SCDA for 3D lattice gases with repulsive interaction

The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. Received 7 August 2002 / Received in final form 22 January 2003 Published online 24 April 2003     

Tumor Hypoxia Heterogeneity Affects Radiotherapy: Inverse-Percolation Shell-Model Monte Carlo Simulations

Tumor hypoxia was discovered a century ago, and the interference of hypoxia with all radiotherapies is well known. Here, we demonstrate the potentially extreme effects of hypoxia heterogeneity on radiotherapy and combination radiochemotherapy. We observe that there is a decrease in hypoxia from tumor periphery to tumor center, due to oxygen diffusion, resulting in a gradient of radiative cell-kill probability, mathematically expressed as a probability gradient of occupied space removal. The radiotherapy-induced break-up of the tumor/TME network is modeled by the physics model of inverse percolation in a shell-like medium, using Monte Carlo simulations. The different shells now have different probabilities of space removal, spanning from higher probability in the periphery to lower probability in the center of the tumor. Mathematical results regarding the variability of the critical percolation concentration show an increase in the critical threshold with the applied increase in the probability of space removal. Such an observation will have an important medical implication: a much larger than expected radiation dose is needed for a tumor breakup enabling successful follow-up chemotherapy. Information on the TME’s hypoxia heterogeneity, as shown here with the numerical percolation model, may enable personalized precision radiation oncology therapy.     

Fractal to classical crossover of chemical reactions

Computer simulations on binary reactions of random walkers (A + A → A) on two- and three-dimensional percolation clusters bear out the recent superuniversality conjecture (integrated reaction rate α t²¹³). Moreover, the fractal-to-euclidean crossover (t²¹³ to t dependence) parallels that of the single walker.     

Single random walker on disordered lattices

Random walks on square lattice percolating clusters were followed for up to 2×105 steps. The mean number of distinct sites visited (S _N > gives a spectral dimension ofd _s = 1.30±0.03 consistent with superuniversality (d _s =4J3) but closer to the alternatived _s = 182/139, based on the low dimensionality correction. Simulations are also given for walkers on anenergetically disordered lattice, with a jump probability that depends on the local energy mismatch and the temperature. An apparent fractal behavior is observed for a low enough reduced temperature. Above this temperature, the walker exhibits a crossover from fractal-to-Euclidean behavior. Walks on two- and three-dimensional lattices are similar, except that those in three dimensions are more efficient.Supported by NSF Grant No. DMR 8303919 and Nato Grant No. SA 5205 RG 295J82.     

Percolation of randomly distributed growing clusters: the low initial density regime

We investigate the problem of growing clusters, which is modeled by two dimensional disks and three dimensional droplets. In this model we place a number of seeds on random locations on a lattice with an initial occupation probability, p. The seeds simultaneously grow with a constant velocity to form clusters. When two or more clusters eventually touch each other they immediately stop their growth. The probability that such a system will result in a percolating cluster depends on the density of the initially distributed seeds and the dimensionality of the system. For very low values of p we find a power law behavior for several properties that we investigate, namely for the size of the largest and second largest cluster, for the probability for a spanning cluster to occur, and for the mean radius of the finally formed droplets. We report the values of the corresponding scaling exponents. Finally, we show that for very low initial concentration of seeds the final coverage takes a constant value which depends on the system dimensionality.     

Computational study of energy transfer in two-dimensional J-aggregates

We perform a computational analysis of the intra- and interband energy transfer in two-dimensional J-aggregates. Each aggregate is represented as a two-dimensional array (LB-film or self-assembled film) of two kinds of cyanine dyes. We consider the J-aggregate whose J-band is located at a shorter wavelength to be a donor and an aggregate or a small impurity with longer wavelength to be an acceptor. Light absorption in the blue wing of the donor aggregate gives rise to the population of its excitonic states. The depopulation of these states is possible by (a) radiative transfer to the ground state, (b) intraband energy transfer, and (c) interband energy transfer to the acceptor. We study the dependence of energy transfer on properties such as the energy gap, the diagonal disorder, and the exciton–phonon interaction strength. Experimentally observable parameters, such as the position and form of luminescence spectrum, and results of the kinetic spectroscopy measurements strongly depend upon the density of states in excitonic bands, rates of energy exchange between states and oscillator strengths for luminescent transitions originating from these states.     

Fracture mechanics analysis of arc shaped specimens for pipe grade polymers

Instrumented three-point bend impact fracture tests are widely used to evaluate pipe grade polymers. Often specimens cut from small-diameter pipe are used, and these are necessarily arc-shaped. Because the orientation and thermal history may differ between extruded pipe and compression moulded plaque material, this additional difference in geometry must be properly accounted for, or it may mask any effects on material properties. This paper modifies a previously published solution for the geometry-dependent energy correction factor for arc-shaped specimens, and extends it to a wider range of standard pipe geometries. When the results are properly corrected, the effects of processing on a commercial PE100 appear to be minor.     

Exciton states in organic alloys: Naphthalene-perdeuteronaphthalene

The lower band-edge energy of the first single exciton of naphthalene has been determined as a function of concentration in a C₁₀H₈/C₁₀D₈ alloy. Experimentally, the vibronic 0–512 fluorescence at 2 K and 1 cm^?1 resolution has been measured. Theoretically, the coherent potential approximation (CPA) and the negative factor counting (NFC) results have been derived from the work of Hong and Kopelman. Agreement is good within the experimental and computational uncertainties (2–3 cm^?1).