The past decade has seen an upsurge of interest in quantum dots and nanostructures. These are essentially structures of size 1to10nm. We discuss a simplified model of a quantum dot in which we employ the effective mass approximation and the BenDaniel-Duke boundary condition. The latter accounts for the fact that the effective carrier mass inside the well, mi, is different from the mass outside, m0. The energies and the charge distributions in the nanostructure are determined by the mass discontinuity factor β=mi∕m0. The charge density at the interface becomes larger as β→0. We propose a novel quantum scale σ∼β2V0L2, where V0 is the barrier height and L is the well size. The scale σ represents a mass modified potential strength. An asymptotic analysis shows that the charge densities and energies of the carrier depend simply on σ. We also propose a definition of the penetration depth analogous to the one proposed by Garrett. Our study of tunneling reveals that the one-dimensional analog of the Ramsauer-Townsend resonances becomes increasingly sharp and well defined as β→0.

Cellulitis is a bacterial infection of the dermis and subcutaneous tissues occupying a large proportion of hospital beds. This study was conducted for analysis of patients with cellulitis according to their demographics and clinical presentation and to examine their comorbidities, complications, and its management. This observational cross-sectional study was conducted in the Department of Surgery at Santosh Medical College and Hospitals involving a total of 60 cases having cellulitis and other soft tissue infections of lower limb. Analysis of their demographic profile, management, and complications was done. Cellulitis is seen commonly in males, 46 (76.6%). The mean age of patients affected by cellulitis in the study was 36.4 ± 1.23 years. The most common site affected is leg involving more people in field jobs. The most common risk factor was trauma in 46.6%, and other factors were diabetes mellitus and smoking, while abscess formation was the most common complication observed in 36.6% of cases. A total of 56.6% cases were managed conservatively, while 43.3% cases required surgical intervention. Mean hospital stay in this study was 5.02 ± 0.23 days. It was concluded that cellulitis is subcutaneous, spreading bacterial infection is more common in males, and its incidence is highest in working age group population. Lower limb is commonly involved. Trauma, smoking, and diabetes are significant risk factors for development of cellulitis. Abscess is the most common complication. About 50% patients with cellulitis can be managed conservatively and the rest require surgical intervention.