The Ground State Energy of Dilute Bose Gas in Potentials with Positive Scattering Length

The leading term of the ground state energy/particle of a dilute gas of bosons with mass $m$ in the thermodynamic limit is $2\pi \hbar^2 a \rho/m$ when the density of the gas is $\rho$, the interaction potential is non-negative and the scattering length $a$ is positive. In this paper, we generalize the upper bound part of this result to any interaction potential with positive scattering length, i.e, $a>0$ and the lower bound part to some interaction potentials with shallow and/or narrow negative parts.Comment: Latex 28 page

The ground state energy of the weakly interacting Bose gas at high density

We prove the Lee-Huang-Yang formula for the ground state energy of the 3D Bose gas with repulsive interactions described by the exponential function, in a simultaneous limit of weak coupling and high density. In particular, we show that the Bogoliubov approximation is exact in an appropriate parameter regime, as far as the ground state energy is concerned.Comment: RevTeX4, 16 page

Free Energies of Dilute Bose gases: upper bound

We derive a upper bound on the free energy of a Bose gas system at density $\rho$ and temperature $T$. In combination with the lower bound derived previously by Seiringer \cite{RS1}, our result proves that in the low density limit, i.e., when $a^3\rho\ll 1$, where $a$ denotes the scattering length of the pair-interaction potential, the leading term of $\Delta f$ the free energy difference per volume between interacting and ideal Bose gases is equal to 4\pi a (2\rho^2-[\rho-\rhoc]^2_+). Here, \rhoc(T) denotes the critical density for Bose-Einstein condensation (for the ideal gas), and $[\cdot ]_+$ $=$ $\max\{\cdot, 0\}$ denotes the positive part.Comment: 56 pages, no figure

Skyrmions in Higher Landau Levels

We calculate the energies of quasiparticles with large numbers of reversed spins (``skyrmions'') for odd integer filling factors 2k+1, k is greater than or equals 1. We find, in contrast with the known result for filling factor equals 1 (k = 0), that these quasiparticles always have higher energy than the fully polarized ones and hence are not the low energy charged excitations, even at small Zeeman energies. It follows that skyrmions are the relevant quasiparticles only at filling factors 1, 1/3 and 1/5.Comment: 10 pages, RevTe

The Second Order Upper Bound for the Ground Energy of a Bose Gas

Consider $N$ bosons in a finite box $\Lambda= [0,L]^3\subset \mathbf R^3$ interacting via a two-body smooth repulsive short range potential. We construct a variational state which gives the following upper bound on the ground state energy per particle $$\bar\lim_{\rho\to0} \bar \lim_{L \to \infty, N/L^3 \to \rho} (\frac{e_0(\rho)- 4 \pi a \rho}{(4 \pi a)^{5/2}(\rho)^{3/2}})\leq \frac{16}{15\pi^2},$$ where $a$ is the scattering length of the potential. Previously, an upper bound of the form $C 16/15\pi^2$ for some constant $C > 1$ was obtained in \cite{ESY}. Our result proves the upper bound of the the prediction by Lee-Yang \cite{LYang} and Lee-Huang-Yang \cite{LHY}.Comment: 62 pages, no figure

Physical principles of ion-beam processing of polymeric materials and applications

Irradiation of polymeric materials with energetic ions in the range of several hundreds of keV to several MeV causes drastic changes in physical, chemical, and mechanical properties. Studies indicate that irradiation produces many active radicals which then react with each other, transforming spaghetti-like tangled polymer chains into a highly cross-linked network structure. Analysis of experimental data shows that the most important parameter for cross-linking is the deposited energy density along the ion track, often expressed in terms of linear energy transfer (LET) in units of eV/nm. High LET produces a high number of free radicals over many neighboring molecular chains and thereby facilitates cross-linking. On the other hand, under low LET conditions, radicals are produced so sparsely that cross-linking efficiency decreases. Moreover, the deposited energy in the chain often leads to chain scission when there are no radicals in the neighboring chains for crosslinking. This paper reviews the current understanding of cross-linking mechanisms in terms of nuclear and electronic stopping and their impact on materials` properties

effect of butyric acid on the performance and carcass yield of broiler chickens

Short-chain fatty acids such as butyrate are considered potential alternatives to antibiotic growth promoters. The efficacy of butyric acid on performance and carcass characteristics of broiler chickens was tested in two studies. The effect of dietary butyrate on the ability to withstand coccidial oocyte challenge also was investigated. In experiment 1, male broiler chickens were fed diets supplemented with 0 or 11 ppm virginiamycin or 0.2 or 0.4% butyric acid (as mono-, di-, and triglyceride). In experiment 2, broilers were fed bacitracin methylene disalicylate or 0.1 or 0.2% butyric acid. In another trial, birds vaccinated against coccidiosis were challenged with oocytes at 21 d and examined 6 d later. In experiment 1, diet treatments had no effect on body weight gain. Feed intake of the birds fed 0.4% butyric acid was decreased (P < 0.01) compared with birds fed the nonmedicated diet during the starter period, whereas birds fed 0.2% butyric acid had similar feed intake to the control birds. In experiment 2, diet treatments did not affect the performance of broiler chicks while carcass weight and breast meat yield increased (P < 0.01) in birds fed 0.2% butyric acid. With oocyte challenge, birds that had received butyric acid before challenge showed higher growth rate following the challenge compared with birds that received nonmedicated feed. Bacitracin decreased (P < 0.05%) duodenal villi crypt depth, whereas villus length was similar in birds fed butyric acid or the nonmedicated control diet. These results show that 0.2% butyric acid can help to maintain the performance and carcass quality of broilers, especially in vaccinated birds challenged with coccidiosis

Nano encapsulation of Drug-loaded Lipid by Temperature induced Phase Transition

Pluronic nanoparticles (NPs) were prepared by means of a temperature-induced phase transition in the mixture composed of Pluronic F-68 and liquid Tween 80/soybean oil containing model drugs such as orlistat, caffeine, and ibuprofen sodium salt. Liquid soybean oil/Tween 80 was used as a solubilizer for model drugs, and Pluronic F-68 was the polymer that stabilizes liquid soybean oil/Tween 80 containing model drugs. Field-emission scanning electron microscopy and particle size analyzer were used to observe the morphology and size distribution of the prepared NPs. X-ray diffractometer was used to understand relationship between the crystalline state of the model drug and its solubility in the aqueous media. To observe the feasibility of Pluronic NPs as a drug delivery system, the release pattern of model drugs was observed

Second-order corrections to mean field evolution for weakly interacting Bosons. I

Inspired by the works of Rodnianski and Schlein and Wu, we derive a new nonlinear Schr\"odinger equation that describes a second-order correction to the usual tensor product (mean-field) approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation. We show that our new equation, if it has solutions with appropriate smoothness and decay properties, implies a new Fock space estimate. We also show that for an interaction potential $v(x)= \epsilon \chi(x) |x|^{-1}$, where $\epsilon$ is sufficiently small and $\chi \in C_0^{\infty}$, our program can be easily implemented locally in time. We leave global in time issues, more singular potentials and sophisticated estimates for a subsequent part (part II) of this paper

Nano encapsulation of Drug-loaded Lipid by Temperature induced Phase Transition

Pluronic nanoparticles (NPs) were prepared by means of a temperature-induced phase transition in the mixture composed of Pluronic F-68 and liquid Tween 80/soybean oil containing model drugs such as orlistat, caffeine, and ibuprofen sodium salt. Liquid soybean oil/Tween 80 was used as a solubilizer for model drugs, and Pluronic F-68 was the polymer that stabilizes liquid soybean oil/Tween 80 containing model drugs. Field-emission scanning electron microscopy and particle size analyzer were used to observe the morphology and size distribution of the prepared NPs. X-ray diffractometer was used to understand relationship between the crystalline state of the model drug and its solubility in the aqueous media. To observe the feasibility of Pluronic NPs as a drug delivery system, the release pattern of model drugs was observed