Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation

We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a zero-Hamiltonian solution of a fourth-order nonlinear eigenvalue problem

Ring-type singular solutions of the biharmonic nonlinear Schrodinger equation

We present new singular solutions of the biharmonic nonlinear Schrodinger equation in dimension d and nonlinearity exponent 2\sigma+1. These solutions collapse with the quasi self-similar ring profile, with ring width L(t) that vanishes at singularity, and radius proportional to L^\alpha, where \alpha=(4-\sigma)/(\sigma(d-1)). The blowup rate of these solutions is 1/(3+\alpha) for 4/d\le\sigma<4, and slightly faster than 1/4 for \sigma=4. These solutions are analogous to the ring-type solutions of the nonlinear Schrodinger equation.Comment: 21 pages, 13 figures, research articl

Thermal collapse of a granular gas under gravity

Free cooling of a gas of inelastically colliding hard spheres represents a central paradigm of kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity, which brings inhomogeneity, affect the cooling? We combine molecular dynamics simulations, a numerical solution of hydrodynamic equations and an analytic theory to show that a granular gas cooling under gravity undergoes thermal collapse: it cools down to zero temperature and condenses on the bottom of the container in a finite time.Comment: 4 pages, 12 eps figures, to appear in PR

Velocity fluctuations of noisy reaction fronts propagating into a metastable state: testing theory in stochastic simulations

The position of a reaction front, propagating into a metastable state, fluctuates because of the shot noise of reactions and diffusion. A recent theory [B. Meerson, P.V. Sasorov, and Y. Kaplan, Phys. Rev. E 84, 011147 (2011)] gave a closed analytic expression for the front diffusion coefficient in the weak noise limit. Here we test this theory in stochastic simulations involving reacting and diffusing particles on a one-dimensional lattice. We also investigate a small noise-induced systematic shift of the front velocity compared to the prediction from the spatially continuous deterministic reaction-diffusion equation.Comment: 5 pages, 5 figure

Psychological interventions for caregivers of people with bipolar disorder: A systematic review and meta-analysis

AIMS: Clinical guidelines recommend psychological interventions be offered to caregivers of people with bipolar disorder. However, there is little clarity about the efficacy of such interventions. This review examined the efficacy of psychological interventions in improving caregiver-focused outcomes, including burden, psychological symptoms and knowledge. METHOD: A systematic search for controlled trials was conducted using a combination of electronic database searches (PsycINFO, MEDLINE, and CENTRAL), and hand searches. Risk of bias was assessed using the Cochrane Collaboration tool. Outcomes were meta-analysed using Review Manager (RevMan). RESULTS: Nine studies met inclusion criteria. All meta-analyses compared psychoeducation to a control. At post-treatment there was a large effect of psychoeducation on burden (g = -0.8, 95% CI: -1.32, -0.27). However, there was high heterogeneity, confidence intervals were wide, and the effect was not maintained at follow-up. The apparent effect of psychoeducation on psychological symptoms was driven by a single outlying study. There was a very large effect on knowledge at post-treatment (g = 2.60, 95% CI: 1.39, 3.82) and follow-up (g =2.41, 95% CI: 0.85, 3.98). LIMITATIONS: There was considerable diversity in study methodology and quality. The number of included studies and sample sizes were small. CONCLUSIONS: This review provides tentative meta-analytic evidence for the efficacy of psychoeducation in improving caregiver burden at post-treatment, and knowledge at post-treatment and follow-up. Services could consider offering psychoeducation as part of a multi-disciplinary package of care. However, more methodologically rigorous research is needed before clinical recommendations can be made with confidence

'Between a rock and a hard place': family members' experiences of supporting a relative with bipolar disorder

Purpose: Clinical guidelines emphasise the central role of family members in supporting people with bipolar disorder. However, there has been little focus on the challenges family members face in supporting their relative. This qualitative study explored the challenges of providing support to a relative with bipolar disorder, and how family members attempted to meet these challenges. Factors that helped or hindered their efforts were also explored, including experiences of professional support. Methods: Semi-structured interviews were conducted with 18 family members (partners, parents, adult children, and siblings). Transcripts were analysed using the Framework approach. Results: Participants faced numerous challenges pertaining to the nature of the disorder and specific illness phases, their relative’s responses to their attempts to help, and the limitations of support from healthcare professionals. Although participants were resourceful in managing these challenges, they strongly valued professional input. Six themes were identified: ‘Not knowing: like being in a minefield’, ‘It’s out of my control: sitting waiting for the next thing to happen’, ‘Treading on eggshells’, ‘Picking up on signs’, ‘Times of crisis: between a rock and a hard place’, and ‘I have to make my voice heard’. Conclusions: Family members supporting a relative with bipolar disorder face significant challenges but show considerable resourcefulness in managing them. The findings underline the importance of input from healthcare professionals to help family members effectively support their relative and manage the challenges they face. Professional support should be strengths-based, and tailored to family members’ needs

Extinction of metastable stochastic populations

We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling (scenario A) or attracting (scenario B) point of the deterministic rate equation. In scenario A the metastable stochastic population resides in the vicinity of an attracting fixed point next to the repelling point n=0. In scenario B there is an intermediate repelling point n=n_1 between the attracting point n=0 and another attracting point n=n_2 in the vicinity of which the metastable population resides. The crux of the theory is WKB method which assumes that the typical population size in the metastable state is large. Starting from the master equation, we calculate the quasi-stationary probability distribution of the population sizes and the (exponentially long) mean time to extinction for each of the two scenarios. When necessary, the WKB approximation is complemented (i) by a recursive solution of the quasi-stationary master equation at small n and (ii) by the van Kampen system-size expansion, valid near the fixed points of the deterministic rate equation. The theory yields both entropic barriers to extinction and pre-exponential factors, and holds for a general set of multi-step processes when detailed balance is broken. The results simplify considerably for single-step processes and near the characteristic bifurcations of scenarios A and B.Comment: 19 pages, 7 figure

Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.Comment: 4 pages, 7 figure

Weak-coupling phase diagrams of bond-aligned and diagonal doped Hubbard ladders

We study, using a perturbative renormalization group technique, the phase diagrams of bond-aligned and diagonal Hubbard ladders defined as sections of a square lattice with nearest-neighbor and next-nearest-neighbor hopping. We find that for not too large hole doping and small next-nearest-neighbor hopping the bond-aligned systems exhibit a fully spin-gapped phase while the diagonal systems remain gapless. Increasing the next-nearest-neighbor hopping typically leads to a decrease of the gap in the bond-aligned ladders, and to a transition into a gapped phase in the diagonal ladders. Embedding the ladders in an antiferromagnetic environment can lead to a reduction in the extent of the gapped phases. These findings suggest a relation between the orientation of hole-rich stripes and superconductivity as observed in LSCO.Comment: Published version. The set of RG equations in the presence of magnetization was corrected and two figures were replace