Global exponential convergence to variational traveling waves in cylinders

We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The convergence to this traveling wave is exponentially fast. The obtained result is mainly a consequence of the gradient flow structure of the considered equation in the exponentially weighted spaces and does not depend on the precise details of the problem. It strengthens our earlier generic propagation and selection result for "pushed" fronts.Comment: 23 page

Response of Seven Crystallographic Orientations of Sapphire Crystals to Shock Stresses of 16 to 86 GPa

Shock-wave profiles of sapphire (single-crystal Al2O3) with seven crystallographic orientations were measured with time-resolved VISAR interferometry at shock stresses in the range 16 to 86 GPa. Shock propagation was normal to the surface of each cut. The angle between the c-axis of the hexagonal crystal structure and the direction of shock propagation varied from 0 for c-cut up to 90 degrees for m-cut in the basal plane. Based on published shock-induced transparencies, shock-induced optical transparency correlates with the smoothness of the shock-wave profile. The ultimate goal was to find the direction of shock propagation in sapphire that is most transparent as a window. Particle velocity histories were recorded at the interface between a sapphire crystal and a LiF window. In most cases measured wave profiles are noisy as a result of heterogeneity of deformation. Measured values of Hugoniot Elastic Limits (HELs) depend on direction of shock compression and peak shock stress. The largest HEL values were recorded for shock loading along the c-axis and perpendicular to c along the m-direction. Shock compression along the m- and s-directions is accompanied by the smallest heterogeneity of deformation and the smallest rise time of the plastic shock wave. m- and s-cut sapphire most closely approach ideal elastic-plastic flow, which suggests that m- and s-cut sapphire are probably the orientations that remains most transparent to highest shock pressures. Under purely elastic deformation sapphire has very high spall strength, which depends on load duration and peak stress. Plastic deformation of sapphire causes loss of its tensile strength.Comment: 18 pages, 18 figure

Entropy-Dominated Dissipation in Sapphire Shock-Compressed up to 400 GPa (4 Mbar)

Sapphire (single-crystal Al2O3) is a representative Earth material and is used as a window and/or anvil in shock experiments. Pressure, for example, at the core-mantle boundary is about 130 gigapascals (GPa). Defects induced by 100-GPa shock waves cause sapphire to become opaque, which precludes measuring temperature with thermal radiance. We have measured wave profiles of sapphire crystals with several crystallographic orientations at shock pressures of 16, 23, and 86 GPa. At 23 GPa plastic-shock rise times are generally quite long (~100 ns) and their values depend sensitively on the direction of shock propagation in the crystal lattice. The long rise times are probably caused by the high strength of inter-atomic interactions in the ordered three-dimensional sapphire lattice. Our wave profiles and recent theoretical and laser-driven experimental results imply that sapphire disorders without significant shock heating up to about 400 GPa, above which Al2O3 is amorphous and must heat. This picture suggests that the characteristic shape of shock compression curves of many Earth materials at 100 GPa pressures is caused by a combination of entropy and temperature.Comment: 12 pages, 4 figure

Flame Enhancement and Quenching in Fluid Flows

We perform direct numerical simulations (DNS) of an advected scalar field which diffuses and reacts according to a nonlinear reaction law. The objective is to study how the bulk burning rate of the reaction is affected by an imposed flow. In particular, we are interested in comparing the numerical results with recently predicted analytical upper and lower bounds. We focus on reaction enhancement and quenching phenomena for two classes of imposed model flows with different geometries: periodic shear flow and cellular flow. We are primarily interested in the fast advection regime. We find that the bulk burning rate v in a shear flow satisfies v ~ a*U+b where U is the typical flow velocity and a is a constant depending on the relationship between the oscillation length scale of the flow and laminar front thickness. For cellular flow, we obtain v ~ U^{1/4}. We also study flame extinction (quenching) for an ignition-type reaction law and compactly supported initial data for the scalar field. We find that in a shear flow the flame of the size W can be typically quenched by a flow with amplitude U ~ alpha*W. The constant alpha depends on the geometry of the flow and tends to infinity if the flow profile has a plateau larger than a critical size. In a cellular flow, we find that the advection strength required for quenching is U ~ W^4 if the cell size is smaller than a critical value.Comment: 14 pages, 20 figures, revtex4, submitted to Combustion Theory and Modellin

Subexponential estimations in Shirshov's height theorem (in English)

In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: "Suppose that F_{2, m} is a 2-generated associative ring with the identity x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential growth?" We show that the nilpotency degree of l-generated associative algebra with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l (nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by this result. It is the consequence of one fact, which is based on combinatorics of words. Let l, n and d>n be positive integers. Then all the words over alphabet of cardinality l which length is greater than Psi(n,d,l) are either n-divided or contain d-th power of subword, where a word W is n-divided, if it can be represented in the following form W=W_0 W_1...W_n such that W_1 >' W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov proved that the set of non n-divided words over alphabet of cardinality l has bounded height h over the set Y consisting of all the words of degree <n. Original Shirshov's estimation was just recursive, in 1982 double exponent was obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation. We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55

Methodological limitations of psychosocial interventions in patients with an implantable cardioverter-defibrillator (ICD) A systematic review

<p>Abstract</p> <p>Background</p> <p>Despite the potentially life-saving benefits of the implantable cardioverter-defibrillator (ICD), a significant group of patients experiences emotional distress after ICD implantation. Different psychosocial interventions have been employed to improve this condition, but previous reviews have suggested that methodological issues may limit the validity of such interventions. Aim: To review the methodology of previously published studies of psychosocial interventions in ICD patients, according to CONSORT statement guidelines for non-pharmacological interventions, and provide recommendations for future research.</p> <p>Methods</p> <p>We electronically searched the PubMed, PsycInfo and Cochrane databases. To be included, studies needed to be published in a peer-reviewed journal between 1980 and 2008, to involve a human population aged 18+ years and to have an experimental design.</p> <p>Results</p> <p>Twelve studies met the eligibility criteria. Samples were generally small. Interventions were very heterogeneous; most studies used cognitive behavioural therapy (CBT) and exercise programs either as unique interventions or as part of a multi-component program. Overall, studies showed a favourable effect on anxiety (6/9) and depression (4/8). CBT appeared to be the most effective intervention. There was no effect on the number of shocks and arrhythmic events, probably because studies were not powered to detect such an effect. Physical functioning improved in the three studies evaluating this outcome. Lack of information about the indication for ICD implantation (primary vs. secondary prevention), limited or no information regarding use of anti-arrhythmic (9/12) and psychotropic (10/12) treatment, lack of assessments of providers' treatment fidelity (12/12) and patients' adherence to the intervention (11/12) were the most common methodological limitations.</p> <p>Conclusions</p> <p>Overall, this review supports preliminary evidence of a positive effect of psychosocial interventions on anxiety and physical functioning in ICD patients. However, these initial findings must be interpreted cautiously because of important methodological limitations. Future studies should be designed as large RCTs, whose design takes into account the specific challenges associated with the evaluation of behavioural interventions.</p

Protocol for a systematic review of screening tools for fear of recurrent illness in common life threatening diseases

This is the authors' accepted version of an article published in Systematic Reviews, 2015.A myocardial infarction (MI) (‘heart attack’) can be intensely stressful, and the impact of this event can leave patients with clinically significant post-MI stress symptoms. Untreated stress can make heart disease worse. Few tools are available that screen for specific thoughts or beliefs that can trigger post-MI stress responses. In other life-threatening illnesses, fear of recurrence (FoR) of illness has been identified as a key stressor, and screening tools have been developed to identify this. The aim of this review is to identify FoR screening tools used in other common life-threatening diseases that report on the development of the tool, to assess if there are any that can be adapted for use in MI survivors so that those with high levels of FoR can be identified and helped

Somatic mosaicism and common genetic variation contribute to the risk of very-early-onset inflammatory bowel disease

Abstract: Very-early-onset inflammatory bowel disease (VEO-IBD) is a heterogeneous phenotype associated with a spectrum of rare Mendelian disorders. Here, we perform whole-exome-sequencing and genome-wide genotyping in 145 patients (median age-at-diagnosis of 3.5 years), in whom no Mendelian disorders were clinically suspected. In five patients we detect a primary immunodeficiency or enteropathy, with clinical consequences (XIAP, CYBA, SH2D1A, PCSK1). We also present a case study of a VEO-IBD patient with a mosaic de novo, pathogenic allele in CYBB. The mutation is present in ~70% of phagocytes and sufficient to result in defective bacterial handling but not life-threatening infections. Finally, we show that VEO-IBD patients have, on average, higher IBD polygenic risk scores than population controls (99 patients and 18,780 controls; P < 4 × 10−10), and replicate this finding in an independent cohort of VEO-IBD cases and controls (117 patients and 2,603 controls; P < 5 × 10−10). This discovery indicates that a polygenic component operates in VEO-IBD pathogenesis