Duality in matrix lattice Boltzmann models

The notion of duality between the hydrodynamic and kinetic (ghost) variables of lattice kinetic formulations of the Boltzmann equation is introduced. It is suggested that this notion can serve as a guideline in the design of matrix versions of the lattice Boltzmann equation in a physically transparent and computationally efficient way.Comment: 12 pages, 3 figure

Dimensional versus cut-off renormalization and the nucleon-nucleon interaction

The role of dimensional regularization is discussed and compared with that of cut-off regularization in some quantum mechanical problems with ultraviolet divergence in two and three dimensions with special emphasis on the nucleon-nucleon interaction. Both types of renormalizations are performed for attractive divergent one- and two-term separable potentials, a divergent tensor potential, and the sum of a delta function and its derivatives. We allow energy-dependent couplings, and determine the form that these couplings should take if equivalence between the two regularization schemes is to be enforced. We also perform renormalization of an attractive separable potential superposed on an analytic divergent potential.Comment: 19 pages + one postscript figur

Performance of a prototype active veto system using liquid scintillator for a dark matter search experiment

We report the performance of an active veto system using a liquid scintillator with NaI(Tl) crystals for use in a dark matter search experiment. When a NaI(Tl) crystal is immersed in the prototype detector, the detector tags 48% of the internal K-40 background in the 0-10 keV energy region. We also determined the tagging efficiency for events at 6-20 keV as 26.5 +/- 1.7% of the total events, which corresponds to 0.76 +/- 0.04 events/keV/kg/day. According to a simulation, approximately 60% of the background events from U, Th, and K radioisotopes in photomultiplier tubes are tagged at energies of 0-10 keV. Full shielding with a 40-cm-thick liquid scintillator can increase the tagging efficiency for both the internal K-40 and external background to approximately 80%.Comment: Submitted to Nuclear Instruments and Methods in Physics Research Section

Universal aspects of barrier crossing under bias

The thermal activation process by which a system passes from one local energy minimum to another is a recurring motif in physics, chemistry, and biology. For instance, biopolymer chains are typically modeled in terms of energy landscapes, with folded and unfolded conformations represented by two distinct wells separated by a barrier. The rate of transfer between wells depends primarily on the height of the barrier, but it also depends on the details of the shape of the landscape along the trajectory. We consider the case of bias due to an external force, analogous to the pulling force applied in optical tweezer experiments on biopolymers. Away from the Arrhenius-law limit and well out of equilibrium, somewhat idiosyncratic behavior might be expected. Instead, we identify universal behavior of the biased activated-barrier-crossing process and demonstrate that data collapse on a universal curve can be achieved for simulated data over a wide variety of energy landscapes having barriers of different height and shape and for loading rates spanning many orders of magnitude

Effective Nonlinear Schr\"odinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity

In the case of tight transverse confinement (cigar-shaped trap) the three-dimensional (3D) nonlinear Schr\"odinger equation, describing superfluid Fermi atoms at unitarity (infinite scattering length $|a|\to \infty$), is reduced to an effective one-dimensional form by averaging over the transverse coordinates. The resultant effective equation is a 1D nonpolynomial Schrodinger equation, which produces results in good agreement with the original 3D one. In the limit of small and large fermion number $N$ the nonlinearity is of simple power-law type. A similar reduction of the 3D theory to a two-dimensional form is also performed for a tight axial confinement (disk-shaped trap). The resultant effective 2D nonpolynomial equation also produces results in agreement with the original 3D equation and has simple power-law nonlinearity for small and large $N$. For both cigar- and disk-shaped superfluids our nonpolynomial Schr\"odinger equations are quite attractive for phenomenological application.Comment: 22 pages, 5 figure

Reliable extraction of energy landscape properties from critical force distributions

The structural dynamics of a biopolymer is governed by a process of diffusion through its conformational energy landscape. In pulling experiments using optical tweezers, features of the energy landscape can be extracted from the probability distribution of the critical force at which the polymer unfolds. The analysis is often based on rate equations having Bell-Evans form, although it is understood that this modeling is inadequate and leads to unreliable landscape parameters in many common situations. Dudko et al. [Phys. Rev. Lett. 96, 108101 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.108101] have emphasized this critique and proposed an alternative form that includes an additional shape parameter (and that reduces to Bell-Evans as a special case). Their fitting function, however, is pathological in the tail end of the pulling force distribution, which presents problems of its own. We propose a modified closed-form expression for the distribution of critical forces that correctly incorporates the next-order correction in pulling force and is everywhere well behaved. Our claim is that this new expression provides superior parameter extraction and is valid even up to intermediate pulling rates. We present results based on simulated data that confirm its utility