Existence and stability of singular patterns in a Ginzburg–Landau equation coupled with a mean field

We study singular patterns in a particular system of parabolic partial differential equations which consist of a Ginzburg–Landau equation and a mean field equation. We prove the existence of the three simplest concentrated periodic stationary patterns (single spikes, double spikes, double transition layers) by composing them of more elementary patterns and solving the corresponding consistency conditions. In the case of spike patterns we prove stability for sufficiently large spatial periods by first showing that the eigenvalues do not tend to zero as the period goes to infinity and then passing in the limit to a nonlocal eigenvalue problem which can be studied explicitly. For the two other patterns we show instability by using the variational characterization of eigenvalues

2s Hyperfine Structure in Hydrogen Atom and Helium-3 Ion

The usefulness of study of hyperfine splitting in the hydrogen atom is limited on a level of 10 ppm by our knowledge of the proton structure. One way to go beyond 10 ppm is to study a specific difference of the hyperfine structure intervals 8 Delta nu_2 - Delta nu_1. Nuclear effects for are not important this difference and it is of use to study higher-order QED corrections.Comment: 10 pages, presented at Hydrogen Atom II meeting (2000

The Covalent Interaction between Dihydrogen and Gold: a Rotational Spectroscopic Study of H₂-AuCl

The pure rotational transitions of H2-AuCl have been measured using a pulsed-jet cavity Fourier transform microwave spectrometer equipped with a laser ablation source. The structure was found to be T-shaped, with the H-H bond interacting with the gold atom. Both 35Cl and 37Cl isotopologues have been measured for both ortho and para states of H2. Rotational constants, quartic centrifugal distortion constants, and nuclear quadrupole coupling constants for gold and chlorine have been determined. The use of the nuclear spin-nuclear spin interaction terms Daa, Dbb, and Dcc for H2 were required to fit the ortho state of hydrogen, as well as a nuclear-spin rotation constant Caa. The values of the nuclear quadrupole coupling constant of gold are Xaa=-817.9929(35) MHz, Xbb=504.0(27) MHz, and Xcc=314.0(27). This is large compared to the eQq of AuCl, 9.63 312(13) MHz, which indicates a strong, covalent interaction between gold and dihydrogen

Interleukin-6 and interleukin-6 receptor secretion by chronic lymphatic leukaemia and normal B lymphocytes: effect of PMA and PWM

Interleukin-6 (IL-6) and soluble interleukin-6 receptor (sIL-6R) were detected in supernatants of cultures of B chronic lymphatic leukaemia (CLL) lymphocytes. Phorbol-12-myristate 13 acetate (PMA) caused a decrease in the levels of IL-6 in 14 out of 16 cultures and an increase in levels of sIL6R in all 15 cases. The effect of pokeweed mitogen (PWM) was variable and not significant. The levels of IL-6 were below the detection limit (60 pg/ml) in sera of 13 CLL patients whereas sIL-6R was detected (13 ng/ml to 97 ng/ml) in the 13 sera. IL6 was not detected in cultures of unstimulated or stimulated with PMA or PWM normal human B cells. Levels of sIL-6R were minimal in cultures of normal B lymphocytes and were increased in PMA stimulated cultures. The results are consistent with the view that B-CLL cells produce spontaneously IL-6 which could act in an autocrine fashion to cause shedding of surface IL-6R and account for the correlation found between serum levels of sIL-6R and B-CLL lymphocyte numbers. The fall in levels of IL-6 in PMA stimulated CLL cultures might express masking or degradation of IL-6 after combination with the receptor

Cost-effectiveness of financial incentives to promote adherence to depot antipsychotic medication: economic evaluation of a cluster-randomised controlled trial

Background: Offering a modest financial incentive to people with psychosis can promote adherence to depot antipsychotic medication, but the cost-effectiveness of this approach has not been examined. Methods: Economic evaluation within a pragmatic cluster-randomised controlled trial. 141 patients under the care of 73 teams (clusters) were randomised to intervention or control; 138 patients with diagnoses of schizophrenia, schizo-affective disorder or bipolar disorder participated. Intervention participants received £15 per depot injection over 12 months, additional to usual acute, mental and community primary health services. The control group received usual health services. Main outcome measures: incremental cost per 20% increase in adherence to depot antipsychotic medication; incremental cost of ‘good’ adherence (defined as taking at least 95% of the prescribed number of depot medications over the intervention period). Findings: Economic and outcome data for baseline and 12-month follow-up were available for 117 participants. The adjusted difference in adherence between groups was 12.2% (73.4% control vs. 85.6% intervention); the adjusted costs difference was £598 (95% CI -£4 533, £5 730). The extra cost per patient to increase adherence to depot medications by 20% was £982 (95% CI -£8 020, £14 000). The extra cost per patient of achieving 'good' adherence was £2 950 (CI -£19 400, £27 800). Probability of cost-effectiveness exceeded 97.5%at willingness-to-pay values of £14 000 for a 20% increase in adherence and £27 800 for good adherence. Interpretation: Offering a modest financial incentive to people with psychosis is cost-effective in promoting adherence to depot antipsychotic medication. Direct healthcare costs (including costs of the financial incentive) are unlikely to be increased by this intervention. Trial Registration: ISRCTN.com 7776928

Boolean Models of Bistable Biological Systems

This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex differential equations models. The motivation for this work comes from mathematical systems biology. While Boolean mechanisms do not provide information about exact concentration rates or time scales, they are often sufficient to capture steady states and other key dynamics. Due to their intuitive nature, such models are very appealing to researchers in the life sciences. This paper is focused on dynamical systems that exhibit bistability and are desc ribedby delay equations. It is shown that if a certain motif including a feedback loop is present in the wiring diagram of the system, the Boolean model captures the bistability of molecular switches. The method is appl ied to two examples from biology, the lac operon and the phage lambda lysis/lysogeny switch

Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlinearity is "supercritical" in the case of two and three space dimensions. Thus the standard methods used for studying semilinear hyperbolic equations are not very effective in the present case. Nevertheless, we have recently proven the global existence and dissipativity of strong solutions in the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case with small inertial coefficient and arbitrary growth rate of the nonlinearity. The present contribution studies the long-time behavior of rather weak (energy) solutions of that equation and it is a natural complement of the results of our previous papers. Namely, we prove here that the attractors for energy and strong solutions coincide for both the cases mentioned above. Thus, the energy solutions are asymptotically smooth. In addition, we show that the non-smooth part of any energy solution decays exponentially in time and deduce that the (smooth) exponential attractor for the strong solutions constructed previously is simultaneously the exponential attractor for the energy solutions as well

Longtime behavior of nonlocal Cahn-Hilliard equations

Here we consider the nonlocal Cahn-Hilliard equation with constant mobility in a bounded domain. We prove that the associated dynamical system has an exponential attractor, provided that the potential is regular. In order to do that a crucial step is showing the eventual boundedness of the order parameter uniformly with respect to the initial datum. This is obtained through an Alikakos-Moser type argument. We establish a similar result for the viscous nonlocal Cahn-Hilliard equation with singular (e.g., logarithmic) potential. In this case the validity of the so-called separation property is crucial. We also discuss the convergence of a solution to a single stationary state. The separation property in the nonviscous case is known to hold when the mobility degenerates at the pure phases in a proper way and the potential is of logarithmic type. Thus, the existence of an exponential attractor can be proven in this case as well

On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities

We study a non-local variant of a diffuse interface model proposed by Hawkins--Darrud et al. (2012) for tumour growth in the presence of a chemical species acting as nutrient. The system consists of a Cahn--Hilliard equation coupled to a reaction-diffusion equation. For non-degenerate mobilities and smooth potentials, we derive well-posedness results, which are the non-local analogue of those obtained in Frigeri et al. (European J. Appl. Math. 2015). Furthermore, we establish existence of weak solutions for the case of degenerate mobilities and singular potentials, which serves to confine the order parameter to its physically relevant interval. Due to the non-local nature of the equations, under additional assumptions continuous dependence on initial data can also be shown.Comment: 28 page