Classical Time Crystals

We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary orbits of an angular variable as lowest-energy trajectories for nonsingular Lagrangian systems. Dynamics within orbits of broken symmetry provide a natural arena for formation of time crystals. We exhibit models of that kind, including a model with traveling density waves.Comment: 5 pages, 1 figur

Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach

We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular demonstrating different forms for SIS and SIR disease spreading (e.g. under the SIR model our method counts self-avoiding walks). In comparison to existing methods to infer the spreading efficiency of different nodes in the network (based on degree, k-shell decomposition analysis and different centrality measures), our method directly considers the spreading process and, as such, is unique in providing estimation of actual numbers of infections. Crucially, in simulating infections on various real-world networks with the SIR model, we show that our walks-based method improves the inference of effectiveness of nodes over a wide range of infection rates compared to existing methods. We also analyse the trade-off between estimate accuracy and computational cost, showing that the better accuracy here can still be obtained at a comparable computational cost to other methods.Comment: 6 page

Hydrodynamic flow patterns and synchronization of beating cilia

We calculate the hydrodynamic flow field generated far from a cilium which is attached to a surface and beats periodically. In the case of two beating cilia, hydrodynamic interactions can lead to synchronization of the cilia, which are nonlinear oscillators. We present a state diagram where synchronized states occur as a function of distance of cilia and the relative orientation of their beat. Synchronized states occur with different relative phases. In addition, asynchronous solutions exist. Our work could be relevant for the synchronized motion of cilia generating hydrodynamic flows on the surface of cells.Comment: 5 pages, 4 figures, v2: minor correction

Thermal spin transport and spin-orbit interaction in ferromagnetic/non-magnetic metals

In this article we extend the currently established diffusion theory of spin-dependent electrical conduction by including spin-dependent thermoelectricity and thermal transport. Using this theory, we propose new experiments aimed at demonstrating novel effects such as the spin-Peltier effect, the reciprocal of the recently demonstrated thermally driven spin injection, as well as the magnetic heat valve. We use finite-element methods to model specific devices in literature to demonstrate our theory. Spin-orbit effects such as anomalous-Hall, -Nernst, anisotropic magnetoresistance and spin-Hall are also included in this model

Low-energy QCD: Chiral coefficients and the quark-quark interaction

A detailed investigation of the low-energy chiral expansion is presented within a model truncation of QCD. The truncation allows for a phenomenological description of the quark-quark interaction in a framework which maintains the global symmetries of QCD and permits a $1/N_c$ expansion. The model dependence of the chiral coefficients is tested for several forms of the quark-quark interaction by varying the form of the running coupling, $\alpha (q^2)$, in the infrared region. The pattern in the coefficients that arises at tree level is consistent with large $N_c$ QCD, and is related to the model truncation.Comment: 28 pages, Latex, 6 postscript figures available on request to [email protected]

DDGun: An untrained method for the prediction of protein stability changes upon single and multiple point variations

Background: Predicting the effect of single point variations on protein stability constitutes a crucial step toward understanding the relationship between protein structure and function. To this end, several methods have been developed to predict changes in the Gibbs free energy of unfolding (\u3b4\u3b4G) between wild type and variant proteins, using sequence and structure information. Most of the available methods however do not exhibit the anti-symmetric prediction property, which guarantees that the predicted \u3b4\u3b4G value for a variation is the exact opposite of that predicted for the reverse variation, i.e., \u3b4\u3b4G(A \u2192 B) = -\u3b4\u3b4G(B \u2192 A), where A and B are amino acids. Results: Here we introduce simple anti-symmetric features, based on evolutionary information, which are combined to define an untrained method, DDGun (DDG untrained). DDGun is a simple approach based on evolutionary information that predicts the \u3b4\u3b4G for single and multiple variations from sequence and structure information (DDGun3D). Our method achieves remarkable performance without any training on the experimental datasets, reaching Pearson correlation coefficients between predicted and measured \u3b4\u3b4G values of ~ 0.5 and ~ 0.4 for single and multiple site variations, respectively. Surprisingly, DDGun performances are comparable with those of state of the art methods. DDGun also naturally predicts multiple site variations, thereby defining a benchmark method for both single site and multiple site predictors. DDGun is anti-symmetric by construction predicting the value of the \u3b4\u3b4G of a reciprocal variation as almost equal (depending on the sequence profile) to -\u3b4\u3b4G of the direct variation. This is a valuable property that is missing in the majority of the methods. Conclusions: Evolutionary information alone combined in an untrained method can achieve remarkably high performances in the prediction of \u3b4\u3b4G upon protein mutation. Non-trained approaches like DDGun represent a valid benchmark both for scoring the predictive power of the individual features and for assessing the learning capability of supervised methods

Riemann-Einstein Structure from Volume and Gauge Symmetry

It is shown how a metric structure can be induced in a simple way starting with a gauge structure and a preferred volume, by spontaneous symmetry breaking. A polynomial action, including coupling to matter, is constructed for the symmetric phase. It is argued that assuming a preferred volume, in the context of a metric theory, induces only a limited modification of the theory.Comment: LaTeX, 13 pages; Added additional reference in Reference

Non-universal equilibrium crystal shape results from sticky steps

The anisotropic surface free energy, Andreev surface free energy, and equilibrium crystal shape (ECS) z=z(x,y) are calculated numerically using a transfer matrix approach with the density matrix renormalization group (DMRG) method. The adopted surface model is a restricted solid-on-solid (RSOS) model with "sticky" steps, i.e., steps with a point-contact type attraction between them (p-RSOS model). By analyzing the results, we obtain a first-order shape transition on the ECS profile around the (111) facet; and on the curved surface near the (001) facet edge, we obtain shape exponents having values different from those of the universal Gruber-Mullins-Pokrovsky-Talapov (GMPT) class. In order to elucidate the origin of the non-universal shape exponents, we calculate the slope dependence of the mean step height of "step droplets" (bound states of steps) using the Monte Carlo method, where p=(dz/dx, dz/dy)$, and represents the thermal averag |p| dependence of , we derive a |p|-expanded expression for the non-universal surface free energy f_{eff}(p), which contains quadratic terms with respect to |p|. The first-order shape transition and the non-universal shape exponents obtained by the DMRG calculations are reproduced thermodynamically from the non-universal surface free energy f_{eff}(p).Comment: 31 pages, 21 figure