Scattering theory without large-distance asymptotics

In conventional scattering theory, to obtain an explicit result, one imposes a precondition that the distance between target and observer is infinite. With the help of this precondition, one can asymptotically replace the Hankel function and the Bessel function with the sine functions so that one can achieve an explicit result. Nevertheless, after such a treatment, the information of the distance between target and observer is inevitably lost. In this paper, we show that such a precondition is not necessary: without losing any information of distance, one can still obtain an explicit result of a scattering rigorously. In other words, we give an rigorous explicit scattering result which contains the information of distance between target and observer. We show that at a finite distance, a modification factor --- the Bessel polynomial --- appears in the scattering amplitude, and, consequently, the cross section depends on the distance, the outgoing wave-front surface is no longer a sphere, and, besides the phase shift, there is an additional phase (the argument of the Bessel polynomial) appears in the scattering wave function

Crossing w=−1w=-1 by a single scalar field coupling with matter and the observational constraints

Motivated by Yang-Mills dark energy model, we propose a new model by introducing a logarithmic correction. we find that this model can avoid the coincidence problem naturally and gives an equation of state $w$ smoothly crossing -1 if an interaction between dark energy and dark matter exists. It has a stable tracker solution as well. To confront with observations based on the combined data of SNIa, BAO, CMB and Hubble parameter, we obtain the best fit values of the parameters with $1\sigma, 2\sigma, 3\sigma$ errors for the noncoupled model: $\Omega_m=0.276\pm0.008^{+0.016+0.024}_{-0.015-0.022}$, $h=0.699\pm0.003\pm0.006\pm0.008$, and for the coupled model with a decaying rate $\gamma=0.2$: $\Omega_m=0.291\pm0.004^{+0.008+0.012}_{-0.007-0.011}$, $h=0.701\pm0.002\pm0.005\pm0.007$. In particular, it is found that the non-coupled model has a dynamic evolution almost undistinguishable to $\Lambda$CDM at the late-time Universe.Comment: 12 pages, 3 figures, the published versio

PocketCare: Tracking the Flu with Mobile Phones using Partial Observations of Proximity and Symptoms

Mobile phones provide a powerful sensing platform that researchers may adopt to understand proximity interactions among people and the diffusion, through these interactions, of diseases, behaviors, and opinions. However, it remains a challenge to track the proximity-based interactions of a whole community and then model the social diffusion of diseases and behaviors starting from the observations of a small fraction of the volunteer population. In this paper, we propose a novel approach that tries to connect together these sparse observations using a model of how individuals interact with each other and how social interactions happen in terms of a sequence of proximity interactions. We apply our approach to track the spreading of flu in the spatial-proximity network of a 3000-people university campus by mobilizing 300 volunteers from this population to monitor nearby mobile phones through Bluetooth scanning and to daily report flu symptoms about and around them. Our aim is to predict the likelihood for an individual to get flu based on how often her/his daily routine intersects with those of the volunteers. Thus, we use the daily routines of the volunteers to build a model of the volunteers as well as of the non-volunteers. Our results show that we can predict flu infection two weeks ahead of time with an average precision from 0.24 to 0.35 depending on the amount of information. This precision is six to nine times higher than with a random guess model. At the population level, we can predict infectious population in a two-week window with an r-squared value of 0.95 (a random-guess model obtains an r-squared value of 0.2). These results point to an innovative approach for tracking individuals who have interacted with people showing symptoms, allowing us to warn those in danger of infection and to inform health researchers about the progression of contact-induced diseases

Where is Mr. Berg ?

Where is Mr. Berg? is a narrative short film that contemplates the relationship between parents and their children. This paper documents the growth of the story, how the story gets shaped and blossomed from the seed, and how the film is produced with minimal compromise to the original idea during the pandemic. I, as the Director and Director of Photography in this film, will break down the tangible process from different mindsets and visions in this thesis from scene to screen

Synthesis, structure and photoluminescence of (HgCl3)n (C6NO2H6)n(C6NO2H5)n•nH2O

A new isonicotinic acid compound with infinite mercury halide anionic chains, (HgCl3)n (C6NO2H6)n(C6NO2H5)n•nH2O (1), was obtained from the hydrothermal reaction and structurally characterized by X-ray single diffraction. The title compound is characteristic of a one-dimensional structure, based on one-dimensional (HgCl3)- anionic chains, protonated isonicotinic acid, neutral isonicotinic acid molecules and lattice water molecules. The protonated isonicotinic acid, neutral isonicotinic acid molecules and lattice water molecules are interconnected via hydrogen bonds to form a three-dimensional supramolecular framework. The (HgCl3)- anionic chains are anchored in the voids of the supramolecular framework via hydrogen bonds. Photoluminescent investigation reveals that the title compound displays a strong emission in blue region. The emission band is identified as the π-π* transitions of the isonicotinic acid moieties.KEY WORDS: Crystal, Isonicotinic, Halide, Mercury, Photoluminescence  Bull. Chem. Soc. Ethiop. 2011, 25(2), 233-238

Hydrodynamic Modeiingfor Tanjung Kepah, Perak

The objective ofthis report is to detail the progress ofthe computer simulation of coastal hydrodynamic, which is MIKE 21. Firstly, a study has been carried out at Tanjung Kepah, Lumut to study the impacts of wave distribution patterns in that area. Tanjung Kepah is chosen because there are erosion activities going on at the coast. Tanjung Kepah is studied and modeled with the MIKE 21 software to provide the best solution to prevent the erosion acivities. The primary data and secondary data on oceanographical condition, site topography and bathymetry are collected from various sources. Thus, the existing hydraulic environment conditions are analyzed based on the parameters relating to currents, tides, waves and wind. And also, the wave data analysis is carried out to predict the extreme wave heights in various return periods. The execution of computer modeling will cover several phases, which are bathymetry modeling, simulation of wave analysis, and simulation of coastal hydrodynamic incorporated with wave radiation stress. The simulation has been successfully completed, the results are interpreted and analyzed. From the analysis, the incoming waves at a distance of 100 meter from the Tanjung Kepah coast have a maximum wave height of 0.70 meter above ACD during spring high tide at return period of 50 years. The incoming current flow is 0.22 m/s at 320° during flood tide and outgoing current flow is 0.27 m/s at 138° during ebb tide. Thus, this report can be used by the authorities as a reference in order to study the existing coastal hydrodynamic of Tanjung Kepah and decide the preventive actions to be taken to protect the coast. Besides that, the authorities can use this report to do a preliminary design of protective structure, such as breakwaters

Dynamical Mean Field Theory for the Bose-Hubbard Model

The dynamical mean field theory (DMFT), which is successful in the study of strongly correlated fermions, was recently extended to boson systems [Phys. Rev. B {\textbf 77}, 235106 (2008)]. In this paper, we employ the bosonic DMFT to study the Bose-Hubbard model which describes on-site interacting bosons in a lattice. Using exact diagonalization as the impurity solver, we get the DMFT solutions for the Green's function, the occupation density, as well as the condensate fraction on a Bethe lattice. Various phases are identified: the Mott insulator, the Bose-Einstein condensed (BEC) phase, and the normal phase. At finite temperatures, we obtain the crossover between the Mott-like regime and the normal phase, as well as the BEC-to-normal phase transition. Phase diagrams on the $\mu/U-\tilde{t}/U$ plane and on the $T/U-\tilde{t}/U$ plane are produced ($\tilde{t}$ is the scaled hopping amplitude). We compare our results with the previous ones, and discuss the implication of these results to experiments.Comment: 11 pages, 8 figure

Probability Thermodynamics and Probability Quantum Field

In this paper, we introduce probability thermodynamics and probability quantum fields. By probability we mean that there is an unknown operator, physical or nonphysical, whose eigenvalues obey a certain statistical distribution. Eigenvalue spectra define spectral functions. Various thermodynamic quantities in thermodynamics and effective actions in quantum field theory are all spectral functions. In the scheme, eigenvalues obey a probability distribution, so a probability distribution determines a family of spectral functions in thermodynamics and in quantum field theory. This leads to probability thermodynamics and probability quantum fields determined by a probability distribution. There are two types of spectra: lower bounded spectra, corresponding to the probability distribution with nonnegative random variables, and the lower unbounded spectra, corresponding to probability distributions with negative random variables. For lower unbounded spectra, we use the generalized definition of spectral functions. In some cases, we encounter divergences. We remove the divergence by a renormalization procedure. Moreover, in virtue of spectral theory in physics, we generalize some concepts in probability theory. For example, the moment generating function in probability theory does not always exist. We redefine the moment generating function as the generalized heat kernel, which makes the concept definable when the definition in probability theory fails. As examples, we construct examples corresponding to some probability distributions. Thermodynamic quantities, vacuum amplitudes, one-loop effective actions, and vacuum energies for various probability distributions are presented