The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. II. Theoretical Model

The observed powerlaw distributions of solar flare parameters can be interpreted in terms of a nonlinear dissipative system in the state of self-organized criticality (SOC). We present a universal analytical model of a SOC process that is governed by three conditions: (i) a multiplicative or exponential growth phase, (ii) a randomly interrupted termination of the growth phase, and (iii) a linear decay phase. This basic concept approximately reproduces the observed frequency distributions. We generalize it to a randomized exponential-growth model, which includes also a (log-normal) distribution of threshold energies before the instability starts, as well as randomized decay times, which can reproduce both the observed occurrence frequency distributions and the scatter of correlated parametyers more realistically. With this analytical model we can efficiently perform Monte-Carlo simulations of frequency distributions and parameter correlations of SOC processes, which are simpler and faster than the iterative simulations of cellular automaton models. Solar cycle modulations of the powerlaw slopes of flare frequency distributions can be used to diagnose the thresholds and growth rates of magnetic instabilities responsible for solar flares.Comment: Part II of Paper I: The State of Self-Organized Criticality of the Sun During the Last Three Solar Cycles. I. Observation

Analysis of tumor as an inverse problem provides a novel theoretical framework for understanding tumor biology and therapy

We use a novel “inverse problem” technique to construct a basic mathematical model of the interacting populations at the tumor-host interface. This approach assumes that invasive cancer is a solution to the set of state equations that govern the interactions of transformed and normal cells. By considering the invading tumor edge as a traveling wave, the general form of the state equations can be inferred. The stability of this traveling wave solution imposes constraints on key biological quantities which appear as parameters in the model equations. Based on these constraints, we demonstrate the limitations of traditional therapeutic strategies in clinical oncology that focus solely on killing tumor cells or reducing their rate of proliferation. The results provide insights into fundamental mechanisms that may prevent these approaches from successfully eradicating most common cancers despite several decades of research. Alternative therapies directed at modifying the key parameters in the state equations to destabilize the propagating solution are proposed

Viral Retinitis following Intraocular or Periocular Corticosteroid Administration: A Case Series and Comprehensive Review of the Literature.

Abstract Purpose: To describe viral retinitis following intravitreal and periocular corticosteroid administration. Methods: Retrospective case series and comprehensive literature review. Results: We analyzed 5 unreported and 25 previously published cases of viral retinitis following local corticosteroid administration. Causes of retinitis included 23 CMV (76.7%), 5 HSV (16.7%), and 1 each VZV and unspecified (3.3%). Two of 22 tested patients (9.1%) were HIV positive. Twenty-one of 30 (70.0%) cases followed one or more intravitreal injections of triamcinolone acetonide (TA), 4 (13.3%) after one or more posterior sub-Tenon injections of TA, 3 (10.0%) after placement of a 0.59-mg fluocinolone acetonide implant (Retisert), and 1 (3.3%) each after an anterior subconjunctival injection of TA (together with IVTA), an anterior chamber injection, and an anterior sub-Tenon injection. Mean time from most recent corticosteroid administration to development of retinitis was 4.2 months (median 3.8; range 0.25-13.0). Twelve patients (40.0%) had type II diabetes mellitus. Treatments used included systemic antiviral agents (26/30, 86.7%), intravitreal antiviral injections (20/30, 66.7%), and ganciclovir intravitreal implants (4/30, 13.3%). Conclusions: Viral retinitis may develop or reactivate following intraocular or periocular corticosteroid administration. Average time to development of retinitis was 4 months, and CMV was the most frequently observed agent. Diabetes was a frequent co-morbidity and several patients with uveitis who developed retinitis were also receiving systemic immunosuppressive therapy

Generation of Porous Particle Structures using the Void Expansion Method

The newly developed "void expansion method" allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions using the discrete element method. Particles are randomly placed under addition of much smaller "void-particles". Then, the void-particle radius is increased repeatedly, thereby rearranging the structural particles until formation of a dense particle packing. The structural particles' mean coordination number was used to characterize the evolving microstructures. At some void radius, a transition from an initially low to a higher mean coordination number is found, which was used to characterize the influence of the various simulation parameters. For structural and void-particle stiffnesses of the same order of magnitude, the transition is found at constant total volume fraction slightly below the random close packing limit. For decreasing void-particle stiffness the transition is shifted towards a smaller void-particle radius and becomes smoother.Comment: 9 pages, 8 figure

Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four-dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomophic theory of gravity could be inconsistent with a theorem of the dual unitary quantum field theory.Comment: 18 pages, v2: reference added, v3: comments on more recent literature added in response to referee's reques

Spin dynamics of wave packets evolving with the Dirac Hamiltonian in atoms with high Z

The motion of circular WP for one electron in central Coulomb field with high Z is calculated. The WP is defined in terms of solutions of the Dirac equation in order to take into account all possible relevant effects in particular the spin-orbit potential. A time scale is defined within which spin dynamics must be taken into account mainly in the atoms with high Z. Within this time scale there exists a mechanism of collapses and revivals of the spin already shown by the authors for harmonic oscillator potential and called the 'spin-orbit pendulum'. However this effect has not the exact periodicity of the simpler model, but the WP's spatial motion is nevertheless quite similar.Comment: 17 pages, 9 figures, LaTeX2e, uses IOP style files (included). Title changed, one reference adde

The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February 2012

Anisotropic Superparamagnetism of Monodispersive Cobalt-Platinum Nanocrystals

Based on the high-temperature organometallic route (Sun et al. Science 287, 1989 (2000)), we have synthesized powders containing CoPt_3 single crystals with mean diameters of 3.3(2) nm and 6.0(2) nm and small log-normal widths sigma=0.15(1). In the entire temperature range from 5 K to 400 K, the zero-field cooled susceptibility chi(T) displays significant deviations from ideal superparamagnetism. Approaching the Curie temperature of 450(10) K, the deviations arise from the (mean-field) type reduction of the ferromagnetic moments, while below the blocking temperature T_b, chi(T) is suppressed by the presence of energy barriers, the distributions of which scale with the particle volumes obtained from transmission electron microscopy (TEM). This indication for volume anisotropy is supported by scaling analyses of the shape of the magnetic absorption chi''(T,omega) which reveal distribution functions for the barriers being also consistent with the volume distributions observed by TEM. Above 200 K, the magnetization isotherms M(H,T) display Langevin behavior providing 2.5(1) mu_B per CoPt_3 in agreement with reports on bulk and thin film CoPt_3. The non-Langevin shape of the magnetization curves at lower temperatures is for the first time interpreted as anisotropic superparamagnetism by taking into account an anisotropy energy of the nanoparticles E_A(T). Using the magnitude and temperature variation of E_A(T), the mean energy barriers and 'unphysical' small switching times of the particles obtained from the analyses of chi''(T,omega) are explained. Below T_b hysteresis loops appear and are quantitatively described by a blocking model, which also ignores particle interactions, but takes the size distributions from TEM and the conventional field dependence of E_A into account.Comment: 12 pages with 10 figures and 1 table. Version accepted for publication in Phys. Rev. B . Two-column layou

A Field-theoretical Interpretation of the Holographic Renormalization Group

A quantum-field theoretical interpretation is given to the holographic RG equation by relating it to a field-theoretical local RG equation which determines how Weyl invariance is broken in a quantized field theory. Using this approach we determine the relation between the holographic C theorem and the C theorem in two-dimensional quantum field theory which relies on the Zamolodchikov metric. Similarly we discuss how in four dimensions the holographic C function is related to a conjectured field-theoretical C function. The scheme dependence of the holographic RG due to the possible presence of finite local counterterms is discussed in detail, as well as its implications for the holographic C function. We also discuss issues special to the situation when mass deformations are present. Furthermore we suggest that the holographic RG equation may also be obtained from a bulk diffeomorphism which reduces to a Weyl transformation on the boundary.Comment: 24 pages, LaTeX, no figures; references added, typos corrected, paragraph added to section