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We study in detail a one-dimensional lattice model of a continuum, conserved field (mass) that is transferred deterministically between neighbouring random sites. The model falls in a wider class of lattice models capturing the joint effect of random advection and diffusion and encompassing as specific cases, some models studied in the literature, like the Kang-Redner, Kipnis-Marchioro-Presutti, Takayasu-Taguchi, etc. The motivation for our setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. For finite lattices, we study both the coalescence of an initially spread field (interpreted as roughening), and the statistical steady-state properties. We distinguish two main size-dependent regimes, depending on the strength of the diffusion term and on the lattice size. Using numerical simulations and mean-field approach, we study the statistics of the field. For weak diffusion, we unveil a characteristic hierarchical structure of the field. We also connect the model and the iterated function systems concept., Comment: Revised version, to be published in Physical Review E

After a zero temperature quench, we study the kinetics of the one-dimensional Ising model with long-range interactions between spins at distance $r$ decaying as $r^{-\alpha}$, with $\alpha \le 1$. As shown in our recent study [SciPost Phys 10, 109 (2021)] that only a fraction of the non-equilibrium trajectories is characterized by the presence of coarsening domains while in the remaining ones the system is quickly driven towards a magnetised state. Restricting to realisations displaying coarsening we compute numerically the probability distribution of the size of the domains and find that it exhibits a scaling behaviour with an unusual $\alpha$-dependent power-law decay. This peculiar behaviour is also related to the divergence of the average size of domains with system size at finite times. Such a scenario differs from the one observed when $\alpha>1$, where the distribution decays exponentially. Finally, based on numerical results and on analytical calculations we argue that the average domain size grows asymptotically linearly in time., Comment: 10 pages

The Arecchi-Bonifacio (or Maxwell-Bloch) model is the benchmark for the description of active optical media. However, in the presence of a fast relaxation of the atomic polarization, its implementation is a challenging task even in the simple ring-laser configuration, due to the presence of multiple time scales. In this Article we show that the dynamics is nearly Hamiltonian over time scales much longer than those of the cavity losses. More precisely, we prove that it can be represented as a pseudo spatio-temporal pattern generated by a nonlinear wave equation equipped with a Toda potential. The existence of two constants of motion (identified as pseudo energies), thereby, elucidates the reason why it is so hard to simplify the original model: the adiabatic elimination of the polarization must be accurate enough to describe the dynamics correctly over unexpectedly long time scales. Finally, since the nonlinear wave equation with Toda potential can be simulated on much longer times than the previous models, this opens up the route to the numerical (and theoretical) investigation of realistic setups.

The atmospheric C/O ratio of exoplanets is widely used to constrain their formation. To guarantee that the C/O ratio provides robust information, we need to accurately quantify the amount of C and O in exoplanetary atmospheres. In the case of O, water and carbon monoxide are generally studied as the two key carriers. However, oxygen is a very reactive element and does not bind with carbon; depending on the temperature, it also binds to refractory elements. Estimating the amount of oxygen bound to refractory elements is therefore critical for unbiased estimates of the C/O ratio. In this work, we investigate the oxygen deficit due to refractory elements and its effects on the atmospheric C/O ratio of giant exoplanets as a function of their metallicity and equilibrium temperature. We model the composition of planetary atmospheres assuming chemical equilibrium and using as input physically justified elemental mixtures arising from detailed planet formation simulations. Our results show how the interplay between the atmospheric temperature and non-solar abundances of oxygen and refractory elements can sequester large fractions of oxygen, introducing significant biases in evaluating the C/O ratio when this effect is not accounted for. We apply our results to the case of Jupiter in the Solar System and show how the currently estimated water abundance points to a true oxygen abundance that is four times the solar one., Comment: 13 pages, 10 figures, accepted for publication on the journal MNRAS

We consider a simple, purely stochastic model characterized by two conserved quantities (mass density $a$ and energy density $h$) which is known to display a condensation transition when $h > 2a^2$: in the localized phase a single site hosts a finite fraction of the whole energy. Its equilibrium properties in the thermodynamic limit are known and in a recent paper (Gabriele Gotti, Stefano Iubini, Paolo Politi, Phys. Rev. E 103, 052133 (2021)) we studied the transition for finite systems. Here we analyze finite-size effects on the energy distribution and on the relaxation dynamics, showing that extremely large systems should be studied in order to observe the asymptotic distribution and even larger systems should be simulated in order to observe the expected relaxation dynamics., Comment: 7 pages

Spin-Vertical Cavity Surface Emitting Lasers (spin-VCSELs) are undergoing increasing research effort for new paradigms in high-speed optical communications and photon-enabled computing. To date research in spin-VCSELs has mostly focused on Quantum-Well (QW) devices. However, novel Quantum-Dot (QD) spin-VCSELs, offer enhanced parameter controls permitting the effective, dynamical and ultrafast manipulation of their light emissions polarization. In the present contribution we investigate in detail the operation of QD spin-VCSELs subject to polarization modulation for their use as ultrafast light sources in optical communication systems. We reveal that QD spin-VCSELs outperform their QW counterparts in terms of modulation efficiency, yielding a nearly two-fold improvement. We also analyse the impact of key device parameters in QD spin-VCSELs (e.g. photon decay rate and intra-dot relaxation rate) on the large signal modulation performance with regard to optical modulation amplitude and eye-diagram opening penalty. We show that in addition to exhibiting enhanced polarization modulation performance for data rates up to 250Gbps, QD spin-VCSELs enable operation in dual (ground and excited state) emission thus allowing future exciting routes for multiplexing of information in optical communication links.

Raising the temperature of a material enhances the thermal motion of particles. Such an increase in thermal energy commonly leads to the melting of a solid into a fluid and eventually vaporises the liquid into a gaseous phase of matter. Here, we study the finite-temperature physics of dipolar quantum fluids and find surprising deviations from this general phenomenology. In particular, we describe how heating a dipolar superfluid from near-zero temperatures can induce a phase transition to a supersolid state with a broken translational symmetry. The predicted effect agrees with experimental measurements on ultracold dysprosium atoms, which opens the door for exploring the unusual thermodynamics of dipolar quantum fluids., Comment: 4 pages, 3 figures

The Discrete Nonlinear Schr\"odinger (DNLS) equation is a Hamiltonian model displaying an extremely slow relaxation process when discrete breathers appear in the system. In [Iubini S, Chirondojan L, Oppo G L, Politi A and Politi P 2019 Physical Review Letters 122 084102], it was conjectured that the frozen dynamics of tall breathers is due to the existence of an adiabatic invariant (AI). Here, we prove the conjecture in the simplified context of a unidirectional DNLS equation, where the breather is "forced" by a background unaffected by the breather itself. We first clarify that the nonlinearity of the breather dynamics and the deterministic nature of the forcing term are both necessary ingredients for the existence of a frozen dynamics. We then derive perturbative expressions of the AI by implementing a canonical perturbation theory and via a more phenomenological approach based on the estimate of the energy flux. The resulting accurate identification of the AI allows revealing the presence and role of sudden jumps as the main breather destabilization mechanism, with an unexpected similarity with L\'evy processes., Comment: 23 pages. Abstract and Introduction fully rewritten, also other minor changes

Several lattice models display a condensation transition in real space when the density of a suitable order parameter exceeds a critical value. We consider one of such models with two conservation laws, in a one-dimensional open setup where the system is attached to two external reservoirs. Both reservoirs impose subcritical boundary conditions at the chain ends. When such boundary conditions are equal, the system is in equilibrium below the condensation threshold and no condensate can appear. Instead, when the system is kept out of equilibrium, localization may arise in an internal portion of the lattice. We discuss the origin of this phenomenon, the relevance of the number of conservation laws, and the effect of the pinning of the condensate on the dynamics of the out-of-equilibrium state., Comment: 9 pages, 7 figures

Peridynamic (PD) theories have gained widespread diffusion among various research areas, due to the ability of modeling discontinuities formation and evolution in materials. Bond-Based Peridynamics (BB-PD), notwithstanding some modeling limitations, is widely employed in numerical simulations, due to its easy implementation combined with physical intuitiveness and stability. In the present paper, several aspects of bond-based peridynamic models have been reviewed and investigated. A detailed description of peridynamics theory, applications and numerical models has been presented. Employed BB-PD integral kernels have been displayed, together with their differences and commonalities; then, some consequences of their mathematical structure have been discussed. The kinematic role of nonlocality, the relation between kernel structure and material impenetrability, and the role of PD kernel nonlinearity in cracks formation prediction have been critically analyzed and commented. Finally the idea of extending BB-PD to fluids is proposed and presented in the framework of fading memory material, drawing some perspectives for a deeper and more comprehensive understanding of the peridynamics in fluids., Comment: Accepted for pubblication in Advances in Continuous and Discrete Models: Theory and Applications

In this paper, the dynamic of inertial capsules into microfluidic bifurcations is studied. The fluid evolution is based on the solution of the BGK -- lattice Boltzmann scheme including a forcing term accounting for immersed geometries. The dynamic-Immersed Boundary forcing strategy is adopted for imposing no-slip boundary conditions on moving deformable or rigid structures, while, on fixed immersed geometries the Bouzidi-Firdaouss-Lallemand second-order bounce back technique is implemented. The proposed computational framework is employed to detail dynamics and deformation of rigid and deformable capsules traveling into a branching duct. This journey is characterized in terms of i) the capsule/bifurcation interaction depending on the sharpness of the branching channels junction; ii) daughter branches aperture angle; iii) occlusion ratio, the ratio between capsule size and main channel diameter; iv) flowing capsules stiffness; v) number of flowing particles.

In this manuscript, an original numerical procedure for the nonlinear peridynamics on arbitrarily--shaped two-dimensional (2D) closed manifolds is proposed. When dealing with non parameterized 2D manifolds at the discrete scale, the problem of computing geodesic distances between two non-adjacent points arise. Here, a routing procedure is implemented for computing geodesic distances by re-interpreting the triangular computational mesh as a non-oriented graph; thus returning a suitable and general method. Moreover, the time integration of the peridynamics equation is demanded to a P-(EC)$^k$ formulation of the implicit $\beta$-Newmark scheme. The convergence of the overall proposed procedure is questioned and rigorously proved. Its abilities and limitations are analyzed by simulating the evolution of a two-dimensional sphere. The performed numerical investigations are mainly motivated by the issues related to the insurgence of singularities in the evolution problem. The obtained results return an interesting picture of the role played by the nonlocal character of the integrodifferential equation in the intricate processes leading to the spontaneous formation of singularities in real materials.

Giant planets can interact with multiple and chemically diverse environments in protoplanetary discs while they form and migrate to their final orbits. The way this interaction affects the accretion of gas and solids shapes the chemical composition of the planets and of their atmospheres. Here we investigate the effects of different chemical structures of the host protoplanetary disc on the planetary composition. We consider both scenarios of molecular (inheritance from the pre-stellar cloud) and atomic (complete chemical reset) initial abundances in the disc. We focus on four elemental tracers of different volatility: C, O, N, and S. We explore the entire extension of possible formation regions suggested by observations by coupling the disc chemical scenarios with N-body simulations of forming and migrating giant planets. The planet formation process produces giant planets with chemical compositions significantly deviating from that of the host disc. We find that the C/N, N/O, and S/N ratios follow monotonic trends with the extent of migration. The C/O ratio shows a more complex behaviour, dependent on the planet accretion history and on the chemical structure of the formation environment. The comparison between S/N* and C/N* (where * indicates normalisation to the stellar value), constrains the relative contribution of gas and solids to the total metallicity. Giant planets whose metallicity is dominated by the contribution of the gas are characterised by N/O* > C/O* > C/N* and allow for constraining the disc chemical scenario. When the planetary metallicity is instead dominated by the contribution of the solids we find that C/N* > C/O* > N/O*., Comment: 27 pages, 10 figures, 1 table. Published in The Astrophysical Journal

Quantized vortices are the prototypical feature of superfluidity. Pervasive in all natural systems, vortices are yet to be observed in dipolar quantum gases. Here, we exploit the anisotropic nature of the dipole-dipole interaction of a dysprosium Bose-Einstein condensate to induce angular symmetry breaking in an otherwise cylindrically symmetric pancake-shaped trap. Tilting the magnetic field towards the radial plane deforms the cloud into an ellipsoid through magnetostriction, which is then set into rotation. At stirring frequencies approaching the radial trap frequency, we observe the generation of dynamically unstable surface excitations, which cause angular momentum to be pumped into the system through vortices. Under continuous rotation, the vortices arrange into a stripe configuration along the field--in close corroboration with simulations--realizing a long sought-after prediction for dipolar vortices., Comment: 13 pages, 4+3 figures