Random billiards with wall temperature and associated Markov chains

By a random billiard we mean a billiard system in which the standard specular reflection rule is replaced with a Markov transition probabilities operator P that, at each collision of the billiard particle with the boundary of the billiard domain, gives the probability distribution of the post-collision velocity for a given pre-collision velocity. A random billiard with microstructure (RBM) is a random billiard for which P is derived from a choice of geometric/mechanical structure on the boundary of the billiard domain. RBMs provide simple and explicit mechanical models of particle-surface interaction that can incorporate thermal effects and permit a detailed study of thermostatic action from the perspective of the standard theory of Markov chains on general state spaces. We focus on the operator P itself and how it relates to the mechanical/geometric features of the microstructure, such as mass ratios, curvatures, and potentials. The main results are as follows: (1) we characterize the stationary probabilities (equilibrium states) of P and show how standard equilibrium distributions studied in classical statistical mechanics, such as the Maxwell-Boltzmann distribution and the Knudsen cosine law, arise naturally as generalized invariant billiard measures; (2) we obtain some basic functional theoretic properties of P. Under very general conditions, we show that P is a self-adjoint operator of norm 1 on an appropriate Hilbert space. In a simple but illustrative example, we show that P is a compact (Hilbert-Schmidt) operator. This leads to the issue of relating the spectrum of eigenvalues of P to the features of the microstructure;(3) we explore the latter issue both analytically and numerically in a few representative examples;(4) we present a general algorithm for simulating these Markov chains based on a geometric description of the invariant volumes of classical statistical mechanics

Solving the Initial Value Problem of two Black Holes

We solve the elliptic equations associated with the Hamiltonian and momentum constraints, corresponding to a system composed of two black holes with arbitrary linear and angular momentum. These new solutions are based on a Kerr-Schild spacetime slicing which provides more physically realistic solutions than the initial data based on conformally flat metric/maximal slicing methods. The singularity/inner boundary problems are circumvented by a new technique that allows the use of an elliptic solver on a Cartesian grid where no points are excised, simplifying enormously the numerical problem.Comment: 4 pages, 3 figures. Minor corrections, some points clarified, and one reference added. To appear in Phys. Rev. Let

Stability and collapse of rapidly rotating, supramassive neutron stars: 3D simulations in general relativity

We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $\Gamma = 2$ and focus on uniformly rotating stars. We find that the onset of dynamical instability along mass-shedding sequences nearly coincides with the onset of secular instability. Unstable stars collapse to rotating black holes within about one rotation period. We also study the collapse of stable stars which have been destabilized by pressure depletion (e.g. via a phase transition) or mass accretion. In no case do we find evidence for the formation of massive disks or any ejecta around the newly formed Kerr black holes, even though the progenitors are rapidly rotating.Comment: 16 pages, to appear in Phys. Rev.

The discomforting rise of ' public geographies': a 'public' conversation.

In this innovative and provocative intervention, the authors explore the burgeoning ‘public turn’ visible across the social sciences to espouse the need to radically challenge and reshape dominant and orthodox visions of ‘the academy’, academic life, and the role and purpose of the academic

Critical Behavior of a Three-State Potts Model on a Voronoi Lattice

We use the single-histogram technique to study the critical behavior of the three-state Potts model on a (random) Voronoi-Delaunay lattice with size ranging from 250 to 8000 sites. We consider the effect of an exponential decay of the interactions with the distance,$J(r)=J_0\exp(-ar)$, with $a>0$, and observe that this system seems to have critical exponents $\gamma$ and $\nu$ which are different from the respective exponents of the three-state Potts model on a regular square lattice. However, the ratio $\gamma/\nu$ remains essentially the same. We find numerical evidences (although not conclusive, due to the small range of system size) that the specific heat on this random system behaves as a power-law for $a=0$ and as a logarithmic divergence for $a=0.5$ and $a=1.0$Comment: 3 pages, 5 figure

CXD101 and nivolumab in patients with metastatic microsatellite-stable colorectal cancer (CAROSELL): a multicentre, open-label, single-arm, phase II trial.

BACKGROUND: Patients with microsatellite stable (MSS) colorectal carcinoma (CRC) do not respond to immune checkpoint inhibitors. Preclinical models suggested synergistic anti-tumour activity combining CXD101 and anti-programmed cell death protein 1 treatment; therefore, we assessed the clinical combination of CXD101 and nivolumab in heavily pre-treated patients with MSS metastatic CRC (mCRC). PATIENTS AND METHODS: This single-arm, open-label study enrolled patients aged 18 years or older with biopsy-confirmed MSS CRC; at least two lines of systemic anticancer therapies (including oxaliplatin and irinotecan); at least one measurable lesion; Eastern Cooperative Oncology Group performance status of 0, 1 or 2; predicted life expectancy above 3 months; and adequate organ and bone marrow function. Nine patients were enrolled in a safety run-in study to define a tolerable combination schedule of CXD101 and nivolumab, followed by 46 patients in the efficacy assessment phase. Patients in the efficacy assessment cohort were treated orally with 20 mg CXD101 twice daily for 5 consecutive days every 3 weeks, and intravenously with 240 mg nivolumab every 2 weeks. The primary endpoint was immune disease control rate (iDCR). RESULTS: Between 2018 and 2020, 55 patients were treated with CXD101 and nivolumab. The combination therapy was well tolerated with the most frequent grade 3 or 4 adverse events being neutropenia (18%) and anaemia (7%). Immune-related adverse reactions commonly ascribed to checkpoint inhibitors were surprisingly rare although we did see single cases of pneumonitis, hypothyroidism and hypopituitarism. There were no treatment-related deaths. Of 46 patients assessable for efficacy, 4 (9%) achieved partial response and 18 (39%) achieved stable disease, translating to an immune disease control rate of 48%. The median overall survival (OS) was 7.0 months (95% confidence interval 5.13-10.22 months). CONCLUSIONS: The primary endpoint was met in this phase II study, which showed that the combination of CXD101 and nivolumab, at full individual doses in the treatment of advanced or metastatic MSS CRC, was both well tolerated and efficacious

Initial Data and Coordinates for Multiple Black Hole Systems

We present here an alternative approach to data setting for spacetimes with multiple moving black holes generalizing the Kerr-Schild form for rotating or non-rotating single black holes to multiple moving holes. Because this scheme preserves the Kerr-Schild form near the holes, it selects out the behaviour of null rays near the holes, may simplify horizon tracking, and may prove useful in computational applications. For computational evolution, a discussion of coordinates (lapse function and shift vector) is given which preserves some of the properties of the single-hole Kerr-Schild form