Considerations for Management of Longitudinal Melanonychia During the COVID-19 Pandemic: An International Perspective

To the editor: 34 Longitudinal melanonychia (LM) is the presenting sign of nail unit melanoma (NUM) in 2/3 35 of cases and is therefore among the most important conditions managed by dermatologists. In 36 normal times, referral for LM would prompt an expedited appointment for clinical 37 examination and dermoscopy.1 However, due to SARS-CoV-2, dermatologists have been 38 asked to reconsider “urgent/emergency” conditions. The COVID-19 pandemic has propelled 39 physicians to unexpectedly adopt telemedicine without adequate guidance for managing LM 40 patients

Does the Boltzmann principle need a dynamical correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived [M. Bianucci, R. Mannella, B. J. West, and P. Grigolini, Phys. Rev. E 51, 3002 (1995)] which differs from the one that follows from the Boltzmann principle S = k log (Omega(E)) via the thermodynamic relation 1/T= dS/dE by additional terms of "dynamical" character, which are argued to correct and generalize the Boltzmann principle for small systems (here Omega(E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker-Planck formalism of Bianucci et al. is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the "volume" entropy S = k log (Phi(E)) via the thermodynamic relation above for systems of any number of degrees of freedom (Phi(E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al. and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.Comment: REVTeX 4, 10 pages, 2 figures. Accepted to J. Stat. Phy

Magnetism in small bimetallic Mn-Co clusters

Effects of alloying on the electronic and magnetic properties of Mn$_{x}$Co$_{y}$ ($x+y$=$n$=2-5; $x$=0-$n$) and Mn$_2$Co$_{11}$ nanoalloy clusters are investigated using the density functional theory (DFT). Unlike the bulk alloy, the Co-rich clusters are found to be ferromagnetic and the magnetic moment increases with Mn-concentration, and is larger than the moment of pure Co$_n$ clusters of same size. For a particular sized cluster the magnetic moment increases by 2 $\mu_B$/Mn-substitution, which is found to be independent of the size and composition. All these results are in good agreement with recent Stern-Gerlach (SG) experiments [Phys. Rev. B {\bf 75}, 014401 (2007) and Phys. Rev. Lett. {\bf 98}, 113401 (2007)]. Likewise in bulk Mn$_x$Co$_{1-x}$ alloy, the local Co-moment decreases with increasing Mn-concentration.Comment: 11 pages, 15 figures. To appear in Physical Review

Thermodynamics of Na_8 and Na_{20} clusters studied with ab-initio electronic structure methods

We study the thermodynamics of Na_8 and Na_{20} clusters using multiple-histogram methods and an ab initio treatment of the valence electrons within density functional theory. We consider the influence of various electron kinetic-energy functionals and pseudopotentials on the canonical ionic specific heats. The results for all models we consider show qualitative similarities, but also significant temperature shifts from model to model of peaks and other features in the specific-heat curves. The use of phenomenological pseudopotentials shifts the melting peak substantially (~ 50--100 K) when compared to ab-initio results. It is argued that the choice of a good pseudopotential and use of better electronic kinetic-energy functionals has the potential for performing large time scale and large sized thermodynamical simulations on clusters.Comment: LaTeX file and EPS figures. 24 pages, 13 figures. Submitted to Phys. Rev.

Classification of phase transitions in small systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let

Thermal Degradation of Adsorbed Bottle-Brush Macromolecules: Molecular Dynamics Simulation

The scission kinetics of bottle-brush molecules in solution and on an adhesive substrate is modeled by means of Molecular Dynamics simulation with Langevin thermostat. Our macromolecules comprise a long flexible polymer backbone with $L$ segments, consisting of breakable bonds, along with two side chains of length $N$, tethered to each segment of the backbone. In agreement with recent experiments and theoretical predictions, we find that bond cleavage is significantly enhanced on a strongly attractive substrate even though the chemical nature of the bonds remains thereby unchanged. We find that the mean bond life time decreases upon adsorption by more than an order of magnitude even for brush molecules with comparatively short side chains $N=1 \div 4$. The distribution of scission probability along the bonds of the backbone is found to be rather sensitive regarding the interplay between length and grafting density of side chains. The life time declines with growing contour length $L$ as $\propto L^{-0.17}$, and with side chain length as $\propto N^{-0.53}$. The probability distribution of fragment lengths at different times agrees well with experimental observations. The variation of the mean length $L(t)$ of the fragments with elapsed time confirms the notion of the thermal degradation process as a first order reaction.Comment: 15 pages, 7 figure

Excitation and relaxation in atom-cluster collisions

Electronic and vibrational degrees of freedom in atom-cluster collisions are treated simultaneously and self-consistently by combining time-dependent density functional theory with classical molecular dynamics. The gradual change of the excitation mechanisms (electronic and vibrational) as well as the related relaxation phenomena (phase transitions and fragmentation) are studied in a common framework as a function of the impact energy (eV...MeV). Cluster "transparency" characterized by practically undisturbed atom-cluster penetration is predicted to be an important reaction mechanism within a particular window of impact energies.Comment: RevTeX (4 pages, 4 figures included with epsf

Evolution of electronic and ionic structure of Mg-clusters with the growth cluster size

The optimized structure and electronic properties of neutral and singly charged magnesium clusters have been investigated using ab initio theoretical methods based on density-functional theory and systematic post-Hartree-Fock many-body perturbation theory accounting for all electrons in the system. We have systematically calculated the optimized geometries of neutral and singly charged magnesium clusters consisting of up to 21 atoms, electronic shell closures, binding energies per atom, ionization potentials and the gap between the highest occupied and the lowest unoccupied molecular orbitals. We have investigated the transition to the hcp structure and metallic evolution of the magnesium clusters, as well as the stability of linear chains and rings of magnesium atoms. The results obtained are compared with the available experimental data and the results of other theoretical works.Comment: 30 pages, 10 figures, 3 table

Quantifying erosion rates and weathering pathways that maximize soil organic carbon storage

Primary minerals that enter soils through bedrock weathering and atmospheric deposition can generate poorly crystalline minerals (PCM) that preferentially associate with soil organic carbon (SOC). These associations hinder microbial decomposition and the release of CO₂ from soils to the atmosphere, making them a critical geochemical control on terrestrial carbon abundance and persistence. Studies that explore these relationships are typically derived from soil chronosequences that experience negligible erosion and thus do not readily translate to eroding landscapes. Here, we propose a theoretical framework to estimate steady-state PCM density and stocks for hilly and mountainous settings by coupling geochemical and geomorphic mass balance equations that account for soil production from bedrock and dust, soil erosion, PCM formation from weathering, and the transformation of PCMs into crystalline phases. We calculate an optimal erosion rate for maximum PCM abundance that arises because PCMs are limited by insufficient weathering at faster erosion rates and loss via “ripening” into more crystalline forms at slower erosion rates. The optimal erosion rate for modeled hilltop soil is modulated by reaction rate constants that govern the efficiency of primary mineral weathering and PCM ripening. By comparing our analysis with global compilations of erosion and soil production rates derived from cosmogenic nuclides, we show that landscapes with slow-to-moderate erosion rates may be optimal for harboring abundant PCM stocks that can facilitate SOC sequestration and limit turnover. Given the growing array of erosion-topography metrics and the widespread availability of high-resolution topographic data, our framework demonstrates how weathering and critical zone processes can be coupled to inform landscape prioritization for persistent SOC storage potential across a broad range of spatial and temporal scales