Nonequilibrium phase transitions in models of adsorption and desorption

The nonequilibrium phase transition in a system of diffusing, coagulating particles in the presence of a steady input and evaporation of particles is studied. The system undergoes a transition from a phase in which the average number of particles is finite to one in which it grows linearly in time. The exponents characterizing the mass distribution near the critical point are calculated in all dimensions.Comment: 10 pages, 2 figures (To appear in Phys. Rev. E

Quantum-fluctuation-induced repelling interaction of quantum string between walls

Quantum string, which was brought into discussion recently as a model for the stripe phase in doped cuprates, is simulated by means of the density-matrix-renormalization-group method. String collides with adjacent neighbors, as it wonders, owing to quantum zero-point fluctuations. The energy cost due to the collisions is our main concern. Embedding a quantum string between rigid walls with separation d, we found that for sufficiently large d, collision-induced energy cost obeys the formula \sim exp (- A d^alpha) with alpha=0.808(1), and string's mean fluctuation width grows logarithmically \sim log d. Those results are not understood in terms of conventional picture that the string is `disordered,' and only the short-wave-length fluctuations contribute to collisions. Rather, our results support a recent proposal that owing to collisions, short-wave-length fluctuations are suppressed, but instead, long-wave-length fluctuations become significant. This mechanism would be responsible for stabilizing the stripe phase

Quantum-fluctuation-induced collisions and subsequent excitation gap of an elastic string between walls

An elastic string embedded between rigid walls is simulated by means of the density-matrix renormalization group. The string collides against the walls owing to the quantum-mechanical zero-point fluctuations. Such ``quantum entropic'' interaction has come under thorough theoretical investigation in the context of the stripe phase observed experimentally in doped cuprates. We found that the excitation gap opens in the form of exponential singularity DeltaE ~ exp(-Ad^sigma) (d: wall spacing) with the exponent sigma =0.6(3), which is substantially smaller than the meanfield value sigma=2. That is, the excitation gap is much larger than that anticipated from meanfield, suggesting that the string is subjected to robust pinning potential due to the quantum collisions. This feature supports Zaanen's ``order out of disorder'' mechanism which would be responsible to the stabilization of the stripe phase

Vortex Dynamics and Defects in Simulated Flux Flow

We present the results of molecular dynamic simulations of a two-dimensional vortex array driven by a uniform current through random pinning centers at zero temperature. We identify two types of flow of the driven array near the depinning threshold. For weak disorder the flux array contains few dislocation and moves via correlated displacements of patches of vortices in a {\it crinkle} motion. As the disorder strength increases, we observe a crossover to a spatially inhomogeneous regime of {\it plastic} flow, with a very defective vortex array and a channel-like structure of the flowing regions. The two regimes are characterized by qualitatively different spatial distribution of vortex velocities. In the crinkle regime the distribution of vortex velocities near threshold has a single maximum that shifts to larger velocities as the driving force is increased. In the plastic regime the distribution of vortex velocities near threshold has a clear bimodal structure that persists upon time-averaging the individual velocities. The bimodal structure of the velocity distribution reflects the coexistence of pinned and flowing regions and is proposed as a quantitative signature of plastic flow.Comment: 12 pages, 13 embedded PostScript figure

Kang-Redner Anomaly in Cluster-Cluster Aggregation

The large time, small mass, asymptotic behavior of the average mass distribution \pb is studied in a $d$-dimensional system of diffusing aggregating particles for $1\leq d \leq 2$. By means of both a renormalization group computation as well as a direct re-summation of leading terms in the small reaction-rate expansion of the average mass distribution, it is shown that \pb \sim \frac{1}{t^d} (\frac{m^{1/d}}{\sqrt{t}})^{e_{KR}} for $m \ll t^{d/2}$, where $e_{KR}=\epsilon +O(\epsilon ^2)$ and $\epsilon =2-d$. In two dimensions, it is shown that \pb \sim \frac{\ln(m) \ln(t)}{t^2} for $m \ll t/ \ln(t)$. Numerical simulations in two dimensions supporting the analytical results are also presented.Comment: 11 pages, 6 figures, Revtex

Statistics and geometry of cosmic voids

We introduce new statistical methods for the study of cosmic voids, focusing on the statistics of largest size voids. We distinguish three different types of distributions of voids, namely, Poisson-like, lognormal-like and Pareto-like distributions. The last two distributions are connected with two types of fractal geometry of the matter distribution. Scaling voids with Pareto distribution appear in fractal distributions with box-counting dimension smaller than three (its maximum value), whereas the lognormal void distribution corresponds to multifractals with box-counting dimension equal to three. Moreover, voids of the former type persist in the continuum limit, namely, as the number density of observable objects grows, giving rise to lacunar fractals, whereas voids of the latter type disappear in the continuum limit, giving rise to non-lacunar (multi)fractals. We propose both lacunar and non-lacunar multifractal models of the cosmic web structure of the Universe. A non-lacunar multifractal model is supported by current galaxy surveys as well as cosmological $N$-body simulations. This model suggests, in particular, that small dark matter halos and, arguably, faint galaxies are present in cosmic voids.Comment: 39 pages, 8 EPS figures, supersedes arXiv:0802.038

Subgraphs in random networks

Understanding the subgraph distribution in random networks is important for modelling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as \mean{G} ~ N^{n-g}. However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find new scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as P(k) ~ k^{-\gamma}. Considering the power exponent of the degree distribution, \gamma, as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime the subgraph number of appearances follows a different scaling law, \mean{G} ~ N^{\alpha}, where \alpha=n-g+s-1 for \gamma<2, \alpha=n-g+s+1-\gamma for 2<\gamma<\gamma_c, and \alpha=n-g for \gamma>\gamma_c, s is the maximal outdegree in the subgraph, and \gamma_c=s+1. We find that certain subgraphs appear much more frequently than in Erdos networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.Comment: 8 pages, 5 figure

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

An Extreme Solar Event of 20 January 2005: Properties of the Flare and the Origin of Energetic Particles

The extreme solar and SEP event of 20 January 2005 is analyzed from two perspectives. Firstly, we study features of the main phase of the flare, when the strongest emissions from microwaves up to 200 MeV gamma-rays were observed. Secondly, we relate our results to a long-standing controversy on the origin of SEPs arriving at Earth, i.e., acceleration in flares, or shocks ahead of CMEs. All emissions from microwaves up to 2.22 MeV line gamma-rays during the main flare phase originated within a compact structure located just above sunspot umbrae. A huge radio burst with a frequency maximum at 30 GHz was observed, indicating the presence of a large number of energetic electrons in strong magnetic fields. Thus, protons and electrons responsible for flare emissions during its main phase were accelerated within the magnetic field of the active region. The leading, impulsive parts of the GLE, and highest-energy gamma-rays identified with pi^0-decay emission, are similar and correspond in time. The origin of the pi^0-decay gamma-rays is argued to be the same as that of lower energy emissions. We estimate the sky-plane speed of the CME to be 2000-2600 km/s, i.e., high, but of the same order as preceding non-GLE-related CMEs from the same active region. Hence, the flare itself rather than the CME appears to determine the extreme nature of this event. We conclude that the acceleration, at least, to sub-relativistic energies, of electrons and protons, responsible for both the flare emissions and the leading spike of SEP/GLE by 07 UT, are likely to have occurred simultaneously within the flare region. We do not rule out a probable contribution from particles accelerated in the CME-driven shock for the leading GLE spike, which seemed to dominate later on.Comment: 34 pages, 14 Postscript figures. Solar Physics, accepted. A typo corrected. The original publication is available at http://www.springerlink.co

HOPX functions as a tumour suppressor in head and neck cancer.

Head and neck squamous cell carcinoma (HNSCC) is generalized term that encompasses a diverse group of cancers that includes tumours of the oral cavity (OSCC), oropharynx (OPSCC) and nasopharynx (NPC). Genetic alterations that are common to all HNSCC types are likely to be important for squamous carcinogenesis. In this study, we have investigated the role of the homeodomain-only homeobox gene, HOPX, in the pathogenesis of HNSCC. We show that HOPX mRNA levels are reduced in OSCC and NPC cell lines and tissues and there is a general reduction of HOPX protein expression in these tumours and OPSCCs. HOPX promoter methylation was observed in a subset of HNSCCs and was associated with a worse overall survival in HPV negative tumours. RNAseq analysis of OSCC cells transfected with HOPX revealed a widespread deregulation of the transcription of genes related to epithelial homeostasis and ectopic over-expression of HOPX in OSCC and NPC cells inhibited cell proliferation, plating efficiency and migration, and enhanced sensitivity to UVA-induced apoptosis. Our results demonstrate that HOPX functions as a tumour suppressor in HNSCC and suggest a central role for HOPX in suppressing epithelial carcinogenesis