Packing Hyperspheres in High-Dimensional Euclidean Spaces

We present the first study of disordered jammed hard-sphere packings in four-, five- and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions $d=4$, 5 and 6 to be $\phi_{MRJ} \simeq 0.46$, 0.31 and 0.20, respectively. To a good approximation, the MRJ density obeys the scaling form $\phi_{MRJ}= c_1/2^d+(c_2 d)/2^d$, where $c_1=-2.72$ and $c_2=2.56$, which appears to be consistent with high-dimensional asymptotic limit, albeit with different coefficients. Calculations of the pair correlation function $g_{2}(r)$ and structure factor $S(k)$ for these states show that short-range ordering appreciably decreases with increasing dimension, consistent with a recently proposed ``decorrelation principle,'' which, among othe things, states that unconstrained correlations diminish as the dimension increases and vanish entirely in the limit $d \to \infty$. As in three dimensions (where $\phi_{MRJ} \simeq 0.64$), the packings show no signs of crystallization, are isostatic, and have a power-law divergence in $g_{2}(r)$ at contact with power-law exponent $\simeq 0.4$. Across dimensions, the cumulative number of neighbors equals the kissing number of the conjectured densest packing close to where $g_{2}(r)$ has its first minimum. We obtain estimates for the freezing and melting desnities for the equilibrium hard-sphere fluid-solid transition, $\phi_F \simeq 0.32$ and $\phi_M \simeq 0.39$, respectively, for $d=4$, and $\phi_F \simeq 0.19$ and $\phi_M \simeq 0.24$, respectively, for $d=5$.Comment: 28 pages, 9 figures. To appear in Physical Review

Protective Role of S-Adenosylmethionine Against Fructose-Induced Oxidative Damage in Obesity

Introduction. It has been shown that S-adenosylmethionine (S-AMe) stimulates glutathione synthesis and increases cell resistance to the cytotoxic action of free radicals and pro-inflammatory cytokines. The aim of this study was to determine the effect of S-adenosylmethionine on the oxidative stress in adipose tissue in a model of fructose-induced obesity. Methods. The study was performed on male Wistar rats divided into 3 groups: control, fructose fed (HFD) (35%, 16 weeks), and HFD + S-AMe (20 mg/kg). We examined the changes in the ratio of retroperitoneal adipose tissue weight / body weight; levels of reduced glutathione (GSH) and malondialdehyde (MDA) in the retroperitoneal adipose tissue, and serum levels of GSH and TNF-α. Results. Significant increases in the retroperitoneal adipose tissue, MDA, and serum TNF-α were identified, as well as decreased tissue and serum levels of GSH in rats fed with a high-fructose diet as compared with the control group. In the group fed with HFD and S-AMe, we found significant reduction in the retroperitoneal adipose tissue and decreased levels of MDA and serum TNF-α, as well as increased tissue and serum levels of GSH as compared with the group only on HFD. In conclusion, our results show that fructose-induced obesity causes oxidative stress in hypertrophic visceral adipose tissue. The administration of S-AMe improves the antioxidative protection of adipocytes, and reduces oxidative damage and excessive accumulation of lipids and inflammation