Casimir effect and gravitational balance: A search for stable configurations

Tensile fatigue evolution in sandstone under lower cyclic stress: Coupled Brazilian disc experiments and enhanced mesoscale damage modeling

Dynamic source seeking via multi-agent formation with nonconvex scalar fields

Visualizing the large-scale datasets output by HPC resources presents a difficult challenge, as the memory and compute power required become prohibitively expensive for end user systems. Novel view synthesis techniques can address this by producing a small, interactive model of the data, requiring only a set of training images to learn from. While these models allow accessible visualization of large data and complex scenes, they do not provide the interactions needed for scientific volumes, as they do not support interactive selection of transfer functions and lighting parameters. To address this, we introduce Volume Encoding Gaussians (VEG), a 3D Gaussian-based representation for volume visualization that supports arbitrary color and opacity mappings. Unlike prior 3D Gaussian Splatting (3DGS) methods that store color and opacity for each Gaussian, VEG decouple the visual appearance from the data representation by encoding only scalar values, enabling transfer function-agnostic rendering of 3DGS models. To ensure complete scalar field coverage, we introduce an opacity-guided training strategy, using differentiable rendering with multiple transfer functions to optimize our data representation. This allows VEG to preserve fine features across a dataset's full scalar range while remaining independent of any specific transfer function. Across a diverse set of volume datasets, we demonstrate that our method outperforms the state-of-the-art on transfer functions unseen during training, while requiring a fraction of the memory and training time.

SurfaceNets is a powerful visualization technique typically used to contour non-continuous, discrete, volumetric scalar fields such as segmentation label maps. Label maps are ubiquitous to medical computing, biological studies, and materials characterization, used in applications ranging from anatomical atlas creation to nanotechnology analysis. Due to the uniform spacing of volume data, however, representing data with highly variable resolution is challenging. Consequently we have developed a generalized high-performance, parallel SurfaceNets algorithm that processes unorganized, labeled point clouds. Based on a scalable, meshless Voronoi approach, the algorithm independently processes each Voronoi hull in parallel using a hierarchical neighborhood point search metric. By employing novel topological constructs, the resulting meshless tessellation can be readily transformed into a connected conformal mesh, from which multiple, valid contour surfaces can be simultaneously extracted and smoothed. Additional contributions include a general API for locating points proximal to Voronoi hulls; the definition of topological coordinates used to detect and eliminate numerical degeneracies, merge coincident points, rapidly produce the dual Delaunay triangulation, and build smoothing stencils; and the construction of a Voronoi adjacency graph along with associated necessary conditions to ensure the generation of valid tessellations. Characterization of parallel performance is also quantified, including producing Voronoi and Delaunay tessellations of 128 million hulls and more than 750 million tetrahedra. A software implementation is available from the open source the Visualization Toolkit (VTK) system at vtk.org.

The present investigation explores baryogenesis within the purview of Hořava-Lifshitz cosmology, assuming a background evolution governed by generalised holographic dark energy coupled with generalised Chaplygin gas. To set up the scalar-field sector, we employ the Starobinsky potential. It is demonstrated that the reconstructed scalar field and the potential associated with it are consistent with the observed accelerated expansion of the Universe. In Hořava-Lifshitz gravity, the parameter that corresponds to the equation-of-state (EoS) exhibits quintessence-type behaviour for the coupled dark-energy system.We further analyse baryogenesis in general and gravitational baryogenesis in this scenario and demonstrate that the predicted baryon-to-entropy ratio agrees with observational bounds. Furthermore, the model suggests that either the generalised sec ond rule of thermodynamics continues to apply or the baryon and antibaryon densities will eventually equalise. In addition, the statistically investigation establishes that the model values of the Hubble parameter fit good according to the observed values of the Hubble parameter.

Abstract We develop an augmented characteristic, first-order formulation of the field equations in f(R) gravity governing the global evolution of a (possibly) massive scalar field $\phi$ under spherical symmetry. This formulation is designed to isolate the genuine dynamical degrees of freedom while preserving the geometric structure of the theory. By treating the spacetime scalar curvature as an independent unknown, we obtain a closed first-order nonlocal system for the pair (\phi,R). This augmentation eliminates the higher-derivative character of the original equations at the level of the principal part. Our formulation allows us to pose the characteristic initial value problem and to establish several structural properties of solutions. More precisely, we work in generalized Bondi–Sachs coordinates and prescribe initial data on an asymptotically flat future light cone with vertex at the center of symmetry, and we identify the minimal regularity conditions required at the center. These regularity conditions are shown to be precisely those ensuring equivalence between the reduced system and the full f(R) equations. Extending Christodoulou’s method for the Einstein–scalar-field system, we recast the f(R) field equations as an integro-differential system of two coupled, first-order, nonlocal, nonlinear hyperbolic equations, whose principal unknowns are the scalar field and the spacetime scalar curvature. In deriving this reduced two-equation system, we impose natural assumptions on the scalar-field potential and on the function f(R) governing the gravitational Lagrangian density. These hypotheses correspond to standard viability and positivity conditions commonly imposed in the f(R) literature.
We prove several equivalence and monotonicity properties, including for the Hawking mass in this setting.The proposed formulation separates the essential null evolution from the radial constraint reconstruction (via explicit integral relations) on the future domain of dependence of the initial light cone. This structure makes the system amenable to characteristic energy estimates and to stable numerical implementation in spherical symmetry.

Multistate density functional theory (MSDFT) generalizes Kohn-Sham density functional theory to a finite subspace of interacting states through a Hamiltonian matrix functional of the matrix density D(r). A central challenge is to construct matrix functionals that preserve subspace unitary invariance while encoding nontrivial state coupling. Here we show that any local, unitary-covariant matrix functional of D(r) must be codiagonalizable with D(r), and is therefore completely specified by a scalar generator acting on its eigenvalues. This establishes a one-to-all mapping from a scalar generator to the full matrix functional. As a consequence, the construction of N2 matrix elements is reduced to a single scalar mapping evaluated on the eigenvalue spectrum at each spatial grid point. The formalism is illustrated using a four-state Hubbard model, where exact reconstruction is achieved with a known scalar function, and deviations from this mapping can be systematically corrected within the spectral framework. The results provide a rigorous foundation for constructing local matrix exchange-correlation functionals with computational complexity comparable to Kohn-Sham DFT, and offer a practical route toward scalable MSDFT approximations.

An introduction to homogeneous scalar fields in cosmology

Abstract Recent observations from the DESI survey have reignited the debate on the true nature of dark energy, challenging the standard model of cosmology. The results suggest a preference for dynamical dark energy rather than a constant. Several recent analyses of DESI data indicate that the universe’s expansion may not be accelerating in the way suggested by supernova based cosmology. Motivated by these studies, we investigated a tachyon type scalar field $$\phi $$ ϕ as a model for dark energy, assuming an exponential potential for the field and performed parameter estimation using MCMC techniques. Such a model offers solutions that have $$w\sim -1$$ w ∼ - 1 and are decelerating without requiring a phantom like equation of state (EoS). The present day value of EoS parameter is treated as a free parameter. However, for the reference model, we fix its present value to $$-1$$ - 1 . The analysis is carried out using Pantheon+ and BAO measurements from DESI. The results show that both types of datasets consistently predict a turnaround in the EoS, regardless of whether $$w_{\phi 0}$$ w ϕ 0 is treated as a free parameter or fixed to $$-1$$ - 1 . The corresponding deceleration parameter also exhibits a future turnaround for both datasets when $$w_{\phi 0}$$ w ϕ 0 is free. However, in the reference model with $$w_{\phi 0}=-1$$ w ϕ 0 = - 1 , the deceleration parameter instead approaches $$-1$$ - 1 asymptotically. A model comparison shows that the Pantheon+ dataset favors free $$w_{\phi 0}$$ w ϕ 0 , while BAO observations prefer $$w_{\phi 0} = -1$$ w ϕ 0 = - 1 . This indicates a disagreement in the future evolution predicted by the two datasets within the tachyon dark energy model.

Abstract We focus on the use of the functional Wilsonian renormalization group framework characterized by a proper time regulator and test its use in the search of the scaling solutions and the critical properties of an O ( N )-invariant scalar field multiplet coupled to gravity in $$d=4$$ d = 4 and $$d=3$$ d = 3 dimensions. We employ the same background-fluctuation splitting and gauge fixing procedure, already adopted in a previous study based, instead, on the effective average action framework and a similar truncation of the effective action. Our main goal is to compare the results for the scaling solutions and some of the associated critical exponents. In this analysis, performed in a different framework, most of the picture previously uncovered is confirmed both at qualitative and quantitative level. There are, nevertheless, few differences both at finite N and in its large value limit, depending also on the schemes which in both frameworks are called “improved”.

We consider various possible consequences of time-varying dark energy due to a quintessence scalar field whose energy density is partially converted to particles as the field evolves down its potential. This particle production acts as a source of thermal friction on the field that can make it difficult to distinguish whether dark energy is due to a radiating field rolling down a steep potential, a purely self-interacting field moving down a flatter potential, or a cosmological constant. By reducing the acceleration of the scalar field, thermal friction increases the amount of accelerated expansion and can cause a sizable bump in the quintessence equation of state. We take special interest in the case where a steep potential rapidly changes from positive to negative as the field evolves, resulting in the end of cosmic expansion and the beginning of contraction. Even in this case, we find that thermal friction lengthens the period of accelerated expansion and consequently delays the end of cosmic expansion, making it challenging to detect the impending transition to contraction using conventional cosmological tests. However, particle production can also provide alternative avenues for detection by generating a background of thermal dark radiation, partly comprised of neutrinos or other particles, whose energy density exceeds the remnant photon energy density.

This paper provides a systematic and complete study of thermal field theory with fermion fields of any kind for generic equilibrium density matrices, which feature arbitrary values not only of temperature and chemical potentials, but also average angular momentum. This extends a previous study that focused on scalar fields, to all fermion-scalar theories. Both Dirac and Majorana fermions and both Dirac and Majorana masses are covered. A general technique to compute ensemble averages is provided. Path-integral methods are developed to study thermal Green's functions (with an arbitrary number of points) in generic interacting fermion-scalar theories, which cover both the real-time and imaginary-time formalism. These general results are applied to physical situations typical of neutron stars, which are often quickly rotating: The Fermi surface and Fermi momentum, the average energy, number density and angular momentum for degenerate fermions and particle production (such as neutrino production from rotating neutron stars, e.g. pulsars). In particular, it is shown that the neutrino production rate due to the direct URCA (DU) processes grows indefinitely as the angular velocity approaches the inverse linear size of the plasma and, therefore, rotation can significantly increase this rate.

We investigate the quasinormal modes (QNMs) of a massive scalar field in the background of a regular black hole arising from the proper-time flow in asymptotically safe gravity. This quantum-corrected geometry, characterized by a deformation parameter q , smoothly interpolates between a near-extremal regular black hole and the Schwarzschild solution. Employing both the WKB approximation with Padé resummation and time-domain integration, we compute the complex frequencies for various values of the scalar field mass μ, multipole number ℓ, and deformation parameter q. We observe that the real parts of the QNMs increase with the field mass, while the imaginary parts exhibit behavior indicative of long-lived modes. Although quasi-resonances are not detected in the time-domain profiles due to the dominance of late-time tails, we find that the asymptotic decay follows an oscillatory slowly decaying behavior with the power-law envelope.

Well-designed and trained deep neural networks can solve inverse electromagnetic problems much faster than conventional solvers. However, they need a physics framework to ensure producing physically correct results. Since most physics-guided deep learning inverse solvers require substantial training with numerous epochs, each involving solving a forward problem, their accuracy and efficiency are largely defined by the utilized forward solver, which becomes a bottleneck for their practical training. Thus, a fast and accurate self-supervised deep learning forward solver is presented. The solver uses a physics-based framework that divides the domain into two regions: an interior region, which includes any scatterers, and an exterior region, which represents the background medium. A hybrid loss function, incorporating Maxwell's curl equation and integral equation with the well-defined scalar background's Green's function, is employed to guide the scattered field generated from the neural network, ensuring global and local accuracy. To verify the generality of the solver, it is trained on random objects and tested on realistic models, showing high global and local metrics accuracy. For example, more than 95% of testing cases using the proposed method achieve less than 0.15 root-mean-square error in the calculated scattered field and dielectric properties of the imaged domain compared to the ground truth. In contrast, two recent deep learning methods could only realize that level of accuracy for less than 50% of the tested cases. The reported method is 97% faster than conventional solvers, enabling the development of reliable deep-learning inverse solvers.

We construct a novel exact solution of the Einstein-scalar-Maxwell equations describing a dynamical black hole immersed in an external, time-dependent electromagnetic field. Motivated by the need for more realistic analytical black hole models, our construction incorporates two key ingredients often neglected in exact solutions: a fully dynamical cosmological background and the non-perturbative backreaction of external electromagnetic fields. The compact object is obtained by dressing a Schwarzschild black hole with a radially and temporally dependent scalar field, yielding a time-dependent generalization of the Fisher-Janis-Newman-Winicour solution within the Fonarev framework. The external electromagnetic field is generated via a Lie point symmetry of the Einstein-scalar-Maxwell system, which exports the effect of a Harrison transformation to dynamical settings provided a spacelike Killing vector is present. The resulting spacetime combines a spherically symmetric dynamical horizon with an axisymmetric electromagnetic field and exhibits a rich asymptotic structure mixing Friedmann-Lemaître-Robertson-Walker and Levi-Civita geometries. We show that the time dependence of the configuration plays a crucial role in potentially cloaking curvature singularities, which would otherwise be generically naked in the stationary limit. We analyze the geometric and physical properties of the solution, including its asymptotic behavior, algebraic classification, and the structure of trapped surfaces defining the dynamical horizon.Possible implications for primordial black holes and some astrophysical applications, as well as extensions to higher dimensions, are also discussed.

In this work we provide the missing link between two approaches aimed at characterizing the effect of long perturbation modes in Inflation. We consider the Inflationary Fossils' approach (Phys. Rev. Lett. 108 (2012) 251301 and related works) that characterizes the power-spectrum of the inflaton field in presence of other long and non dynamical fossil fields, and a technique, appeared in JCAP 2106 (2021) 051, that computes, beyond perturbation theory, the power-spectrum of a scalar field in presence of a large fluctuation of a second field. We clarify a few points on the applicability of the non-perturbative technique. We prove in six distinct cases, one involving a violation of the consistency conditions, that the non-perturbative approach, once expanded to first order in the coupling, matches the perturbative result following the Fossils' approach. We believe that this non-perturbative technique extends to all orders the Fossils' approach, resumming infinitely many diagrams of standard in-in perturbation theory.

We propose a novel gravitational mechanism for the non-thermal production of dark matter driven by curvature-induced tachyonic instabilities after inflation. Departing from the commonly studied non-minimal couplings to gravity, our framework considers a real spectator scalar field coupled quadratically to spacetime curvature invariants. We show that the rapid reorganization of spacetime curvature at the end of inflation can dynamically render the dark matter field tachyonic, triggering a short-lived phase of spontaneous symmetry breaking and explosive particle production. As a concrete and theoretically controlled example, we focus on the Gauss-Bonnet topological invariant. By combining analytical estimates with 3+1 classical lattice simulations in the spectator field approximation, we track the out-of-equilibrium evolution of the system and compute the resulting dark matter abundance. We find that this purely gravitational mechanism can robustly reproduce the observed dark matter relic density over a wide range of masses and inflationary scales, providing also a simple fitting function that enables a lattice-independent application of our results.

We study stochastic inflation in the presence of higher-curvature terms non-minimally coupled to the inflaton. Focusing on quadratic curvature invariants, we single out the Gauss–Bonnet term which is known to avoid ghosts, while having non-trivial effects on the background and scalar mode evolution when coupled to the scalar field. Stochastic Klein–Gordon and Langevin equations are derived in the presence of the Gauss–Bonnet coupling, and their slow-roll and ultra-slow-roll limits are studied. By using first-passage time method, scalar power spectrum and PBH mass fraction are estimated in these limits. Stochastic evolution of a Gauss–Bonnet-coupled spectator field in de Sitter vacuum is also discussed.

The radial quadrature (RQ) method proposed recently for evaluating the beam shape coefficients (BSCs) of structured light (more exactly, electromagnetic) beams is applied to acoustical beams, based on the strong analogy between the acoustical scattering and light scattering. The BSCs of the scalar field of the acoustical beam are formulated in double integrals. For the on-axis located acoustical beams, which have axisymmetric structures, the integral expressions of the BSCs can be simplified to the closed-forms, thus, allowing efficient calculation. The Gaussian beam and high-order Bessel beam are studied with numerical calculations. The RQ method may serve as an alternative tool in studying the acoustical scattering and relevant applications.