Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling

We simulated a growth model in 1+1 dimensions in which particles are aggregated according to the rules of ballistic deposition with probability p or according to the rules of random deposition with surface relaxation (Family model) with probability 1-p. For any p>0, this system is in the Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover from the Edwards-Wilkinson class (EW) for small p. From the scaling of the growth velocity, the parameter p is connected to the coefficient of the nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma = 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and strong corrections to scaling for small lambda. This picture is consistent with a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8), in agreement with scaling theories and renormalization group analysis. Some consequences of the slow crossover in this problem are discussed and may help investigations of more complex models.Comment: 16 pages, 7 figures; to appear in Phys. Rev.

Persistence properties of a system of coagulating and annihilating random walkers

We study a d-dimensional system of diffusing particles that on contact either annihilate with probability 1/(q-1) or coagulate with probability (q-2)/(q-1). In 1-dimension, the system models the zero temperature Glauber dynamics of domain walls in the q-state Potts model. We calculate P(m,t), the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly (m-1) coagulations. Using perturbative renormalization group analysis for d < 2, we show that, if the number of coagulations m is much less than the typical number M(t), then P(m,t) ~ m^(z/d) t^(-theta), with theta=d Q + Q(Q-1/2) epsilon + O(epsilon^2), z=(2Q-1) epsilon + (2 Q-1) (Q-1)(1/2+A Q) epsilon^2 +O(epsilon^3), where Q=(q-1)/q, epsilon =2-d and A =-0.006. M(t) is shown to scale as t^(d/2-delta), where delta = d (1 -Q)+(Q-1)(Q-1/2) epsilon+ O(epsilon^2). In two dimensions, we show that P(m,t) ~ ln(t)^(Q(3-2Q)) ln(m)^((2Q-1)^2) t^(-2Q) for m << t^(2 Q-1). The 1-dimensional results corresponding to epsilon=1 are compared with results from Monte Carlo simulations.Comment: 12 pages, revtex, 5 figure

Moving Towards Self-Reliance: Living Conditions of Refugee Camps in Lebanon and Opportunities for Development

Refugee camps in Lebanon are harsh, continuously and rapidly deteriorating environments. In addition to poverty, numerous wars and the restrictions of civil rights, refugee camps that were not designed as a long-term settlement were made to accommodate their residents in addition to their descendents for a period that has lasted over 59 years. Since the establishment of the camps in 1948 the Palestinian refugees in Lebanon have fallen victim to multiple wars and as a result most camps have witnessed major destruction of homes and infrastructure, and a few were entirely destroyed. Today, the planning and development of the camps are highly restricted by the local government, building material is banned from entering the camps and horizontal as well as vertical expansion is prohibited by Lebanese law. According to the United Nations Relief and Work Agency (UNRWA) the hundreds of thousands of Palestinian refugees in Lebanon have the highest rate of people living in abject poverty in the Middle East. Meanwhile, the refugee community and the international aid agencies working in the camps are caught in the dilemma of investing in the development of a sustainable environment in a settlement with a temporary purpose and an uncertain future. This thesis explores the problems facing the built-environment in the camps within the political and socio-economic context, and takes the camp of Burj El Barajneh as a case study for deeper investigation. It then suggests three possible solution approaches that address the environmental problems within different future scenarios. The thesis also looks at the feasibility and requirements of an energy generation plant to provide part of the energy needs of the camp of Burj El Barjneh. Finally, a set of conclusions and recommendations are derived that address the refugee community, the international aid agencies and the host country. The significance of this study is to mitigate a possible humanitarian and environmental crisis in the most dire of refugee situations in the Middle East, with the hope that conclusions drawn from this study can be applied to refugee communities elsewhere in the region