Evolution of Human-like Social Grooming Strategies regarding Richness and Group Size

Human beings tend to cooperate with close friends, therefore they have to construct strong social relationships to recieve cooperation from others. Therefore they should have acquired their strategies of social relationship construction through an evolutionary process. The behavior of social relationship construction is know as "social grooming." In this paper, we show that there are four classes including a human-like strategy in evolutionary dynamics of social grooming strategies based on an evolutionary game simulation. Social relationship strengths (as measured by frequency of social grooming) often show a much skewed distribution (a power law distribution). It may be due to time costs constraints on social grooming, because the costs are too large to ignore for having many strong social relationships. Evolution of humans' strategies of construction of social relationships may explain the origin of human intelligence based on a social brain hypothesis. We constructed an individual-based model to explore the evolutionary dynamics of social grooming strategies. The model is based on behavior to win over others by strengthening social relationships with cooperators. The results of evolutionary simulations show the four classes of evolutionary dynamics. The results depend on total resources and the ratio of each cooperator's resource to the number of cooperators. One of the four classes is similar to a human strategy, i.e. the strategies based on the Yule--Simon process of power law.Comment: 21 pages, 10 figure

Lax pair formulation in the simultaneous presence of boundaries and defects

Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equations of motion on the defect point are accordingly extracted. We consider a specific prototype i.e. the vector non-linear Schr\"{o}dinger (NLS) model to exemplify our construction. This model displays a highly non-trivial behavior and allows the existence of two distinct types of boundary conditions based on the reflection algebra or the twisted Yangian.Comment: 19 pages, Latex. A few comments and clarifications added. Version to appear in J. Phys.

Printing High Viscosity Fluids using Ultrasonic Droplet Generation

A new printing technology based on ultrasonic actuation (~1 MHz) is presented that has the potential to print high viscosity fluids. In this paper, we describe the print-head’s operating principles and construction. Acoustic focusing in the nozzles produces high pressure gradients that help eject the fluid which, under the proper conditions, forms droplets. Two types of models are presented to attempt to predict print-head behavior over a range of conditions. The first model borrows from simple fully developed, laminar flows to estimate printing conditions based on fluid properties, as well as printing pressures. The second model captures the dynamic behavior of the print-head to estimate cavity resonances that lead to acoustic focusing and potentially droplet generation. We report on experiments with several types of fluids that demonstrate the technology’s potential.Mechanical Engineerin

Oscillations and traveling waves of calcium: a simplified model

We construct a heuristic model of calcium oscillations in pancreatic acinar cells. The model is based on the two-state model of Sneyd et al. (Sneyd, J., A. LeBeau and D. Yule, 2000, Traveling waves of calcium in pancreatic acinar cells: model construction and bifurcation analysis, Physica D, in press) and is similar in spirit to the FitzHugh reduction of the Hodgkin-Huxley equations. The simpli¯ed model successfully reproduces the oscillatory behavior and wave behaviour of the more complex model. In particular, the simpli¯ed model provides an example of a simple, physiologically relevant model that has a T-point and an associated spiral branch of homoclinic orbits

General-relativistic Model of Magnetically Driven Jet

The general scheme for the construction of the general-relativistic model of the magnetically driven jet is suggested. The method is based on the usage of the 3+1 MHD formalism. It is shown that the critical points of the flow and the explicit radial behavior of the physical variables may be derived through the jet ``profile function."Comment: 12 pages, LaTex, no figure

A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement

Ground Energy of the Magnetic Laplacian in Polyhedral Bodies

The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the model problems (continuity, semi-continuity, existence of generalized eigenfunctions). We prove estimates for the remainders of our asymptotic formula. Lower bounds are obtained with the help of a classical IMS partition based on adequate coverings of the polyhedral domain, whereas upper bounds are established by a novel construction of quasimodes, qualified as sitting or sliding according to spectral properties of local model problems.Comment: 59 page