Kinetics and mechanism of proton transport across membrane nanopores

We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across the membrane diffusively in single-file chains of hydrogen-bonded water molecules. Proton passage through the membrane is opposed by a high barrier along the effective potential, reflecting the large electrostatic penalty for desolvation and reminiscent of charge exclusion in biological water channels. At neutral pH, we estimate a translocation rate of about 1 proton per hour and tube.Comment: 4 pages, 4 figure

Relation between macroscopic and microscopic dielectric relaxation times in water dynamics

A simplified derivation for the ratio of macroscopic to microscopic relaxation times of polar liquids is based on the Mori-Zwanzig projection-operator technique, with added statistical assumptions. We obtain several useful forms for the lifetime ratio, which we apply to the dynamics of liquid water. Our theoretical single-molecule relaxation times agree with the second Debye relaxation times as measured by frequency-domain dielectric spectroscopy of water and alcohols. From the theory, fast relaxation modes couple to the Debye relaxation time, τD, through very large water clusters, and their temperature dependence is similar to that of τD. Slower modes are localized to smaller water clusters and exhibit weaker temperature dependence. This is exemplified by the lifetime ratios measured by time-domain dielectric spectroscopy and optical Kerr effect spectroscopy, respectively

Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.Comment: 18 pages, 3 figure

Green functions and dimensional reduction of quantum fields on product manifolds

We discuss Euclidean Green functions on product manifolds P=NxM. We show that if M is compact then the Euclidean field on P can be approximated by its zero mode which is a Euclidean field on N. We estimate the remainder of this approximation. We show that for large distances on N the remainder is small. If P=R^{D-1}xS^{beta}, where S^{beta} is a circle of radius beta, then the result reduces to the well-known approximation of the D dimensional finite temperature quantum field theory to D-1 dimensional one in the high temperature limit. Analytic continuation of Euclidean fields is discussed briefly.Comment: 17 page

International recommendations for the assessment of autoantibodies to cellular antigens referred to as anti-nuclear antibodies.

Anti-nuclear antibodies (ANA) are fundamental for the diagnosis of autoimmune diseases, and have been determined by indirect immunofluorescence assay (IIFA) for decades. As the demand for ANA testing increased, alternative techniques were developed challenging the classic IIFA. These alternative platforms differ in their antigen profiles, sensitivity and specificity, raising uncertainties regarding standardisation and interpretation of incongruent results. Therefore, an international group of experts has created recommendations for ANA testing by different methods. Two groups of experts participated in this initiative. The European autoimmunity standardization initiative representing 15 European countries and the International Union of Immunologic Societies/World Health Organization/Arthritis Foundation/Centers for Disease Control and Prevention autoantibody standardising committee. A three-step process followed by a Delphi exercise with closed voting was applied. Twenty-five recommendations for determining ANA (1-13), anti-double stranded DNA antibodies (14-18), specific antibodies (19-23) and validation of methods (24-25) were created. Significant differences between experts were observed regarding recommendations 24-25 (p<0.03). Here, we formulated recommendations for the assessment and interpretation of ANA and associated antibodies. Notably, the roles of IIFA as a reference method, and the importance of defining nuclear and cytoplasmic staining, were emphasised, while the need to incorporate alternative automated methods was acknowledged. Various approaches to overcome discrepancies between methods were suggested of which an improved bench-to-bedside communication is of the utmost importance. These recommendations are based on current knowledge and can enable harmonisation of local algorithms for testing and evaluation of ANA and related autoantibodies. Last but not least, new more appropriate terminologies have been suggested

Residence time and collision statistics for exponential flights: the rod problem revisited

Many random transport phenomena, such as radiation propagation, chemical/biological species migration, or electron motion, can be described in terms of particles performing {\em exponential flights}. For such processes, we sketch a general approach (based on the Feynman-Kac formalism) that is amenable to explicit expressions for the moments of the number of collisions and the residence time that the walker spends in a given volume as a function of the particle equilibrium distribution. We then illustrate the proposed method in the case of the so-called {\em rod problem} (a 1d system), and discuss the relevance of the obtained results in the context of Monte Carlo estimators.Comment: 9 pages, 8 figure

Magnetic calculus and semiclassical trace formulas

The aim of these notes is to show how the magnetic calculus developed in \cite{MP, IMP1, IMP2, MPR, LMR} permits to give a new information on the nature of the coefficients of the expansion of the trace of a function of the magnetic Schr\"odinger operator whose existence was established in \cite{HR2}

On the existence of traveling waves in the 3D Boussinesq system

We extend earlier work on traveling waves in premixed flames in a gravitationally stratified medium, subject to the Boussinesq approximation. For three-dimensional channels not aligned with the gravity direction and under the Dirichlet boundary conditions in the fluid velocity, it is shown that a non-planar traveling wave, corresponding to a non-zero reaction, exists, under an explicit condition relating the geometry of the crossection of the channel to the magnitude of the Prandtl and Rayleigh numbers, or when the advection term in the flow equations is neglected.Comment: 15 pages, to appear in Communications in Mathematical Physic

The critical dimension for a 4th order problem with singular nonlinearity

We study the regularity of the extremal solution of the semilinear biharmonic equation \bi u=\f{\lambda}{(1-u)^2}, which models a simple Micro-Electromechanical System (MEMS) device on a ball B\subset\IR^N, under Dirichlet boundary conditions $u=\partial_\nu u=0$ on $\partial B$. We complete here the results of F.H. Lin and Y.S. Yang \cite{LY} regarding the identification of a "pull-in voltage" \la^*>0 such that a stable classical solution u_\la with 0 exists for \la\in (0,\la^*), while there is none of any kind when \la>\la^*. Our main result asserts that the extremal solution $u_{\lambda^*}$ is regular $(\sup_B u_{\lambda^*} <1)$ provided $N \le 8$ while $u_{\lambda^*}$ is singular ($\sup_B u_{\lambda^*} =1$) for $N \ge 9$, in which case $1-C_0|x|^{4/3}\leq u_{\lambda^*} (x) \leq 1-|x|^{4/3}$ on the unit ball, where $C_0:= (\frac{\lambda^*}{\overline{\lambda}})^{1/3}$ and $\bar{\lambda}:= {8/9} (N-{2/3}) (N- {8/3})$.Comment: 19 pages. This paper completes and replaces a paper (with a similar title) which appeared in arXiv:0810.5380. Updated versions --if any-- of this author's papers can be downloaded at this http://www.birs.ca/~nassif

Magnetic strip waveguides

We analyze the spectrum of the "local" Iwatsuka model, i.e. a two-dimensional charged particle interacting with a magnetic field which is homogeneous outside a finite strip and translationally invariant along it. We derive two new sufficient conditions for absolute continuity of the spectrum. We also show that in most cases the number of open spectral gaps of the model is finite. To illustrate these results we investigate numerically the situation when the field is zero in the strip being screened, e.g. by a superconducting mask.Comment: 22 pages, a LaTeX source file with three eps figure