Evolutionary dynamics on strongly correlated fitness landscapes

We study the evolutionary dynamics of a maladapted population of self-replicating sequences on strongly correlated fitness landscapes. Each sequence is assumed to be composed of blocks of equal length and its fitness is given by a linear combination of four independent block fitnesses. A mutation affects the fitness contribution of a single block leaving the other blocks unchanged and hence inducing correlations between the parent and mutant fitness. On such strongly correlated fitness landscapes, we calculate the dynamical properties like the number of jumps in the most populated sequence and the temporal distribution of the last jump which is shown to exhibit a inverse square dependence as in evolution on uncorrelated fitness landscapes. We also obtain exact results for the distribution of records and extremes for correlated random variables

Number of adaptive steps to a local fitness peak

We consider a population of genotype sequences evolving on a rugged fitness landscape with many local fitness peaks. The population walks uphill until it encounters a local fitness maximum. We find that the statistical properties of the walk length depend on whether the underlying fitness distribution has a finite mean. If the mean is finite, all the walk length cumulants grow with the sequence length but approach a constant otherwise. Experimental implications of our analytical results are also discussed

Quantifying the pathway and predicting spontaneous emulsification during material exchange in a two phase liquid system

Kinetic restriction of a thermodynamically favourable equilibrium is a common theme in materials processing. The interfacial instability in systems where rate of material exchange is far greater than the mass transfer through respective bulk phases is of specific interest when tracking the transient interfacial area, a parameter integral to short processing times for productivity streamlining in all manufacturing where interfacial reaction occurs. This is even more pertinent in high-temperature systems for energy and cost savings. Here the quantified physical pathway of interfacial area change due to material exchange in liquid metal-molten oxide systems is presented. In addition the predicted growth regime and emulsification behaviour in relation to interfacial tension as modelled using phase-field methodology is shown. The observed in-situ emulsification behaviour links quantitatively the geometry of perturbations as a validation method for the development of simulating the phenomena. Thus a method is presented to both predict and engineer the formation of micro emulsions to a desired specification

CSLM, XCT Couple interrogation of the emulsification interaction between free steel droplets suspended in steel making slags

Small Fe-based droplets have been heated to a molten phase suspended within a slag medium to replicate a partial environment within the Basic Oxygen Furnace (BOF). The confocal scanning laser microscope (CSLM) has been used as a heating platform as it offers the high heating rates necessary for slag and metal to become molten in close time proximity avoiding gradual equilibration during heating. The effect of impurities and their transfer across the metal/slag interface, on the emulsification of the droplet into the slag medium was then examined through X-ray Computer Tomography (XCT) scanning of the quenched sample. This gives the mapping of emulsion dispersion in 3D space, calculating the changing of interfacial area between the two materials, and changes of material volume due to material transfer between metal and slag. Samples were then sectioned and radial chemical analysis is used to identify component surface enrichment or lack thereof. Replication of the previously reported study by Assis et al1 has also been carried out, to show repeatability of the experimental set up and conditions through different users

Efficient organic-inorganic hybrid perovskite solar cells processed in air

Organic-inorganic hybrid perovskite solar cells with fluorine doped tin oxide/titanium dioxide/CH3NH3PbI3-xClx/poly(3-hexylthiophene)/silver were made in air with more than 50% humidity. The best devices showed an open circuit voltage of 640 mV, a short circuit current density of 18.85 mA cm-2, a fill factor of 0.407 and a power conversion efficiency of 5.67%. The devices showed external quantum efficiency varying from 60 to 80% over a wavelength region of 350 nm to 750 nm of the solar spectrum. The morphology of the perovskite was investigated using scanning electron microscopy and it was found to be porous in nature. This study provides insights into air-stability of perovskite solar cells

Semiclassical energy formulas for power-law and log potentials in quantum mechanics

We study a single particle which obeys non-relativistic quantum mechanics in R^N and has Hamiltonian H = -Delta + V(r), where V(r) = sgn(q)r^q. If N \geq 2, then q > -2, and if N = 1, then q > -1. The discrete eigenvalues E_{n\ell} may be represented exactly by the semiclassical expression E_{n\ell}(q) = min_{r>0}\{P_{n\ell}(q)^2/r^2+ V(r)}. The case q = 0 corresponds to V(r) = ln(r). By writing one power as a smooth transformation of another, and using envelope theory, it has earlier been proved that the P_{n\ell}(q) functions are monotone increasing. Recent refinements to the comparison theorem of QM in which comparison potentials can cross over, allow us to prove for n = 1 that Q(q)=Z(q)P(q) is monotone increasing, even though the factor Z(q)=(1+q/N)^{1/q} is monotone decreasing. Thus P(q) cannot increase too slowly. This result yields some sharper estimates for power-potential eigenvlaues at the bottom of each angular-momentum subspace.Comment: 20 pages, 5 figure

Nonlinear deterministic equations in biological evolution

We review models of biological evolution in which the population frequency changes deterministically with time. If the population is self-replicating, although the equations for simple prototypes can be linearised, nonlinear equations arise in many complex situations. For sexual populations, even in the simplest setting, the equations are necessarily nonlinear due to the mixing of the parental genetic material. The solutions of such nonlinear equations display interesting features such as multiple equilibria and phase transitions. We mainly discuss those models for which an analytical understanding of such nonlinear equations is available.Comment: Invited review for J. Nonlin. Math. Phy

Relativistic wave equations for interacting massive particles with arbitrary half-intreger spins

New formulation of relativistic wave equations (RWE) for massive particles with arbitrary half-integer spins s interacting with external electromagnetic fields are proposed. They are based on wave functions which are irreducible tensors of rank $n ($n=s-\frac12$) antisymmetric w.r.t. n pairs of indices, whose components are bispinors. The form of RWE is straightforward and free of inconsistencies associated with the other approaches to equations describing interacting higher spin particles