstract: A canonical analysis for general relativity is performed on a null surface without fixing the diffeomorphism gauge, and the canonical pairs of configuration and momentum variables are derived. Next to the well-known spin-2 pair, also spin-1 and spin-0 pairs are identified. The boundary action for a null boundary segment of spacetime is obtained, including terms on codimension two corners.

Higher derivative field theories: degeneracy conditions and classes

Abstract: We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of “half” degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.

Hořava Gravity is Asymptotically Free in 2+1 Dimensions.

Abstract: We compute the β functions of marginal couplings in projectable Hořava gravity in 2+1 spacetime dimensions. We show that the renormalization group flow has an asymptotically free fixed point in the ultraviolet (UV), establishing the theory as a UV-complete model with dynamical gravitational degrees of freedom. Therefore, this theory may serve as a toy model to study fundamental aspects of quantum gravity. Our results represent a step forward towards understanding the UV properties of realistic versions of Hořava gravity.

Superfluid Brillouin optomechanics

Abstract: An optomechanical system made of an optical cavity filled with superfluid liquid helium provides the means to study phenomena involving different degrees of freedom than those in traditional solid-state resonators.

A Class of Minimally Modified Gravity Theories

Abstract: We investigate the Hamiltonian structure of a class of gravitational theories whose actions are linear in the lapse function. We derive the necessary and sufficient condition for a theory in this class to have two or less local physical degrees of freedom. As an application we then find several concrete examples of modified gravity theories in which the total number of local physical degrees of freedom in the gravity sector is two.

Holography as deep learning

Abstract: Quantum many-body problem with exponentially large degrees of freedom can be reduced to a tractable computational form by neural network method [G. Carleo and M. Troyer, Science 355 (2017) 602, arX...

Observable Supertranslations

Abstract: We show that large gauge transformations in asymptotically flat spacetime can be implemented by sandwiching a shell containing the ingoing hard particles between two finite-width shells of soft gauge excitations Integration of the graviton Dirac bracket implies that our observable soft degrees of freedom obey the algebra imposed by Strominger on unobservable boundary degrees of freedom Thus, we provide both a derivation and an observable realization of this algebra The conservation laws associated with asymptotic symmetries are seen to arise physically from free propagation of infrared modes This explains in physical terms our recent result that soft charges fail to constrain the hard scattering problem, and so cannot be relevant to the black hole information paradox

Degrees of Freedom in SEM: Are We Testing the Models That We Claim to Test?

Abstract: Structural equation modeling (SEM) has been a staple of the organizational sciences for decades. It is common to report degrees of freedom (df) for tested models, and it should be possible for a re...

3‐D range of motion envelopes reveal interacting degrees of freedom in avian hind limb joints

Abstract: Measuring range of motion (ROM) is a valuable technique that can link bone morphology to joint function in both extant and extinct taxa. ROM results are commonly presented as tables or graphs of maxima and minima for each rotational degree of freedom. We investigate the interactions among three degrees of freedom using X-ray reconstruction of moving morphology (XROMM) to measure ROM of the main hind limb joints of Helmeted Guineafowl (Numida meleagris). By plotting each rotation on an axis, we generate three-dimensional ROM volumes or envelopes composed of hundreds of extreme joint positions for the hip, knee, and intertarsal joints. We find that the shapes of ROM volumes can be quite complex, and that the contribution of long-axis rotation is often substantial. Plotting in vivo poses from individual birds executing different behaviors shows varying use of potential rotational combinations within their ROM envelopes. XROMM can provide unprecedented high-resolution data on the spatial relationship of skeletal elements and thereby illuminate/elucidate the complex ways in which soft and hard tissues interact to produce functional joints. In joints with three rotational degrees of freedom, two-dimensional representations of ROM (flexion/extension and abduction/adduction) are incomplete.

Degrees of Freedom of OAM-Based Line-of-Sight Radio Systems

Abstract: This paper studies the degrees of freedom (DOFs) of a line-of-sight (LOS) communication system, employing orbital angular momentum (OAM)-based orthogonal multiplexing to enhance the spectral efficiency. Aperture and ring receive domains are considered, and analytical expressions of the DOF numbers are obtained. For both cases, the DOF numbers are found to be strongly dependent on the relative sizes between the transmitter and the receiver because of the divergence of the OAM-carrying beams. It is also found that the DOF number of an OAM-based system is less than that of a comparable system allowed to use any supported waves, suggesting that OAM-based multiplexing does not offer any additional performance benefits over traditional spatial multiplexing techniques. Some practical implications of the OAM-based radio are discussed. A numerical study is also presented to evaluate the analytical findings and to address the impacts of the assumptions adopted to reach these findings. The analytical DOF expressions are evidenced to have very good performance in both high-DOF and low-DOF scenarios.

Mutual Information, Neural Networks and the Renormalization Group

Abstract: Physical systems differring in their microscopic details often display strikingly similar behaviour when probed at macroscopic scales. Those universal properties, largely determining their physical characteristics, are revealed by the powerful renormalization group (RG) procedure, which systematically retains "slow" degrees of freedom and integrates out the rest. However, the important degrees of freedom may be difficult to identify. Here we demonstrate a machine learning algorithm capable of identifying the relevant degrees of freedom and executing RG steps iteratively without any prior knowledge about the system. We introduce an artificial neural network based on a model-independent, information-theoretic characterization of a real-space RG procedure, performing this task. We apply the algorithm to classical statistical physics problems in one and two dimensions. We demonstrate RG flow and extract the Ising critical exponent. Our results demonstrate that machine learning techniques can extract abstract physical concepts and consequently become an integral part of theory- and model-building.

Reversible time travel with freedom of choice.

Abstract: General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or more generally local operations, lead to inconsistencies and should thus be forbidden. Here we consider the most general deterministic dynamics connecting classical degrees of freedom defined on a set of bounded space-time regions, requiring that it is compatible with arbitrary operations performed in the local regions. We find that any such dynamics can be realised through reversible interactions. We further find that consistency with local operations is compatible with non-trivial time travel: Three parties can interact in such a way to be all both in the future and in the past of each other, while being free to perform arbitrary local operations.

Testing self-energy embedding theory in combination with GW

Abstract: We present a theoretical framework and implementation details for self-energy embedding theory (SEET) with the GW approximation for the treatment of weakly correlated degrees of freedom and configuration interactions solver for handing the strongly correlated degrees. On a series of molecular examples, for which the exact results are known within a given basis, we demonstrate that SEET(CI/GW) is a systematically improvable and well controlled method capable of giving accurate results and well behaved causal self-energies and Green's functions. We compare the theoretical framework of SEET(CI/GW) to that of GW+DMFT and comment on differences between these to approaches that aim to treat both strongly and weakly correlated simultaneously.

Balancing exploration and exploitation in reinforcement learning using a value of information criterion

Abstract: In this paper, we consider an information-theoretic approach for addressing the exploration-exploitation dilemma in reinforcement learning. We employ the value of information, a criterion that provides the optimal trade-off between the expected returns and a policy's degrees of freedom. As the degrees of freedom are reduced, an agent will exploit more than explore. As the policy degrees of freedom increase, an agent will explore more than exploit. We provide an efficient computational procedure for constructing policies using the value of information. The performance is demonstrated on a standard reinforcement learning benchmark problem.

What is modified gravity and how to differentiate it from particle dark matter

Abstract: An obvious criterion to classify theories of modified gravity is to identify their gravitational degrees of freedom and their coupling to the metric and the matter sector. Using this simple idea, we show that any theory which depends on the curvature invariants is equivalent to general relativity in the presence of new fields that are gravitationally coupled to the energy-momentum tensor. We show that they can be shifted into a new energy-momentum tensor. There is no a priori reason to identify these new fields as gravitational degrees of freedom or matter fields. This leads to an equivalence between dark matter particles gravitationally coupled to the standard model fields and modified gravity theories designed to account for the dark matter phenomenon. Due to this ambiguity, it is impossible to differentiate experimentally between these theories and any attempt of doing so should be classified as a mere interpretation of the same phenomenon.

Bottom-up discrete symmetries for Cabibbo mixing

Abstract: We perform a bottom-up search for discrete non-Abelian symmetries capable of quantizing the Cabibbo angle that parameterizes CKM mixing. Given a particular Abelian symmetry structure in the up and down sectors, we construct representations of the associated residual generators which explicitly depend on the degrees of freedom present in our effective mixing matrix. We then discretize those degrees of freedom and utilize the Groups, Algorithms, Programming (GAP) package to close the associated finite groups. This short study is performed in the context of recent results indicating that, without resorting to special model-dependent corrections, no small-order finite group can simultaneously predict all four parameters of the three-generation CKM matrix and that only groups of 𝒪(102) can predict the analogous parameters of the leptonic PMNS matrix, regardless of whether neutrinos are Dirac or Majorana particles. Therefore, a natural model of flavour might instead incorporate small(er) finite groups whose pre...

E11, Romans theory and higher level duality relations

Abstract: From the underlying nonlinear realisation, we compute the complete E11 invariant equations of motion in eleven dimensions, at the linearised level, up to and including level four in the fields. Thus, we include the metric, the three and six forms, the dual graviton and three fields at level four. The fields are linked by a set of duality equations, which are first-order in derivatives and transform into each other under the E11 symmetries. From these duality relations, we deduce second-order equations of motion, including those for the usual supergravity fields. As a result the on-shell degrees of freedom are those of the eleven-dimensional supergravity. We also show that the level four fields provide an eleven-dimensional origin of Romans theory and lead to a novel duality relation.