Hydrodynamic limit and Newtonian limit from the relativistic Boltzmann equation to the classical Euler equations

The hydrodynamic limit and Newtonian limit are important in the relativistic kinetic theory. We justify rigorously the validity of the two independent limits from the special relativistic Boltzmann equation to the classical Euler equations without assuming any dependence between the Knudsen number $\varepsilon$ and the light speed $\mathfrak{c}$. The convergence rates are also obtained. This is achieved by Hilbert expansion of relativistic Boltzmann equation. New difficulties arise when tacking the uniform in $\mathfrak{c}$ and $\varepsilon$ estimates for the Hilbert expansion, which have been overcome by establishing some uniform-in-$\mathfrak{c}$ estimate for relativistic Boltzmann operators.Comment: 63 pages. All comments are welcom

The Global Well-Posedness of the Relativistic Boltzmann Equation with Diffuse Reflection Boundary Condition in Bounded Domains

The relativistic Boltzmann equation in bounded domains has been widely used in physics and engineering, for example, Tokamak devices in fusion reactors.In spite of its importance, there has, to the best of our knowledge, been no mathematical theory on the global existence of solutions to the relativistic Boltzmann equation in bounded domains. In the present paper, assuming that the motion of single-species relativistic particles in a bounded domain is governed by the relativistic Boltzmann equation with diffuse reflection boundary conditions of non-isothermal wall temperature of small variations around a positive constant, and regarding the speed of light $\mathfrak{c}$ as a large parameter, we first construct a unique non-negative stationary solution $F_{*}$, and further establish the dynamical stability of such stationary solution with exponential time decay rate. We point out that the $L^{\infty}$-bound of perturbations for both steady and non-steady solutions are independent of the speed of light $\mathfrak{c}$, and such uniform in $\mathfrak{c}$ estimates will be useful in the study of Newtonian limit in the future.Comment: 61 pages. Comments are welcom

SART-Type Image Reconstruction from Overlapped Projections

To maximize the time-integrated X-ray flux from multiple X-ray sources and shorten the data acquisition process, a promising way is to allow overlapped projections from multiple sources being simultaneously on without involving the source multiplexing technology. The most challenging task in this configuration is to perform image reconstruction effectively and efficiently from overlapped projections. Inspired by the single-source simultaneous algebraic reconstruction technique (SART), we hereby develop a multisource SART-type reconstruction algorithm regularized by a sparsity-oriented constraint in the soft-threshold filtering framework to reconstruct images from overlapped projections. Our numerical simulation results verify the correctness of the proposed algorithm and demonstrate the advantage of image reconstruction from overlapped projections

Nonlocal interaction engineering of 2D roton-like dispersion relations in acoustic and mechanical metamaterials

The interior of the synthetic unit cells and their interactions determine the wave properties of metamaterials composed of periodic lattices of these cells. While local interactions with the nearest neighbors are well appreciated, nonlocal beyond-nearest-neighbor interactions are often considered as a nuisance. Here, by introducing a versatile effectively two-dimensional metamaterial platform for airborne sound and elastic waves, we exploit nonlocal effects as a powerful design tool. Within a simplified discrete model, we analytically show that the lowest band can be engineered by Fourier synthesis, where the N-th order Fourier coefficient is determined by the N-th nearest-neighbor interaction strength. Roton-like dispersion relations are an example. The results of the discrete model agree well with a refined model and with numerical calculations. In addition, we engineer the passage of waves from a local metamaterial into a nonlocal metamaterial by carefully tailoring the transition region between the two

Phonon transmission through a nonlocal metamaterial slab

Previous theory and experiment has shown that introducing strong (nonlocal) beyond-nearest-neighbor interactions in addition to (local) nearest-neighbor interactions into rationally designed periodic lattices called metamaterials can lead to unusual wave dispersion relations of the lowest band. For roton-like dispersions, this especially includes the possibility of multiple solutions for the wavenumber at a given frequency. Here, we study the one-dimensional frequency-dependent acoustical phonon transmission of a slab of such nonlocal metamaterial in a local surrounding. In addition to the usual Fabry-Perot resonances, we find a series of bound states in the continuum. In their vicinity, sharp Fano-type transmission resonances occur, with sharp zero-transmission minima next to sharp transmission maxima. Our theoretical discussion starts with a discrete mass-and-spring model. We compare these results with solutions of a generalized wave equation for heterogeneous nonlocal effective media. We validate our findings by numerical calculations on three-dimensional metamaterial microstructures for one-dimensional acoustical wave propagation

Selective thermal emission and infrared camouflage based on layered media

Infrared camouflage based on artificial thermal metasurfaces has recently attracted significant attention. By eliminating thermal radiation differences between the object and the background, it is possible to hide a given object from infrared detection. Infrared camouflage is an important element that increases the survivability of aircraft and missiles, by reducing target susceptibility to infrared guided threats. Herein, a simple and practicable design is theoretically presented based on a multilayer film for infrared stealth, with distinctive advantages of scalability, flexible fabrication, and structural simplicity. The multilayer medium consists of silicon substrate, carbon layer and zinc sulfide film, the optical properties of which are determined by transfer matrix method. By locally changing the thickness of the coating film, the spatial tunability and continuity in thermal emission are demonstrated. A continuous change of emissive power is further obtained and consequently implemented to achieve thermal camouflage functionality. In addition, other functionalities, like thermal illusion and thermal coding, are demonstrated by thickness-engineered multilayer films

Effect of microencapsulation of egg yolk immunoglobulin Y by sodium alginate/chitosan/sodium alginate on the growth performance, serum parameters, and intestinal health of broiler chickens

Objective Egg yolk immunoglobulin (IgY) is an antibiotic alternative to prevent and fight intestinal pathogenic infections. This study aimed to investigate the effects of sodium alginate/chitosan/sodium alginate IgY microcapsules on the growth performance, serum parameters, and intestinal health of broiler chickens. Methods One-day-old broilers (Ross 308) were divided into five treatments, each with 10 replicates of five chickens. The dietary treatments were maintained for 28 days and consisted of a basal diet (NC), basal diet + 500 mg chlortetracycline/kg diet (CH), basal diet + 50 mg non-microencapsulated IgY/kg diet (NM), basal diet + 600 mg low levels microencapsulated IgY/kg diet (LM), and basal diet + 700 mg high levels microencapsulated IgY/kg diet (HM). Results Throughout the 28-day trial period, the NM, LM, HM, and CH groups increased average daily gain compared with the NC group (p<0.05), and the HM group reduced feed conversion ratio compared with the CH group (p<0.05). The LM and HM groups increased relative organ weights of thymus and spleen compared with the CH and NM groups (p< 0.05). The HM group improved the duodenal, jejunal and ileum villi height (VH) and villus height to crypt depth ratio (VH:CD) compared with the CH and NM groups (p<0.05). Compared with the CH group, the HM group increased serum immunoglobulin (IgA), immunoglobulin G (IgG), superoxide dismutase, total antioxidant capacity, and glutathione peroxidase levels (p<0.05), and decreased serum malondialdehyde levels (p<0.05). Compared with the NC group, the NM, LM, HM, and CH groups reduced colonic Escherichia coli and Salmonella levels (p<0.05). and the HM group promoted the levels of lactic acid bacteria and bifidobacteria compared with the CH group (p<0.05). Conclusion Microencapsulation could be considered as a way to improve the efficiency of IgY. The 700 mg high levels microencapsulated IgY/kg diet could potentially be used as an alternative to antibiotics to improve the immune performance and intestinal health, leading to better performance of broiler chickens

From transients to permanent residents: the existence of obligate aerobic microorganisms in the goat rumen

The rumen serves as a complex ecosystem, harboring diverse microbial communities that play crucial ecological roles. Because previous studies have predominantly focused on anaerobic microorganisms, limited attention has been given to aerobic microorganisms in the goat rumen. This study aims to explore the diversity of aerobic microorganisms in the rumen and understand their niche and ecological roles. Rumen fluid samples were collected from 6 goats at different time points post-morning feeding. pH, NH3-N, and volatile fatty acid (TVFA) concentrations were measured, while In vitro cultivation of aerobic microorganisms was performed using PDA medium. Internal Transcribed Spacer (ITS) and 16S sequencing unveiled microbial diversity within the rumen fluid samples. Evidence of obligate aerobic microorganisms in the goat rumen suggests their potential contribution to ecological functionalities. Significantly, certain aerobic microorganisms exhibited correlations with TVFA levels, implying their involvement in TVFA metabolism. This study provides evidence of the existence and potential ecological roles of obligate aerobic microorganisms in the goat rumen. The findings underscore the significance of comprehensively deciphering goat rumen microbial communities and their interactions, with aerobes regarded as permanent residents rather than transients. These insights form a solid foundation for advancing our understanding of the intricate interplay between goat and their aerobic microorganisms in the rumen

Status of Muon Collider Research and Development and Future Plans

The status of the research on muon colliders is discussed and plans are outlined for future theoretical and experimental studies. Besides continued work on the parameters of a 3-4 and 0.5 TeV center-of-mass (CoM) energy collider, many studies are now concentrating on a machine near 0.1 TeV (CoM) that could be a factory for the s-channel production of Higgs particles. We discuss the research on the various components in such muon colliders, starting from the proton accelerator needed to generate pions from a heavy-Z target and proceeding through the phase rotation and decay ($\pi \to \mu \nu_{\mu}$) channel, muon cooling, acceleration, storage in a collider ring and the collider detector. We also present theoretical and experimental R & D plans for the next several years that should lead to a better understanding of the design and feasibility issues for all of the components. This report is an update of the progress on the R & D since the Feasibility Study of Muon Colliders presented at the Snowmass'96 Workshop [R. B. Palmer, A. Sessler and A. Tollestrup, Proceedings of the 1996 DPF/DPB Summer Study on High-Energy Physics (Stanford Linear Accelerator Center, Menlo Park, CA, 1997)].Comment: 95 pages, 75 figures. Submitted to Physical Review Special Topics, Accelerators and Beam