We obtain upper bound on the heat kernel of Keller-Segel type finite particle system that exhibit blow up effects. The proof exploits a connection with certain non-local operators.

We investigate X-shaped radio galaxies (XRGs) with optical double-peaked narrow emission lines (DPNELs) as potential hosts of dual or binary supermassive black holes (SMBHs). Using available optical spectra from the SDSS and DESI surveys, we identify 55 DPNEL sources among a sample of 187 XRGs. We find that the occurrence of [O III] DPNELs in XRGs is $\sim$30 %, which is substantially higher than the $\sim$1 % observed in the general galaxy population. Using optical (involving {[O III]$\lambda$5007}, H$\alpha$, H$\beta$, {[N II]$\lambda$,6584}, and {[S II]$\lambda\lambda$6716,6731}) and mid-infrared diagnostic diagrams, we found that both components are predominantly AGN-powered, implying a $\sim$95 % probability of hosting dual AGN systems. In comparison, a stellar-mass-, color-, and redshift-matched control sample of non-XRG DPNEL galaxies shows a lower dual AGN fraction, which depends strongly on radio luminosity, rising from ~25 % in radio-undetected to ~54 % in radio-detected galaxies, and reaching ~95 % in radio-bright XRGs and FR-II radio galaxies. Interestingly, more than 30 % of DPNEL XRGs have companion galaxies, supporting a merger-driven origin for these systems. Finally, we analyze parsec-scale radio structure in 7 XRGs using VLBA observations at 1.4, 4.3, and 7.6 GHz, resolving the core in only one source. Nevertheless, flat radio spectral indices, AGN-like emission-line properties, and radio-optical VLBA-Gaia positional offsets found in 5 cases together support the interpretation that XRGs are strong dual/binary AGN candidates.

We develop a closed-form analytical theory for the transport of a chiral active Brownian particle in three dimensions, moving through a fluctuating local density field that models steric and dynamical interactions in a dense active medium. The density field is modeled as an Ornstein--Uhlenbeck process with finite correlation time $\tau$ and fluctuation strength $\sigma_\rho^2$, capturing both spatial fluctuations and temporal memory. Within this framework, we derive exact expressions for the mean-squared displacement and time-dependent diffusivity, revealing how chirality and density coupling jointly renormalise orientational persistence and generate nontrivial dynamical crossovers. The theory predicts: (i) anomalously high initial diffusivity for particles starting in locally denser regions, arising from a transient active drift driven by local swim-pressure gradients; (ii) a finite crossover time $t_c$ for homogenising density inhomogeneities, with a transient dependence of the dynamics on the initial local density environment which arises from the non-equilibrium evolution of density fluctuations and does not persist when averaging over stationary initial conditions ($\rho_0 = \rho_\infty$); (iii) a non-monotonic $t_c(\Omega)$ with a global minimum at intermediate chirality, and a three-regime suppression of long-time diffusivity $D_\infty(\Omega)$, consistent with micro-clustered phases observed in simulations; and (iv) a resonance-like peak in the early-time oscillatory strength of the mean-squared displacement at an optimal chirality $\Omega^*$, set by the interplay of orientational diffusion, density-field decorrelation, and imposed rotation. The framework captures the qualitative dependence of $D_\infty$ on $Pe$ and $\Omega$, {where Pe denotes the Péclet number}, while uncovering chirality-dependent transport features in active matter.

We introduce the notion of polynomial-depth duality transformations, which relates two sets of operator algebras through a conjugation by a poly-depth quantum circuit, and make use of this to construct efficient Gibbs samplers for a variety of interesting quantum Hamiltonians as they are poly-depth dual to classical Hamiltonians. This is for example the case for the 2D toric code, which is demonstrated to be poly-depth dual to two decoupled classical Ising spin chains for any system size, and we give evidence that such dualities hold for a wide class of stabilizer Hamiltonians. Additionally, we extend the above notion of duality to Lindbladians in order to show that mixing times and other quantities such as the spectral gap or the modified logarithmic Sobolev inequality are preserved under duality.

The Landau-Lifshitz-Gilbert (LLG) equations are widely used to study spin dynamics in Mott insulators. However, because energy damping is typically introduced phenomenologically, their validity for describing nonequilibrium processes and their connection to the microscopic origin of dissipation in real materials remains unclear. In this paper, we derive generalized stochastic LLG equations from first principles for spin-orbital coupled Mott insulators, explicitly incorporating the coupling between electronic degrees of freedom and lattice vibrations. Our approach is based on a path-integral formalism formulated along the Keldysh contour, which naturally accounts for dissipation and thermal fluctuations through interactions with a phonon bath and emergent stochastic noise. We benchmark our theoretical framework by numerically integrating the equations of motion for a two-orbital spin chain coupled to Einstein phonons. The resulting energy relaxation mimics realistic cooling dynamics, exhibits nontrivial transient behavior during thermalization, and accurately reproduces thermodynamic properties upon equilibration. We further demonstrate how electron-phonon coupling induces hybridization between electronic and phononic modes in the excitation spectrum and show that the conventional LLG equations are recovered as a limiting case of our microscopic theory. These results establish a robust and reliable framework for capturing dissipative spin dynamics in strongly correlated systems, both in and out of equilibrium.

The interdependence of position and momentum, as highlighted by the Heisenberg uncertainty principle, is a cornerstone of quantum physics. Yet, position-momentum correlations have received little systematic attention. Motivated by recent developments in bosonic quantum physics that underscore their relevance in quantum thermodynamics, metrology, and computing, we establish a general framework to study and quantify position-momentum correlations in quantum states. We introduce symplectic coherence, a faithful and easily computable measure defined as the Frobenius norm of the block of the covariance matrix encoding position-momentum correlations, and demonstrate that symplectic coherence is monotone under relevant operations and robust under small perturbations. Furthermore, using a recent mapping by Barthe et al. (Phys. Rev. Lett. 134, 070604) which relates the covariance matrix of a bosonic state to the density matrix of a finite-dimensional system, we show that position-momentum correlations correspond to beyond-classical correlations in a virtual finite-dimensional quantum state, with symplectic coherence mapping naturally to geometric quantum discord. Taking energy constraints into account, we determine the maximal position-momentum correlations achievable at fixed energy, revealing structural insights about the corresponding optimal states. Finally, we illustrate the operational relevance of symplectic coherence through several examples in quantum information tasks and quantum thermodynamics. In the process, we establish new technical results on matrix norms and quantum covariance matrices, and demonstrate the conceptual significance of viewing covariance matrices as density matrices of virtual quantum states.

Quantum mechanics is compatible with scenarios where physical processes happen in an indefinite order. In theory, this feature could be detected through violations of inequalities on the observed correlations, analogous to Bell inequalities. However, experimental demonstrations of such violations have been missing until recently due to the complexity of the required setup. Here we report an experimental violation of a Bell-like inequality involving the correlations of four parties, one of which is spacelike separated from the others. Our demonstration employs 3 km fiber spools to simulate spacelike separation, and achieves high-speed operations in photonic time-bin encoding, nanosecond synchronization, and accurate temperature stabilization. These experimental advances enable a violation by 5.7 standard deviations and open a path towards a certification of indefinite order in conditions that guarantee spacelike separation with existing state-of-the-art devices. However, the certification is not device-independent, as it relies on knowledge about the setup to exclude bidirectional signaling--a loophole inherent to implementations in classical acyclic spacetimes, which may be resolved in future quantum-spacetime tests.

A unified framework sheltering the type-I Dirac seesaw, based on the $\Delta(27)$ group supplemented by other cyclic symmetries is proposed, preserving the naturalness of Yukawa couplings. It helps to visualize mass matrices within the lepton and quark sectors in terms of \textit{three universal parameters}: $\Sigma_1$, $\Sigma_2$, and $\Sigma_3$, highlighting that the down-type quark and light neutrino mass matrices exhibit a \textit{Hermitian} texture. Several phenomenological aspects, such as lepton flavour violation and nonunitarity of the lepton mixing matrix are explored. The stability of the proposed texture under renormalization group evolution is also investigated.

Conceptual design and performance evaluation of HL-LHC based antimuon-proton collider (${\mu}$LHC) are presented. Leveraging the ${\mu}$TRISTAN concept based on established J-PARC ultra-cold ${\mu}^{+}$ beam technology, ${\mu}$LHC will give the opportunity to achieve a 5.3 TeV center-of-mass energy, significantly surpassing EIC and LHeC. Two booster ring options for ${\mu}^{+}$ acceleration, namely, a ${\mu}$TRISTAN-based and a repurposed LHeC ERL-based systems, are explored. Achievable luminosities are predicted to exceed $10^{33} cm^{-2}s^{-1}$. The ${\mu}$LHC offers substantially wider kinematic plane coverage, particularly in small-x and high-$Q^{2}$ regions, significantly contributing to QCD basics and Higgs boson properties. Its unique potential for BSM physics extends to muon-related phenomena like excited muons, color-octet muons, leptoquarks, and contact interactions. A possible detector concept is also outlined. Given the maturity of ultra-cold ${\mu}^{+}$ beam technology, ${\mu}$LHC is highly feasible for earlier realization than the muon collider, positioning it as a critical tool for the future of high energy physics.

We introduce a novel extension of the volume-averaged correlation function (VACF) framework by replacing the traditional spherical smoothing kernels with anisotropic, ellipsoidal windows. This generalized approach enables the study of shape-dependent clustering statistics and captures directional information encoded in large-scale structure, particularly in redshift space where galaxy distribution is distorted by peculiar velocities. We define and compute ellipsoidal VACFs $\bar{\xi}_J (r_{\parallel}, r_{\perp})$ and the corresponding reduced cumulants $s_J (r_{\parallel}, r_{\perp})$, allowing for joint sensitivity to both scale and anisotropy across arbitrary statistical order J. Using a suite of COLA N-body simulations spanning a grid of cosmologies with varying $\Omega_M$ and $\sigma_8$, we analyze the behavior of ellipsoidal VACFs and cumulants in both real and redshift space. We find that the shape of the smoothing kernel that maximizes the clustering signal depends strongly on the redshift-space distortion regime: spherical in real space, prolate in the Fingers-of-God-dominated regime, and oblate in the Kaiser squashing-dominated regime. While the standard VACF amplitude is mainly sensitive to ${\sigma}_8$, the shape-dependence of redshift-space skewness shows a coherent response to the combined growth parameter $f \sigma_8$, with a typical sensitivity at the 1-3 $\sigma$ level between neighboring models. Our results demonstrate that ellipsoidal VACFs offer a computationally efficient and information-rich generalization of counts-in-cells analysis, with promising applications to galaxy survey data, halo catalogs, and cosmological tests of gravity beyond $\Lambda CDM$.

Topologically Associating Chromatin Domains are spatially distinct chromatin regions that regulate transcription by segregating active and inactive genomic elements. Empirical studies show that their formation correlates with local patterns of epigenetic markers, yet the precise mechanisms linking 1D epigenetic landscapes to 3D chromatin folding remain unclear. Recent models represent chromatin as a spin system, where nucleosomes are treated as discrete-state variables coupled by interaction strengths derived from genomic and epigenetic data. Classical samplers struggle with these models due to high frustration and dense couplings. Here, we present a quantum annealing (QA) approach to efficiently sample chromatin states, embedding an epigenetic Ising model into the topology of D-Wave quantum processors. Rather than reconstructing exact TAD size distributions or insulation scores, our method reproduces statistical features, such as mean marker incidences and intra-/inter-nucleosome correlations, while generating configurations that exhibit TAD-like structural motifs. These results demonstrate QA as an alternative to explore the chromatin architecture and provide a foundation in epigenetic modeling.

We investigate the static properties of $0-\pi$ Josephson junctions and their potential application as superconducting qubits. We show that fractional vortex and fractional antivortex configurations give rise to a bistable free-energy landscape with stable minima corresponding to topologically distinct fractional-vortex states. In the long-junction limit the two configurations correspond to stable equilibrium states, whereas in the short-junction limit the reduced barrier suggests enhanced quantum tunneling and hybridization between them. These results suggest that $0-\pi$ Josephson junctions may provide a physically meaningful platform for qubit-like two-level dynamics, provided that a finite tunneling amplitude exists between the fractional-vortex and fractional-antivortex states.

Quantum teleportation is a quintessential quantum communication protocol that enables the transmission of an arbitrary quantum state between two distant parties without physically transmitting the state with the help of shared entanglement and limited classical communication. We show that it is possible to relax the entanglement requirement in quantum teleportation if we have access to a certain strain of superposition of quantum processes. Two types of superposition of quantum processes are generally considered in the literature: superposition of paths identified with quantum maps and superposition of indefinite causal orders of the maps. We find that when superposition of paths is incorporated in the protocol, quantum teleportation with unit fidelity becomes possible with nonzero probability of 1/4 even when the two parties share certain classes of separable states, including pure product states. In contrast, the assistance of superposition of indefinite causal order of quantum maps in teleportation protocol does not enable any quantum advantage for shared pure product states. Furthermore, we show that separable Werner states can also yield quantum advantage in quantum teleportation assisted by the superposition of paths. Finally, we establish that the presence of quantum coherence in the control qubit is both necessary and sufficient to achieve quantum advantage in quantum teleportation assisted with superposition of paths. The results potentially uncover yet another role of quantum superposition, in general, in teleportation versus entanglement.

Delta-kick cooling is a technique employed to achieve low kinetic temperatures by decreasing momentum width at the cost of increased position width. In an ideal implementation, this method uses a harmonic potential to deliver a single near-instantaneous momentum kick. In practice, potentials that are approximately harmonic near their center are commonly used. As a result, the breakdown of the harmonic approximation far from the center limits the cooling performance. Inspired by aberration cancellation in optics, we propose to use compound matter-wave lens systems for $\delta-$kick cooling with Gaussian potentials. By strategically combining attractive and repulsive kicks, we show that it is possible to mimic the effect of a harmonic potential. For a test case with reasonable experimental parameters, our method suggests a reduction in kinetic temperature by a factor of $2.5$ using a 2-pulse sequence and by a factor of $3.2$ using a 3-pulse sequence.

Active filament translocation through confined spaces is central to processes ranging from DNA transport through nanopores to cytoskeletal dynamics in cell migration. Here, we use living filamentous \textit{Tubifex tubifex} worms as a model system to investigate how activity and filament conformation govern transport in confinement. By tuning activity via temperature and tracking worm dynamics in a two-chamber geometry connected by a narrow bridge, we quantify their translocation behavior and conformational states. In contrast to passive polymers and filaments, we find that contour length has negligible influence on trapping dynamics, while activity and reorientation jointly control escape. Strikingly, translocation efficiency is maximized at an intermediate temperature ($20^\circ$C), where a balance between directed propulsion and rotational diffusion optimizes exploration. We show that trapping times are governed by the interplay between the timescale of conformational rearrangements and the conformational entropy, quantifying the diversity of accessible shapes. Simulations of tangentially driven active filaments quantitatively reproduce the experimental observations and provide a minimal physical framework to rationalize the existence of an optimal activity. More broadly, our results identify general principles governing active filament transport in confinement, with implications for both biological systems and the design of synthetic active slender objects.

Driven-dissipative quantum systems can undergo transitions from stationary to dynamical phases, reflecting the emergence of collective non-equilibrium behavior. We study such a transition in a Bose-Einstein condensate coupled to an optical cavity and develop a cavity-assisted Bragg spectroscopy technique to resolve its collective modes. We observe dissipation-induced synchronization at the quasiparticle level, where two roton-like modes coalesce at an exceptional point. This reveals how dissipation microscopically drives collective dynamics and signals a precursor to a dynamical phase transition.

We present a theoretical model for a transversally driven Bose-Einstein condensate coupled to an optical cavity. We focus on the interplay between different coherent couplings, which can trigger a structural phase transition, known as the superradiant phase transition. Our approach, based on band structure theory and a mean-field description, enables a comprehensive analysis of the nature of the system's excited modes, precursing the phase transitions. By incorporating dissipative couplings, intrinsic to these systems, we find non-Hermitian phenomena such as the coalescence of crossing precursor modes and the emergence of exceptional points (EPs). The general formulation of our model allows us to explain the role of an angle between transverse pump and the cavity deviating from $90^\circ$. This offers us a unified perspective on the plethora of different implementations of such systems.

Previously, it was shown that both the concurrence and $n$-tangle on $2n$-qubit pure quantum states can be expressed in terms of Cayley's first hyperdeterminant \cite{dobes2024qubits}, indicating that Cayley's first hyperdeterminant, denoted $\mathrm{hdet}$, captures some aspects of a state's $2n$-way entanglement. In this paper, we rigorously prove that on both pure and mixed states, $|\mathrm{hdet}|^{2/d}$ is identically zero on separable states, is an LU invariant, and is non-increasing on average under LOCC, thus demonstrating that $|\mathrm{hdet}|^{d/2}$ is a physically meaningful and legitimate entanglement measure. Moreover, we discuss a few key examples to illustrate the particular type of entanglement Cayley's first hyperdeterminant is detecting: genuine full $d$-level GHZ-type entanglement across all $2n$ parties. Combined, this establishes Cayley's first hyperdeterminant (or $|\mathrm{hdet}|^{2/d}$ to be precise), as a physically significant generalization of the $G$-concurrence and the $n$-tangle to $2n$-qudit states.

We study the counts-in-cells reduced skewness $s_3$ for dark matter, halo, and galaxy distributions in both real and redshift space, using the ELEPHANT ($\textit{Extended LEnsing PHysics with ANalytical ray Tracing}$) suite of $N$-body simulations. We compare General Relativity (GR) with two extended (EG) gravity models: $f(R)$ gravity with chameleon screening and the normal-branch Dvali-Gabadadze-Porrati (nDGP) model with Vainshtein screening. We quantify the suppression of $s_3$ by redshift-space distortions (RSD), finding that while small-scale skewness is strongly reduced, the $F5$ model retains a $\sim 4\%$ deviation from GR in galaxy samples, corresponding to a $2\sigma$ significance. We show that the ratio $s_3^{\mathrm{RSD}}/s_3^{\mathrm{real}}$ is approximately independent of the gravity model across tracers and redshifts. Our results demonstrate that real-space predictions can help reliably infer redshift-space skewness in both GR and extended gravity, providing a new tool for testing gravity with current and forthcoming galaxy redshift surveys.

Many-body interactions arise naturally in the perturbative treatment of classical and quantum many-body systems and play a crucial role in the description of condensed matter systems. In the case of three-body interactions, the Axilrod-Teller-Muto (ATM) potential is highly relevant for the quantitative prediction of material properties. This work solves the long-standing issue of the numerical computation of the resulting energies in $d$-dimensional lattice systems. We present an efficiently computable representation of many-body lattice sums in terms of singular integrals over products of Epstein zeta functions. For three-body interactions in three dimensions, this approach reduces the runtime for computing the ATM lattice sum from weeks to minutes. Our approach further extends to a broad class of $n$-body lattice sums. We demonstrate that the computational cost of our method only increases linearly with $n$, evading the exponential increase in complexity of direct summation. We discuss techniques for numerically computing the arising singular integrals and compare the accuracy of our results against computable special cases and against direct summation in low dimensions, achieving full precision for exponents greater than the system dimension. Finally, we apply our method to study the stability of a three-dimensional lattice system with Lennard-Jones two-body interactions under the inclusion of an ATM three-body term at finite pressure, finding a transition from the face-centered-cubic to the body-centered-cubic lattice structure with increasing ATM coupling strength. This work establishes both the numerical and analytical foundation for an ongoing investigation into the influence of many-body interactions on the stability of matter.

Atomically thin moiré materials behave like elastic membranes where at very small twist angles, the van der Waals adhesion energy much exceeds the strain energy. In this ``marginal twist" regime, regions with low adhesion energy expand, covering most of the moiré unit cell, while all the unfavorable energy configurations shrink to form topological defects linked by a periodic network of domain walls. We find analytical expressions that successfully capture this strong-coupling regime for both the triangular soliton network and the honeycomb soliton network matching predictions from LAMMPS molecular dynamics simulations, and numerical solutions of continuum elasticity theory. There is an emergent universality where the theory is characterized by a single twist-angle dependent parameter. Our formalism is essential to understand experiments on a wide-range of materials of current interest including twisted bilayer graphene, both parallel and antiparallel stacked tWSe2 and tMoTe2, and any other twisted homobilayer with the same stacking symmetry.

Generalizing the result of H. Ellis who embedded a warp bubble in the background of a black hole, we introduce a warp bubble in a de Sitter universe. We show that under certain conditions (namely, that the bubble is moving in the radial direction at a velocity equal to the speed of the expansion of the universe), it is possible for the bubble to have strictly non--negative energy density, with the weak and null energy satisfied up to a total divergence term that averages to zero. We discuss the implications of this result and its possible applications to models of dark energy like "dark fluid" and quintessence, as well as to physical systems like Casimir cavities and analogue gravity setups.

We introduce affordable computational strategies for calculating orbital and pair-orbital energies in atomic and molecular systems. Our methods are based on the pair Coupled Cluster Doubles (pCCD) ansatz and its orbital-optimized variant. The computed orbital and pair-orbital energies are then subsequently used to approximate ionization potentials (IPs), electron affinities (EAs), the resulting charge gaps, double ionization potentials (DIPs), and double electron affinities (DEAs). Our methodology builds on the standard Koopmans' theorem and refines it for a pCCD-based wave function. Furthermore, we incorporate pCCD electron correlation effects into the model utilizing canonical Hartree-Fock or natural pCCD-optimized orbitals. The latter represents a diagonal approximation to the (D)IP/D(EA) equation of motion pCCD models. We benchmarked our newly developed models against theoretical and available experimental data for selected atoms in various basis set sizes and a set of 24 organic acceptor molecules. Our numerical results show that the Koopmans' approach based on pCCD natural orbitals provides a balanced treatment of occupied and virtual orbital energies, resulting in reliable predictions of charge gaps at a low computational cost.

The Epstein zeta function generalises the classical Riemann zeta function to oscillatory lattice sums in higher dimensions and has recently emerged as a key tool in the simulation of long-range interacting classical and quantum many-body systems. Its computation and analytic properties are therefore of significant interest, yet a rigorous and comprehensive treatment has been lacking. We address this gap by introducing a superexponentially convergent algorithm, complete with error bounds, for computing the Epstein zeta function in any dimension with arbitrary real parameters. Our approach is accompanied by a detailed analysis of the analytic properties of the Epstein zeta function. We first present a concise reformulation of its meromorphic continuation, functional equation, and symmetries. We then establish, for the first time, its joint holomorphic continuation in all parameters and offer a complete characterization of the resulting complex singularity structure, which governs convergence rates in numerical algorithms based on the function. Recognizing that the function can be decomposed into power-law singularities and a regularised analytic part, we provide an algorithm for removing singularities without cancellation error. This facilitates the evaluation of integrals and enables fast precomputations through interpolation methods. We present the first high-performance implementation for arbitrary real arguments in EpsteinLib, a C library with Python and Julia bindings, and rigorously benchmark its performance and accuracy, achieving full-precision evaluation against known analytic results in dimensions 1,2,3,4,6, and 8 and against an arbitrary precision implementation across the entire parameter range. Finally, we apply our methods to the computation of quantum dispersion relations in spin systems and Casimir energies in three-dimensional geometries.

We study integrals appearing in one-loop amplitudes in string theory, and in particular their analytic continuation based on a string theoretic analog of the $i\varepsilon$-prescription of quantum field theory. For various zero- and two-point one-loop amplitudes of both open and closed strings, we prove that this analytic continuation is equivalent to a regularization using generalized exponential integrals. Our approach provides exact expressions in terms of the degeneracies at each mass level. For one-loop amplitudes with boundaries, our result takes the form of a linear combination of three partition functions at different temperatures depending on a variable $T_0$, yet their sum is independent of this variable. The imaginary part of the amplitudes can be read off in closed form, while the real part is amenable to numerical evaluation. While the expressions are rather different, we demonstrate agreement of our approach with the contour put forward by Eberhardt-Mizera (2023) following the Hardy-Ramanujan-Rademacher circle method, and compare these two approaches. We include applications to the Ramond-Ramond sector of the vacuum amplitude and two-point amplitudes of Type I superstring theory.

The Ekman boundary layer, a fundamental concept in geophysical fluid mechanics, describes the near-boundary fluid motion subject to rotation. Within the singular limit framework of rapid rotation and vanishing viscosity, classical studies of Ekman theory (e.g., Desjardins and Grenier (1999), Masmoudi (2000)) are predominantly restricted to flat or small-amplitude boundary assumptions. The conventional flat-boundary assumption obscures the complex mechanisms induced by topographic curvature; moreover, even small-amplitude perturbations reduce topographic effects to simple linear forcing terms. Consequently, this paper investigates the singular limit behavior of rotating fluids over a non-flat boundary $z=B(x,y)$ of $\mathcal{O}(1)$ amplitude with uniformly bounded slope and curvature. We elucidate how such topography modulates fluid dissipation through two distinct mechanisms: macroscopic topographic forcing and microscopic anisotropic pumping. First, using multi-scale asymptotic analysis, we construct a class of approximate solutions that explicitly depend on the boundary's geometric characteristics, yielding a two-dimensional limit system fundamentally distinct from classical models. A key innovation of this system is the introduction of a generalized velocity field defined via the topographic metric tensor. This formulation not only generalizes the traditional isotropic linear damping to anisotropic geometric damping but also couples rotational effects to macroscopic vertical acceleration. Furthermore, using energy methods, we establish the $L^2$ convergence of these variable-thickness approximate solutions to the weak solutions of the original three-dimensional system. Finally, we analyze the multiple mechanisms governing rotating fluid motion over large-amplitude topography using a representative class of boundary geometries.

We provide a new proof of the splitting theorems from Lorentzian geometry, in which simplicity is gained by sacrificing linearity of the d'Alembertian to recover ellipticity. We exploit a negative homogeneity (non-uniformly) elliptic $p$-d'Alembert operator for this purpose. This allows us to bring the Eschenburg, Galloway, and Newman Lorentzian splitting theorems into a framework closer to the Cheeger-Gromoll splitting theorem from Riemannian geometry.

We present an approach to detecting (linear) gravitational wave memory in a Galactic core-collapse supernova using current interferometers. Gravitational wave memory is an important prediction of general relativity that has yet to be confirmed. Our approach uses a combination of Linear Prediction Filtering and Matched-Filtering. We present the results of our approach on data from core-collapse supernova simulations that span a range of progenitor mass and metallicity. We are able to detect gravitational wave memory out to 10 kpc. We also present the False Alarm Probabilities assuming an On-Source Window compatible with the presence of a neutrino detection. Errata: The neutrino-induced gravitational waveforms, a component of the total waveforms used to demonstrate the efficacy of the proposed detection method for gravitational wave memory, were computed incorrectly. They were underestimated by a factor of $4\pi$. As a result, the detection results improve and, most important, our primary conclusions are reinforced. In particular, with the corrected waveforms, see Fig. 1 and Fig. 3, the signal for D9.6-3D is in fact detectable at 1 kiloparsec, see Fig. 6 and Fig. 4. The corrected fit parameters are presented in Table 1. The false alarm probability for all three signals is impacted, as shown in Fig. 5. Fig. 5 demonstrates that our proposed method can reliably detect the D9.6-3D signal at 1 kpc for all cutoff values, but our conclusions regarding the inability to detect this signal at 10 and 100 kpc remain the same. We see a boost in the detectability of the D15-3D and D25-3D signals. We now obtain a lower false alarm probability at 10 and 100 kpc. The authors would like to acknowledge Lella et al. [87] for pointing out the discrepancy between our computed neutrino-induced waveforms and theirs, which prompted us to investigate the discrepancy and which led to the discovery of our error.

The facilitated simple exclusion process (FEP) is a one-dimensional exclusion process with a dynamical constraint. We establish bounds on the mixing time of the FEP on the segment, with closed boundaries, and the circle. The FEP on these spaces exhibits transient states that, if the macroscopic density of particles is at least $1/2$, the process will eventually exit to reach an ergodic component. If the macroscopic density is less than $1/2$ the process will hit an absorbing state. We show that the symmetric FEP (SFEP) on the segment $\{1,\ldots,N\}$, with $k>N/2$ particles, has mixing time of order $N^{2}\log(N-k)$ and exhibits the pre-cutoff phenomenon. For the asymmetric FEP (AFEP) on the segment, we show that there exists initial conditions for which the hitting time of the ergodic component is exponentially slow in the number of holes $N-k$. In particular, when $N-k$ is large enough, the hitting time of the ergodic component determines the mixing time. For the SFEP on the circle of size $N$, and macroscopic particle density $\rho \in(1/2,1)$, we establish bounds on the mixing time of order $N^{2}\log N$ for the process restricted to its ergodic component. We also give an upper bound on the hitting time of the ergodic component of order $N^{2}\log N$ for a large class of initial conditions. The proofs rely on couplings with exclusion processes (both open and closed boundaries) via a novel lattice path (height function) construction of the FEP.

We introduce a higher spin vertex model on a strip with fused vertex weights. This model can be regarded as a generalization of both the unfused six-vertex model on a strip arXiv:2212.09111 and an 'integrable two-step Floquet dynamics' model introduced in arXiv:1711.08884. We solve for the stationary measure using a fused version of the matrix product ansatz and then characterize it in terms of the Askey-Wilson process. Using this characterization, we obtain the limits of the mean density along an arbitrary down-right path. It turns out that all these models share a common phase diagram, which, after an appropriate mapping, matches the phase diagram of open ASEP. This provides evidence for the universality of this phase diagram.