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Statistical Physics of Complex Systems

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Statistical Physics of Complex Systems Statistical Physics of Complex Systems European Physical Society 7-11 May 2019 Nordita, Stockholm ii Contributed talks and posters (in alphabetic order of 1st author) 1 Liquid phase separation controlled by pH Omar Adame-Arana1, Christoph. A Weber1, Vasily Zaburdaev2, Jacques Prost3, and Frank J¨ulicher1 1Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany 2Friedrich-Alexander Universit¨atErlangen-N¨urnberg, Cauerstr. 11, 91058 Erlangen, Germany 3Institut Curie, 26 rue d’Ulm, 75248 Paris Cedex 05, France Abstract Recent developments at the interface of biology and physics brought to light the importance of phase separation in explaining biological processes in the cell. It has been shown that some proteins are able to phase separate in solution and form liquid-like droplets in the cytoplasm that carry out a distinct biological function. Particularly, a drop in the cytosolic pH leads to a widespread protein assembly in the cytoplasm, this phenomenon triggered our interest to the mechanism of protein phase separation as a function of pH. In order to study this mechanism, we define a model of a mixture composed of macromolecules which can exist in three different charge states and have a tendency to phase separate. The pH dependence is introduced in terms of chemical reactions which control the charge state of the macromolecules. Using conservation laws and chemical equilibrium, we identify the conjugate variables of the system. We then perform a Legendre transform which defines the free energy corresponding to a fixed pH ensemble. We conclude by showing phase diagrams as a function of pH, where we find that under most conditions, phase separation is most pronounced near the isolectric point. Replica Analysis of the Performance of Image Processing by Compressed Sensing Toshiaki Aida1 1 Okayama University, Japan Compressed sensing is one of the most effective signal processing methods based on the sparse representation of inferred data, in which dictionary matrices play an essential role as a set of overcomplete basis vectors. They are learned from data, e.g. images or signals, by feature extraction methods such as K-SVD ones. Therefore, in general, it requires a considerable amount of computational cost to construct a dictionary matrix. In this work, we analytically evaluate the performance of image processing by compressed sensing, utilizing the replica method of statistical physics. For this pur- pose, we have derived the expression of the probability distribution followed by a dictionary matrix for image processing, assuming that grey scale images are gener- ated by the Gaussian model [1]. Also, we have adopted the framework of replica analysis by Kabashima et al. to analytically evaluate the performance of compressed sensing based on Lp-norm minimization [2]. Recently, we have found an analytical solution of the saddle point equations, which are satisfied by the order parameters of an image restoration model with com- pressed sensing taken into account. The solution has made clear, for example, the scaling relation between the complexity of images and the optimal size of dictionary matrices, which has been addressed not in an analytical way but only in a numerical one so far. [1] T. Aida, Covariance Matrix of a Probability Distribution for Image Dictio- naries in Compressed Sensing, Proceedings of 2018 18th International Conference on Control, Automation and Systems, pp. 829-832, 2018. [2] Y. Kabashima, T. Wadayama and T. Tanaka, A typical reconstruction limit for compressed sensing based on Lp-norm minimization, Journal of Statistical Me- chanics: Theory and Experiment, (2009) L09003. Keywords: Replica method, Image processing, Compressed sensing Dynamical properties and scaling behavior of biological systems: Langevin Equation Treatment L. Amallaha,*, A. Hadera,d, H. Sbiaaia, I. Achikb and Y.Boughaleba,c a LBGIM, Ecole Normale Supérieure, University Hassan II. Casablanca, Morocco bLPMC , Faculty of sciences Ben M’sik . University Hasan II. Casablanca, Morocco cLPMC , University Chouaib Doccali. El Jadida, Morocco d Centre régional des métiers d’éducation et de formation Casablanca- Settat/ établissement Settat, Morocco *corresponding author: [email protected] Abstract: Many animal groups as fishing schools and bird flocks are definitely constitutional, with the literal of organisms so coordinated. They may change form and direction; they appear to be a coherent single entity. Many of the collective behaviors presented by such groups can be understood only by considering the very large number of interactions between the group components. That’s why physicists have made a great effort to study widely the motion of these biological systems, in order to better understand the physical mechanisms that govern the out-of-equilibrium dynamics of these systems. In our work, attention is drawn to propose a new approach to explicitly identify dynamic properties and scaling behavior of self- propelled particles for a given system in collective motion rather than Vicsek model. To address our problems, we are choosing the Langevin equation as a stochastic differential equation. This dynamic has been affected by the use only of the repulsive zone of radius R. The results show that the system velocity increases with time and reaches to finite value at the equilibrium phase. This result is more consisting with the one of the Vicsek model. However, the system velocity decreases exponentially with the applied noise, without taking the Zero value for the highest noise value. Keywords: Collective motion; System Biological; Noise; complex systems; Self-organized particles; Scaling behavior; Langevin dynamic. Contributed talk: Statistical Physics of Power Grids Title: Characterizing the statistic characteristics of power demand Firsrt author: Mehrnaz Anvari, Max Planck Institute for the Physics of Complex Systems Second author: Elisavet Proedrou, DLR Institute of Networked En- ergy Systems Recent studies on power grid frequency fluctuations show the non-Gaussian nature of these variations. Given the critical importance of the power grid for the functioning of our society, answering precisely the question concerning the sources of non-Gaussianity in power grid frequency fluctuations is vital to realize the stability of the network. Three highly probable reasons for the significant deviation of the grid power frequency from its nominal value are: (i) Renewable energy; (ii) Energy trading market; (iii) Power demand (or load). In the last years novel researches showed, on one hand, the statistic characteristics of renewable energies as a replacement of traditional power plants, and, on the other hand, the response of power grids with different topologies to feed-in fluctuations induced by renewable energies. As the existence of the balance between the energy supply and its consumption is one basic principle in power grids, this work, unlike previous studies looking at the fluctuations from generators side and ther effect on power network, shows the underling dynamics and statistics of demand. The intermittent characteristic of demand fluctuations is demonstrated, and the response of the power network to this type of perturbations is discussed. Towards an effective mean-field model for transitional plane Couette flow. Crist´obalArratia1 1Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden Abstract The coexistence between laminar and turbulent regions is generic to the subcritical transition to turbulence of wall-bounded shear flows. An effective description with a reaction-diffusion model for a scalar q (’turbu- lence intensity‘) in a double-well potential is instructive (Pomeau. Phys. D, 23(1):3 – 11, 1986), but in such a simplified model most of the distinc- tive dynamics of the laminar/turbulent interfaces is lost. In the case of pipe flow, a remarkable breakthrough was achieved in the last few years by Barkley (J. Fluid Mech., 803, Sep 2016.) who, by analogy with excitable media, was able to mimic the evolution of laminar/turbulent interfaces throughout the transitional regime by adding a single variable u. Physi- cally, this new variable u plays a double role in modelling the effects of (i) the mean shear relevant to locally inhibit/promote turbulence, and (ii) the large-scale advection of the laminar/turbulent interfaces. For two dimensionally extended shear flows, of which plane Couette flow is the pro- totypical example, the laminar/turbulent interfaces display a complex and largely unexplained transitional dynamics which includes the formation of striking laminar-turbulent patterns (Manneville. Entropy, 19(7), 2017). A specific rationale for extending Barkley’s model to plane Couette flow is proposed. This is based on a pair of variables q and s, where s represents the effect of mean shear (i), but not the large-scale advection (ii) which is described in terms of spatial gradients. While this leaves potentially a very large parameter space, heuristic arguments suggest terms which ap- pear in a certain extension of the Swift-Hohenberg equation (SHE) known to display complex spatiotemporal behaviour and patterns. Most remark- ably, this extended SHE has been shown to generically govern the order parameter around bifurcations of codimension 3 involving the appearance of bi-stability together with the onset of a long-wave Turing instability; all ingredients which are naturally brought in to this case. Thus, deriva- tion of the extended SHE from a suitable extension of
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