Abstract:
The thermodynamics and dynamics of supercooled liquids correlate with their elasticity. In particular for covalent networks, the jump of specific heat is small and the liquid is {\it strong} near the threshold valence where the network acquires rigidity. By contrast, the jump of specific heat and the fragility are large away from this threshold valence. In a previous work [Proc. Natl. Acad. Sci. U.S.A., 110, 6307 (2013)], we could explain these behaviors by introducing a model of supercooled liquids in which local rearrangements interact via elasticity. However, in that model the disorder characterizing elasticity was frozen, whereas it is itself a dynamic variable in supercooled liquids. Here we study numerically and theoretically adaptive elastic network models where polydisperse springs can move on a lattice, thus allowing for the geometry of the elastic network to fluctuate and evolve with temperature. We show numerically that our previous results on the relationship between structure and thermodynamics hold in these models. We introduce an approximation where redundant constraints (highly coordinated regions where the frustration is large) are treated as an ideal gas, leading to analytical predictions that are accurate in the range of parameters relevant for real materials. Overall, these results lead to a description of supercooled liquids, in which the distance to the rigidity transition controls the number of directions in phase space that cost energy and the specific heat.

Abstract:
We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak non-covalent interactions. We show that at low-temperature, these interactions considerably affect the network topology near the rigidity transition that occurs as the coordination increases. As a result, this transition becomes mean-field and does not present a line of critical points previously argued for, the "rigidity window". Vibrational modes are then not fractons, but instead are similar to the anomalous modes observed in packings of particles near jamming. These results suggest an alternative interpretation for the intermediate phase observed in chalcogenides.

Abstract:
Molecular dynamics simulation is employed to study the structural evolution of low density amorphous ice during its compression from one atmosphere to 2.5\,GPa. Calculated results show that high density amorphous ice is formed at an intermediate pressure of $\sim $1.0\,GPa; the O--O--O bond angle ranges from 83$^{\circ}$ to 113$^{\circ}$, and the O--H$\cdots$O bond is bent from 112$^{\circ}$ to 160$^{\circ}$. Very high density amorphous ice is obtained by quenching to 80\,K and decompressing the ice to ambient pressure from 160\,K/1.3\,GPa or 160\,K/1.7\,GPa; and the next-nearest O--O length is found to be 0.310\,nm, just 0.035\,nm beyond the nearest O--O distance of 0.275\,nm.

Abstract:
Text message stream which is produced by Instant Messager and Internet Relay Chat poses interesting and challenging problems for information technologies. It is beneficial to extract the conversations in this kind of chatting message stream for information management and knowledge finding. However, the data in text message stream are usually very short and incomplete, and it requires efficiency to monitor thousands of continuous chat sessions. Many existing text mining methods encounter challenges. This paper focuses on the conversation extraction in dynamic text message stream. We design the dynamic representation for messages to combine the text content information and linguistic feature in message stream. A memory structure of reversed maximal similar relationship is developed for renewable assignments when grouping messages into conversations. We finally propose a double time window algorithm based on above methods to extract conversations in dynamic text message stream. Experiments on a real dataset shows that our method outperforms two baseline methods introduced in a recent related paper about 47% and 15% in terms of F measure respectively.

Abstract:
Super-cooled liquids are characterized by their fragility: the slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure controls fragility remains a challenge. Surprisingly, experiments indicate that the linear elasticity of the glass -- a purely local property of the free energy landscape -- is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations, which are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.

Abstract:
Tracing magnetic fields is crucial as magnetic fields play an important role in many astrophysical processes. Earlier studies have demonstrated that Ground State Alignment (GSA) is a unique way to detect weak magnetic fields (1G> B> 1exp(-15)G) in diffuse media, they consider the situation when the pumping source is a point source, which applies when the star is very far away from the diffuse media. In this paper, we explore the GSA in the presence of extended radiation fields. For the radiation fields with a clear geometric structure, we consider the alignment in circumstellar medium, binary systems, disc, and Local Interstellar Medium (LISM). For the radiation fields with unidentified pumping sources, we apply the method of multipole expansion and discuss the GSA induced by each component. We demonstrate that for general radiation fields, it is adequate to consider the contribution from dipole and quadrupole radiation components. We find that in general polarization of absorption arizing from GSA coincides with the projection of magnetic field in the 2D sky with 90 degree degeneracy. We conclude that the GSA is a unique tool to detect the direction of weak magnetic field, and it can be applied to diffuse media in any radiation field.

Abstract:
We study theoretically the erosion threshold of a granular bed forced by a viscous fluid. We first introduce a novel model of interacting particles driven on a rough substrate. It predicts a continuous transition at some threshold forcing $\theta_c$, beyond which the particle current grows linearly $J\sim \theta-\theta_c$, in agreement with experiments. The stationary state is reached after a transient time $t_{\rm conv}$ which diverges near the transition as $t_{\rm conv}\sim |\theta-\theta_c|^{-z}$ with $z\approx 2.5$. The model also makes quantitative testable predictions for the drainage pattern: the distribution $P(\sigma)$ of local current is found to be extremely broad with $P(\sigma)\sim J/\sigma$, spatial correlations for the current are negligible in the direction transverse to forcing, but long-range parallel to it. We explain some of these features using a scaling argument and a mean-field approximation that builds an analogy with $q$-models. We discuss the relationship between our erosion model and models for the depinning transition of vortex lattices in dirty superconductors, where our results may also apply.

Abstract:
We study three instances of log-correlated processes on the interval: the logarithm of the Gaussian unitary ensemble (GUE) characteristic polynomial, the Gaussian log-correlated potential in presence of edge charges, and the Fractional Brownian motion with Hurst index $H \to 0$ (fBM0). In previous collaborations we obtained the probability distribution function (PDF) of the value of the global minimum (equivalently maximum) for the first two processes, using the freezing-duality conjecture (FDC). Here we study the PDF of the position of the maximum $x_m$ through its moments. Using replica, this requires calculating moments of the density of eigenvalues in the $\beta$-Jacobi ensemble. Using Jack polynomials we obtain an exact and explicit expression for these moments for arbitrary $\beta >0$ and positive integer $n$ in terms of sums over partitions. This expression agrees with a very recent independent derivation by Mezzadri and Reynolds. We check our results against a contour integral formula derived recently by Borodin and Gorin (presented in the Appendix A from these authors) which, remarkably, also allows to calculate negative moments. The duality necessary for the FDC to work is proved, and on our expressions, found to correspond to exchange of partitions with their dual. Performing the limit $n \to 0$ and to negative Dyson index $\beta \to -2$, we obtain the moments of $x_m$ and give explicit expressions for the lowest ones. Numerical checks for the GUE polynomials, performed independently by N. Simm, indicate encouraging agreement. Some results are also obtained for moments in Laguerre, Hermite-Gaussian, as well as circular and related ensembles. The correlations of the position and the value of the field at the minimum are also analyzed.

Abstract:
Finding the global minimum of a cost function given by the sum of a quadratic and a linear form in N real variables over (N-1)- dimensional sphere is one of the simplest, yet paradigmatic problems in Optimization Theory known as the "trust region subproblem" or "constraint least square problem". When both terms in the cost function are random this amounts to studying the ground state energy of the simplest spherical spin glass in a random magnetic field. We first identify and study two distinct large-N scaling regimes in which the linear term (magnetic field) leads to a gradual topology trivialization, i.e. reduction in the total number N_{tot} of critical (stationary) points in the cost function landscape. In the first regime N_{tot} remains of the order $N$ and the cost function (energy) has generically two almost degenerate minima with the Tracy-Widom (TW) statistics. In the second regime the number of critical points is of the order of unity with a finite probability for a single minimum. In that case the mean total number of extrema (minima and maxima) of the cost function is given by the Laplace transform of the TW density, and the distribution of the global minimum energy is expected to take a universal scaling form generalizing the TW law. Though the full form of that distribution is not yet known to us, one of its far tails can be inferred from the large deviation theory for the global minimum. In the rest of the paper we show how to use the replica method to obtain the probability density of the minimum energy in the large-deviation approximation by finding both the rate function and the leading pre-exponential factor.