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Density-valued solutions for the Boltzmann-Enskog process
Get PDFThe time evolution of a moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed in [1] and further studied in [12, 13]. The process is given by the solution of a McKean-Vlasov equation driven by a Poisson random measure with the compensator depending on the distribution of the solution [1, 12]. The existence of a marginal probability density function at each time for the measure-valued solution is established in this article by using a functional-analytic criterion on Besov spaces [8, 11]. In addition to existence, the density is shown to reside in a Besov space. The support of the velocity marginal distribution is shown to be the whole of R3
Supercongruences Arising from Ramanujan-Sato Series
No full textRecently, the authors with Lea Beneish established a recipe for constructing Ramanujan-Sato series for 1/π, and used this to construct 11 explicit examples of Ramanujan-Sato series arising from modular forms for arithmetic triangle groups of non-compact type. Here, we use work of Chisholm, Deines, Long, Nebe and the third author to prove a general p-adic supercongruence theorem through an explicit connection to CM hypergeometric elliptic curves that provides p-adic analogues of these Ramanujan-Sato series. We further use this theorem to construct explicit examples related to each of our explicit Ramanujan-Sato series examples
The Hass Avocado Boom as a Catalyst for Socio-Natural Regime Transitions in the Global South: Insights from Northern Caldas, Colombia
No full textQuantum-assisted master clock in the sky: Global synchronization from satellites at subnanosecond precision
No full textThis paper develops a protocol to synchronize clocks on board a network of satellites equipped with quantum resources. We show that, in such a constellation, satellites reinforce each other\u27s sync capabilities, forming a common clock that is more stable and precise than its constituents. We envision the resulting network as a master clock able to distribute time across the globe, providing the basis for a future quantum global navigation satellite system or a space-based quantum network. As an example of its capabilities, we show that a constellation of 50 satellites equipped with modest quantum resources, and distributed amongst five orbits at an altitude of 500 km, allows the synchronization of clocks spread across the globe at subnanosecond precision
Prompt periodicity in the GRB 211211A precursor: Black-hole or magnetar engine?
No full textThe merger origin long GRB 211211A was a class (re-)defining event. A precursor was identified with a s separation from the main burst, as well as a claimed candidate quasi-periodic oscillation (QPO) with a frequency Hz. Here, we explore the implications of the precursor, assuming the quasi-periodicity is real. The precursor variability time-scale requires relativistic motion with a Lorentz factor, and implies an engine-driven jetted outflow. The declining amplitude of the consecutive pulses requires an episodic engine with an \u27on/off\u27 cycle consistent with the QPO. For a black-hole central engine, the QPO can have its origin in Lense-Thirring precession of the inner disc at (gravitational radii) for a mass M, and for 4.5]]\u3e M
Explaining Nonmerger Gamma-Ray Bursts and Broad-lined Supernovae with Close Binary Progenitors with Black Hole Central Engines
No full textFor over 25 yr, the origin of long-duration gamma-ray bursts (lGRBs) has been linked to the collapse of rotating massive stars. However, we have yet to pinpoint the stellar progenitor powering these transients. Moreover, the dominant engine powering the explosions remains open to debate. Observations of both lGRBs, supernovae associated with these GRBs, such as broad-line (BL) stripped-envelope (type Ic) supernovae (hereafter, Ic-BL), supernovae (SNe), and perhaps superluminous SNe, fast blue optical transients, and fast x-ray transients, may provide clues to both engines and progenitors. In this paper, we conduct a detailed study of the tight-binary formation scenario for lGRBs, comparing this scenario to other leading progenitor models. Combining this progenitor scenario with different lGRB engines, we can compare to existing data and make predictions for future observational tests. We find that the combination of the tight-binary progenitor scenario with the black hole accretion disk engine can explain lGRBs, low-luminosity GRBs, ultra-long GRBs, and Ic-BL. We discuss the various progenitor properties required for these different subclasses and note such systems would be future gravitational-wave merger sources. We show that the current literature on other progenitor-engine scenarios cannot explain all of these transient classes with a single origin, motivating additional work. We find that the tight-binary progenitor with a magnetar engine is excluded by existing observations. The observations can be used to constrain the properties of stellar evolution, the nature of the GRB, and the associated SN engines in lGRBs and Ic-BL. We discuss the future observations needed to constrain our understanding of these rare, but powerful, explosions
The luminous, slow-rising orphan afterglow AT2019pim as a candidate moderately relativistic outflow
No full textClassical gamma-ray bursts (GRBs) have two distinct emission episodes: prompt emission from ultrarelativistic ejecta and afterglow from shocked circumstellar material. While both components are extremely luminous in known GRBs, a variety of scenarios predict the existence of luminous afterglow emission with little or no associated high-energy prompt emission. We present AT 2019pim, the first spectroscopically confirmed afterglow with no observed high-energy emission to be identified. Serendipitously discovered during follow-up observations of a gravitational-wave trigger and located in a contemporaneous TESS sector, it is hallmarked by a fast-rising ( h), luminous ( mag) optical transient with accompanying luminous X-ray and radio emission. No gamma-ray emission consistent with the time and location of the transient was detected by Fermi-GBM or by Konus, placing constraining limits on an accompanying GRB. We investigate several independent observational aspects of the afterglow in the context of constraints on relativistic motion and find all of them are consistent with an initial Lorentz factor of 10-30 for the on-axis material, significantly lower than in any well-observed GRB and consistent with the theoretically predicted \u27dirty fireball\u27 scenario in which the high-energy prompt emission is stifled by pair production. However, we cannot rule out a structured jet model in which only the line-of-sight material was ejected at low-, off-axis from a classical high- jet core, and an on-axis GRB with below-average gamma-ray efficiency also remains a possibility. This event represents a milestone in orphan afterglow searches, demonstrating that luminous optical afterglows lacking detected GRB counterparts can be identified and spectroscopically confirmed in real time
Reducing classical communication costs in multiplexed quantum repeaters using hardware-aware quasi-local policies
Get PDFFuture quantum networks will have nodes equipped with multiple quantum memories, allowing for multiplexing and entanglement distillation strategies for long-distance entanglement distribution. In this work, we focus on quasi-local policies for multiplexed quantum repeater chains. In fully-local policies, nodes use the knowledge of only their own states, whereas more efficient global policies use knowledge of the entire network state. The classical communication costs of using this knowledge have not been explored in existing literature. We show that quasi-local policies not only obtain improved performance over local policies, but also reduce classical communication costs considerably. Our policies also outperform the widely studied nested purification and doubling policy in practical parameter regimes. We identify parameter regimes where distillation is useful and address the question: “Should we distill before swapping, or vice versa?” Finally, we propose an implementation scheme for a multiplexed repeater chain, experimentally demonstrate the key element, a high-dimensional biphoton frequency comb, and evaluate its anticipated performance using our multiplexing-based policies