Coarsening Dynamics of a One-Dimensional Driven Cahn-Hilliard System

We study the one-dimensional Cahn-Hilliard equation with an additional driving term representing, say, the effect of gravity. We find that the driving field $E$ has an asymmetric effect on the solution for a single stationary domain wall (or `kink'), the direction of the field determining whether the analytic solutions found by Leung [J.Stat.Phys.{\bf 61}, 345 (1990)] are unique. The dynamics of a kink-antikink pair (`bubble') is then studied. The behaviour of a bubble is dependent on the relative sizes of a characteristic length scale $E^{-1}$, where $E$ is the driving field, and the separation, $L$, of the interfaces. For $EL \gg 1$ the velocities of the interfaces are negligible, while in the opposite limit a travelling-wave solution is found with a velocity $v \propto E/L$. For this latter case ($EL \ll 1$) a set of reduced equations, describing the evolution of the domain lengths, is obtained for a system with a large number of interfaces, and implies a characteristic length scale growing as $(Et)^{1/2}$. Numerical results for the domain-size distribution and structure factor confirm this behavior, and show that the system exhibits dynamical scaling from very early times.Comment: 20 pages, revtex, 10 figures, submitted to Phys. Rev.

Dynamics of Ordering of Heisenberg Spins with Torque --- Nonconserved Case. I

We study the dynamics of ordering of a nonconserved Heisenberg magnet. The dynamics consists of two parts --- an irreversible dissipation into a heat bath and a reversible precession induced by a torque due to the local molecular field. For quenches to zero temperature, we provide convincing arguments, both numerically (Langevin simulation) and analytically (approximate closure scheme due to Mazenko), that the torque is irrelevant at late times. We subject the Mazenko closure scheme to systematic numerical tests. Such an analysis, carried out for the first time on a vector order parameter, shows that the closure scheme performs respectably well. For quenches to $T_c$, we show, to ${\cal O}(\epsilon^2)$, that the torque is irrelevant at the Wilson-Fisher fixed point.Comment: 13 pages, REVTEX, and 19 .eps figures, compressed, Submitted to Phys. Rev.

Spinodal Decomposition and the Tomita Sum Rule

The scaling properties of a phase-ordering system with a conserved order parameter are studied. The theory developed leads to scaling functions satisfying certain general properties including the Tomita sum rule. The theory also gives good agreement with numerical results for the order parameter scaling function in three dimensions. The values of the associated nonequilibrium decay exponents are given by the known lower bounds.Comment: 15 pages, 6 figure

The identification of mitochondrial DNA variants in glioblastoma multiforme

Background: Mitochondrial DNA (mtDNA) encodes key proteins of the electron transfer chain (ETC), which produces ATP through oxidative phosphorylation (OXPHOS) and is essential for cells to perform specialised functions. Tumor-initiating cells use aerobic glycolysis, a combination of glycolysis and low levels of OXPHOS, to promote rapid cell proliferation and tumor growth. Glioblastoma multiforme (GBM) is an aggressively malignant brain tumor and mitochondria have been proposed to play a vital role in GBM tumorigenesis. Results: Using next generation sequencing and high resolution melt analysis, we identified a large number of mtDNA variants within coding and non-coding regions of GBM cell lines and predicted their disease-causing potential through in silico modeling. The frequency of variants was greatest in the D-loop and origin of light strand replication in non-coding regions. ND6 was the most susceptible coding gene to mutation whilst ND4 had the highest frequency of mutation. Both genes encode subunits of complex I of the ETC. These variants were not detected in unaffected brain samples and many have not been previously reported. Depletion of HSR-GBM1 cells to varying degrees of their mtDNA followed by transplantation into immunedeficient mice resulted in the repopulation of the same variants during tumorigenesis. Likewise, de novo variants identified in other GBM cell lines were also incorporated. Nevertheless, ND4 and ND6 were still the most affected genes. We confirmed the presence of these variants in high grade gliomas. Conclusions: These novel variants contribute to GBM by rendering the ETC. partially dysfunctional. This restricts metabolism to anaerobic glycolysis and promotes cell proliferation

Evolution of speckle during spinodal decomposition

Time-dependent properties of the speckled intensity patterns created by scattering coherent radiation from materials undergoing spinodal decomposition are investigated by numerical integration of the Cahn-Hilliard-Cook equation. For binary systems which obey a local conservation law, the characteristic domain size is known to grow in time $\tau$ as $R = [B \tau]^n$ with n=1/3, where B is a constant. The intensities of individual speckles are found to be nonstationary, persistent time series. The two-time intensity covariance at wave vector ${\bf k}$ can be collapsed onto a scaling function $Cov(\delta t,\bar{t})$, where $\delta t = k^{1/n} B |\tau_2-\tau_1|$ and $\bar{t} = k^{1/n} B (\tau_1+\tau_2)/2$. Both analytically and numerically, the covariance is found to depend on $\delta t$ only through $\delta t/\bar{t}$ in the small-$\bar{t}$ limit and $\delta t/\bar{t} ^{1-n}$ in the large-$\bar{t}$ limit, consistent with a simple theory of moving interfaces that applies to any universality class described by a scalar order parameter. The speckle-intensity covariance is numerically demonstrated to be equal to the square of the two-time structure factor of the scattering material, for which an analytic scaling function is obtained for large $\bar{t}.$ In addition, the two-time, two-point order-parameter correlation function is found to scale as $C(r/(B^n\sqrt{\tau_1^{2n}+\tau_2^{2n}}),\tau_1/\tau_2)$, even for quite large distances $r$. The asymptotic power-law exponent for the autocorrelation function is found to be $\lambda \approx 4.47$, violating an upper bound conjectured by Fisher and Huse.Comment: RevTex: 11 pages + 12 figures, submitted to PR

Optimal Location of Sources in Transportation Networks

We consider the problem of optimizing the locations of source nodes in transportation networks. A reduction of the fraction of surplus nodes induces a glassy transition. In contrast to most constraint satisfaction problems involving discrete variables, our problem involves continuous variables which lead to cavity fields in the form of functions. The one-step replica symmetry breaking (1RSB) solution involves solving a stable distribution of functionals, which is in general infeasible. In this paper, we obtain small closed sets of functional cavity fields and demonstrate how functional recursions are converted to simple recursions of probabilities, which make the 1RSB solution feasible. The physical results in the replica symmetric (RS) and the 1RSB frameworks are thus derived and the stability of the RS and 1RSB solutions are examined.Comment: 38 pages, 18 figure

Phase-ordering of conserved vectorial systems with field-dependent mobility

The dynamics of phase-separation in conserved systems with an O(N) continuous symmetry is investigated in the presence of an order parameter dependent mobility M(\phi)=1-a \phi^2. The model is studied analytically in the framework of the large-N approximation and by numerical simulations of the N=2, N=3 and N=4 cases in d=2, for both critical and off-critical quenches. We show the existence of a new universality class for a=1 characterized by a growth law of the typical length L(t) ~ t^{1/z} with dynamical exponent z=6 as opposed to the usual value z=4 which is recovered for a<1.Comment: RevTeX, 8 pages, 13 figures, to be published in Phys. Rev.

Phase Separation Kinetics in a Model with Order-Parameter Dependent Mobility

We present extensive results from 2-dimensional simulations of phase separation kinetics in a model with order-parameter dependent mobility. We find that the time-dependent structure factor exhibits dynamical scaling and the scaling function is numerically indistinguishable from that for the Cahn-Hilliard (CH) equation, even in the limit where surface diffusion is the mechanism for domain growth. This supports the view that the scaling form of the structure factor is "universal" and leads us to question the conventional wisdom that an accurate representation of the scaled structure factor for the CH equation can only be obtained from a theory which correctly models bulk diffusion.Comment: To appear in PRE, figures available on reques

CRISPR interference at the FAAH-OUT genomic region reduces FAAH expression

FAAH-OUT encodes a putative long non-coding RNA which is located next to the FAAH gene on human chromosome 1. Recently an ~8 kb microdeletion, that removes upstream regulatory elements and the first 2 exons of FAAH-OUT, was reported in a pain insensitive patient (PFS) with additional clinical symptoms including a happy, non-anxious disposition, fast wound healing, fear and memory deficits, and significant post-operative nausea and vomiting induced by morphine. PFS also carries a hypomorphic SNP in FAAH that significantly reduces the activity of the encoded fatty-acid amide hydrolase enzyme. The FAAH and FAAH-OUT mutations identified in PFS result in elevated levels of anandamide (AEA), palmitoylethanolamide (PEA) and oleoylethanolamine (OEA) measured in peripheral blood. These bioactive lipids, which are normally degraded by FAAH, have diverse biological functions including known roles in pain pathways. Here we report the first mechanistic insights into how the FAAH-OUT microdeletion affects FAAH function. Gene editing in a human cell line to mimic the FAAH-OUT microdeletion observed in PFS results in reduced expression of FAAH. Furthermore, CRISPRi experiments targeting the promoter region of FAAH-OUT or a short highly evolutionarily conserved element in the first intron of FAAH-OUT also result in reduced expression of FAAH. These experiments confirm the importance of FAAH-OUT and specific genomic elements within the ~8 kb microdeleted sequence to normal FAAH expression. Our results also highlight the potential of CRISPRi and gene editing strategies that target the FAAH-OUT region for the development of novel FAAH-based analgesic and anxiolytic therapies

Optimal Resource Allocation in Random Networks with Transportation Bandwidths

We apply statistical physics to study the task of resource allocation in random sparse networks with limited bandwidths for the transportation of resources along the links. Useful algorithms are obtained from recursive relations. Bottlenecks emerge when the bandwidths are small, causing an increase in the fraction of idle links. For a given total bandwidth per node, the efficiency of allocation increases with the network connectivity. In the high connectivity limit, we find a phase transition at a critical bandwidth, above which clusters of balanced nodes appear, characterised by a profile of homogenized resource allocation similar to the Maxwell's construction.Comment: 28 pages, 11 figure