Phase Distribution in a Disordered Chain and the Emergence of a Two-parameter Scaling in the Quasi-ballistic to the Mildly Localized Regime

We study the phase distribution of the complex reflection coefficient in different configurations as a disordered 1D system evolves in length, and its effect on the distribution of the 4-probe resistance $R_4$. The stationary ($L \to \infty$) phase distribution is almost always strongly non-uniform and is in general double-peaked with their separation decaying algebraically with growing disorder strength to finally give rise to a single narrow peak at infinitely strong disorder. Further in the length regime where the phase distribution still evolves with length (i.e., in the quasi-ballistic to the mildly localized regime), the phase distribution affects the distribution of the resistance in such a way as to make the mean and the variance of $log(1+R_4)$ diverge independently with length with different exponents. As $L \to \infty$, these two exponents become identical (unity). Obviously, these facts imply two relevant parameters for scaling in the quasi-ballistic to the mildly localized regime finally crossing over to one-parameter scaling in the strongly localized regime.Comment: 12 LaTeX pages plus 3 EPS figure

Human Wounds and Its Burden: An Updated Compendium of Estimates

Significance: A 2018 retrospective analysis of Medicare beneficiaries identified that ∼8.2 million people had wounds with or without infections. Medicare cost estimates for acute and chronic wound treatments ranged from $28.1 billion to$96.8 billion. Highest expenses were for surgical wounds followed by diabetic foot ulcers, with a higher trend toward costs associated with outpatient wound care compared with inpatient. Increasing costs of health care, an aging population, recognition of difficult-to-treat infection threats such as biofilms, and the continued threat of diabetes and obesity worldwide make chronic wounds a substantial clinical, social, and economic challenge. Recent Advances: Chronic wounds are not a problem in an otherwise healthy population. Underlying conditions ranging from malnutrition, to stress, to metabolic syndrome, predispose patients to chronic, nonhealing wounds. From an economic point of view, the annual wound care products market is expected to reach $15–22 billion by 2024. The National Institutes of Health's (NIH) Research Portfolio Online Reporting Tool (RePORT) now lists wounds as a category. Future Directions: A continued rise in the economic, clinical, and social impact of wounds warrants a more structured approach and proportionate investment in wound care, education, and related research

Electronic transport in a randomly amplifying and absorbing chain

We study localization properties of a one-dimensional disordered system characterized by a random non-hermitean hamiltonian where both the randomness and the non-hermiticity arises in the local site-potential; its real part being ordered (fixed), and a random imaginary part implying the presence of either a random absorption or amplification at each site. The transmittance (forward scattering) decays exponentially in either case. In contrast to the disorder in the real part of the potential (Anderson localization), the transmittance with the disordered imaginary part may decay slower than that in the case of ordered imaginary part.Comment: 7 LaTex pages plus 2 PS figures; e-mail: [email protected]

Spherically confined isotropic harmonic oscillator

The generalized pseudospectral Legendre method is used to carry out accurate calculations of eigenvalues of the spherically confined isotropic harmonic oscillator with impenetrable boundaries. The energy of the confined state is found to be equal to that of the unconfined state when the radius of confinement is suitably chosen as the location of the radial nodes in the unconfined state. This incidental degeneracy condition is numerically shown to be valid in general. Further, the full set of pairs of confined states defined by the quantum numbers [(n+1, \ell) ; (n, \ell+2)], n = 1,2,.., and with the radius of confinement {(2 \ell +3)/2}^{1/2} a.u., which represents the single node in the unconfined (1, \ell) state, is found to display a constant energy level separation exactly given by twice the oscillator frequency. The results of similar numerical studies on the confined Davidson oscillator with impenetrable boundary as well as the confined isotropic harmonic oscillator with finite potential barrier are also reported .The significance of the numerical results are discussed.Comment: 28 pages, 4 figure