Pulse propagation in discrete systems of coupled excitable cells

Propagation of pulses in myelinated fibers may be described by appropriate solutions of spatially discrete FitzHugh-Nagumo systems. In these systems, propagation failure may occur if either the coupling between nodes is not strong enough or the recovery is too fast. We give an asymptotic construction of pulses for spatially discrete FitzHugh-Nagumo systems which agrees well with numerical simulations and discuss evolution of initial data into pulses and pulse generation at a boundary. Formulas for the speed and length of pulses are also obtained.Comment: 16 pages, 10 figures, to appear in SIAM J. Appl. Mat

Promoting a local brand: Assessing the Economic Benefits of the Texas Superstar® and Earth-Kind® Promotion on Place (POP) Program

This paper aims to evaluate consumer’s awareness and willingness-to-pay (WTP) for two ornamental brands in Texas: Texas Superstar® and Earth-Kind®, after a Promotion on Place (POP) Program was developed by the Texas Department of Agriculture (TDA). Consumer’s characteristics that are more likely to influence brand awareness and WTP are identified.Brand recognition, Willingness to pay, Consumer preferences, Ornamentals, Consumer/Household Economics, Marketing,

Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators

We present a stability theory for kink propagation in chains of coupled oscillators and a new algorithm for the numerical study of kink dynamics. The numerical solutions are computed using an equivalent integral equation instead of a system of differential equations. This avoids uncertainty about the impact of artificial boundary conditions and discretization in time. Stability results also follow from the integral version. Stable kinks have a monotone leading edge and move with a velocity larger than a critical value which depends on the damping strength.Comment: 11 figure

Oscillatory wave fronts in chains of coupled nonlinear oscillators

Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for $F_{cd} < |F| < F_{cs}$ stable static and moving wave fronts coexist, and for $|F| > F_{cs}$ (static Peierls stress) there are only stable moving wave fronts. For piecewise linear models, extending an exact method of Atkinson and Cabrera's to chains with damped dynamics corroborates this description. For smooth nonlinearities, an approximate analytical description is found by means of the active point theory. Generically for small or zero damping, stable wave front profiles are non-monotone and become wavy (oscillatory) in one of their tails.Comment: 18 pages, 21 figures, 2 column revtex. To appear in Phys. Rev.

Dynamics of Coherent States in Regular and Chaotic Regimes of the Non-integrable Dicke Model

The quantum dynamics of initial coherent states is studied in the Dicke model and correlated with the dynamics, regular or chaotic, of their classical limit. Analytical expressions for the survival probability, i.e. the probability of finding the system in its initial state at time $t$, are provided in the regular regions of the model. The results for regular regimes are compared with those of the chaotic ones. It is found that initial coherent states in regular regions have a much longer equilibration time than those located in chaotic regions. The properties of the distributions for the initial coherent states in the Hamiltonian eigenbasis are also studied. It is found that for regular states the components with no negligible contribution are organized in sequences of energy levels distributed according to Gaussian functions. In the case of chaotic coherent states, the energy components do not have a simple structure and the number of participating energy levels is larger than in the regular cases.Comment: Contribution to the proceedings of the Escuela Latinoamericana de F\'isica (ELAF) Marcos Moshinsky 2017. (9 pages, 4 figures

Effects of disorder on the wave front depinning transition in spatially discrete systems

Pinning and depinning of wave fronts are ubiquitous features of spatially discrete systems describing a host of phenomena in physics, biology, etc. A large class of discrete systems is described by overdamped chains of nonlinear oscillators with nearest-neighbor coupling and subject to random external forces. The presence of weak randomness shrinks the pinning interval and it changes the critical exponent of the wave front depinning transition from 1/2 to 3/2. This effect is derived by means of a recent asymptotic theory of the depinning transition, extended to discrete drift-diffusion models of transport in semiconductor superlattices and confirmed by numerical calculations.Comment: 4 pages, 3 figures, to appear as a Rapid Commun. in Phys. Rev.

Searching for Communities in Bipartite Networks

Bipartite networks are a useful tool for representing and investigating interaction networks. We consider methods for identifying communities in bipartite networks. Intuitive notions of network community groups are made explicit using Newman's modularity measure. A specialized version of the modularity, adapted to be appropriate for bipartite networks, is presented; a corresponding algorithm is described for identifying community groups through maximizing this measure. The algorithm is applied to networks derived from the EU Framework Programs on Research and Technological Development. Community groups identified are compared using information-theoretic methods.Comment: 12 pages, 4 figures, to appear in "Proceedings of the 5th Jagna International Workshop: Stochastic and Quantum Dynamics of Biomolecular Systems," C. C. Bernido and M. V. Carpio-Bernido, editors. A version with full-quality figures and larger file size is available at http://ccm.uma.pt/publications/Barber-Faria-Streit-Strogan-2008.pd

Molecular line probes of activity in galaxies

The use of specific tracers of the dense molecular gas phase can help to explore the feedback of activity on the interstellar medium (ISM) in galaxies. This information is a key to any quantitative assessment of the efficiency of the star formation process in galaxies. We present the results of a survey devoted to probe the feedback of activity through the study of the excitation and chemistry of the dense molecular gas in a sample of local universe starbursts and active galactic nuclei (AGNs). Our sample includes also 17 luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs). From the analysis of the LIRGs/ULIRGs subsample, published in Gracia-Carpio et al.(2007) we find the first clear observational evidence that the star formation efficiency of the dense gas, measured by the L_FIR/L_HCN ratio, is significantly higher in LIRGs and ULIRGs than in normal galaxies. Mounting evidence of overabundant HCN in active environments would even reinforce the reported trend, pointing to a significant turn upward in the Kennicutt-Schmidt law around L_FIR=10^11 L_sun. This result has major implications for the use of HCN as a tracer of the dense gas in local and high-redshift luminous infrared galaxies.Comment: 4 pages, 2 figures, contributed paper to Far-Infrared Workshop 07 (FIR 2007