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We study complete spacelike hypersurfaces immersed in an open region of the de Sitter space $\mathbb{S}^{n+1}_{1}$ which is known as the steady state space $\mathcal{H}^{n+1}$. In this setting, under suitable constraints on the behavior of the higher order mean curvatures of these hypersurfaces, we prove that they must be spacelike hyperplanes of $\mathcal{H}^{n+1}$. Nonexistence results concerning these spacelike hypersurfaces are also given. Our approach is based on a suitable extension of the Omori-Yau's generalized maximum principle due to Al\'{\i}as, Impera and Rigoli in [5].

We consider theories which break the invariance under diffeomorphisms (Diff) down to transverse diffeomorphisms (TDiff) in the matter sector, consisting of multiple scalar fields. In particular, we regard shift-symmetric models with two free TDiff scalar fields in a flat Robertson-Walker spacetime (FLRW) and use the perfect fluid approach to study their dynamics. As a consequence of the symmetry breaking, an effective interaction between the fields is induced from the conservation of the total energy-momentum tensor, without the necessity to introduce any explicit interacting term in the Lagrangian. We study the different single-field domination regimes and analyze the energy exchange between the fields. Thereupon, we introduce an application of these models for the description of interactions in the dark sector, and compare the theoretical predictions of our model to observational data from Type Ia supernovae., Comment: V2: 14 pages, 7 figures. New section 4.3, figure 5 updated, new references added, this version matches published version. V1: 12 pages, 7 figures

A method for generating narratives by analyzing single images or image sequences is presented, inspired by the time immemorial tradition of Narrative Art. The proposed method explores the multimodal capabilities of GPT-4o to interpret visual content and create engaging stories, which are illustrated by a Stable Diffusion XL model. The method is supported by a fully implemented tool, called ImageTeller, which accepts images from diverse sources as input. Users can guide the narrative's development according to the conventions of fundamental genres - such as Comedy, Romance, Tragedy, Satire or Mystery -, opt to generate data-driven stories, or to leave the prototype free to decide how to handle the narrative structure. User interaction is provided along the generation process, allowing the user to request alternative chapters or illustrations, and even reject and restart the story generation based on the same input. Additionally, users can attach captions to the input images, influencing the system's interpretation of the visual content. Examples of generated stories are provided, along with details on how to access the prototype.

Consider the family of semilinear parabolic problems \begin{equation*} \left\{ \begin{array}{lll} u_{t}(x,t) = \Delta u(x,t) - au(x,t) + f(u(x,t)), \,\,\, x \in \Omega_{\epsilon}, t > 0, \\ \frac{\partial u}{\partial N} (x,t) = g(u(x,t)), \,\,\, x \in \partial \Omega_{\epsilon}, t > 0, \end{array} \right. \end{equation*} where $a > 0$, $\Omega$ is the unit square, $\Omega_{\epsilon} = h_{\epsilon}(\Omega)$, $h_{\epsilon}$ is a family of $C^{m}$ - diffeomorphisms, $m \geq 1$, which converge to the identity of $\Omega$ in $C^{\alpha}$ norm, if $\alpha <1$ but do not converge in the $C^{1}$ - norm and, $f,g: \mathbb{R} \rightarrow \mathbb{R}$ are real functions. We show that a weak version of this problem, transported to the fixed domain $\Omega$ by a ``pull-back'' procedure, is well posed for $0 <\epsilon \leq \epsilon_{0}$, $\epsilon_{0} > 0$, in a suitable phase space, the associated semigroup has a global attractor $\mathcal{A}_{\epsilon}$ and the family $\{ \mathcal{A}_{\epsilon} \}_{0 \, < \, \epsilon \, \leq \, \epsilon_{0}}$ converges as $\epsilon \to 0$ to the attractor of the limiting problem: \begin{equation*}\ \left\{ \begin{array}{lll} u_{t}(x,t) = \Delta u(x,t) - au(x,t) + f(u(x,t)), \,\,\, x \in \Omega, t > 0, \\ \frac{\partial u}{\partial N} (x,t) = g(u(x,t))\mu, \,\,\, x \in \partial \Omega, t > 0, \end{array} \right. \end{equation*} where $\mu$ is essentially the limit of the Jacobian determinant of the diffeomorphism ${h_{\epsilon}}_{| \partial \Omega} : \partial \Omega \rightarrow \partial h_{\epsilon}(\Omega)$ (but does not depend on the particular family $h_{\epsilon})$.

Kondo physics and heavy-fermion behavior have been predicted and observed in moir\'e materials. The electric tunability of moir\'e materials allows an in-situ study of Kondo lattices' phase diagrams, which is not possible with their intermetallic counterparts. However, moir\'e platforms rely on twisting, which introduces twisting angle disorder and undesired buckling. Here we propose device layouts for one- and two-dimensional gate-defined superlattices in Bernal bilayer graphene where localized states couple to dispersive valley-helical modes. We show that, under electronic interactions, these superlattices are described by an electrically tunable Kondo-Heisenberg model., Comment: 13 pages, 5 figures

We explore the consequences of the breaking of diffeomorphism (Diff) invariance in the electromagnetic sector. We consider the breaking of Diff symmetry down to the subgroup of transverse diffeomorphisms (TDiff) and analyse its impact on the generation and evolution of cosmic magnetic fields. We show that Diff breaking induces a breaking of conformal invariance that modifies the way in which magnetic fields evolve on super-Hubble scales. The effects of the highly conductive plasma in the evolution are also analysed. We obtain the magnetic power spectrum today and discuss the parameter regions that yield intergalactic magnetic fields compatible with current observations., Comment: 6 pages, 2 figures

Theories formulated in the arena of teleparallel geometries are generically plagued by ghost-like instabilities or other pathologies that are ultimately caused by the breaking of some symmetries. In this work, we construct a class of ghost-free theories based on a symmetry under Transverse Diffeomorphisms that is naturally realised in symmetric teleparallelism. We explicitly show their equivalence to a family of theories with an extra scalar field plus a global degree of freedom and how Horndeski theories and healthy couplings to matter fields can be readily accommodated., Comment: 11 pages, no figures. V2: 13 pages, added clarifications and references, matches published version

Most studies of triple flames in counterflowing streams of fuel and oxidizer have been focused on the symmetric problem in which the stoichiometric mixture fraction is $1/2$. There then exist lean and rich premixed flames of roughly equal strengths, with a diffusion flame trailing behind from the stoichiometric point at which they meet. In the majority of realistic situations, however, the stoichiometric mixture fraction departs appreciably from unity, typically being quite small. With the objective of clarifying the influences of stoichiometry, attention is focused on one of the simplest possible models, addressed here mainly by numerical integration. When the stoichiometric mixture fraction departs appreciably from $1/2$, one of the premixed wings is found to be dominant to such an extent that the diffusion flame and the other premixed flame are very weak by comparison. These curved, partially premixed flames are expected to be relevant in realistic configurations. In addition, a simple kinematic balance is shown to predict the shape of the front and the propagation velocity reasonably well in the limit of low stretch and low curvature.

Numerical computations employing detailed chemistry are used to characterize the different combustion modes emerging in mixing layers separating nitrogen-diluted counterflowing planar streams of hydrogen and oxygen. Attention is focused on high degrees of dilution, resulting in near-limit flames, with peak temperatures close to the crossover temperature. A bifurcation diagram is presented in a plane, having the stoichiometric mixture fraction and normalized strain rate as coordinates, that identifies six different combustion regimes involving four different flame types, namely, diffusion-flame sheets, advancing and retreating edge flames, multiple flame tubes, and single isolated flame tubes. Multiple-tube flame configurations vary from small, round, widely separated flame strings at high strain rates to wide, flat, densely packed flame strips, with narrow flame-free gaps between them, at lower strain rates, and they are steady and stable in various arrays over a continuum of tube-separation distances. The observed flame behavior exhibits hysteresis in a certain range of parameters, with the structure that is established depending on the ignition mechanism, as it also does at high strain rates, and a continuum of different stable steady-state flame configurations exists, each accessed from a different initial condition.

This paper shows how to construct genre patterns, whose purpose is to guide interactive story composition in a way that enforces thematic consistency. To start the discussion we argue, based on previous seminal works, for the existence of five fundamental genres, namely comedy, romance - in the sense of epic plots, flourishing since the twelfth century -, tragedy, satire, and mystery. To construct the patterns, a simple two-phase process is employed: first retrieving examples that match our genre characterizations, and then applying a form of most specific generalization to the groups of examples in order to find their commonalities. In both phases, AI agents are instrumental, with our PatternTeller prototype being called to operate the story composition process, offering the opportunity to generate stories from a given premise of the user, to be developed under the guidance of the chosen pattern and trying to accommodate the user's suggestions along the composition stages., Comment: Added publication details to references that were published after the submission of the previous version (references [18] and [19])

Despite many reports of valley-related phenomena in graphene and its multilayers, current transport experiments cannot probe valley phenomena without the application of external fields. Here we propose a gate-defined valley splitter as a direct transport probe for valley phenomenon in graphene multilayers. First, we show how the device works, its magnetotransport response, and its robustness against fabrication errors. Secondly, we present two applications for valley splitters: (i) resonant tunneling of quantum dots probed by a valley splitter shows the valley polarization of dot levels; (ii) a combination of two valley splitters resolves the nature of order parameters in mesoscopic samples., Comment: 16 pages, 7 figures

We study the dynamics of Abelian gauge fields invariant under transverse diffeomorphisms (TDiff) in cosmological contexts. We show that in the geometric optics approximation, very much as for Diff invariant theories, the corresponding massless gauge bosons propagate along null geodesics and particle number is conserved. In addition, the polarization vectors are orthogonal to the propagation direction and the physical (transverse projection) polarization is parallel transported along the geodesics. We also consider TDiff invariant Dirac spinors, study the coupling to the gauge fields and analyze the conditions in order to avoid violations of Einstein's Equivalence Principle. The contributions to the energy-momentum tensor of the gauge field are also analyzed. We find that, in general, the breaking of Diff invariance makes the electric and magnetic parts of the vector field to gravitate in a different way. In the sub-Hubble regime we recover the standard radiation-like behaviour of the energy density, however in the super-Hubble regime the behaviour is totally different to the Diff case, thus opening up a wide range of possibilities for cosmological model building. In particular, possible effects on the evolution of large-scale primordial magnetic fields are discussed., Comment: 22 pages. Final version published in PRD with a corrected typo in Eq. (110)

We explore the idea of restoring the full diffeomorphism (Diff) invariance in theories with only transverse diffeomorphisms (TDiff) by the introduction of additional fields. In particular, we consider in detail the case of a TDiff invariant scalar field and how Diff symmetry can be restored preserving locality by introducing an additional vector field. We reobtain the corresponding dynamics and energy-momentum tensor from the covariantized action and analyze the potential and kinetic domination regimes. For the former, the theory describes a cosmological constant-type behaviour, while for the latter we show that the theory can describe an adiabatic perfect fluid whose equation of state and speed of sound is obtained in a straightforward way. Furthermore, the reformulation with the full symmetry allows us to analyze the gravitational properties of the theory beyond those particular regimes. In particular, we find the general expression for the effective speed of sound of the non-adiabatic perfect fluid, which provides us with physically reasonable conditions that should be satisfied by the coupling functions. Finally, we investigate the particular models leading to an adiabatic fluid., Comment: V2: 24 pages, new section V, new appendix, new applications, conclusions unchanged, version accepted for publication in PRD. V1: 9 pages, 1 Appendix

Using a single-site mean-field approximation (MFA) and Monte Carlo simulations, we examine Ising-like models on directed regular random graphs. The models are directed-network implementations of the Ising model, Ising model with absorbing states, and majority voter models. When these nonequilibrium models are driven by the heat-bath dynamics, their stationary characteristics, such as magnetization, are correctly reproduced by MFA as confirmed by Monte Carlo simulations. It turns out that MFA reproduces the same result as the generating functional analysis that is expected to provide the exact description of such models. We argue that on directed regular random graphs, the neighbors of a given vertex are typically uncorrelated, and that is why MFA for models with heat-bath dynamics provides their exact description. For models with Metropolis dynamics, certain additional correlations become relevant, and MFA, which neglects these correlations, is less accurate. Models with heat-bath dynamics undergo continuous phase transition, and at the critical point, the power-law time decay of the order parameter exhibits the behavior of the Ising mean-field universality class. Analogous phase transitions for models with Metropolis dynamics are discontinuous., Comment: 14 pages

We demonstrate that Andreev modes that propagate along a transparent Josephson junction have a perfect transmission at the point where three junctions meet. The chirality and the number of quantized transmission channels is determined by the topology of the Fermi surface and the vorticity of the superconducting phase differences at the trijunction. We explain this chiral adiabatic transmission (CAT) as a consequence of the adiabatic evolution of the scattering modes both in momentum and real space. The dispersion relation of the junction then separates the scattering trajectories by introducing inaccesible regions of phase space. We expect that CAT is observable in nonlocal conductance and thermal transport measurements. Furthermore, because it does not rely on particle-hole symmetry, CAT is also possible to observe directly in metamaterials., Comment: 14 pages, 8 figures

In this work we present a unified model for the cosmological dark sector. The theory is based on a simple minimally coupled scalar field whose action only contains a canonical kinetic term and is invariant under transverse diffeomorphisms (TDiff). The model has the same number of free parameters as $\Lambda$CDM. We confront the predictions of the model at the background level with data from Planck 2018 CMB distance priors, Pantheon+ and SH0ES SNIa distance moduli, BAO data points from 6dFGS, BOSS, eBOSS and DES and measurements of the Hubble parameter from cosmic chronometers. The model provides excellent results in the joint fit analysis, showing very strong evidence compared to $\Lambda$CDM in the deviance information criterion (DIC). We also show that the Hubble tension between Planck 2018 and SH0ES measurements can be alleviated in the unified TDiff model although further analysis is still needed., Comment: 17 pages, 8 figures. Final version published in PRD

The achievement of valley-polarized electron currents is a cornerstone for the realization of valleytronic devices. Here, we report on ballistic coherent transport experiments where two opposite quantum point contacts (QPCs) are defined by electrostatic gating in a bilayer graphene (BLG) channel. By steering the ballistic currents with an out-of-plane magnetic field we observe two current jets, a consequence of valley-dependent trigonal warping. Tuning the BLG carrier density and number of QPC modes (m) with a gate voltage we find that the two jets are present for m=1 and up to m=6, indicating the robustness of the effect. Semiclassical simulations which account for size quantization and trigonal warping of the Fermi surface quantitatively reproduce our data without fitting parameters, confirming the origin of the signals. In addition, our model shows that the ballistic currents collected for non-zero magnetic fields are valley-polarized independently of m, but their polarization depends on the magnetic field sign, envisioning such devices as ballistic current sources with tuneable valley-polarization., Comment: 15 pages, 11 figures

Directional fluid flow in perivascular spaces surrounding cerebral arteries is hypothesized to play a key role in brain solute transport and clearance. While various drivers for pulsatile flow, such as cardiac or respiratory pulsations, are well quantified, the question remains as to which mechanisms could induce directional flow within physiological regimes. To address this question, we develop theoretical and numerical reduced-order models to quantify the directional (net) flow induceable by peristaltic pumping in periarterial networks. Each periarterial element is modeled as a slender annular space bounded internally by a circular tube supporting a periodic traveling (peristaltic) wave. Under the reasonable assumptions of small Reynolds number flow, small radii, and small-amplitude peristaltic waves, we use lubrication theory and regular perturbation methods to derive theoretical expressions for the directional net flow and pressure distribution in the perivascular network. The reduced model is used to derive closed-form analytical expressions for the net flow for simple network configurations of interest, including single elements, two elements in tandem, and a three element bifurcation, with results compared with numerical predictions. In particular, we provide a computable theoretical estimate of the net flow induced by peristaltic motion in perivascular networks as a function of physiological parameters, notably wave length, frequency, amplitude and perivascular dimensions. Quantifying the maximal net flow for specific physiological regimes, we find that vasomotion may induce net pial periarterial flow velocities on the order of a few to tens of mum/s and that sleep-related changes in vasomotion pulsatility may drive a threefold flow increase.

We study the cosmological implications of gravity models which break diffeomorphisms (Diff) invariance down to transverse diffeomorphisms (TDiff). We start from the most general gravitational action involving up to quadratic terms in derivatives of the metric tensor and identify TDiff models as the only stable theories consistent with local gravity tests. These models propagate an additional scalar graviton and although they are indistinguishable from GR at the post-Newtonian level, their cosmological dynamics exhibits a rich phenomenology. Thus we show that the model includes standard $\Lambda$CDM as a solution when the extra scalar mode is not excited, but different cosmological evolutions driven by the new term are possible. In particular, we show that for a soft Diff breaking, the new contribution always behaves as a cosmological constant at late times. When the extra contribution is not negligible, generically its evolution either behaves as dark energy or tracks the dominant background component. Depending on the initial conditions, solutions in which the universe evolves from an expanding to a contracting phase, eventually recollapsing are also possible., Comment: 13 pages, 9 figures. Final version to appear in PRD

We reflect on the possibility of having a matter action that is invariant only under transverse diffeomorphisms. This possibility is particularly interesting for the dark sector, where no restrictions arise based on the weak equivalence principle. In order to implement this idea we consider a scalar field which couples to gravity minimally but via arbitrary functions of the metric determinant. We show that the energy-momentum tensor of the scalar field takes the perfect fluid form when its velocity vector is time-like. We analyze the conservation of this tensor in detail, obtaining a seminal novel result for the energy density of this field in the kinetic dominated regime. Indeed, in this regime the fluid is always adiabatic and we obtain an explicit expression for the speed of sound. Furthermore, to get insight in the gravitational properties of these theories, we consider the fulfillment of the energy conditions, concluding that nontrivial physically reasonable matter violates the strong energy condition in the potential domination regime. On the other hand, we present some shift-symmetric models of particular interest. These are: constant equation of state models (which may provide us with a successful description of dark matter or dark radiation) and models presenting different gravitational domains (characterized by the focusing or possible defocusing of time-like geodesics), as it happens in unified dark matter-energy models., Comment: V2: 26 pages, 1 figure, new comments included, appendix added, conclusions unchanged, version accepted for publication in JHEP

Assuming that the term 'metaverse' could be understood as a computer-based implementation of multiverse applications, we started to look in the present work for a logic that would be powerful enough to handle the situations arising both in the real and in the fictional underlying application domains. Realizing that first-order logic fails to account for the unstable behavior of even the most simpleminded information system domains, we resorted to non-conventional extensions, in an attempt to sketch a minimal composite logic strategy. The discussion was kept at a rather informal level, always trying to convey the intuition behind the theoretical notions in natural language terms, and appealing to an AI agent, namely ChatGPT, in the hope that algorithmic and common-sense approaches can be usefully combined.

We report on multiterminal measurements in a ballistic bilayer graphene (BLG) channel where multiple spin and valley-degenerate quantum point contacts (QPCs) are defined by electrostatic gating. By patterning QPCs of different shapes and along different crystallographic directions, we study the effect of size quantization and trigonal warping on the transverse electron focusing (TEF) spectra. Our TEF spectra show eight clear peaks with comparable amplitude and weak signatures of quantum interference at the lowest temperature, indicating that reflections at the gate-defined edges are specular and transport is phase coherent. The temperature dependence of the scattering rate indicates that electron-electron interactions play a dominant role in the charge relaxation process for electron doping and temperatures below 100 K. The achievement of specular reflection, which is expected to preserve the pseudospin information of the electron jets, is promising for the realization of ballistic interconnects for new valleytronic devices., Comment: 22 pages, 16 figures

The quantum geometry in the momentum space of semiconductors and insulators, described by the quantum metric of the valence band Bloch state, has been an intriguing issue owing to its connection to various material properties. Because the Brillouin zone is periodic, the integration of quantum metric over momentum space represents an average distance between neighboring Bloch states, of which we call the fidelity number. We show that this number can further be expressed in real space as a fidelity marker, which is a local quantity that can be calculated directly from diagonalizing the lattice Hamiltonian. A linear response theory is further introduced to generalize the fidelity number and marker to finite temperature, and moreover demonstrates that they can be measured from the global and local optical absorption power against linearly polarized light. In particular, the fidelity number spectral function in 2D systems can be easily measured from the opacity of the material. Based on the divergence of quantum metric, a nonlocal fidelity marker is further introduced and postulated as a universal indicator of any quantum phase transitions provided the crystalline momentum remains a good quantum number, and it may be interpreted as a Wannier state correlation function. The ubiquity of these concepts is demonstrated for a variety of topological insulators and topological phase transitions in different dimensions., Comment: 11 pages, 5 figures

We study scalar field theories invariant under transverse diffeomorphisms in cosmological contexts. We show that in the geometric optics approximation, the corresponding particles move along geodesics and contribute with the same active mass (energy) to the gravitational field as in Diff invariant theories. However, for low-frequency (super-Hubble) modes, the contributions to the energy-momentum tensor differ from that of Diff invariant theories. This opens up a wide range of possibilities for cosmological model building. As an example, we show that the simplest TDiff invariant scalar field theory with only kinetic term could drive inflation and generate a nearly scale invariant (red-tilted) spectrum of density fluctuations. We also present a detailed analysis of cosmological perturbations and show that the breaking of full Diff invariance generically induces new non-adiabatic pressure perturbations. A simple scalar field dark matter model based on a purely kinetic term that exhibits the same clustering properties as standard cold dark matter is also presented., Comment: 16 pages. New section and references included. Final version to appear in JCAP