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We use conformal geometry methods and the construction of Friedrich's cylinder at spatial infinity to study the propagation of spin-$0$ fields (solutions to the wave equation) on $n$-dimensional Minkowski spacetimes in a neighbourhood of spatial and null infinity. We obtain formal solutions written in terms of series expansions close to spatial and null infinity and use them to compute non-trivial asymptotic spin-$0$ charges. It is shown that if one considers the most general initial data within the class considered in this paper, the expansion is poly-homogeneous and hence of restricted regularity at null infinity. Furthermore, we derive the conditions on the initial data needed to obtain regular solutions and well-defined limits for the asymptotic charges at the critical sets where null infinity and spatial infinity meet. In four dimensions, we find that there are infinitely many well-defined asymptotic charges at the critical sets, while for higher dimensions there is only a finite number of non-trivial asymptotic charges that remain regular at the critical sets., Comment: 17 pages, 1 figure

We give an overview exploring the role of kinetics in multicomponent mixtures. Compared to the most commonly studied binary (single species plus solvent) case, multicomponent fluids show a rich interplay between kinetics and thermodynamics due to the possibility of fractionation, interdiffusion of mixture components and collective motion. This leads to a competition between multiple timescales that change depending on the underlying kinetics. At high densities, crowding effects are relevant and non-equilibrium structures can become long-lived. We present the main approaches for the study of kinetic effects in multicomponents mixtures, including the role of crowding, and explore their consequences for equilibrium and non-equilibrium scenarios. We conclude by identifying the main challenges in the field.

Ultrasound imaging is a cost-effective and radiation-free modality for visualizing anatomical structures in real-time, making it ideal for guiding surgical interventions. However, its limited field-of-view, speckle noise, and imaging artifacts make it difficult to interpret the images for inexperienced users. In this paper, we propose a new 2D ultrasound to 3D CT registration method to improve surgical guidance during ultrasound-guided interventions. Our approach adopts a dense feature matching method called LoFTR to our multimodal registration problem. We learn to predict dense coarse-to-fine correspondences using a Transformer-based architecture to estimate a robust rigid transformation between a 2D ultrasound frame and a CT scan. Additionally, a fully differentiable pose estimation method is introduced, optimizing LoFTR on pose estimation error during training. Experiments conducted on a multimodal dataset of ex vivo porcine kidneys demonstrate the method's promising results for intraoperative, trackerless ultrasound pose estimation. By mapping 2D ultrasound frames into the 3D CT volume space, the method provides intraoperative guidance, potentially improving surgical workflows and image interpretation., Comment: Accepted to SPIE Medical Imaging 2024

Extending the famous Model B for the time evolution of a liquid mixture, we derive an approximate expression for the mobility matrix that couples the different mixture components. This approach is based on a single component fluid with particles that are artificially grouped into separate species labelled by ``colors''. The resulting mobility matrix depends on a single dimensionless parameter, which can be determined efficiently from experimental data or numerical simulations, and includes existing standard forms as special cases. We identify two distinct mobility regimes, corresponding to collective motion and interdiffusion, respectively, and show how they emerge from the microscopic properties of the fluid. As a test scenario, we study the dynamics after a thermal quench, providing a number of general relations and analytical insights from a Gaussian theory. Specifically, for systems with two or three components, analytical results for the time evolution of the equal time correlation function compare well to results of Monte Carlo simulations of a lattice gas. A rich behavior is observed, including the possibility of transient fractionation.

We investigate the future asymptotics of spatially homogeneous space-times with a positive cosmological constant by using and further developing geometric conformal methods in General Relativity. For a large class of source fields, including fluids with anisotropic stress, we prove that the space-times are future asymptotically simple and geometrically conformally regular. We use that result in order to show the global conformal regularity of the Einstein-Maxwell system as well as the Einstein-radiation, Einstein-dust, massless Einstein-Vlasov and particular Einstein-scalar field systems for Bianchi space-times. Taking into account previous results, this implies the future non-linear stability of some of those space-times in the sense that, for small perturbations, the space-times approach locally the de Sitter solution asymptotically in time. This extends some cosmic no-hair theorems to almost spatially homogeneous space-times. However, we find that the conformal Einstein field equations preserve the Bianchi type even at conformal infinity, so the resulting asymptotic space-times have conformal hair., Comment: 43 pages

We are interested in the global dynamics of a massive scalar field evolving under its own gravitational field and, in this paper, we study spherically symmetric solutions to Einstein's field equations coupled with a Klein-Gordon equation with quadratic potential. For the initial value problem we establish a global existence theory when initial data are prescribed on a future light cone with vertex at the center of symmetry. A suitably generalized solution in Bondi coordinates is sought which has low regularity and possibly large but finite Bondi mass. A similar result was established first by Christodoulou for massless fields. In order to deal with massive fields, we must overcome several challenges and significantly modify Christodoulou's original method. First of all, we formulate the Einstein-Klein-Gordon system in spherical symmetry as a non-local and nonlinear hyperbolic equation and, by carefully investigating the global dynamical behavior of the massive field, we establish various estimates concerning the Einstein operator, the Hawking mass, and the Bondi mass, including positivity and monotonicity properties. Importantly, in addition to a regularization at the center of symmetry we find it necessary to also introduce a regularization at null infinity. We also establish new energy and decay estimates for, both, regularized and generalized solutions., Comment: 43 pages

We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a future null cone with a wider range of decaying profiles than previously considered. New estimates are then derived in order to prove that, for small data, the system has a unique global classical solution. We also show that the solution decays exponentially in (Bondi) time and that the radial decay is essentially polynomial, although containing logarithmic factors in some special cases. This improved asymptotic analysis allows us to show that, under appropriate and natural decaying conditions on the initial data, the future asymptotic solution is differentiable, up to and including spatial null-infinity, and approaches the de Sitter solution, uniformly, in a neighborhood of infinity. Moreover, we analyze the decay of derivatives of the solution up to second order showing the (uniform) $C^2$-asymptotic stability of the de Sitter attractor in this setting. This corresponds to a surprisingly strong realization of the cosmic no-hair conjecture., Comment: 42 pages

Motivated by cosmological models of the early universe we analyse the dynamics of the Einstein equations with a minimally coupled scalar field with monomial potentials $V(\phi)=\frac{(\lambda\phi)^{2n}}{2n}$, $\lambda>0$, $n\in\mathbb{N}$, interacting with a perfect fluid with linear equation of state $p_\mathrm{pf}=(\gamma_\mathrm{pf}-1)\rho_\mathrm{pf}$, $\gamma_\mathrm{pf}\in(0,2)$, in flat Robertson-Walker spacetimes. The interaction is a friction-like term of the form $\Gamma(\phi)=\mu \phi^{2p}$, $\mu>0$, $p\in\mathbb{N}\cup\{0\}$. The analysis relies on the introduction of a new regular 3-dimensional dynamical systems' formulation of the Einstein equations on a compact state space, and the use of dynamical systems' tools such as quasi-homogeneous blow-ups and averaging methods involving a time-dependent perturbation parameter. We find a bifurcation at $p=n/2$ due to the influence of the interaction term. In general, this term has more impact on the future (past) asymptotics for $pn/2$). For $pn/2$ the future asymptotics is similar to the case with no interaction. Finally, we show that irrespective of the parameters, an inflationary quasi-de-Sitter solution always exists towards the past, and therefore the cases with $p\leq(n-2)/2$ may provide new cosmological models of quintessential inflation., Comment: 63 pages, 54 figures

Understanding the phase behavior of mixtures with many components is important in many contexts, including as a key step toward a physics-based description of intracellular compartmentalization. Here, we study the instabilities of a mixture model where the second virial coefficients are taken as random Gaussian variables. Using tools from free probability theory we obtain the exact spinodal curve and the nature of instabilities for a mixture with an arbitrary composition, thus lifting the assumption of uniform mixture component densities pervading previous studies. We show that, by controlling the volume fraction of only a few components, one can systematically change the nature of the spinodal instability and achieve demixing for realistic scenarios by a strong {\em composition imbalance amplification}. This results from a non-trivial interplay of entropic effects due to non-uniform composition and complexity in the interactions. Our approach allows for the inclusion of any finite number of structured interactions, leading to a competition between different forms of demixing as density is varied.

The existence of magnetic fields in the universe is unmistakable. They are observed at all scales from stars to galaxy clusters. However, the origin of these fields remains enigmatic. It is believed that magnetic field seeds may have emerged from inflation, under certain conditions. This possibility is analised in the context of an alternative theory of gravity with non-minimal coupling between curvature and matter. We find, through the solution of the generalised Maxwell equations in the context of non-minimal models, that for general slow-roll inflationary scenarios with low reheating temperatures, $T_{RH}\simeq10^{10}$GeV, the generated magnetic fields can be made compatible with observations at large scales, $\lambda \sim 1 Mpc$., Comment: 12 pages; corrections in section 3; conclusions unchanged

We investigate the numerical stability of accelerated AdS black holes against linear scalar perturbations. In particular, we study the evolution of a probe non-minimally coupled scalar field on Schwarzschild and Reissner-Nordstr\"om AdS black holes with small accelerations by computing the quasinormal modes of the perturbation spectrum. We decompose the scalar field Klein-Gordon equation and study the eigenvalue problem for its angular and radial-temporal parts using different numerical methods. The angular part is written in terms of the Heun solution and expanded through the Frobenius method which turns out to give eigenvalues qualitatively similar to the ones obtained through the spherical harmonics representation. The radial-temporal evolution renders a stable field profile which is decomposed in terms of damped and purely imaginary oscillations of the quasinormal modes. We calculate the respective frequencies for different spacetime parameters showing the existence of a fine-structure in the modes, for both real and imaginary parts, which is not present in the non-accelerated AdS black holes. Our results indicate that the Schwarzschild and Reissner-Nordstr\"om AdS black holes with small accelerations are stable against linear scalar perturbations., Comment: 23 pages, 3 figures

The extendibility of spacetime and the existence of weak solutions to the Einstein field equations beyond Cauchy horizons, is a crucial ingredient to examine the limits of General Relativity. Strong Cosmic Censorship serves as a firewall for gravitation by demanding inextendibility of spacetime beyond the Cauchy horizon. For asymptotically flat spacetimes, the predominance of the blueshift instability and the subsequent formation of a mass-inflation singularity at the Cauchy horizon have, so far, substantiated the conjecture. Accelerating black holes, described by the $C-$metric, are exact solutions of the field equations without a cosmological constant, which possess an acceleration horizon with similar causal properties to the cosmological horizon of de Sitter spacetime. Here, by considering linear scalar field perturbations, we provide numerical evidence for the stability of the Cauchy horizon of charged accelerating black holes. In particular, we show that the stability of Cauchy horizons in accelerating charged black holes is connected to quasinormal modes, we discuss the regularity requirement for which weak solutions to the field equations exist at the Cauchy horizon and show that Strong Cosmic Censorship may be violated near extremality., Comment: 7 pages, 2 figures, minor corrections, accepted for publication in PRD, title changed to match published version

Black holes found in binaries move at very high velocities relative to our own reference frame and can accelerate due to the emission of gravitational radiation. Here, we investigate the numerical stability and late-time behavior of linear scalar perturbations in accelerating black holes described by the $C-$metric. We identify a family of quasinormal modes associated with the photon surface and a brand new family of purely imaginary modes associated with the boost parameter of the accelerating black hole spacetime. When the accelerating black hole is charged, we find a third family of modes which dominates the ringdown waveform near extremality. Our frequency and time domain analysis indicate that such spacetimes are stable under scalar fluctuations, while the late-time behavior follows an exponential decay law, dominated by quasinormal modes. This result is in contrast with the common belief that such perturbations, for black holes without a cosmological constant, always have a power-law cutoff. In this sense, our results suggest that the asymptotic structure of black hole backgrounds does not always dictate how radiative fields behave at late times., Comment: 15 pages, 8 figures, matches published version

We consider a characteristic initial value problem, with initial data given on a future null cone, for the Einstein (massless) scalar field system with a positive cosmological constant, in Bondi coordinates. We prove that, for small data, this system has a unique global classical solution which is causally geodesically complete to the future and decays polynomially in radius and exponentially in Bondi time, approaching the de Sitter solution., Comment: 25 pages, to appear in Journal of Hyperbolic Differential Equations

We study lattice gas systems on the honeycomb lattice where particles exclude neighboring sites up to order $k$ ($k=1\ldots5$) from being occupied by another particle. Monte Carlo simulations were used to obtain phase diagrams and characterize phase transitions as the system orders at high packing fractions. For systems with first neighbors exclusion (1NN), we confirm previous results suggesting a continuous transition in the 2D-Ising universality class. Exclusion up to second neighbors (2NN) lead the system to a two-step melting process where, first, a high density columnar phase undergoes a first order phase transition with non-standard scaling to a solid-like phase with short range ordered domains and, then, to fluid-like configurations with no sign of a second phase transition. 3NN exclusion, surprisingly, shows no phase transition to an ordered phase as density is increased, staying disordered even to packing fractions up to 0.98. The 4NN model undergoes a continuous phase transition with critical exponents close to the 3-state Potts model. The 5NN system undergoes two first order phase transitions, both with non-standard scaling. We, also, propose a conjecture concerning the possibility of more than one phase transition for systems with exclusion regions further than 5NN based on geometrical aspects of symmetries., Comment: 14 pages, 28 figures