A generalization of Turaev's virtual string cobracket and self-intersections of virtual strings

Previously we defined an operation µ that generalizes Turaev’s cobracket for loops on a surface. We showed that, in contrast to the cobracket, this operation gives a formula for the minimum number of self-intersections of a loop in a given free homotopy class. In this paper we consider the corresponding question for virtual strings, and conjecture that µ gives a formula for the minimum number of self-intersection points of a virtual string in a given virtual homotopy class. To support the conjecture, we show that µ gives a bound on the minimal self-intersection number of a virtual string which is stronger than a bound given by Turaev’s virtual string cobracket. We also use Turaev’s based matrices to describe a large set of strings α such that µ gives a formula for the minimal self-intersection number α. Finally, we construct an example that shows the bound on the minimal self-intersection number given by µ is always at least as good as, and sometimes stronger than, the bound ρ given by Turaev’s based matrix invariant

Entropy production in phase field theories

Allen-Cahn (Ginzburg-Landau) dynamics for scalar fields with heat conduction is treated in rigid bodies using a non-equilibrium thermodynamic framework with weakly nonlocal internal variables. The entropy production and entropy flux is calculated with the classical method of irreversible thermodynamics by separating full divergences.Comment: 5 pages, no figure

Two Stages in the evolution of binary alkali Bose-Einstein condensate mixtures towards phase segregation

Two stages of quantum spinodal decomposition is proposed and analyzed for this highly non-equilibrium process. Both time and spatial scales for the process are found. Qualitative agreement with existing data is found. Some cases the agreements are quantitative. Further experimental verifications are indicated.Comment: late

Two Modes of Solid State Nucleation - Ferrites, Martensites and Isothermal Transformation Curves

When a crystalline solid such as iron is cooled across a structural transition, its final microstructure depends sensitively on the cooling rate. For instance, an adiabatic cooling across the transition results in an equilibrium `ferrite', while a rapid cooling gives rise to a metastable twinned `martensite'. There exists no theoretical framework to understand the dynamics and conditions under which both these microstructures obtain. Existing theories of martensite dynamics describe this transformation in terms of elastic strain, without any explanation for the occurence of the ferrite. Here we provide evidence for the crucial role played by non-elastic variables, {\it viz.}, dynamically generated interfacial defects. A molecular dynamics (MD) simulation of a model 2-dimensional (2d) solid-state transformation reveals two distinct modes of nucleation depending on the temperature of quench. At high temperatures, defects generated at the nucleation front relax quickly giving rise to an isotropically growing `ferrite'. At low temperatures, the defects relax extremely slowly, forcing a coordinated motion of atoms along specific directions. This results in a twinned critical nucleus which grows rapidly at speeds comparable to that of sound. Based on our MD results, we propose a solid-state nucleation theory involving the elastic strain and non-elastic defects, which successfully describes the transformation to both a ferrite and a martensite. Our work provides useful insights on how to formulate a general dynamics of solid state transformations.Comment: 3 pages, 4 B/W + 2 color figure

Clinical-epidemiological features of HIV-infected patients diagnosed at age of 50 years or older

HIV/AIDS prevention and care efforts are directed to individuals of reproductive age (15–49 yrs). With the extension of sexual life of older people, they became a growing population at risk of HIV infection, usually not included in prevention strategies. In order to evaluate clinical profile of HIV/AIDS pts diagnosed at 50 yrs or older assisted in an HIV outpatient center in Buenos Aires, we retrospectively assessed clinical records of pts initiating care between Jan 1986 and Dec 2011. Age, CD4 cells and viral load (pVL) at HIV diagnosis and most recent value, opportunistic infections (OIs), co-morbidities and antiretroviral therapy (ARV) were recorded. Of 10,998 pts assisted in the 26-yr period, 495 (4.5%) were≥50 yrs old at HIV diagnosis; median annual diagnoses: 18.5 (IQR 3.3–30.3) without significant changes in the last 20 yrs. Demographics: median age 54.7 yrs (IQR 51.8–59.2, rank 50–80), 76.6% male. Risk behavior: HTX 61.4%, MSM 34.1%, others 4.4%. 55.4% of HIV diagnoses occurred during hospitalization or simultaneously with acute OIs. One third (n=176) had AIDS at diagnosis, 24% had history of STDs. HCV co-infection 5.7%, past HBV infection 28.1% and chronic HBV infection 5.1%. Median CD4 cells at HIV diagnosis: 223.5 (13.7%) (IQR 98.8–420.3), initial pVL 60,000 cp/mL (IQR 9,995.5–208,391). 69.3% of pts started ARV therapy during follow-up (FU), and the median time between diagnosis and treatment initiation was 3.4 mo (IQR 0.7–14); 56.9% of them started a non-nucleoside-based regimen (ZDV/3TC/EFV), 28.3% a PI-based regimen (ZDV/3TC/IDV) and 14.6% a nucleoside-based regimen (ZDV/ddI pre-HAART era). After a year (±6 mo), 63.8% pts achieved undetectable pVL and gained 136 CD4 cells from BSL (IQR 83–204). After 40.6 mo of FU (IQR 6.7-89.8), 66.3% are alive, 7.1% died (68.6% of HIV-related diseases) and 26.7% are lost to FU. Co-morbidities were present in 125 (25.3%), mainly hypertension, increased lipids, CVD and DBT. Among treated pts, 70.6% achieved pVL<50 cp/mL, with a median increase of CD4 cells up to 410 (22%) (IQR 281.5–563.9) from BSL. 51% (176) changed ARV therapy due to toxicity/AE: 54.5%, ARV failure: 29.5% and simplification: 14.8%. Stable HIV epidemic in older people reinforce the need of specific prevention approaches, while growing age of HIV individuals in care highlights to consider risks associated to older age. Late presentation to care needs to be specifically addressed. Response to treatment is remarkable high in this population

Azimuthal Correlation in Lepton-Hadron Scattering via Charged Weak-Current Processes

We consider the azimuthal correlation of the final-state particles in charged weak-current processes. This correlation provides a test of perturbative quantum chromodynamics. The azimuthal asymmetry is large in the semi-inclusive processes in which we identify a final-state hadron, say, a charged pion compared to that in the inclusive processes in which we do not identify final-state particles and use only the calorimetric information. In semi-inclusive processes the azimuthal asymmetry is more conspicuous when the incident lepton is an antineutrino or a positron than when the incident lepton is a neutrino or an electron. We analyze all the possible charged weak-current processes and study the quantitative aspects of each process. We also compare this result to the ep scattering with a photon exchange.Comment: 25 pages, 2 Postscript figures, uses RevTeX, fixes.st