On the solvable multi-species reaction-diffusion processes

A family of one-dimensional multi-species reaction-diffusion processes on a lattice is introduced. It is shown that these processes are exactly solvable, provided a nonspectral matrix equation is satisfied. Some general remarks on the solutions to this equation, and some special solutions are given. The large-time behavior of the conditional probabilities of such systems are also investigated.Comment: 13 pages, LaTeX2

Perturbative spectrum of Trapped Weakly Interacting Bosons in Two Dimensions

We study a trapped Bose-Einstein condensate under rotation in the limit of weak, translational and rotational invariant two-particle interactions. We use the perturbation-theory approach (the large-N expansion) to calculate the ground-state energy and the excitation spectrum in the asymptotic limit where the total number of particles N goes to infinity while keeping the total angular momentum L finite. Calculating the probabilities of different configurations of angular momentum in the exact eigenstates gives us a clear view of the physical content of excitations. We briefly discuss the case of repulsive contact interaction.Comment: Revtex, 10 pages, 1 table, to appear in Phys. Rev.

A Fredholm Determinant Representation in ASEP

In previous work the authors found integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice. The dynamics are uniquely determined once the initial state is specified. In this note we restrict our attention to the case of step initial condition with particles at the positive integers, and consider the distribution function for the m'th particle from the left. In the previous work an infinite series of multiple integrals was derived for this distribution. In this note we show that the series can be summed to give a single integral whose integrand involves a Fredholm determinant. We use this determinant representation to derive (non-rigorously, at this writing) a scaling limit.Comment: 12 Pages. Version 3 includes a scaling conjectur

A new class of integrable diffusion-reaction processes

We consider a process in which there are two types of particles, A and B, on an infinite one-dimensional lattice. The particles hop to their adjacent sites, like the totally asymmetric exclusion process (ASEP), and have also the following interactions: A+B -> B+B and B+A -> B+B, all occur with equal rate. We study this process by imposing four boundary conditions on ASEP master equation. It is shown that this model is integrable, in the sense that its N-particle S-matrix is factorized into a product of two-particle S-matrices and, more importantly, the two-particle S-matrix satisfy quantum Yang-Baxter equation. Using coordinate Bethe-ansatz, the N-particle wavefunctions and the two-particle conditional probabilities are found exactly. Further, by imposing four reasonable physical conditions on two-species diffusion-reaction processes (where the most important ones are the equality of the reaction rates and the conservation of the number of particles in each reaction), we show that among the 4096 types of the interactions which have these properties and can be modeled by a master equation and an appropriate set of boundary conditions, there are only 28 independent interactions which are integrable. We find all these interactions and also their corresponding wave functions. Some of these may be new solutions of quantum Yang-Baxter equation.Comment: LaTex,16 pages, some typos are corrected, will be appeared in Phys. Rev. E (2000

Generalized Green Functions and current correlations in the TASEP

We study correlation functions of the totally asymmetric simple exclusion process (TASEP) in discrete time with backward sequential update. We prove a determinantal formula for the generalized Green function which describes transitions between positions of particles at different individual time moments. In particular, the generalized Green function defines a probability measure at staircase lines on the space-time plane. The marginals of this measure are the TASEP correlation functions in the space-time region not covered by the standard Green function approach. As an example, we calculate the current correlation function that is the joint probability distribution of times taken by selected particles to travel given distance. An asymptotic analysis shows that current fluctuations converge to the ${Airy}_2$ process.Comment: 46 pages, 3 figure

Rising minimum daily flows in northern Eurasian rivers: A growing influence of groundwater in the high-latitude hydrologic cycle

A first analysis of new daily discharge data for 111 northern rivers from 1936-1999 and 1958-1989 fmds an overall pattern of increasing minimum daily flows (or "low flows") throughout Russia. These increases are generally more abundant than are increases in mean flow and appear to drive much of the overall rise in mean flow observed here and in previous studies. Minimum flow decreases have also occurred but are less abundant. The minimum flow increases are found in summer as well as winter and in nonpermafrost as well as permafrost terrain. No robust spatial contrasts are found between the European Russia, Ob', Yenisey, and Lena/eastern Siberia sectors. A subset of 12 unusually long discharge records from 1935-2002, concentrated in south central Russia, suggests that recent minimum flow increases since ∼1985 are largely unprecedented in the instrumental record, at least for this small group of stations. If minimum flows are presumed sensitive to groundwater and unsaturated zone inputs to river discharge, then the data suggest a broad-scale mobilization of such water sources in the late 20th century. We speculate that reduced intensity of seasonal ground freezing, together with precipitation increases, might drive much of the well documented but poorly understood increases in river discharge to the Arctic Ocean

T-bet controls intestinal mucosa immune responses via repression of type 2 innate lymphoid cell function

Innate lymphoid cells (ILCs) play an important role in regulating immune responses at mucosal surfaces. The transcription factor T-bet is crucial for the function of ILC1s and NCR+ ILC3s and constitutive deletion of T-bet prevents the development of these subsets. Lack of T-bet in the absence of an adaptive immune system causes microbiota-dependent colitis to occur due to aberrant ILC3 responses. Thus, T-bet expression in the innate immune system has been considered to dampen pathogenic immune responses. Here, we show that T-bet plays an unexpected role in negatively regulating innate type 2 responses, in the context of an otherwise intact immune system. Selective loss of T-bet in ILCs leads to the expansion and increased activity of ILC2s, which has a functionally important impact on mucosal immunity, including enhanced protection from Trichinella spiralis infection and inflammatory colitis. Mechanistically, we show that T-bet controls the intestinal ILC pool through regulation of IL-7 receptor signalling. These data demonstrate that T-bet expression in ILCs acts as the key transcriptional checkpoint in regulating pathogenic vs. protective mucosal immune responses, which has significant implications for the understanding of the pathogenesis of inflammatory bowel diseases and intestinal infections

From Vicious Walkers to TASEP

We propose a model of semi-vicious walkers, which interpolates between the totally asymmetric simple exclusion process and the vicious walkers model, having the two as limiting cases. For this model we calculate the asymptotics of the survival probability for $m$ particles and obtain a scaling function, which describes the transition from one limiting case to another. Then, we use a fluctuation-dissipation relation allowing us to reinterpret the result as the particle current generating function in the totally asymmetric simple exclusion process. Thus we obtain the particle current distribution asymptotically in the large time limit as the number of particles is fixed. The results apply to the large deviation scale as well as to the diffusive scale. In the latter we obtain a new universal distribution, which has a skew non-Gaussian form. For $m$ particles its asymptotic behavior is shown to be $e^{-\frac{y^{2}}{2m^{2}}}$ as $y\to -\infty$ and $e^{-\frac{y^{2}}{2m}}y^{-\frac{m(m-1)}{2}}$ as $y\to \infty$.Comment: 37 pages, 4 figures, Corrected reference

Evidence for orbital and North Atlantic climate forcing in alpine Southern California between 125 and 10 ka from multi-proxy analyses of Baldwin Lake

We employed a new, multi-proxy record from Baldwin Lake (∼125–10 ka) to examine drivers of terrestrial Southern California climate over long timescales. Correlated bulk organic and biogenic silica proxy data demonstrated high-amplitude changes from 125 to 71 ka, suggesting that summer insolation directly influenced lake productivity during MIS 5. From 60 to 57 ka, hydrologic state changes and events occurred in California and the U.S. Southwest, though the pattern of response varied geographically. Intermediate, less variable levels of winter and summer insolation followed during MIS 3 (57–29 ka), which likely maintained moist conditions in Southern California that were punctuated with smaller-order, millennial-scale events. These Dansgaard-Oeschger events brought enhanced surface temperatures (SSTs) to the eastern Pacific margin, and aridity to sensitive terrestrial sites in the Southwest and Southern California. Low temperatures and reduced evaporation are widespread during MIS 2, though there is increasing evidence for moisture extremes in Southern California from 29 to 20 ka. Our record shows that both orbital-scale radiative forcing and rapid North Atlantic temperature perturbations were likely influences on Southern California climate prior to the last glacial. However, these forcings produced a hydroclimatic response throughout California and the U.S. Southwest that was geographically complex. This work highlights that it is especially urgent to improve our understanding of the response to rapid climatic change in these regions. Enhanced temperature and aridity are projected for the rest of the 21st century, which will place stress on water resources

Low-Temperature Specific Heat of an Extreme-Type-II Superconductor at High Magnetic Fields

We present a detailed study of the quasiparticle contribution to the low-temperature specific heat of an extreme type-II superconductor at high magnetic fields. Within a T-matrix approximation for the self-energies in the mixed state of a homogeneous superconductor, the electronic specific heat is a linear function of temperature with a linear-$T$ coefficient $\gamma_s(H)$ being a nonlinear function of magnetic field $H$. In the range of magnetic fields H\agt (0.15-0.2)H_{c2} where our theory is applicable, the calculated $\gamma_s(H)$ closely resembles the experimental data for the borocarbide superconductor YNi$_2$B$_2$C.Comment: 7 pages, 2 figures, to appear in Physical Review