Spectral Radii of Products of Random Rectangular Matrices

We consider m independent random rectangular matrices whose entries are independent and identically distributed standard complex Gaussian random variables. Assume the product of the m rectangular matrices is an n by n square matrix. The maximum absolute values of the n eigenvalues of the product matrix is called spectral radius. In this paper, we study the limiting spectral radii of the product when m changes with n and can even diverge. We give a complete description for the limiting distribution of the spectral radius. Our results reduce to those in Jiang and Qi [26] when the rectangular matrices are square ones.Comment: 29 page

Analyses of Magnetic Field Induced around a Tank

A tank is taken to have the shape of a hollow spheroid. Equations for calculating the induced field are derived based on a special coordinate system established around the spheroid. A numerical example to illustrate the magnetic field induced around a tank and its analyses are given

Collapsing domain walls beyond Z2Z_2

Discrete symmetries are widely imposed in particle theories. It is well-known that the spontaneous breaking of discrete symmetries leads to domain walls. Current studies of domain walls have focused on those from the spontaneous breaking of a $Z_2$ symmetry. Larger discrete symmetries have multiple degenerate vacua, leading to the domain walls in principle different from the simplest $Z_2$ domain wall. We take domain walls from $Z_N$ symmetry breaking as an illustrative study, and study in detail the $Z_3$ case, in which semi-analytical results for the tension and thickness of domain walls are derived. Explicit symmetry breaking terms lead to the dynamics of domain walls collapsing more complicated than the $Z_2$ case. Gravitational wave signals deviate from those from $Z_2$ domain walls.Comment: 9 pages, 4 figure

Lagrangian Neural Style Transfer for Fluids

Artistically controlling the shape, motion and appearance of fluid simulations pose major challenges in visual effects production. In this paper, we present a neural style transfer approach from images to 3D fluids formulated in a Lagrangian viewpoint. Using particles for style transfer has unique benefits compared to grid-based techniques. Attributes are stored on the particles and hence are trivially transported by the particle motion. This intrinsically ensures temporal consistency of the optimized stylized structure and notably improves the resulting quality. Simultaneously, the expensive, recursive alignment of stylization velocity fields of grid approaches is unnecessary, reducing the computation time to less than an hour and rendering neural flow stylization practical in production settings. Moreover, the Lagrangian representation improves artistic control as it allows for multi-fluid stylization and consistent color transfer from images, and the generality of the method enables stylization of smoke and liquids likewise.Comment: ACM Transaction on Graphics (SIGGRAPH 2020), additional materials: http://www.byungsoo.me/project/lnst/index.htm

Report of the Topical Group on Electroweak Precision Physics and Constraining New Physics for Snowmass 2021

The precise measurement of physics observables and the test of their consistency within the standard model (SM) are an invaluable approach, complemented by direct searches for new particles, to determine the existence of physics beyond the standard model (BSM). Studies of massive electroweak gauge bosons (W and Z bosons) are a promising target for indirect BSM searches, since the interactions of photons and gluons are strongly constrained by the unbroken gauge symmetries. They can be divided into two categories: (a) Fermion scattering processes mediated by s- or t-channel W/Z bosons, also known as electroweak precision measurements; and (b) multi-boson processes, which include production of two or more vector bosons in fermion-antifermion annihilation, as well as vector boson scattering (VBS) processes. The latter categories can test modifications of gauge-boson self-interactions, and the sensitivity is typically improved with increased collision energy. This report evaluates the achievable precision of a range of future experiments, which depend on the statistics of the collected data sample, the experimental and theoretical systematic uncertainties, and their correlations. In addition it presents a combined interpretation of these results, together with similar studies in the Higgs and top sector, in the Standard Model effective field theory (SMEFT) framework. This framework provides a model-independent prescription to put generic constraints on new physics and to study and combine large sets of experimental observables, assuming that the new physics scales are significantly higher than the EW scale.Comment: 55 pages; Report of the EF04 topical group for Snowmass 202

Towards a Muon Collider

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.Comment: 118 pages, 103 figure