The effect of partial absorption on a diffusive particle which stochastically resets its position with a finite rate r is considered. The particle is absorbed by a target at the origin with absorption 'velocity' a; as the velocity a approaches ∞ the absorption property of the target approaches that of a perfectly-absorbing target. The effect of partial absorption on first-passage time problems is studied, in particular, it is shown that the mean time to absorption (MTA) is increased by an additive term proportional to 1/a. The results are extended to multiparticle systems where independent searchers, initially uniformly distributed with a given density, look for a single immobile target. It is found that the average survival probability P av is modified by a multiplicative factor which is a function of 1/a, whereas the decay rate of the typical survival probability P typ is decreased by an additive term proportional to 1/a.

Parallelizable workloads are ubiquitous and appear across a diverse array of modern computer systems. Data centers, supercomputers, machine learning clusters, distributed computing frameworks, and databases all process jobs designed to be parallelized across many servers or cores. Unlike the jobs in more classical models, such as the M/G/k queue, that each run on a single server, parallelizable jobs are capable of running on multiple servers simultaneously. When a job is parallelized across additional servers or cores, the job receives a speedup and can be completed more quickly.

We investigate the conditions under which a moving condensate may exist in a driven mass transport system. Our paradigm is a minimal mass transport model in which n − 1 particles move simultaneously from a site containing n > 1 particles to the neighbouring site in a preferred direction. In the spirit of a Zero-Range process the rate u(n) of this move depends only on the occupation of the departure site. We study a hopping rate u(n) = 1+b/n α numerically and find a moving strong condensate phase for b > b c (α) for all α > 0. This phase is characterised by a condensate that moves through the system and comprises a fraction of the system's mass that tends to unity. The mass lost by the condensate as it moves is constantly replenished from the trailing tail of low occupancy sites that collectively comprise a vanishing fraction of the mass. We formulate an approximate analytical treatment of the model that allows a reasonable estimate of b c (α) to be obtained. We show numerically (for α = 1) that the transition is of mixed order, exhibiting exhibiting a discontinuity in the order parameter as well as a diverging length scale as b b c .

We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface, are not symmetrically related. On the basis of numerical results and an exact calculation, we argue that these two arrangements represent two distinct universality classes for interfacial growth: while the well-established Kardar-Parisi-Zhang (KPZ) growth is obtained in the "ahead" arrangement, we find an arrested KPZ growth with a smaller roughness exponent in the "behind" arrangement. This suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct.