Applicability of the Fisher Equation to Bacterial Population Dynamics

The applicability of the Fisher equation, which combines diffusion with logistic nonlinearity, to population dynamics of bacterial colonies is studied with the help of explicit analytic solutions for the spatial distribution of a stationary bacterial population under a static mask. The mask protects the bacteria from ultraviolet light. The solution, which is in terms of Jacobian elliptic functions, is used to provide a practical prescription to extract Fisher equation parameters from observations and to decide on the validity of the Fisher equation.Comment: 5 pages, 3 figs. include

Very long optical path-length from a compact multi-pass cell

The multiple-pass optical cell is an important tool for laser absorption spectroscopy and its many applications. For most practical applications, such as trace-gas detection, a compact and robust design is essential. Here we report an investigation into a multi-pass cell design based on a pair of cylindrical mirrors, with a particular focus on achieving very long optical paths. We demonstrate a path-length of 50.31 m in a cell with 40 mm diameter mirrors spaced 88.9 mm apart - a 3-fold increase over the previously reported longest path-length obtained with this type of cell configuration. We characterize the mechanical stability of the cell and describe the practical conditions necessary to achieve very long path-lengths

The case for the development and use of "ecologically valid" measures of executive function in experimental and clinical neuropsychology

This article considers the scientific process whereby new and better clinical tests of executive function might be developed, and what form they might take. We argue that many of the traditional tests of executive function most commonly in use (e.g., the Wisconsin Card Sorting Test; Stroop) are adaptations of procedures that emerged almost coincidentally from conceptual and experimental frameworks far removed from those currently in favour, and that the prolongation of their use has been encouraged by a sustained period of concentration on “construct-driven” experimentation in neuropsychology. This resulted from the special theoretical demands made by the field of executive function, but was not a necessary consequence, and may not even have been a useful one. Whilst useful, these tests may not therefore be optimal for their purpose. We consider as an alternative approach a function-led development programme which in principle could yield tasks better suited to the concerns of the clinician because of the transparency afforded by increased “representativeness” and “generalisability.” We further argue that the requirement of such a programme to represent the interaction between the individual and situational context might also provide useful constraints for purely experimental investigations. We provide an example of such a programme with reference to the Multiple Errands and Six Element tests

An explicit height bound for the classical modular polynomial

For a prime m, let Phi_m be the classical modular polynomial, and let h(Phi_m) denote its logarithmic height. By specializing a theorem of Cohen, we prove that h(Phi_m) <= 6 m log m + 16 m + 14 sqrt m log m. As a corollary, we find that h(Phi_m) <= 6 m log m + 18 m also holds. A table of h(Phi_m) values is provided for m <= 3607.Comment: Minor correction to the constants in Theorem 1 and Corollary 9. To appear in the Ramanujan Journal. 17 pages

Quantum interference effects in p-Si1−xGex quantum wells

Quantum interference effects, such as weak localization and electronelectron interaction (EEI), have been investigated in magnetic fields up to 11 T for hole gases in a set of Si1−xGex quantum wells with 0.13 < x < 0.95. The temperature dependence of the hole phase relaxation time has been extracted from the magneto-resistance between 35 mK and 10 K. The spin-orbit effects that can be described within the Rashba model were observed in low magnetic fields. A quadratic negative magneto-resistance was observed in strong magnetic fields, due to the EEI effect. The hole-phonon scattering time was determined from hole overheating in a strong magnetic field

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

Radiative charge transfer lifetime of the excited state of (NaCa)+^+

New experiments were proposed recently to investigate the regime of cold atomic and molecular ion-atom collision processes in a special hybrid neutral-atom--ion trap under high vacuum conditions. The collisional cooling of laser pre-cooled Ca$^+$ ions by ultracold Na atoms is being studied. Modeling this process requires knowledge of the radiative lifetime of the excited singlet A$^1\Sigma^+$ state of the (NaCa)$^+$ molecular system. We calculate the rate coefficient for radiative charge transfer using a semiclassical approach. The dipole radial matrix elements between the ground and the excited states, and the potential curves were calculated using Complete Active Space Self-Consistent field and M\"oller-Plesset second order perturbation theory (CASSCF/MP2) with an extended Gaussian basis, 6-311+G(3df). The semiclassical charge transfer rate coefficient was averaged over a thermal Maxwellian distribution. In addition we also present elastic collision cross sections and the spin-exchange cross section. The rate coefficient for charge transfer was found to be $2.3\times 10^{-16}$ cm$^3$/sec, while those for the elastic and spin-exchange cross sections were found to be several orders of magnitude higher ($1.1\times 10^{-8}$ cm$^3$/sec and $2.3\times 10^{-9}$ cm$^3$/sec, respectively). This confirms our assumption that the milli-Kelvin regime of collisional cooling of calcium ions by sodium atoms is favorable with the respect to low loss of calcium ions due to the charge transfer.Comment: 4 pages, 5 figures; v.2 - conceptual change

Rendezvous of Heterogeneous Mobile Agents in Edge-weighted Networks

We introduce a variant of the deterministic rendezvous problem for a pair of heterogeneous agents operating in an undirected graph, which differ in the time they require to traverse particular edges of the graph. Each agent knows the complete topology of the graph and the initial positions of both agents. The agent also knows its own traversal times for all of the edges of the graph, but is unaware of the corresponding traversal times for the other agent. The goal of the agents is to meet on an edge or a node of the graph. In this scenario, we study the time required by the agents to meet, compared to the meeting time $T_{OPT}$ in the offline scenario in which the agents have complete knowledge about each others speed characteristics. When no additional assumptions are made, we show that rendezvous in our model can be achieved after time $O(n T_{OPT})$ in a $n$-node graph, and that such time is essentially in some cases the best possible. However, we prove that the rendezvous time can be reduced to $\Theta (T_{OPT})$ when the agents are allowed to exchange $\Theta(n)$ bits of information at the start of the rendezvous process. We then show that under some natural assumption about the traversal times of edges, the hardness of the heterogeneous rendezvous problem can be substantially decreased, both in terms of time required for rendezvous without communication, and the communication complexity of achieving rendezvous in time $\Theta (T_{OPT})$

Vibrational properties of amorphous silicon from tight-binding O(N) calculation

We present an O(N) algorithm to study the vibrational properties of amorphous silicon within the framework of tight-binding approach. The dynamical matrix elements have been evaluated numerically in the harmonic approximation exploiting the short-range nature of the density matrix to calculate the vibrational density of states which is then compared with the same obtained from a standard O($N^4$) algorithm. For the purpose of illustration, an 1000-atom model is studied to calculate the localization properties of the vibrational eigenstates using the participation numbers calculation.Comment: 5 pages including 5 ps figures; added a figure and a few references; accepted in Phys. Rev.