Department of Physics
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Browsing Department of Physics by Subject "01 Mathematical Sciences"
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- Capillary forces on a small particle at a liquid-vapor interface: Theory and simulationTang, Yanfei; Cheng, Shengfeng (American Physical Society, 2018-09-24)
- Crossover From Self-Similar to Self-Affine Structures in PercolationFrey, E.; Täuber, Uwe C.; Schwabl, Franz (Editions Physique, 1994-05-20)We study the crossover from self-similar scaling behavior to asymptotically self-affine (anisotropic) structures. As an example, we consider bond percolation with one preferred direction. Our theory is based on a field-theoretical representation, and takes advantage of a renormalization group approach designed for crossover phenomena. We calculate effective exponents for the connectivity describing the entire crossover region from isotropic to directed percolation, and predict at which scale of the anisotropy the crossover should occur. We emphasize the broad range of applicability of our method.
- John Cardy's scale-invariant journey in low dimensions: a special issue for his 70th birthday PrefaceCalabrese, Pasquale; Fendley, Paul; Täuber, Uwe C. (IOP, 2018-07-13)
- Requirements for the containment of COVID-19 disease outbreaks through periodic testing, isolation, and quarantineMukhamadiarov, Ruslan I.; Deng, Shengfeng; Serrao, Shannon R.; Priyanka; Childs, Lauren M.; Täuber, Uwe C. (IOP, 2022-01-21)We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman–Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections.
- The role of the non-linearity in controlling the surface roughness in the one-dimensional Kardar-Parisi-Zhang growth processPriyanka; Täuber, Uwe C.; Pleimling, Michel J. (IOP, 2021-04-16)We explore linear control of the one-dimensional non-linear Kardar-Parisi-Zhang (KPZ) equation with the goal to understand the effects the control process has on the dynamics and on the stationary state of the resulting stochastic growth kinetics. In linear control, the intrinsic non-linearity of the system is maintained at all times. In our protocol, the control is applied to only a small number nc of Fourier modes. The stationary-state roughness is obtained analytically in the small-nc regime with weak non-linear coupling wherein the controlled growth process is found to result in Edwards-Wilkinson dynamics. Furthermore, when the non-linear KPZ coupling is strong, we discern a regime where the controlled dynamics shows scaling in accordance to the KPZ universality class. We perform a detailed numerical analysis to investigate the controlled dynamics subject to weak as well as strong non-linearity. A first-order perturbation theory calculation supports the simulation results in the weak non-linear regime. For strong non-linearity, we find a temporal crossover between KPZ and dispersive growth regimes, with the crossover time scaling with the number nc of controlled Fourier modes. We observe that the height distribution is positively skewed, indicating that as a consequence of the linear control, the surface morphology displays fewer and smaller hills than in the uncontrolled growth process, and that the inherent size-dependent stationary-state roughness provides an upper limit for the roughness of the controlled system.
- Stabilizing spiral structures and population diversity in the asymmetric May-Leonard model through immigrationSerrao, Shannon R.; Täuber, Uwe C. (Springer, 2021-08-01)We study the induction and stabilization of spiral structures for the cyclic three-species stochastic May-Leonard model with asymmetric predation rates on a spatially inhomogeneous two-dimensional toroidal lattice using Monte Carlo simulations. In an isolated setting, strongly asymmetric predation rates lead to rapid extinction from coexistence of all three species to a single surviving population. Even for weakly asymmetric predation rates, only a fraction of ecologies in a statistical ensemble manages to maintain full three-species coexistence. However, when the asymmetric competing system is coupled via diffusive proliferation to a fully symmetric May-Leonard patch, the stable spiral patterns from this region induce transient plane-wave fronts and ultimately quasi-stationary spiral patterns in the vulnerable asymmetric region. Thus the endangered ecological subsystem may effectively become stabilized through immigration from even a much smaller stable region. To describe the stabilization of spiral population structures in the asymmetric region, we compare the increase in the robustness of these topological defects at extreme values of the asymmetric predation rates in the spatially coupled system with the corresponding asymmetric May{Leonard model in isolation. We delineate the quasi-stationary nature of coexistence induced in the asymmetric subsystem by its diffusive coupling to a symmetric May{Leonard patch, and propose a (semi-)quantitative criterion for the spiral oscillations to be sustained in the asymmetric region.