From the general understanding on sea ice it is known that as the ocean water begins to freeze, small ice crystals called frazil ice form. Strong wind, turbulence and/or the wavy motion inhibit the growth of a monolithic ice sheet and can entrain some ice crystal down the water column. As a part of the crystals are transported deep, additional ice production may take place also away from the surface provided the overcooling is sufficient. When the crystals freeze they expel salt into the surrounding water. Convective fluxes of heat and ice toward the surface, and of salinity toward the bottom, are therefore present. We consider the case in which a turbulent boundary layer forced both by mechanical stress and convection fluxes is present. Through an analytical approach, some limit regime in terms of crystal growth rate, overcooling and ice entrainment are considered. For this limit the vertical profile of salinity and ice concentration are obtained and their stability is analyzed. The ratio between latent heat flux and sensible heat flux is estimated. The case of a strong wind that blown away the frazil ice leaving the water surface exposed to the cold air with strong increase of ice formation and heat transfer to the atmosphere is also considered. In order to estimate the effects of fluctuations and consider intermediate regime, some numerical results are discussed.

Self-organized criticality elucidates the conditions under which physical and biological systems tune themselves to the edge of a second-order phase transition, with scale invariance. Motivated by the empirical observation of bimodal distributions of activity in neuroscience and other fields, we propose and analyze a theory for the self-organization to the point of phase coexistence in systems exhibiting a first-order phase transition. It explains the emergence of regular avalanches with attributes of scale invariance that coexist with huge anomalous ones, with realizations in many fields.

The numerical study of scattering problems finds a wide range of applications in surface science, and in particular quantum reflection (QR). We present a highly optimised, norm-preserving method to compute QR of slow atoms from metallic surfaces by numerically solving the Time-Dependent Schrödinger Equation in 2D. The aim of our study is to provide a proof of principle that QR from 2D uni-axially periodic potential structures can be investigated in a time-dependent fashion. To this end, the numerical procedures used are presented, as well as the first successful comparisons with 1D results for QR from static and oscillating 1D potentials and the first results for QR from a truly 2D nonseparable potential. This enables the first systematic investigation of atom-surface potentials where Casimir interactions are relevant, as well as numerical tests on quantum diffraction.

Each step in a quantum random walk is typically understood to have two basic components: a "coin toss" which produces a random superposition of two states, and a displacement which moves each component of the superposition by different amounts. Here we suggest the realization of a walk in momentum space with a spinor Bose-Einstein condensate subject to a quantum ratchet realized with a pulsed, off-resonant optical lattice. By an appropriate choice of the lattice detuning, we show how the atomic momentum can be entangled with the internal spin states of the atoms. For the coin toss, we propose to use a microwave pulse to mix these internal states. We present experimental results showing an optimized quantum ratchet, and through a series of simulations, demonstrate how our proposal gives extraordinary control of the quantum walk. This should allow for the investigation of possible biases, and classical-to-quantum dynamics in the presence of natural and engineered noise.

The formation of protein filaments is associated with a wide range of cellular functions, including transport and scaffolding, as well as a variety of disorders, such as Alzheimer's, Parkinson's and prion diseases. The complexity and diversity of these phenomena have made it challenging to establish whether a general predictive description can be formulated to account quantitatively for the kinetics of the formation of filaments in the different cases using a unified theoretical framework. We show here that it is possible to achieve this goal by establishing the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.

In this work we study the survival probability of single-species in the context of hostile and heterogeneous environments. Here we use spatially random growth rates with negative mean to model hostile and heterogeneous environments i.e. population dynamics in this environment, as modeled by the Fisher equation, is characterized by negative average growth rate (\( \bar{\mu} \)), except in some random spatially distributed patches that may support life (\(\mu_i>0\)). In particular, we are interested in the phase diagram of the survival probability and the critical size problem, i.e., the minimum patch size required for surviving in the long time limit. We propose a measure for the critical size as being proportional to the participation ratio (PR) of the eigenvector corresponding to the largest eigenvalue of the linearized Fisher dynamics. We numerically obtain the (extinction-survival) phase diagram and the critical patch size distribution for two network topologies, namely, the linear chain and the Peano basin fractal. We show that both topologies share the same qualitative features, but the fractal topology requires higher spatial fluctuations to guarantee species survival, which leads to a slightly larger patch size than the linear chain. In addition, we perform a finite-size scaling and we obtain the associated critical exponents.

The easy access to large data sets has allowed for leveraging methodology in network physics and complexity science todisentangle patterns and processes directly from the data, leading to key insights in the behavior of systems. Here we use to country specific food production data to study binary and weighted topological properties of the bipartite country-food production matrix. This country-food production matrix can be: 1) transformed into overlap matrices which embed information regarding shared production of products among countries, and or shared countries for individual products, 2) identify subsets of countries which produce similar commodities or subsets of commodities shared by a given country allowing for visualization of correlations in large networks, and 3) used to rank country’s fitness (the ability to produce a diverse array of products weighted on the type of food commodities) and food specialization (quantified on the number of countries producing that food product weighted on their fitness). Our results show that, on average, countries with high fitness producing highly specialized food commodities also produce low specialization goods, while nations with low fitness producing a small basket of diverse food products, typically produce low specialized food commodities.

The complex evolution of social networks is affected by two non-trivial mechanisms: the reinforcement of ties (people tend to distribute their social events toward already contacted nodes) and the burstiness of interactions (the inter-event times are broadly distributed). Here we define and analyze an activity-driven model, featuring both characteristics. We build the model and analytically solve the dynamics in the limit of large time and connectivity. We find a non-trivial phase diagram due to the interplay of the two effects and we determine the leading contribution depending on the system parameters. Interestingly, if ties reinforcement is sufficiently strong, burstiness can be suppressed and it can play a sub-leading role also in the presence of large fluctuations. We test our results against numerical simulations, and we compare the analytical predictions with an empirical datasets (Twitter mentions network) finding a good agreement between the two.

Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments are generally regarded as a sign of multifractality in the data. However, this method fails to disclose the correct monofractal nature of self-similar Levy processes, except for the Brownian motion. I prove that for this class of processes it produces apparent multifractality characterised by a piecewise-linear scaling function with two different regimes, which match at the stability index of the considered process.