Applicability of Effective Pair Potentials for Active Brownian Particles

We have performed a case study investigating a recently proposed scheme to obtain an effective pair potential for active Brownian particles [Farage et al., Phys. Rev. E 91, 042310 (2015)]. Applying this scheme to the Lennard-Jones potential, numerical simulations of active Brownian particles are compared to simulations of passive Brownian particles interacting by the effective pair potential. Analyzing the static pair correlations, our results indicate a limited range of activity parameters (speed and orientational correlation time) for which we obtain quantitative, or even qualitative, agreement. Moreover, we find a qualitatively different behavior for the virial pressure even for small propulsion speeds. Combining these findings we conclude that beyond linear response active particles exhibit genuine non-equilibrium properties that cannot be captured by effective pair interaction alone

Global existence for the spherically symmetric Einstein-Vlasov system with outgoing matter

We prove a new global existence result for the asymptotically flat, spherically symmetric Einstein-Vlasov system which describes in the framework of general relativity an ensemble of particles which interact by gravity. The data are such that initially all the particles are moving radially outward and that this property can be bootstrapped. The resulting non-vacuum spacetime is future geodesically complete.Comment: 16 page

Existence of axially symmetric static solutions of the Einstein-Vlasov system

We prove the existence of static, asymptotically flat non-vacuum spacetimes with axial symmetry where the matter is modeled as a collisionless gas. The axially symmetric solutions of the resulting Einstein-Vlasov system are obtained via the implicit function theorem by perturbing off a suitable spherically symmetric steady state of the Vlasov-Poisson system.Comment: 32 page

The formation of black holes in spherically symmetric gravitational collapse

We consider the spherically symmetric, asymptotically flat Einstein-Vlasov system. We find explicit conditions on the initial data, with ADM mass M, such that the resulting spacetime has the following properties: there is a family of radially outgoing null geodesics where the area radius r along each geodesic is bounded by 2M, the timelike lines $r=c\in [0,2M]$ are incomplete, and for r>2M the metric converges asymptotically to the Schwarzschild metric with mass M. The initial data that we construct guarantee the formation of a black hole in the evolution. We also give examples of such initial data with the additional property that the solutions exist for all $r\geq 0$ and all Schwarzschild time, i.e., we obtain global existence in Schwarzschild coordinates in situations where the initial data are not small. Some of our results are also established for the Einstein equations coupled to a general matter model characterized by conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild coordinates for data which are not small is added together with minor modification

Fused Deposition Modeling of Microfluidic Chips in Transparent Polystyrene

Polystyrene (PS) is one of the most commonly used thermoplastic materials worldwide and plays a ubiquitous role in today’s biomedical and life science industry and research. The main advantage of PS lies in its facile processability, its excellent optical and mechanical properties, as well as its biocompatibility. However, PS is only rarely used in microfluidic prototyping, since the structuring of PS is mainly performed using industrial-scale replication processes. So far, microfluidic chips in PS have not been accessible to rapid prototyping via 3D printing. In this work, we present, for the first time, 3D printing of transparent PS using fused deposition modeling (FDM). We present FDM printing of transparent PS microfluidic channels with dimensions as small as 300 µm and a high transparency in the region of interest. Furthermore, we demonstrate the fabrication of functional chips such as Tesla-mixer and mixer cascades. Cell culture experiments showed a high cell viability during seven days of culturing, as well as enabling cell adhesion and proliferation. With the aid of this new PS prototyping method, the development of future biomedical microfluidic chips will be significantly accelerated, as it enables using PS from the early academic prototyping all the way to industrial-scale mass replication