Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories

In this paper we study the kinetics of diffusion-limited, pseudo-first-order A + B -> B reactions in situations in which the particles' intrinsic reactivities vary randomly in time. That is, we suppose that the particles are bearing "gates" which interchange randomly and independently of each other between two states - an active state, when the reaction may take place, and a blocked state, when the reaction is completly inhibited. We consider four different models, such that the A particle can be either mobile or immobile, gated or ungated, as well as ungated or gated B particles can be fixed at random positions or move randomly. All models are formulated on a $d$-dimensional regular lattice and we suppose that the mobile species perform independent, homogeneous, discrete-time lattice random walks. The model involving a single, immobile, ungated target A and a concentration of mobile, gated B particles is solved exactly. For the remaining three models we determine exactly, in form of rigorous lower and upper bounds, the large-N asymptotical behavior of the A particle survival probability. We also realize that for all four models studied here such a probalibity can be interpreted as the moment generating function of some functionals of random walk trajectories, such as, e.g., the number of self-intersections, the number of sites visited exactly a given number of times, "residence time" on a random array of lattice sites and etc. Our results thus apply to the asymptotical behavior of the corresponding generating functions which has not been known as yet.Comment: Latex, 45 pages, 5 ps-figures, submitted to PR

Number of Common Sites Visited by N Random Walkers

We compute analytically the mean number of common sites, W_N(t), visited by N independent random walkers each of length t and all starting at the origin at t=0 in d dimensions. We show that in the (N-d) plane, there are three distinct regimes for the asymptotic large t growth of W_N(t). These three regimes are separated by two critical lines d=2 and d=d_c(N)=2N/(N-1) in the (N-d) plane. For d<2, W_N(t)\sim t^{d/2} for large t (the N dependence is only in the prefactor). For 2<d<d_c(N), W_N(t)\sim t^{\nu} where the exponent \nu= N-d(N-1)/2 varies with N and d. For d>d_c(N), W_N(t) approaches a constant as t\to \infty. Exactly at the critical dimensions there are logaritmic corrections: for d=2, we get W_N(t)\sim t/[\ln t]^N, while for d=d_c(N), W_N(t)\sim \ln t for large t. Our analytical predictions are verified in numerical simulations.Comment: 5 pages, 3 .eps figures include

The roots of "Western European societal evolution". A concept of Europe by Jenő Szűcs

Jenő Szűcs wrote his essay entitled Sketch on the three regions of Europe in the early 1980s in Hungary. During these years, a historically well-argued opinion emphasising a substantial difference between Central European and Eastern European societies was warmly received in various circles of the political opposition. In a wider European perspective Szűcs used the old “liberty topos” which claims that the history of Europe is no other than the fulfillment of liberty. In his Sketch, Szűcs does not only concentrate on questions concerning the Middle Ages in Western Europe. Yet it is this stream of thought which brought a new perspective to explaining European history. His picture of the Middle Ages represents well that there is a way to integrate all typical Western motifs of post-war self-definition into a single theory. Mainly, the “liberty motif”, as a sign of “Europeanism” – in the interpretation of Bibó’s concept, Anglo-saxon Marxists and Weber’s social theory –, developed from medieval concepts of state and society and from an analysis of economic and social structures. Szűcs’s historical aspect was a typical intellectual product of the 1980s: this was the time when a few Central European historians started to outline non-Marxist aspects of social theory and categories of modernisation theories, but concealing them with Marxist terminology

Diffusion with random distribution of static traps

The random walk problem is studied in two and three dimensions in the presence of a random distribution of static traps. An efficient Monte Carlo method, based on a mapping onto a polymer model, is used to measure the survival probability P(c,t) as a function of the trap concentration c and the time t. Theoretical arguments are presented, based on earlier work of Donsker and Varadhan and of Rosenstock, why in two dimensions one expects a data collapse if -ln[P(c,t)]/ln(t) is plotted as a function of (lambda t)^{1/2}/ln(t) (with lambda=-ln(1-c)), whereas in three dimensions one expects a data collapse if -t^{-1/3}ln[P(c,t)] is plotted as a function of t^{2/3}lambda. These arguments are supported by the Monte Carlo results. Both data collapses show a clear crossover from the early-time Rosenstock behavior to Donsker-Varadhan behavior at long times.Comment: 4 pages, 6 figure

N, NH, and NH2 radical densities in a remote Ar-NH3-SiH4 plasma and their role in silicon nitride deposition

The densities of N, NH, and NH2 radicals in a remote Ar-NH3-SiH4 plasma used for high-rate silicon nitride deposition were investigated for different gas mixts. and plasma settings using cavity ringdown absorption spectroscopy and threshold ionization mass spectrometry. For typical deposition conditions, the N, NH, and NH2 radical densities are on the order of 1012 cm-3 and the trends with NH3 flow, SiH4 flow, and plasma source current are reported. We present a feasible reaction pathway for the prodn. and loss of the NHx radicals that is consistent with the exptl. results. Furthermore, mass spectrometry revealed that the consumption of NH3 was typically 40%, while it was over 80% for SiH4. On the basis of the measured N densities we deduced the recombination and sticking coeff. for N radicals on a silicon nitride film. Using this sticking coeff. and reported surface reaction probabilities of NH and NH2 radicals, we conclude that N and NH2 radicals are mainly responsible for the N incorporation in the silicon nitride film, while Si atoms are most likely brought to the surface in the form of SiHx radicals. [on SciFinder (R)

Analysis of Insulin Doses of Chinese Type 2 Diabetic Patients with Intensive Insulin Treatment

BACKGROUND: To investigate the daily insulin doses and the ratio of basal insulin to total daily insulin in Chinese type 2 diabetic patients who received basal bolus insulin therapy. METHODOLOGY/PRINCIPAL FINDINGS: Totally 2480 patients prescribed with pre-meal bolus insulin and bedtime basal insulin were included. The mean daily insulin doses was 38.22 ± 14.92 IU/day, the mean daily insulin doses per weight was 0.58 ± 0.22 IU/kg, the mean bolus insulin dose was 0.44 ± 0.17 IU/kg and the mean basal insulin dose was 0.13 ± 0.08 IU/kg. The mean basal/total daily insulin ratio (BD/TDD) was 0.23 ± 0.08. In most patients (47.94%), the BD/TDD was between 0.20 and 0.30. Diabetic duration, BMI, HbA1c, fasting and postprandial blood glucose level were positively associated with daily insulin dose, while age was negatively associated with daily insulin dose. Diabetic duration, BMI, HbA1c, fasting blood glucose level, and using metformin were positively associated with BD/TDD ratio, while age, postprandial C peptide, postprandial blood glucose level and CRE level were negatively associated with BD/TDD ratio. CONCLUSIONS/SIGNIFICANCE: The daily insulin doses of intensive treatment in Chinese type 2 diabetic patients was 38.22 IU/day, the mean daily insulin doses per weight was 0.58 IU/kg, mean BD/TDD ratio was 0.23

Observational study of the association of first insulin type in uncontrolled type 2 diabetes with macrovascular and microvascular disease

&lt;p&gt;Aims: To compare the risk of vascular disease, HbA1c and weight change, between first prescribed insulins in people with type 2 diabetes.&lt;/p&gt; &lt;p&gt;Methods: People included in THIN United Kingdom primary care record database who began insulin (2000–2007) after poor control on oral glucose-lowering agents (OGLD) were grouped by the number of OGLDs in their treatment regimen immediately before starting insulin (n = 3,485). Within OGLD group, Cox regression compared macrovascular (all-cause mortality, myocardial infarction, acute coronary syndrome and stroke) and microvascular disease (peripheral neuropathy, nephropathy, and retinopathy) between insulin type (basal, pre-mix or Neutral Protamine Hagedorn, NPH) while ANCOVAs compared haemoglobin A1c (HbA1c) and weight change.&lt;/p&gt; &lt;p&gt;Results: Mean follow-up was 3.6 years. Rates of incident macrovascular events were similar when basal insulin was compared to pre-mix or NPH, adjusted hazard ratio versus basal: pre-mix 1.08 (95% CI 0.73, 1.59); NPH 1.00 (0.63, 1.58) after two OGLDs, and pre-mix 0.97 (0.46, 2.02); NPH 0.77 (0.32, 1.86) after three OGLDs. An increased risk of microvascular disease in NPH versus basal after 3 OGLDs, adjusted hazard ratio1.87 (1.04, 3.36), was not seen after two agents or in comparisons of basal and pre-mix. At one year, after two OGLDs, weight increase was less with basal compared with pre-mix. After three OGLDs, mean HbA1c had reduced less in basal versus pre-mix or NPH at 6–8 and at 9–11 months, and versus pre-mix at 12–14 months.&lt;/p&gt; &lt;p&gt;Conclusion: We found no difference in the risk of macrovascular events between first insulins in the medium term when started during poor glycaemia control. The increased risk of microvascular events with NPH warrants further study. In certain groups, first use of basal insulin was associated with less gain in weight and decrease in HbA1c compared to other insulins.&lt;/p&gt