We present a finite-volume based numerical scheme for a nonlocal Cahn-Hilliard equation which combines ideas from recent numerical schemes for gradient flow equations and nonlocal Cahn-Hilliard equations. The equation of interest is a special case of a previously derived and studied system of equations which describes phase separation in ternary mixtures. We prove the scheme is both energy stable and respects the analytical bounds of the solution. Furthermore, we present numerical demonstrations of the theoretical results using both the Flory-Huggins (FH) and Ginzburg-Landau (GL) free-energy potentials.

We establish the existence of a weak solution for a strongly coupled, nonlinear Stokes–Maxwell system, originally proposed by Nika and Vernescu (Z Angew Math Phys71(1):1–19, 2020) in the three-dimensional setting. The model effectively couplesthe Stokes equation with the quasi-static Maxwell’s equations through the Lorentzforce and the Maxwell stress tensor. The proof of existence is premised on: (i) theaugmented variational formulation of Maxwell’s equations, (ii) the definition of a newfunction space for the magnetic induction and the verification of a Poincar’e-typeinequality, and (iii) the deployment of the Altman–Shinbrot fixed point theorem whenthe magnetic Reynolds number, Rm, is small.

We derive two different effective models from a heterogeneous Cosserat continuum taking into account the Cosserat intrinsic length of the constituents. We pass to the limit using homogenization via periodic unfolding and in doing so we provide rigorous proof to the results introduced by Forest, Pradel, and Sab (Int. J. Solids Struct. 38 (26-27): 4585-4608 ’01). Depending on how different characteristic lengths of the domain scale with respect to the Cosserat intrinsic length, we obtain either an effective classical Cauchy continuum or an effective Cosserat continuum. Moreover, we provide some corrector type results for each case.

We derive effective models for a heterogeneous second-gradient elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size of the heterogeneities ℓ, the intrinsic lengths of the constituents ℓSG and ℓchiral, and the overall characteristic length of the domain L. Depending on the different scale interactions between ℓSG, ℓchiral, ℓ, and L we obtain either an effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors’ structure rely on a suitable use of the periodic unfolding operator.

Accurate population data is crucial for assessing exposure in disaster risk assessments. In recent years,there has been a signifcant increase in the development of spatially gridded population datasets.Despite these datasets often using similar input data to derive population fgures, notable diferencesarise when comparing them with direct ground-level observations. This study evaluates the precisionand accuracy of food exposure assessments using both known and generated gridded populationdatasets in Sweden. Specifcally focusing on WorldPop and GHSPop, we compare these datasetsagainst ofcial national statistics at a 100 m grid cell resolution to assess their reliability in foodexposure analyses. Our objectives include quantifying the reliability of these datasets and examiningthe impact of data aggregation on estimated food exposure across diferent administrative levels.The analysis reveals signifcant discrepancies in food exposure estimates, underscoring the challengesassociated with relying on generated gridded population data for precise food risk assessments.Our fndings emphasize the importance of careful dataset selection and highlight the potential foroverestimation in food risk analysis. This emphasises the critical need for validations against groundpopulation data to ensure accurate food risk management strategies.

We derive a generalized heat conduction problem for a rarefied gas at slip regime from a gradient system where the driving functional is the entropy. Specifically, we construct an Onsager system (X,S,Kheat) such that the associated evolution of the system is given by ∂tu=+Kheat(u)DS(u), where the Onsager operator, Kheat(u), contains higher-gradients of the absolute temperature u. Moreover, through Legendre-Fenchel theory we write the Onsager system as a classical gradient system (X,S,G) with an induced gradient flow equation, ∂tu=∇GDS(u). We demonstrate the usefulness of the approach by modeling scale-size thermal effects in periodic media that have been recently observed experimentally.

We propose an enriched microscopic heat conduction model that can account for size effects in heterogeneous media. Benefiting from physically relevant scaling arguments, we improve the regularity of the corrector in the classical problem of periodic homogenization of linear elliptic equations in the three-dimensional setting and, while doing so, we clarify the intimate role that correctors play in measuring the difference between the heterogeneous solution (microscopic) and the homogenized solution (macroscopic). Moreover, if the data are of form f = div F with (Formula presented), then we recover the classical corrector convergence theorem. 

We derive a hierarchy of effective models that can be used to model the biomechanics of human compact bone taking into account scale-size effects observed experimentally. The classification of the effective models depends on the hierarchy of four characteristic lengths: The size of the heterogeneities, two intrinsic lengths of the constituents, and the overall characteristic length of the domain. Depending on the different scale interactions between the size of the heterogeneities, the two intrinsic lengths of the constituents, and the characteristic length of the domain we obtain either an effective Cauchy continuum or an effective Cosserat continuum. The passage to the limit relies on suitable use of the periodic unfolding operator. Moreover, we perform numerical simulations to validate our results. 

We derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion- based electrothermal models with thermistor-type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss–Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.

We prove existence of a weak solution for a hybrid model for the electro-thermal behavior of semiconductor heterostructures. This hybrid model combines an electro-thermal model based on drift-diffusion with thermistor type models in different subregions of the semiconductor heterostructure. The proof uses a regularization method and Schauder's fixed point theorem. For boundary data compatible with thermodynamic equilibrium we verify, additionally, uniqueness. Moreover, we derive bounds and higher integrability properties for the electrostatic potential and the quasi Fermi potentials as well as the temperature.