Electrostatics of ions inside the nanopores and trans-membrane channels

A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical solution is used to calculate the electrostatic potential energy profiles for pores containing charged protein residues. Availability of a semi-exact interionic potential should greatly facilitate the study of ionic transport through nanopores and ion channels

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

Rupture of multiple parallel molecular bonds under dynamic loading

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.Comment: 8 pages, 2 figure

Output of a pulsed atom laser

We study the output properties of a pulsed atom laser consisting of an interacting Bose-Einstein condensate (BEC) in a magnetic trap and an additional rf field transferring atoms to an untrapped Zeeman sublevel. For weak output coupling we calculate the dynamics of the decaying condensate population, of its chemical potential and the velocity of the output atoms analytically.Comment: 4 pages, RevTeX. Full ps file available on http://mpqibmr1.mpq.mpg.de:5000/~man

Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors

In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of GSp(4,F), where F is a non-archimedean local field of characteristic zero with residue field of order q.Comment: 48 pages, 21 tables. Corrected an error in Table 16 for type V* representations (theta_11 and theta_12 were switched

Effects of interatomic collisions on atom laser outcoupling

We present a computational approach to the outcoupling in a simple one-dimensional atom laser model, the objective being to circumvent mathematical difficulties arising from the breakdown of the Born and Markov approximations. The approach relies on the discretization of the continuum representing the reservoir of output modes, which allows the treatment of arbitrary forms of outcoupling as well as the incorporation of non-linear terms in the Hamiltonian, associated with interatomic collisions. By considering a single-mode trapped condensate, we study the influence of elastic collisions between trapped and free atoms on the quasi steady-state population of the trap, as well as the energy distribution and the coherence of the outcoupled atoms.Comment: 25 pages, 11 figures, to appear in J. Phys.

Characterizing black carbon in rain and ice cores using coupled tangential flow filtration and transmission electron microscopy

Antarctic ice cores have been used to study the history of black carbon (BC), but little is known with regards to the physical and chemical characteristics of these particles in the remote atmosphere. Characterization remains limited by ultra-trace concentrations in ice core samples and the lack of adequate methods to isolate the particles unaltered from the melt water. To investigate the physical and chemical characteristics of these particles, we have developed a tangential flow filtration (TFF) method combined with transmission electron microscopy (TEM). Tests using ultrapure water and polystyrene latex particle standards resulted in excellent blanks and significant particle recovery. This approach has been applied to melt water from Antarctic ice cores as well as tropical rain from Darwin, Australia with successful results: TEM analysis revealed a variety of BC particle morphologies, insoluble coatings, and the attachment of BC to mineral dust particles. The TFF-based concentration of these particles has proven to give excellent results for TEM studies of BC particles in Antarctic ice cores and can be used for future studies of insoluble aerosols in rainwater and ice core samples

On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

Coherent Tunneling of Atoms from Bose-condensed Gases at Finite Temperatures

Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green's functions of the isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle u^2 and v^2 amplitudes.Comment: 26 pages, 5 figures, minor changes, to appear in PR