We present the third release of ULYSSES, a Python package for the numerical evaluation of the baryon asymmetry generated through leptogenesis. This version includes code implementing state-of-the-art density matrix equations for low-scale leptogenesis with three quasi-degenerate right-handed neutrinos. We extend the validity of the code in this scenario beyond the 100 GeV right-handed neutrino mass scale, into the regime of resonant leptogenesis, by including neutrino production rates valid in both the relativistic and non-relativistic regimes. In addition, in the high-scale vanilla scenario, we provide routines for computing ΔL=1 scattering processes, enabling full phase-space evolution of the right-handed neutrino and lepton asymmetry. A new --extended parameter interface allows users to pass model-specific inputs beyond the standard leptogenesis runcard without modifying the core infrastructure and demonstrate its use with a toy module that simultaneously solves the vanilla leptogenesis equations and the freeze-in production of dark matter. On top of these improvements, we introduce an alternative parametrisation of the Casas-Ibarra matrix, update the default neutrino oscillation parameters and report cross-checks of the new low-scale leptogenesis module against published benchmarks and independent codes. ULYSSES is publicly available on GitHub https://github.com/earlyuniverse/ulysses and pip-installable from PyPI. PROGRAM SUMMARY Program title: ULYSSESCPC Library link to program files: https://doi.org/10.17632/4cvdr57t2n.1Developer’s repository link: https://github.com/earlyuniverse/ulyssesLicensing provisions: MIT LicenseProgramming language: Python 3Journal reference of previous version: Comput. Phys. Commun. 291 (2023) 108834Does the new version supersede the previous version?: YesReasons for the new version: Extension of the code capabilities to include low-scale leptogenesis scenarios, complete ΔL=1 scattering processes for high-scale leptogenesis, improved user-defined model support, and enhanced usability through a Python API and Jupyter notebook interface.Summary of revisions: Implementation of a unified treatment of low-scale leptogenesis with three right-handed neutrinos; inclusion of complete ΔL=1 scattering processes in the leptogenesis evolution equations; addition of alternative Casas–Ibarra parametrisations; support for user-specified initial heavy-neutrino abundances; extension of the framework to accommodate custom leptogenesis models and parameters; introduction of a Python API and Jupyter notebook workflow.Nature of problem: Numerical solution of coupled Boltzmann and Density Matrix equations governing thermal, resonant, and low-scale leptogenesis, including the evaluation of computationally demanding thermal integrals and reaction rates.Solution method: The evolution equations are solved using the odeint and solve_ivp integrators available in Python. Integrals are evaluated using a Numba-accelerated wrapper around the cquadpack integration library.
We study the forward discrete space-time wave equation on the homogeneous (q+1)-regular tree T_q+1 associated with a two-parameter generalized Laplacian. Under the natural nonnegativity assumption on this operator, we derive explicit formulas for the two fundamental wave kernels. The formulas are given in terms of discrete I-Bessel functions and yield convolution representations for solutions with general initial conditions. In the boundary case corresponding to the bottom of the spectrum, we obtain another explicit representation of the wave kernel in terms of discrete J-Bessel functions. This representation leads to a discrete analogue of the classical I↔J relation. We also perform both analytic and numerical studies of the asymptotic behavior of the wave kernels, including large radial distance, large time, and large degree of the tree. An important feature of our analysis is that the wave kernels are expressed as finite sums; hence, the propagation formulas remain finite for every discrete time.
Let M-n(F) denote the algebra of n & times; n matrices over an algebraically closed field F of characteristic different from 2. For n >= 2, we classify all maps phi : M-n(F) -> M-n(F) satisfying the mixed Jordan-power identity phi(A(k) degrees B) = phi(A)(k) degrees phi(B), for all A, B is an element of M-n(F), where degrees denotes the Jordan product A degrees B := 1 /2 (AB + BA) and k is an element of & Nopf;. We show that every such map is either constant, taking a fixed (k + 1)-potent value, or there exist an invertible matrix T is an element of M-n(F), a ring monomorphism omega : F -> F, and a k-th root of unity epsilon is an element of F such that phi takes one of the forms phi(X) = epsilon T (omega)(X) T (-1) or phi(X) = epsilon T omega(X)(t) T (-1), where omega(X) denotes the matrix obtained by applying omega entrywise to X, and (& centerdot;)(t) denotes matrix transposition. In particular, every nonconstant solution is necessarily additive. The classification relies fundamentally on the preservation of (k + 1)-potents and their intrinsic structural properties.
We study a diffuse-interface model for thermally driven phase separation in viscous incompressible mixtures. The system couples a convective Cahn-Hilliard equation for the order parameter with a Stokes subsystem for the velocity-pressure field and a heat equation for the temperature. Temperature enters the bulk free energy through a Landau-type coefficient, while the phase field feeds back on the flow through concentration-dependent density and viscosity, yielding a phenomenological temperature-coupled Cahn-Hilliard-Stokes-heat system. The model serves as a proxy for temperature-triggered condensation-like phase separation and does not include humidity, latent heat, vapor pressure, or capillary forcing; these effects are absorbed into the choice of the threshold temperature Theta(S). We motivate the chemical potential by a temperature-dependent Landau free energy and derive a priori estimates for the regularized subproblems. On the analytical side, we prove local-in-time existence of weak solutions for a regularized auxiliary model of the coupled system. This regularized formulation serves as an auxiliary analytical model for establishing local existence. On the numerical side, we use a first-order sequential finite-element discretization of a simplified quasi-static formulation. The heat equation is advanced by an implicit diffusion step, the variable-coefficient Stokes problem by a Taylor-Hood discretization, and the Cahn-Hilliard bulk derivative is evaluated at the previous time level, so every algebraic subproblem is linear. An isothermal diffusive test confirms mass conservation to roundoff and exhibits monotone discrete-energy decay for the tested parameter set. Time-step and mesh-refinement studies show first-order temporal and approximately second-order spatial behavior. The remaining computations are qualitative, parameter-specific illustrations, and no global discrete energy law is claimed for the non-isothermal sequential scheme.
Agro-industrial valorization of Satsuma mandarin peels is typically limited to pectin or essential oils, often neglecting valuable non-volatile bioactives. This study investigates high-pressure homogenization (HPH) as an intensive microstructural disruption strategy to recover matrix-bound bioactives and obtain physically stable multi-phase plant-derived fluid systems using water or oil-in-water (o/w) mixtures. HPH treatment (up to 10 passes) effectively disrupted the cellular matrix, achieving a similar to 2.6-fold particle size reduction. In aqueous systems, 5 passes maximized the recovery of total polyphenols and carotenoids. Remarkably, this water-only process achieved total carotenoid analytical accessibility statistically comparable to exhaustive conventional solvent extraction with acetone, indicating that intense physical disruption can effectively liberate sequestered lipophilic compounds without the primary use of organic solvents. In o/w systems, processing enabled a passive physical partitioning of compounds driven by their respective chemical polarities. Mass balance tracking across the physical fractions indicated that lipophilic carotenoids and polymethoxylated flavones (PMFs) preferentially partitioned into the lipid-rich cream phase, while hydrophilic flavonoids (e.g., narirutin) remained in the continuous serum layer. Chromatographic phase profiles and serum depletion data supported these distinct distribution trends for PMFs (e.g., nobiletin) and carotenoids. Isothermal calorimetry validated the functional protective capacity of the resulting colloidal system: the incorporation of 1% HPH-treated peel powder significantly delayed lipid autooxidation in exogenous linseed oil model, yielding an induction time superior to a purified resveratrol standard. These findings demonstrate that HPH effectively releases and distributes mandarin peel bioactives into distinct, multi-phase fluid matrices, offering a sustainable, solvent-free processing pathway for the valorization of citrus by-products.
