The quantum anomalous Hall effect in altermagnets is difficult to realize because spin-up and spin-down states remain degenerate at the $\Gamma$ point in the nonrelativistic limit. We start from the Bernevig-Hughes-Zhang model to incorporate nontrivial band topology. We demonstrate that the combined effects of an external magnetic field, spin canting, and ferroelectric orbital hybridization lift the degeneracy at the $\Gamma$ point, enabling electric-field control of the Chern number. A minimal two-dimensional d-wave altermagnetic model with band inversion then realizes a ferroelectrically tunable Chern insulator with spontaneous spin canting. The ferroelectric polarization controls the topological phase and the orbital angular momentum, enabling a rich phase diagram with C = $\pm 1$ and C = $\pm 2$ through a Berry-curvature reorganization linked to the spin canting response and ferroelectricity. Our results establish a symmetry-consistent route to electrically tunable Chern insulating phases in altermagnetic materials, opening opportunities for low-power topological and orbitronic devices.

We report ground-based coherent VHF radar observations of extreme turbulent field-structures detected in coincidence with a magnetospheric substorm-associated magnetotail dipolarization. The field-structures are observed by the ICEBEAR radar, in the form of Farley-Buneman (FB) waves in the auroral electrojets, and the field-structures themselves move an order of magnitude faster than the saturation speed of the underlying FB waves, implying transient electric field sources up to 330 mV/m in strength. The field-structures are identified and automatically tracked using an unsupervised clustering & tracking algorithm, applied to clutters of ICEBEAR radar backscatter targets, a method that turns the Doppler radar into a tracking radar capable of measuring the ionospheric ExB-drift by proxy. We place this finding in a coordinated multi-instrument context. Three THEMIS spacecraft observed the dipolarization event in-situ in the near-Earth plasma sheet. In the ionosphere, Swarm A, crossing through the guilty auroral arc at the onset of the dipolarization event, recorded clear signatures of propagating Alfvén waves threading the relevant flux tube. We interpret the ICEBEAR transients as the natural ionospheric foot signature of a shear Alfvén pulse launched by the bipolar space-charge (Hall) electric field of the thinned current sheet, with amplification along the converging flux tube, partial reflection at the ionospheric boundary, and spatial sharpening by precipitation-produced Pedersen-conductance gradients on the auroral arc edges. A one-dimensional wave-transmission analysis recovers the observations. Our results elucidate a tightly controlled coupling between magnetotail processes and meter-scale auroral plasma turbulence, and demonstrate the capability of ICEBEAR to resolve extreme, transient electric-field enhancements in the ionosphere.

Cells dynamically generate, transmit, and dissipate stress. Central to these processes is the actomyosin cortex, an active contractile material that drives cellular mechanical behavior. While prior studies have focused on freely contracting actomyosin systems, the role of mechanical constraints such as adhesion to boundaries remains less explored. To address this, we employ reconstituted actomyosin gels to investigate cellular contractility. We study contraction dynamics under pinned boundary conditions, where the gel is adhered transversely to two opposing surfaces, mimicking supracellular actomyosin networks in tissues and embryos. We find that pinned contraction leads to stress buildup, delaying contraction, producing intermittent dynamics, and generating spatially nonuniform strain fields. Stress is relieved through several pathways, including active-stress-driven symmetric constriction and defect-driven processes such as boundary detachment and internal rupture. We develop a hydrodynamic model incorporating elastic, viscous, and active stress contributions that distinguishes between stress-accumulation and stress-release phases and links variations in active stress to the observed intermittent dynamics. The model predicts distinct energy relaxation rates before and after detachment events, providing insight into stress dissipation. We compare experiments with numerical simulations, which reproduce the observed behavior and reveal how internal energy is generated and dissipated during stress buildup and relaxation. Together, our results demonstrate how boundary conditions and spatial heterogeneity govern the mechanical behavior of contractile active gels. These findings provide insight into stress regulation in cellular and tissue-scale systems and may inform the design of adaptive soft materials and bioinspired robotic systems.

Earthquakes propagating faster than the shear wave-speed are commonly thought to undergo a super-shear transition upon which they discontinuously jump from the sub-Rayleigh regime to the super-shear one. The super-Rayleigh regime, i.e., the range of propagation speeds between the Rayleigh and shear wave-speeds, is regarded as "forbidden" by the two-dimensional classical rupture theory. Here, we revisit the assumptions underlying the classical theory and develop a rupture theory that takes into account the dependence of the fault strength (frictional resistance) on the slip rate. The theory quantitatively agrees with numerical simulations nearly up to the Rayleigh wave-speed. Yet, very close to the latter, two-dimensional rupture solutions change their character due to frictional rate nonlinearity and rupture continuously propagates through the "forbidden" super-Rayleigh range into the super-shear regime, without a sharp super-shear transition. These results demonstrate that frictional rate dependence, generically observed in experiments, can have profound implications for fast earthquake propagation.

The second solar spectrum is the spectrum of the Stokes parameter Q (linear polarization) close to the solar limb. It is made of a few polarized lines with Q/I of about 1% (such as CaI, SrI, or BaII), but most lines exhibit weaker polarization. This paper presents processing of unpublished observations made in 2008 with the Meudon solar tower spectropolarimeter, which are of interest for weak and turbulent unresolved magnetic field measurements in the quiet Sun, through the Hanle effect.

The Traveling Salesman Problem (TSP) is a classical NP-hard problem in combinatorial optimization, where determining the shortest route among a set of cities becomes computationally prohibitive as the problem size increases. This work explores quantum computing as an alternative approach to address this complexity. Unlike existing methods that primarily rely on quantum annealing, we propose a quantum iterative framework integrating Quantum Phase Estimation (QPE) and Grover's search algorithm. Route costs are encoded as quantum phases, enabling QPE to efficiently evaluate them, while Amplitude Amplification, implemented via the Grover-Long algorithm, iteratively refines the solution space toward the optimal route. A proof-of-concept case study on a small-scale TSP instance demonstrates the feasibility of this approach and its potential for scaling to larger optimization problems. Furthermore, under an expectation-based analysis, the algorithm exhibits an expected computational complexity of $O(\frac{m^2\log_2(m)\log_2(1/\epsilon)}{\sqrt{\epsilon}})$ which depends on the error tolerance parameter $\epsilon$. This estimation omits the initialization term, which we expect future refinements to render subdominant to Phase Estimation.

The temperature increase in the contact regions between solids in sliding contact can easily reach several hundred Kelvin and thereby dramatically affect friction and wear. Here I extend an earlier multiscale theory for the flash temperature (Ref. \cite{MP}) to the case of accelerated motion, and present numerical results illustrating the theory.

We prove a singularity theorem in which the classical focusing hypothesis of Hawking--Penrose theory is replaced by a condition on asymptotic volume growth. Under the strong energy condition, we introduce asymptotic volume-expansion invariants associated with a compact Cauchy hypersurface and show that a uniform positive lower bound on these invariants implies past timelike geodesic incompleteness. More precisely, we obtain an explicit upper bound on the time-separation from the hypersurface to its chronological past. The theorem extends to globally hyperbolic Lorentzian length spaces satisfying the synthetic strong energy condition $\mathsf{TCD}^e_p(0,N)$, yielding an inextendibility result valid without any smoothness or differentiability assumption. We also prove an area comparison theorem for equidistant hypersurfaces and a volume singularity theorem based on related asymptotic expansion invariants.

Meta-structures that display axial-twist coupling can be achieved through the emerging kinematics in Kresling origami patterns. A central challenge in these structures is understanding their nonlinear mechanical behaviour, specifically their equilibrium branches and bifurcation diagrams. This involves identifying relationships between desired responses and the geometric variables that define the design space, including the Kresling polygon count, initial twist angle, height, radius, and crease lengths. As the number of constituent units increases in an n-layer chain, we track complex equilibrium branches extending into the post-critical regime under successive instabilities, including branch-point bifurcations and limit-point instabilities. This work begins by establishing the relationship between the geometric design variables and the response curves of the assembled chain by modelling the crease lines as axial-load-carrying elements. Subsequently, equilibrium branches and instabilities are systematically investigated via continuation and bifurcation analysis, beginning with the single-layer system and progressively extending to two- and three-layer configurations. Finally, a generalisation strategy is proposed to extend these findings to an n-layer Kresling chain. This strategy enables the predictive construction of equilibrium paths and the inverse design of multi-layer meta-structures, using prescribed critical points to control post-critical behaviour. It provides a foundation for the inverse design and optimisation of architected mechanical metamaterials with programmable responses.

We study statistics of atypical measurement outcomes in the steady states of driven open quantum systems. In equilibrium, the probability distribution over the phase space, as encoded in, e.g., the Wigner function, is analytic in the phase-space coordinates. We show that this property is generically lost in driven dissipative systems: their {\it large-deviation function} develops lines and surfaces across which its derivatives are discontinuous. As an illustrative example, we consider a parametrically driven Kerr oscillator coupled linearly and/or nonlinearly to a dissipative bath. Rare fluctuations in the amplitude and phase of the induced oscillations are governed by semiclassical instanton trajectories of the corresponding Keldysh-Lindblad action. We demonstrate that a given fluctuation can be realized through multiple distinct instanton trajectories. The competition between these trajectories leads to abrupt switching of the dominant instanton and, consequently, to non-analytic features in the large-deviation function.

Veloce EQuilibrium (VEQ) is a compact parametric framework for tokamak modeling workflows that repeatedly query continuous fixed-boundary equilibria at low latency. The VEQPy implementation evaluated here is an axisymmetric fixed-boundary Grad-Shafranov solver whose main solve enforces a variationally induced projected residual. Its active unknowns are MXH-type flux-surface harmonics and shifted-Chebyshev coefficients for radial profile and source closures. Six input routes accept pressure-gradient, toroidal-field-function, poloidal-flux-gradient, enclosed toroidal current, current-density and safety-factor information through route-specific closures, while all routes map to the same finite-dimensional residual operator. Controlled tests show route consistency for smooth, mutually compatible inputs generated from a common reference equilibrium. For Pareto-selected reduced configurations in three G-EQDSK cases, the most accurate selected rows correspond to a D-shaped case (9 active parameters, minor-radius-normalized shape error 1.4e-3, solve-only median 1.6 ms), an H-mode case (65, 1.1e-3, 19 ms), and an X-point case treated as a smoothed fixed-boundary representation of a diverted boundary (94, 1.9e-3, 15 ms). Sampled pointwise strong-form Grad-Shafranov diagnostics show that enriching the active representation mainly improves interior force balance, whereas the global RMS and maximum values for the H-mode and X-point cases remain dominated by near-boundary contributions. In an isolated one-dimensional transport-geometry coupling test against the target geometry read from G-EQDSK, the temperature-profile response remains below about one percent. These results support using VEQ for repeated equilibrium-geometry queries, provided that pointwise diagnostics are retained to screen cases requiring boundary refinement, local correction or higher-fidelity equilibrium solves.

Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance $z$, the real off-diagonal component $c$, and the imaginary off-diagonal component $s$. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.

Frequency conversion of ultrafast lasers is fundamentally constrained by the trade-off between pulse energy and repetition rate, limiting access to regimes critical for fundamental science and industry. Here, we demonstrate a frequency-conversion mechanism in which molecular coherence accumulates across ultrafast pulse trains in gas-filled hollow-core fibers. Unlike conventional nonlinear interactions initiated by individual high-energy pulses, this mechanism relies on the collective buildup of coherent molecular oscillations driven by successive pulses. Using this mechanism, we achieve Raman frequency conversion at repetition rates up to 3 GHz with nanojoule pulse energies. The results establish a regime of nonlinear optical interaction governed by coherence accumulation of gas molecular oscillations with broad implications for ultrafast laser science and frequency conversion technologies.

We establish a rigorous mathematical bridge from quantum many-body path integrals to the cusp catastrophe model by Lyapunov-Schmidt reduction, which provides a theoretical foundation for analyzing superconducting phase transition using the catastrophe theory. First, it is proved that, near the critical point the infinite-dimensional effective action is diffeomorphic to a finite-dimensional catastrophe. Secondly, starting from Ginzburg-Landau free energy functional, the Euler-Lagrange partial differential equation can be reduced to the cusp catastrophe model. Thirdly, the fermionic imaginary-time path integral to the cusp catastrophe is derived through the Hubbard-Stratonovich transformation, Matsubara frequency expansion, and Grassmann algebra. Furthermore, we connect this framework with the adsorption potential theory we proposed, elucidating the catastrophic topological nature of the electron pairing mechanism in high-temperature superconductivity. The precise microscopic derivation of the adsorption potential from first-principles electronic structure calculations would strengthen the predictive power of the theory.

We introduce Fourier integrator molecular dynamics (FIMD), a method for propagating selected vibrational motion of Hamiltonian systems stably and reversibly in time while analyzing and controlling dynamics in the frequency domain. This makes band selection and vibrational analysis features of the integrator rather than post-processing steps. We demonstrate the method with classical force fields, a machine-learned force field trained on quantum data, and semi-empirical quantum chemistry for CO$_2$ and the capped Ace--Phe--Tyr--NMe peptide. The method reproduces spectra within the chosen band, suppresses out-of-band response, reveals mode coupling, and demonstrates force-field dependence of spectral features, especially for the thermodynamically important low frequencies. FIMD offers an efficient and transparent way to probe the vibrational physics underlying spectroscopic and calorimetric observables.

We investigate $J/\psi$ photoproduction off the proton, $\gamma p \to J/\psi p$, to elucidate the nonexistence of hidden-charm pentaquark signals reported by the GlueX and CLAS12 experiments. Within a coupled-channel rescattering mechanism, we employ the transition amplitudes from a previous coupled-channel analysis that dynamically generates the $P_{c\bar{c}}$ states. The kernel amplitudes for the transition to the $J/\psi N$ channel include both $t$-channel heavy-meson exchange and $u$-channel heavy-baryon exchange. We find that the rescattering contributions from the $\bar{D}^{(*)}\Sigma_c$ channels -- indispensable for the formation of the $P_{c\bar{c}}$ resonances -- are about one order of magnitude smaller than those from $\bar{D}^{(*)}\Lambda_c$, since $g_{\bar{D}^{(*)}N\Sigma_c}$ is roughly five times smaller than $g_{\bar{D}^{(*)}N\Lambda_c}$. Since the $P_{c\bar{c}}$ resonances couple to the $J/\psi N$ channel predominantly through the $\bar{D}^{(*)}\Sigma_c$ intermediate states, their suppression prevents the pentaquark signal from appearing in photoproduction. With only a single parameter controlling the overall normalization, the present work describes the GlueX and CLAS12 cross sections well. These results suggest that the null result from photoproduction need not be in conflict with the pentaquark signals observed by the LHCb Collaboration.

Nonreciprocal interactions in active solids violate action-reaction symmetry and produce a net response to strain. Assuming invariance under Euclidean symmetries, we derive a shape-space formulation for the elastohydrodynamics of nonreciprocal slender bodies that separates intrinsic deformation from rigid motion. The resulting nonlinear reaction-advection-diffusion system represents a geometric flow whose activity-driven instabilities generate steady, oscillatory, and chaotic patterns. These manifest as rigid, swimming, and chaotic motion, linking nonreciprocal elastohydrodynamics to geometric pattern formation and unifying recent observations in slender active structures.

We present a high-pressure single-crystal X-ray diffraction study of the atomically precise $\mathrm{Au}_{25}(\mathrm{PET})_{18}^{q}$ cluster ($q=-1,0$) up to 10 GPa under strictly hydrostatic conditions. Our crystallographic analysis provides direct evidence for the pressure-induced phase transitions previously suggested by spectroscopic studies. Structural refinements reveal that the cluster accommodates compression through the reorganization of the flexible ligand shell and secondary distortions of the staple motifs, while the $\mathrm{Au}_{13}$ icosahedral core remains intact. Notably, the internal Au-Au distances exhibit a monotonic contraction that quantitatively mirrors the compressibility of bulk gold. This invariant rigidity at the sub-nanometer scale demonstrates that the fundamental stiffness of the metallic bond is preserved regardless of size. Our findings reconcile previous contradictions in the elasticity of metal nanostructures by isolating the intrinsic mechanical response of the gold kernel from extrinsic structural and experimental artifacts.

Sub-femtosecond electron beams are powerful probes of ultrafast electronic, atomic, and nuclear dynamics, and promising drivers for ultrashort radiation generation from the extreme-ultraviolet to gamma-ray regimes. However, producing such beams at hundred-MeV energies with pC-level charge remains challenging. Here we propose a two-dimensional beam-compression scheme based on transverse--longitudinal coupling, in which dispersive beam optics convert the small transverse emittance of modern electron beams into an ultrashort longitudinal duration. Linear analysis and particle tracking show that, after the dominant longitudinal and energy-spread contributions are cancelled, the compressed bunch length is governed primarily by transverse beam quality and collective-effect growth. We further derive and verify a scaling law showing that, in the relevant parameter range, collective-effect-induced bunch-length degradation increases approximately linearly with bunch charge and decreases with beam energy. Start-to-end simulations of a realistic injector-to-compressor beamline produce a 200 MeV, pC-level bunch with an rms duration of 0.45 fs and a peak current of about 3.5 kA. Jitter studies indicate that sub-femtosecond performance is maintained for most error seeds. These results suggest a feasible route toward compact, high-energy attosecond electron beam sources and may provide a basis for future sub-femtosecond radiation sources based on undulator emission or inverse Compton scattering.

Uncertainty in the terrestrial carbon cycle remains a major constraint in climate projections, partly driven by the uncertainties affecting the land surface representation and variability in Earth system models. To address this limitation, we present a data-driven framework AI4Land, for generating high-resolution historical reconstructions and future projections of key land surface variables. The framework follows a two-phase approach using a U-Net architecture. In the first phase, which is the focus of this work, it reconstructs annual land use and land cover by integrating coarse-resolution scenario data with static geophysical features. In a planned second phase, the resulting high-resolution maps will be used to predict dynamic biophysical variables, particularly leaf area index, at finer temporal scales. Trained on Earth observation data, the models learn to reproduce spatially explicit and physically consistent land surface patterns, extending temporal coverage to periods lacking direct observations. AI4Land was developed and trained on MareNostrum5, demonstrating how GPU-accelerated HPC infrastructure enables global-scale climate AI pipelines. The final product is a suite of open-source emulators designed for real-time coupling with digital twin platforms, such as those developed under the Destination Earth initiative. By delivering realistic and evolving land surface conditions on demand, this work aims to reduce critical uncertainties and improve the predictive power of next-generation climate simulations.

A recent analysis of the centrifugal instability in the case of pressure-supported compressible relativistic rotation, with application to astrophysical jets, yielded a generalisation of the famous Rayleigh criterion for Newtonian flows. According to this criterion, the centrifugal instability is strongly affected by the flow Mach number, and not only in the relativistic fluid dynamics but also in its Newtonian limit. To validate the Newtonian version of this criterion, we performed axisymmetric numerical simulations of non-relativistic transonic rotating flows which are stable according to the original Rayleigh criterion but can be either stable or unstable according to the new one. The results of computer simulations are found to be in perfect agreement with the theory. The hydrodynamic stability of accretion disks is often explained by referring to the original Rayleigh criterion, even if their rotation is highly supersonic. To clarify the matter, we analysed the hydrodynamic stability of flows rotating about central compact object and derived an instability criterion that retains the explicit dependence on the flow Mach number. This criterion turns out to be equivalent to the standard Solberg-Høiland criterion, which does not involve the Mach number. The same applies to the case of pressure-supported rotation, where the role of gravity is played by the centrifugal force.

We study Kohn-Sham Density Functional Theory (DFT) models describing the electronic structure of two-dimensional materials placed in a three-dimensional environment, encapsulated between two parallel conducting electrodes. In this geometry, the Dirichlet boundary conditions at the electrodes screen the Coulomb interaction, which becomes effectively short-ranged, of Yukawa type. We prove that some nonlinear Kohn-Sham DFT models are well-posed in this setting, both for periodic materials (such as graphene) and for quasi-periodic materials (such as twisted bilayer graphene and other moiré materials for generic incommensurate twist angles).

In closed quantum systems, local information spreads throughout the entire system and becomes highly complex under unitary evolution. In contrast, when the system is embedded in an environment, system-environment coupling can transfer information from the system into the environment, thereby reducing the rate of complexity growth within the system. This leads to the environment-induced scrambling transition established in previous works. In this work, we identify entropy injection from the environment as a different physical process that instead enhances many-body chaos. Our setup consists of coupling a system that is already in equilibrium with one environment to another environment, which serves as an entropy reservoir and drives the system into a non-equilibrium state. When entropy flows into the system through either heat transfer or particle transfer, the effective Hilbert space explored by the system enlarges, a mechanism that can enhance many-body chaos. We explicitly demonstrate this idea by constructing a solvable complex Brownian SYK model, in which both the relaxation toward the steady state and the steady-state quantum Lyapunov exponent can be computed analytically. Our results provide a controllable mechanism for tuning quantum scrambling through entropy flow in quantum many-body systems coupled to environments.

We propose a minimal, rotation-free model of magnetohydrodynamic (MHD) dynamo action driven by laminar thermal convection in a regular tetrahedral cavity. Unlike canonical planetary-dynamo settings, where flow helicity is supplied by global rotation, the present system generates robust flow helicity purely through the geometric constraints imposed by tetrahedral boundaries. Direct numerical simulations show exponential amplification of a weak seed magnetic field and a nonlinear saturated state in which the magnetic energy exceeds the kinetic energy. The convective flow organizes into a highly symmetric pattern with \(D_4\) dihedral symmetry. The dynamo-generated magnetic field obeys a corresponding signed \(D_4\) symmetry involving antisymmetry under \(\pi\)-rotations about the two horizontal axes of the tetrahedron. The tetrahedral dynamo provides a conceptually transparent setting for isolating geometry-induced helicity, magnetic-field amplification, and a closed induction cycle in a non-rotating laminar flow.

Topological charges based on Berry phase play the fundamental role in the topological physics. However, such topological charges remain unexplored in quasicrystals, impeding the systematic understanding of topological states in such quasiperiodic systems. In this work, by deriving all the allowed topological charges according to group representation theory and the corresponding low-energy effective Hamiltonians, we establish a universal framework for Berry-phase-based topological charges in two-dimensional quasicrystals. Taking the $C_{8v}$ quasicrystal as an example, we demonstrate and characterize a higher topological charge of $C=4$, which is inaccessible in conventional periodic systems. Applying our framework to photonic quasicrystals, we uncover that the circling of photon momentum around the charge gives a $C$ times winding of the electromagnetic field distribution pattern. Such observable feature provides a direct experimental method to probe the topological charges. Our work paves the way for exploring topological charges in quasiperiodic matter, and fundamentally bridges periodic and quasiperiodic topological band theories.

Originally motivated by creating first-person computer visualizations within Riemannian manifolds -- the author was led to study deformable-body mechanics, as rigid-body mechanics is not available in a generic Riemannian manifold due to its lack of nontrivial isometry group. Hyperelasticity is a particularly nice sub-category of continuum mechanics in which a deformable, elastic body's behavior is determined by a stored energy density function. This allows problems to be posed variationally, and powerful tools brought to bear on studying and solving them. This article presents numerical simulations of static solutions to a particular class of problems in hyperelastic mechanics in 2-dimensional Riemannian manifolds in which a flat hyperelastic body $B$ is embedded into a region $\Omega$ in a nowhere-flat surface $S$ of revolution $z=z\left(r\right)$ such that $\left|K\left(r\right)\right|$ decreases as $r\to\infty$, where $K$ denotes the Gaussian curvature of $S$. For example, the funnel $z=-r^{-1}$ or the paraboloid $z=\frac{1}{2}r^{2}$. Because $B$ is flat, the body can't achieve a zero-stored-energy configuration, and restorative forces arise in the body to move it toward a region of lower stored energy -- meaning, toward a flatter configuration. With the addition of a gravitational potential $U\left(r\right)=z\left(r\right)$ on $S$, forces act on the body to pull it toward $r=0$. If the body has sufficient stiffness and remains within the region $\Omega$, then the body has an equilibrium configuration in which the body's deformation-response forces perfectly cancel the gravitational forces. Such a configuration represents a kind of "levitation" phenomenon within this surface. The numerical implementation of this problem will be detailed and the resulting numerical solutions and various consequences discussed.

The stress concentrations caused by inherent roughness of natural and manufactured surfaces often induce plastic deformation at contact interfaces, a challenge compounded by competing influences of the size effect of plastic deformation and self-affine rough surface topography. To address this, we developed a novel methodology based on stochastic theory using compounded Chapman-Kolmogorov equations, for the first time, to solve elastoplastic contact problems involving scale-dependent hardness. Our approach formulates three integral equations describing the evolution of probability density functions of elastic contact pressure, relative plastic contact area, and relative non-contact area across geometrical scales. We thoroughly investigate the effects of scale-dependent hardness on contact pressure distribution, relative elastic and plastic contact areas, and the area-to-load relationship. By adjusting various mechanical and material properties, our model predicts a smooth transition from linear elasticity to elastic-plastic behavior and finally to full plasticity. A key advancement is the derivation of a new topographic yield parameter incorporating a wider range of material and geometrical properties, aiding identification of contact status. Numerical solutions enable highly precise determination of elastic and plastic limits via curve-fitting, and we also provide a new diagram for rapid identification of contact status. This study pioneers a stochastic process framework for applying the compounded Chapman-Kolmogorov equation to rough surface contact analysis, and the integral equations characterizing how interfacial properties evolve with scale could offer valuable insights for other multidisciplinary fields where multiscale roughness is critical, such as earthquakes, electrical contact, and contact electrification.

Grover's algorithm achieves a quadratic speedup for unstructured search given a global oracle for the target set. In many applications, however, the target set is specified as the intersection of multiple constraint sets. Constructing a global oracle for the intersection can be costly, whereas the individual constraint oracles are often much simpler to implement. We study a randomized Grover search algorithm that directly uses these constraint oracles. At each iteration, one of the corresponding Grover operators is selected at random. For the two-operator case with uniform sampling, we prove that the success probability approaches one after \[ \Theta \left(\frac\pi4\sqrt{\frac{N}{r}}\right) \] iterations, where $r$ is the size of the intersection. Thus, the algorithm achieves the same asymptotic query complexity as standard Grover search but without requiring a global oracle. We then generalize the analysis to arbitrary sampling distributions and an arbitrary number of Grover operators through an auxiliary operator that approximates the expected Grover evolution, while retaining the same asymptotic complexity. We further show that highly biased sampling distributions can still achieve near-unit success probability, enabling cheaper Grover operators to be used more frequently. Finally, we prove asymptotic optimality and support the theoretical results with numerical simulations.

High-frequency focused acoustic beams are promising for selective trapping of cells in fluids, but the related acoustic absorption may generate large acoustothermal effect which could cause thermal heating on cells or microparticles and bring extra acoustic body force due to the thermal gradient. The theory of the bulk acoustic streaming and acoustic radiation force in a focused-beam for the three-dimensional selective trapping of a cell has been developed [Li and Gong, Phys. Rev. Fluids, 11, 054201 (2026)], however, the acoustothermal effect and its feedback on the acoustic field at high frequency with strong absorption remain weakly understood. To solve this issue, we develop a theoretical and numerical model that couples acoustic propagation, bulk acoustic streaming, and acoustothermal effect in water. The acoustic body force is decomposed into a viscous-attenuation-induced acoustic body force $\mathbf{f}_{\mathrm{E}}$ and a temperature-gradient-induced acoustic body force $\mathbf{f}_{\mathrm{T}}$, while the temperature field is fed back to the frequency-domain acoustic calculation through the temperature-dependent material properties. Taking the single focused beam for example, within the pressure range constrained by the mechanical index, $\mathbf{f}_{\mathrm{T}}$ remains weaker than $\mathbf{f}_{\mathrm{E}}$, whereas streaming-induced convection can markedly reduce the temperature rise when the thermal Peclet number ($Pe_T$) exceeds unity. This work establishes a theoretical basis for predicting and controlling the intercoupling of bulk acoustic streaming and acoustothermal effec of high-frequency focused beams which will be helpful for the design of single-beam acoustical tweezers.

We investigate polarization-selective absorption in a visible-wavelength heterostructure consisting of a ReS$_2$ stripe grating, an $\alpha$-MoO$_3$ spacer, and an Au back-reflector using finite-difference time-domain simulations. For an optimized geometry with a grating period of 500 nm, stripe width of 250 nm, and ReS$_2$ thickness of 80 nm, the structure exhibits near-unity absorption of 99.99\% at 650.5 nm under TE-polarized illumination. The resonant field is concentrated near the outer edges of the ReS$_2$ stripe, while absorption power density is localized in the same region, consistent with a localized edge mode. The absorption response depends strongly on polarization, producing a TE--TM resonance separation of 16.2 nm. Replacing either the biaxial ReS$_2$ layer or the anisotropic $\alpha$-MoO$_3$ spacer with isotropic equivalents substantially modifies the spectral response and reduces the polarization-dependent wavelength separation. In addition, rotating the crystal orientation of the ReS$_2$/$\alpha$-MoO$_3$ stack shifts both the resonance wavelength and peak absorption without changing the device geometry. The results show that the combination of anisotropic resonator and spacer layers provides an effective means of controlling resonant absorption and polarization selectivity in van der Waals photonic structures.