Optimal search strategies of space-time coupled random walkers with finite lifetimes

We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new direction with the same speed. We call these walkers "mortal creepers". A mortal creeper may die at any time during its motion according to an exponential decay law characterized by a finite mean death rate $\omega_m$. While still alive, the creeper has a finite mean frequency $\omega$ of change of the direction of motion. In particular, we consider the efficiency of the target search process, characterized by the probability that the creeper will eventually detect the target. Analytic results confirmed by numerical results show that there is an $\omega_m$-dependent optimal frequency $\omega=\omega_{opt}$ that maximizes the probability of eventual target detection. We work primarily in one-dimensional ($d=1$) domains and examine the role of initial conditions and of finite domain sizes. Numerical results in $d=2$ domains confirm the existence of an optimal frequency of change of direction, thereby suggesting that the observed effects are robust to changes in dimensionality. In the $d=1$ case, explicit expressions for the probability of target detection in the long time limit are given. In the case of an infinite domain, we compute the detection probability for arbitrary times and study its early- and late-time behavior. We further consider the survival probability of the target in the presence of many independent creepers beginning their motion at the same location and at the same time. We also consider a version of the standard "target problem" in which many creepers start at random locations at the same time.Comment: 18 pages, 7 figures. The title has been changed with respect to the one in the previous versio

Excitations and S-matrix for su(3) spin chain combining 3{3} and ${3^{*}}

The associated Hamiltonian for a su(3) spin chain combining ${3}$ and ${3^{*}}$ representations is calculated. The ansatz equations for this chain are obtained and solved in the thermodynamic limit, and the ground state and excitations are described. Thus, relations between the number of roots and the number of holes in each level have been found . The excited states are characterized by means of these quantum numbers. Finally, the exact S matrix for a state with two holes is found.Comment: 17 pages, plaintex, harvmac (to be published in J. of Phys. A

Sobre el «grado cero» de la cultura: las condiciones originarias de la sociabilidad. Releer a Lévi-Strauss

Sin resume

On the use of laser-scanning vibrometry for mechanical performance evaluation of 3D printed specimens

In this study, we explored the suitability of laser-scanning vibrometry (LSV) for evaluation of the mechanical behavior of rectangular prisms produced by Fused Filament Fabrication (FFF). Our hypothesis was that LSV would be able to discriminate the mechanical behavior of specimens fabricated with different process parameters combinations. Build orientation, raster angle, nozzle temperature, printing speed and layer thickness were the process parameters of interest. Based on a factorial design of experiment approach, 48 different process parameter combinations were taken into account and 96 polylactic acid (PLA) rectangular prisms were fabricated. The characterization of their dynamical behavior provided frequency data, making possible the computation of an equivalent elastic modulus metric. Statistical analysis of the equivalent elastic modulus dataset confirmed the significant influences of raster angle, build orientation and nozzle temperature. Moreover, multivariate regression models served to rank, not only the significant influences of individual process parameters, but also the significant quadratic and cubic interactions between them. The previous knowledge was then applied to generate an ad hoc model selecting the most important factors (linear and interactions). The predicted equivalent elastic moduli provided by our ad hoc model were used in modal analysis simulations of both 3D printed rectangular prisms and a complex part. The simulated frequencies thus obtained were generally closer to the experimental ones (=11%), as compared to modal analysis simulations based on internal geometry modelling (=33%). The use of LSV appears very promising in the characterization of the mechanical behavior and integrity of 3D printed parts. Other additive manufacturing technologies may benefit from the use of this technique and from the adoption of the presented methodology to test, simulate and optimize the properties of 3D printed products. © 2021 The Author

Reactive dynamics on fractal sets: anomalous fluctuations and memory effects

We study the effect of fractal initial conditions in closed reactive systems in the cases of both mobile and immobile reactants. For the reaction $A+A\to A$, in the absence of diffusion, the mean number of particles $A$ is shown to decay exponentially to a steady state which depends on the details of the initial conditions. The nature of this dependence is demonstrated both analytically and numerically. In contrast, when diffusion is incorporated, it is shown that the mean number of particles $$ decays asymptotically as $t^{-d_f/2}$, the memory of the initial conditions being now carried by the dynamical power law exponent. The latter is fully determined by the fractal dimension $d_f$ of the initial conditions.Comment: 7 pages, 2 figures, uses epl.cl