We study a family of cosmological models featuring dynamical dark energy (DE), based on the idea that the creation of its constituents arises from the gravitational field of the expanding universe, whose non-equilibrium physics is described by a non-zero bulk viscosity coefficient. We consider the complete scenario, in which both matter creation and bulk viscosity are present, together with its two limiting cases, in which only one of the two effects is retained. Once each model is constrained by requiring its present-day deceleration parameter q0 to match specific values, the complete scenario introduces up to two additional free parameters with respect to the Lambda CDM model, one of which is the equation of state parameter w of the created dark energy. We consider two choices for q0: the value predicted by the Lambda CDM model, and one obtained from a background analysis of Fazzari et al. (2025). To perform the analysis, we construct the effective running Hubble constant, i.e. a theoretical function corresponding to the ratio between the Hubble parameter of our models and the Lambda CDM expansion rate. The theoretical predictions for the effective running Hubble constant of the three models are tested against the Master binned sample of Type Ia Supernovae (SNe Ia), through a Markov Chain Monte Carlo procedure with up to four free parameters. The most important result emerging from this analysis is that, when using the cosmographic q0, all three models exhibit a quintessence-to-phantom transition in the effective equation of state parameter of the dark energy; on the contrary, when using the q0 coming from the Lambda CDM limit, the transition cannot happen, and the effective equation of state parameter is entirely of phantom nature across the considered redshift range.
Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative. Their relative performance remains difficult to assess because the two approaches are often compared under different formulations, parameterizations, optimizers, and regularization choices. We present a controlled comparison of adjoint optimization and PINNs for PDE-constrained inverse problems. From a common abstract formulation, we instantiate both methods on identical domains, governing equations, observation models, and regularization terms, while matching the optimizer, unknown parameterization, and arithmetic precision wherever applicable. The benchmarks include unsteady Burgers, noisy Darcy permeability inversion, three-dimensional Allen-Cahn reaction identification, and unsteady Navier-Stokes viscosity identification. The results show that the representation of the unknown largely determines the preferred method: grid-based fields favor the discrete adjoint, whereas neural representations are native to PINNs and relevant for closure and constitutive modeling. For time-dependent problems, adjoint inversion can be dominated by trajectory storage and differentiation, while PINNs provide satisfactory reconstructions at lower cost. A PINN-warm-started adjoint strategy then recovers adjoint-level accuracy at about half the cost.
We review recent progress in understanding certain aspects of condensed matter systems from a high energy theory perspective. We discuss effective field theories that describe collective bulk and localized excitations in a variety of solid and fluid systems. Particular emphasis is placed on the role played by spacetime symmetries and their spontaneous breaking. The resulting Goldstone dynamics can be seen as underlying a wide variety of phenomena. We attempt to bridge the language gap between subfields while underscoring the numerous conceptual similarities.
We study switching among multiple square selections of output functions (melds) drawn from a deck of candidate outputs for nonlinear systems that are static feedback linearizable via outputs. Fixing an operating point, each meld induces a distinct feedback-linearizing coordinate chart defined on a common neighborhood. Switching between melds therefore produces state-dependent coordinate mismatches that are not represented explicitly in standard fixed-coordinate dwell-time formulations. We quantify this effect through Lipschitz bounds on the cross-chart maps over a compact safe set and introduce a reference-compatibility constant that measures mismatch among reference families across melds. We derive an explicit dwell-time condition depending on the controller decay rates, the reference-compatibility constant, and a bound on the desired-jet resets. The resulting condition guarantees exponential decay of the active-output tracking errors between switches, conditional seamless tracking of shared outputs whose desired jets do not reset, and uniform boundedness of the state error within the safe set. Safe-set invariance follows under an explicit margin condition. A planar 3R manipulator illustrates the results.
This work investigates renewable hydrogen integration in high-temperature ceramic kilns as a partial decarbonization pathway for hard-to-abate industries. An integrated modelling framework combines proton exchange membrane (PEM) and alkaline (AEL) electrolyzer models implemented in Aspen Custom Modeler with process simulation in Aspen Plus® v12.1. The PEM model is physics-based and validated against literature experimental data, while the AEL model uses validated semi-empirical correlations. A reference ceramic plant producing 10 million m2/year is analyzed with 20 vol% H2 blending in natural gas. Four hydrogen-supply configurations are evaluated: grid-connected, PV with H2 storage, PV with battery storage, and hybrid PV–battery–H2 storage. Hydrogen blending reduces direct kiln CO2 emissions by ∼ 7% while increasing volumetric fuel flow by ∼ 16%. Calculated LCOH values are 8.4–8.9 €/kg H2 for grid-connected systems and 9.36–10.55 €/kg H2 for the PV–H2-storage configuration. Within the investigated steady-state parametric design space, the hybrid configuration provides the minimum renewable-based LCOH, approximately 8.11 €/kg H2. High-pressure electrolysis reduces downstream compression demand. Oxygen valorization may further improve system performance: internal reuse increases kiln efficiency from 60% to ∼ 61.5%, while external sales can lower hydrogen production costs under favorable market conditions. Overall, hydrogen blending may provide partial direct-emission reduction, provided that hydrogen supply and process-integration requirements are addressed and burner- and installation-specific compatibility is verified before implementation.
