The 3D version of the finite element program FESTER

In this report, a detailed description of the 3-D version finite element pro-gram FESTER is given. This includes: 1. A brief introduction to the package FESTER; 2. Preparing an input data file for the 3D version of FESTER; 3. Principal stress and stress invariant analyses; 4. 2D joint element (surface contact) characterisation and its mathematical formulation; 5. Formulations of the 3D stress-strain analyses for both isotropic and anisotropic materials, plane of weakness and cracking criteria; 6. 3D brick elements, infinity elements and their corresponding shape and mapping functions; 7. Large-displacement formulations; 8. Modifications to the subroutines INVAR, JNTB, TMAT, MOD2 etc; 9. Numerical examples; and 10. Conclusions

Magnetohydrodynamic normal mode analysis of plasma with equilibrium pressure anisotropy

In this work, we generalise linear magnetohydrodynamic (MHD) stability theory to include equilibrium pressure anisotropy in the fluid part of the analysis. A novel 'single-adiabatic' (SA) fluid closure is presented which is complementary to the usual 'double-adiabatic' (CGL) model and has the advantage of naturally reproducing exactly the MHD spectrum in the isotropic limit. As with MHD and CGL, the SA model neglects the anisotropic perturbed pressure and thus loses non-local fast-particle stabilisation present in the kinetic approach. Another interesting aspect of this new approach is that the stabilising terms appear naturally as separate viscous corrections leaving the isotropic SA closure unchanged. After verifying the self-consistency of the SA model, we re-derive the projected linear MHD set of equations required for stability analysis of tokamaks in the MISHKA code. The cylindrical wave equation is derived analytically as done previously in the spectral theory of MHD and clear predictions are made for the modification to fast-magnetosonic and slow ion sound speeds due to equilibrium anisotropy.Comment: 19 pages. This is an author-created, un-copyedited version of an article submitted for publication in Plasma Physics and Controlled Fusion. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Modeling the transmission of Wolbachia in mosquitoes for controlling mosquito-borne diseases

We develop and analyze an ordinary differential equation model to assess the potential effectiveness of infecting mosquitoes with the Wolbachia bacteria to control the ongoing mosquito-borne epidemics, such as dengue fever, chikungunya, and Zika. Wolbachia is a natural parasitic microbe that stops the proliferation of the harmful viruses inside the mosquito and reduces disease transmission. It is difficult to sustain an infection of the maternal transmitted Wolbachia in a wild mosquito population because of the reduced fitness of the Wolbachia-infected mosquitoes and cytoplasmic incompatibility limiting maternal transmission. The infection will only persist if the fraction of the infected mosquitoes exceeds a minimum threshold. Our two-sex mosquito model captures the complex transmission-cycle by accounting for heterosexual transmission, multiple pregnant states for female mosquitoes, and the aquatic-life stage. We identify important dimensionless numbers and analyze the critical threshold condition for obtaining a sustained Wolbachia infection in the natural population. This threshold effect is characterized by a backward bifurcation with three coexisting equilibria of the system of differential equations: a stable disease-free equilibrium, an unstable intermediate-infection endemic equilibrium and a stable high-infection endemic equilibrium. We perform sensitivity analysis on epidemiological and environmental parameters to determine their relative importance to Wolbachia transmission and prevalence. We also compare the effectiveness of different integrated mitigation strategies and observe that the most efficient approach to establish the Wolbachia infection is to first reduce the natural mosquitoes and then release both infected males and pregnant females. The initial reduction of natural population could be accomplished by either residual spraying or ovitraps.Comment: 27 pages, 14 figure; submitted to SIA

Spontaneous Generation of Photons in Transmission of Quantum Fields in PT Symmetric Optical Systems

We develop a rigorous mathematically consistent description of PT symmetric optical systems by using second quantization. We demonstrate the possibility of significant spontaneous generation of photons in PT symmetric systems. Further we show the emergence of Hanbury-Brown Twiss (HBT) correlations in spontaneous generation. We show that the spontaneous generation determines decisively the nonclassical nature of fields in PT symmetric systems. Our work can be applied to other systems like plasmonic structure where losses are compensated by gain mechanisms.Comment: 4 pages, 5 figure

Numerical and Theoretical Studies of Noise Effects in the Kauffman Model

In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a similar kind of behavior, even when the structure of their basins of attraction is quite different. This can be considered as a robust property of these models. We present numerical results for the full range of noise level and obtain approximate analytic expressions for the above crossing time as a function of the noise in the limit cases of small and large noise levels.Comment: 24 pages, 9 figures, Submitted to the Journal of Statistical Physic

Self-organized criticality in the intermediate phase of rigidity percolation

Experimental results for covalent glasses have highlighted the existence of a new self-organized phase due to the tendency of glass networks to minimize internal stress. Recently, we have shown that an equilibrated self-organized two-dimensional lattice-based model also possesses an intermediate phase in which a percolating rigid cluster exists with a probability between zero and one, depending on the average coordination of the network. In this paper, we study the properties of this intermediate phase in more detail. We find that microscopic perturbations, such as the addition or removal of a single bond, can affect the rigidity of macroscopic regions of the network, in particular, creating or destroying percolation. This, together with a power-law distribution of rigid cluster sizes, suggests that the system is maintained in a critical state on the rigid/floppy boundary throughout the intermediate phase, a behavior similar to self-organized criticality, but, remarkably, in a thermodynamically equilibrated state. The distinction between percolating and non-percolating networks appears physically meaningless, even though the percolating cluster, when it exists, takes up a finite fraction of the network. We point out both similarities and differences between the intermediate phase and the critical point of ordinary percolation models without self-organization. Our results are consistent with an interpretation of recent experiments on the pressure dependence of Raman frequencies in chalcogenide glasses in terms of network homogeneity.Comment: 20 pages, 18 figure