Papers

We introduce an information-theoretic framework that uses variational autoencoders (VAEs) to extract compact, physically interpretable manifolds from high-dimensional flow-field data. To this end, the Kullback–Leibler (KL) divergence in the variational objective is decomposed into three complementary information-theoretic terms: the index-code mutual information, the total correlation, and the dimension-wise KL divergence. These terms explicitly regulate data compression, latent disentanglement, and geometric regularization. This establishes a principled basis for targeted latent-space design, allowing enhanced interpretability without sacrificing information capacity, a common drawback of heavily regularized VAE variants. The approach is evaluated on two synthetic unsteady flow datasets. First, we consider a flow around a cylinder in a channel with variable cylinder position, diameter, and Reynolds number. Later, we also consider the flow around a NACA 0012 airfoil at varying angles of attack and subjected to strong vortex gusts with variable intensity, position, and length scale. Comparisons with Principal Component Analysis, Isometric Feature Mapping, and $\beta$-VAE demonstrate clear advantages in disentanglement and physical interpretability. The learned latent coordinates successfully separate distinct physical effects. Moreover, the proposed method demonstrates strong robustness to variations in the loss-weighting parameters, despite involving a larger number of such parameters.

Impurities embedded in a Bose-Einstein Condensate (BEC) of 39K atoms are investigated with a pump-probe ejection spectroscopy sequence. The spectroscopic signal exhibits a strong feature corresponding to a Bose polaron in agreement with prior injection spectroscopy and theory. In addition, significant spectral weight at energies well below the energy of the polaron is observed, which is absent in injection spectroscopy. The energy and spectral weight of this signal are measured as a function of interaction strength and evolution time between the pump and probe pulses. We tentatively compare these results to two different theoretical models: a low-energy impurity state dressed by many bosonic excitations and a bipolaron state formed by two polarons due to attractive interactions mediated by the BEC. Such states can exist due to the large compressibility of the weakly interacting BEC. Both theories predict ejection spectra consistent with the low-energy signal, but only the bipolaron model is compatible with its spectral weight. These results indicate that lowenergy states below the usual polaron exist for strong interactions, calling for further experimental investigations

Two equal and opposite distributed dead loads are applied orthogonally to the axis of an elastic rod in its rectilinear reference configuration, one at the extrados and the other at the intrados, such that the resultant applied force per unit length is uniformly zero. In this configuration, the rod is subjected to a transverse (tensile or compressive) stress, which is usually believed to have no significant effect on the structural response and has therefore not been considered so far. Contrary to this common belief, the asymptotic behavior of an incrementally deformed elastic layer and three different rod models (the first derived as an asymptotic approximation of the elastic layer; the second based on Euler elastica; and the third obtained by homogenization of a discrete model) reveal that this loading condition produces the same deformation in the rod as an axial load. In particular, the transverse load adds to the axial load in a generalized version of the Euler elastica, leading to buckling and nontrivial postcritical deformations when compressive. The critical transverse stress for buckling is found to have the same form as the Euler critical stress under axial force and tends to zero in the limit of vanishing rod inertia. For this reason, instability induced by transverse loading persists even when the rod thickness tends to zero. These theoretical predictions are confirmed by numerical simulations of a slender elastic layer, which show that increasing transverse load can induce buckling and drive the layer along a deformation path that closely follows that predicted by the generalized Euler elastica throughout the entire postcritical regime, even beyond self-intersection. To show that this behavior can be realized in practice, a dedicated experimental setup is developed, and the experimental results fully confirm the theoretical and numerical predictions.

We investigate two hydraulic stimulation stages performed in April 2022 at the Utah FORGE enhanced geothermal system test site using analytical and numerical models for tensile hydraulic fractures and fluid-induced dilatant shear fractures. The two injection stages differ primarily by the viscosity of the fracturing fluid. Despite similar injection rate schedules and well-head pressure responses, the two stages exhibit markedly different post-shut-in microseismic behavior. The cross-linked gel stage shows sustained microseismic activity for several hours after shut-in, whereas the slickwater stage exhibits an immediate decrease. For the cross-linked gel stage, the located microseismic events reveal the development of a planar radial fracture and allow confident retrieval of the fracture extent evolution with time. We demonstrate that this evolution follows the scalings predicted for viscosity-storage-dominated radial hydraulic fracture by analytical models, providing strong evidence for the development of a planar tensile hydraulic fracture. We further show that leak-off is required to reproduce the fracture extent. In contrast, the immediate arrest observed during the slick-water stage suggests either a transition to a toughness- or leak-off-dominated hydraulic fracture regime, or the development of a fluid-induced shear fracture. We show that the slickwater stage could plausibly correspond to a dilatant shear fracture, provided sufficient dilatancy, whereas this hypothesis is invalidated for the cross-linked gel stage. We confirm these insights using a 3D axisymmetric fully-coupled hydro-mechanical numerical model capable of resolving both tensile and shear failure modes, and including leak-off. Finally, we propagate uncertainties in the in-situ stress state and natural fracture orientations through this numerical model to assess their impact on injection pressures.

Non-Hermitian dynamics in open systems can give rise to a variety of fascinating non-equilibrium phenomena, ranging from symmetry-breaking transitions to directional energy flow. Parity-time (PT) symmetry breaking determines the occurrence of dynamical instabilities, while non-reciprocal interactions enable asymmetric energy transfer between modes. Here, we present a versatile optomechanical platform based on a vacuum-levitated nanoparticle that allows full control over the coupling of its mechanical modes, including non-reciprocal and non-conservative interactions. By engineering the spatial ellipticity and polarization of the trapping beam, we continuously tune the system from a reciprocal to a strongly non-reciprocal regime. This allows us to observe PT-symmetry phase transitions and to isolate a unidirectional regime in which one mode remains effectively decoupled while driving the other. We demonstrate that elliptical polarisation of the trapping beam spanning unidirectional and reciprocal regimes induces asymmetric intermodal energy transfer. This results in the spontaneous cooling of one mechanical mode without external feedback. Both modes share identical mass, size, charge, and optical environment, providing a clean and robust setting for exploring non-Hermitian dynamics, exceptional-point physics, and energy redistribution in minimal systems. Combined with recent advances in ground-state cooling, our results provide a direct route to realising non-Hermitian phenomena in the quantum regime.

Do projects learn across space and time? The Olympics, among the largest publicly funded programmes in the world, offer a unique empirical setting. Theoretically, the Games seem ideal for generating "positive learning curves," driving down costs from one iteration to the next. In practice, they do not. Drawing on the concept of "myopia of learning," we argue that spatiotemporality (geographic distance, temporal gaps, and the temporary organisational form of each host committee) combines to block higher-level learning. Our analysis of cost overruns from 1960 to 2024 reveals no sustained improvement over 64 years. Tactical learning abounds, but none aggregates into strategic improvement. We propose four strategies for overcoming the spatiotemporal barrier (incremental, centralising, decentralising, and real options), arguing that radical reform is required.

The PICOSEC Micromegas detector is a~precise-timing gaseous detector that combines a Cherenkov radiator, a~semi-transparent photocathode and a Micromegas amplification stage, targeting time resolutions of tens of picoseconds for minimum ionising particles (MIPs). Initial single-pad prototypes achieved time resolutions of $\sigma<25$ ps, demonstrating strong potential for High Energy Physics (HEP) applications and beyond. The objective of this paper is a comprehensive characterisation of photocathodes, with a strong focus on robust materials while preserving excellent timing performance. The study includes laboratory measurements of optical and resistive properties, along with beam tests using 150 GeV/$c$ muons to evaluate the time resolution and photoelectron yield for various photocathodes. The best performance was obtained by a 5 nm Cesium Iodide (CsI) photocathode, reaching $\sigma = 10.9 \pm 0.3$ ps with more than 30 extracted photoelectrons, representing the most precise time resolution achieved by PICOSEC Micromegas to date. Metallic and carbon-based photocathodes, including Titanium (Ti), Boron Carbide (B$_4$C) and Diamond-Like Carbon (DLC), were also tested, with Ti and B$_4$C emerging as the most promising alternatives, achieving $\sigma \approx 30$ ps with about 5 extracted photoelectrons. These results demonstrate that improved robustness can be achieved while maintaining excellent time resolution, supporting the feasibility of using the PICOSEC Micromegas concept in future experiments.

International commerce has long been seen as a key way to keep the global food system stable, allowing agricultural surpluses in some areas to compensate for shortages in others. This strategy has led to the rise of highly specialised processing hubs that combine significant industrial capacity with agricultural inputs sourced from throughout the world. Türkiye's flour sector – currently the largest wheat flour exporter in the world – represents one of the most prominent examples of this model. However, increasing climate variability and geopolitical fragmentation raise important questions regarding the long-term resilience of food systems that rely heavily on imported biological inputs. Recent research shows the growing probability of synchronised crop failures across multiple agricultural regions due to atmospheric circulation anomalies and climate-induced extreme weather events. The assumption that global markets can consistently rebalance supply disruptions through trade is challenged by such events. Using the flour industry of Türkiye as a case study, this paper investigates the susceptibility of globally integrated grain processing centres. In order to assess the correlation between the scope of industrial processing and the capacity of domestic agricultural production, we introduce the Biophysical Autonomy Ratio~(BAR). The analysis demonstrates that Türkiye's BAR has declined consistently over time, suggesting that its processing sector has expanded beyond the domestic production base. The results suggest that in order to enhance the resilience of the food system in the future, it may be necessary to establish a more precise alignment between biological production systems and industrial food infrastructure. The paper concludes by addressing the policy implications for national food security governance in the context of escalating climate instability.

Accurate modeling of surface catalytic processes often requires methods capable of describing strong correlation, charge transfer, and multiple closely lying electronic states. While density functional theory remains widely used, its limitations for localized electronic states motivate the use of wavefunction-based approaches and, more recently, quantum computing algorithms. However, the performance of quantum ansätze in chemically motivated, multistate settings remains largely unexplored. Here, we benchmark state-averaged factorized unitary coupled cluster with singles and doubles (SA-fUCCSD) and the adaptive, problem-tailored ansatz (SA-ADAPT) using an embedded cluster model of NO adsorption on Rh-doped TiO2(110). The system exhibits pronounced multiconfigurational character and multiple state crossings, providing a stringent test. State-averaged CASSCF serves as a reference, and the quantum ansätze are evaluated as solvers for the corresponding CASCI problem within a fixed orbital basis. We find that SA-fUCCSD improves with increasing circuit depth but requires many parameters and shows sensitivity to initialization. In contrast, SA-ADAPT achieves near-CASSCF accuracy with significantly fewer operators. A modified operator selection scheme, incorporating multiple operators per iteration, substantially accelerates convergence. Our results demonstrate the efficiency of adaptive ansätze for multistate problems and establish a controlled benchmark for quantum algorithms in chemically motivated systems beyond minimal models.

We present a physics based numerical model that estimates the seismic radiation generated by water sediment flows in gravel-bed rivers. The model reproduces the trajectories of individual particles, evaluates impact and rolling forces from grain scale dynamics, and accounts for broadband turbulence and vortex shedding in the water column. Synthetic seismic signals are propagated to the receivers using the Rayleigh wave Green s function approach and synthetic ground-velocity signals are estimated. Application to a controlled test case shows how intermittent, size selective sediment transport mechanisms produce distinct spectral signatures. Comparison with seismic data from a flood event in a mountain torrent in the Tuscan Apennines displays general agreement with the observed frequency bands and clarifies the relative width of particle collisions and turbulent flow. These results show that resolved grain scale dynamics provides a framework for discriminating sediment transport and flow induced contributions to river seismic noise.

The micro-newton cusped field Hall thruster is an electric propulsion device that employs microwave-assisted ionization control. It serves as an actuator in drag-free control systems, ensuring control accuracy and stability by providing continuously adjustable thrust over a wide range. However, a mode transition occurring during the regulation process can lead to a sudden change in anode current, degrading control precision and stability. Therefore, it is necessary to investigate the underlying patterns of mode transition. This study examines the variations in internal plasma parameters and discharge characteristics of the thruster before and after microwave mode transition, primarily through probe diagnostics.Experimental results indicate that before the mode transition, the plasma luminous region is primarily concentrated within the electron cyclotron resonance (ECR) area, approximately 1-3 mm upstream of the anode. After the transition, the luminous region moves further upstream, and the plasma density near the anode exceeds the cutoff density, dropping sharply along the axial direction. The fundamental cause of the change in electron heating mechanism is the alteration in the propagation characteristics of fundamental waves due to this plasma density variation.When the plasma density rises to the cutoff density, the R wave and O wave, which drive ionization, are rapidly attenuated or reflected. At this point, the R-wave cannot reach the resonance layer, causing the dominant ECR ionization to become ineffective. The ionization mechanism shifts from being dominated by the R wave and O wave to being dominated primarily by the O wave. Consequently, the electron heating mechanism transitions from volume heating to surface wave heating......

Coherent structures in aspect ratio 2, axis-switching elliptical jets are studied using direct numerical simulation (DNS). Three different datasets are studied with varying near-nozzle forcing levels. Increasing the forcing level causes the jet to axis switch at an earlier streamwise location. Spectral proper orthogonal decomposition was applied to the dataset to extract the most-energetic coherent structures in the flow, and modes associated with the main symmetries of the flow were identified. The flapping mode was found to decay faster at the high forcing level, a feature that was linked to the axis-switching behavior. The axis-switching phenomenon causes the flapping mode to become a wagging mode relative to the new axis, lowering the growth rate of the structure. Two different coherent structures were found in the SA (dihedral group $D_2$) symmetry for the axis-switching cases: the wagging mode which was dominant in the pre-axis-switch region and a new flapping mode which is dominant in the post-axis-switch region. The new flapping mode was dominant in the low-frequency region of the full-field SPOD spectrum which was overtaken by the wagging mode at $St\approx 0.2$ for the medium-forcing case and at $St\approx 0.4$ for the high-forcing case. This new flapping mode is likely a flapping mode relative to the axis-switched mean flow, which develops due to the slower growth of the shear layer in the major axis.

Recently, Hausmann and Renner have pointed out that several famous paradoxes relating to black holes have a similar character to various Extended Wigner's Friend paradoxes. In this paper I consider what the connection between these things could teach us about the Wigner's Friend scenarios. I argue that if we take the analogy between these cases seriously, the black hole paradoxes appear to favour a certain class of response to the Wigner's Friend scenario - specifically, those which posit intrinsic relationality, rather than effective and emergent relationality, and also those which posit some kind of retrocausality.

Inferring electric potentials from electron phase space density measurements in the lunar wake is complicated by two challenges: the asymmetry between the sunward and anti-sunward sides of the wake driven by the solar wind strahl, and the presence of ion acoustic shocks in the central wake. We develop the Hamiltonian inversion method, which infers the full spatial electric potential profile by exploiting the quasi-static Vlasov equilibrium condition $f = f(H)$, where $H$ is the electron Hamiltonian. The method addresses both challenges through a domain-decomposition strategy: on the two sides of the wake the potential is inferred independently by minimizing the misfit between the observed phase space density and a self-consistently reconstructed $f_\mathrm{interp}(\tilde{H})$, while in the central wake where flat-top trapped electron distributions are present the potential is inferred directly from the flat-top width. We validate the method against particle-in-cell simulation data at two evolutionary stages of the lunar wake: an early stage where strahl asymmetry is strong but no shocks have formed, and a later stage where ion acoustic shocks and flat-top distributions are present. We then apply the method to two ARTEMIS lunar wake crossings at the same evolutionary stages, inferring normalized potential drops of $e\Delta\varphi/T_e \sim 15$ and $\sim 5$ respectively and capturing shock-associated potential enhancements in the central wake. The method is broadly applicable to plasma environments where electrons are in quasi-static equilibrium with a field-aligned electric potential.

Continuous quantum phase transitions are characterized by an order parameter and correlation functions that are often challenging to access experimentally or in direct numerical simulations. The energy of an added impurity can on the other hand be probed by established polaron spectroscopy, or numerically with Monte Carlo methods. We provide evidence from ground-state quantum Monte Carlo calculations that the energy of a mobile impurity interacting weakly with a surrounding lattice Bose gas provides access to the critical behavior of the Mott insulator-superfluid phase transition. Finite-size scaling of the energy reveals that its value is scale invariant at the critical point of the quantum phase transition, and we extract a scaling exponent that is currently unexplained by theory. For a small lattice we further observe a flattening of the impurity-boson density-density correlations at the critical point, which hints at a divergence of a corresponding length scale in the thermodynamic limit. Our results suggest that impurity spectroscopy represents a useful way to probe the critical properties of quantum phase transitions in general.

An analytical solution is obtained for the problem of the slow movement of a small drop of a fluid in another immiscible fluid in an infinitely large reservoir with the boundary condition of the normal slip and(or) tangential partial slip at the liquid-liquid or gas-liquid interface. That generalizes the conventional Navier and Maxwellian boundary conditions of partial slip. Normal slip is accompanied by the density gradient in the fluid and is applicable only if one of the phases in contact at the interface is a gas. At the first time the generalization of the Hadamard-Rybczynski equation (HRE) is discussed within the formalism of two slip lengths. It is proven that each of the two fluids separated by an interface has its own slip length. The slip lengths of the fluids that contact each other through an interface are related by the ratio of the viscosities of these fluids. New equations describing the terminal velocity of gas bubble rise and aerosol falling have been obtained. The theoretical results are in good agreement with the experiments at moderate Knudsen numbers, Kn < 0.25. It has been shown that the gas density within a rising bubble and around a falling droplet in the air is not uniform. The relative magnitude of the density increment increases with the size of the bubble or aerosol. Presumably, the best applicability of the generalized HRE should be expected for the interface of hydrophobic liquid and hydrophilic one (water - hydrocarbons, water - higher alcohols, in general: aqueous emulsions, water - lipophilic organic liquids and oils, etc.). These are quite important emulsions in practical terms, for example, for the oil industry and medicine. Experimental methods for determining the slip length are considered.

Interference is conventionally attributed to path-accumulated phase differences, with measurement treated as a passive readout. Here we demonstrate that single-particle interference is governed by the relative phase between the prepared quantum state and the detector-defined measurement basis – a joint quantity that is operationally inaccessible in any conventional interferometer. Using coherently seeded entangled nonlinear biphoton sources, we show that independently scanning the pump phase difference, the seed phase difference, or the signal interferometric phase each produces identical sinusoidal fringes ($V\approx0.99$) – a three-scan equivalence impossible in any two-mode interferometer. The fringe visibility is continuously controlled through the idler-state overlap, directly encoding quantum distinguishability without idler detection. The same measurement-defined interference law persists from the single-photon to the high-flux regime. The bright-dark collective-state structure demonstrated here unifies coherent population trapping and electromagnetically induced transparency in atomic $\Lambda$-systems, discrete photonic interference, and single-slit diffraction within a common framework differing only in dark-subspace dimensionality, establishing measurement-defined photonic modes as a fundamental resource for quantum photonics.

Space-borne gravitational-wave telescopes are key to extend the observation band below $10\,\mathrm{Hz}$. The use of inter-satellite optical cavities linked by heterodyne interferometry is a promising approach to reach the sensitivity level of $10^{-22}/\sqrt{\mathrm{Hz}}$ in the decihertz band. While heterodyne interferometry is advantageous for relaxing arm-length control requirements, it introduces susceptibility to clock jitter, which can be a significant noise source. In the back-linked Fabry–Perot (BLFP) interferometer aiming at the decihertz band, the required clock stability exceeds that of current space-qualified oscillators by more than an order of magnitude. We propose a clock noise cancellation scheme that uses two heterodyne signals with positive and negative beat-note frequencies, naturally obtained using both incoming and outgoing laser beams of arm cavities without additional clock modulation schemes. By forming a weighted combination of these signals with time-dependent coefficients, clock jitter contributions are eliminated while preserving gravitational-wave information. We present the theoretical framework, analyze performance under realistic arm-length drifts, and validate the approach through time-domain simulations using parameters from the B-DECIGO concept. Results show that the synthesized signal recovers the original sensitivity and even improves the signal-to-noise ratio by a factor of $\sqrt{2}$ for shot noise.

State-of-the-art photon sources based on spontaneous parametric down-conversion (SPDC) currently rely on artificial structuring of the material nonlinearity to satisfy phase-matching conditions. This technique, known as periodic poling, is available only in a limited number of material platforms and introduces additional fabrication steps and errors, which are detrimental to up-scaling efforts. Here, we present a device architecture that enables SPDC of a wide range of frequencies without the need for periodic poling. We present explicit designs and calculations for 4H Silicon Carbide on-insulator, in which SPDC photon generation is so far unavailable, and thin-film Lithium Niobate on-insulator, a state-of-the-art quantum photonics platform. Our design, based on mode conversion and subsequent modal phase-matched SPDC, facilitates a CMOS compatible $\chi^{(2)}$ platform, and simplifies photon sources by removing the requirement of periodic poling and the associated additional fabrication complexity.

Experimental access to many-body quantum systems is often limited by measurement backaction, and key dynamical properties are typically obtained by perturbing a system and measuring its response. Here we replace this active paradigm with a minimally invasive protocol based on a pair of weak quantum measurements that leverages measurement backaction as a strength. By correlating time-separated measurements with the first detecting fluctuations – of any sort – and the second tracking their time evolution, our method directly measures dynamical correlation functions without external perturbation. We demonstrate this technique in an atomic Bose-Einstein condensate using phase-contrast imaging to obtain the two-time density-density correlation function known as the Van Hove function and, through its Fourier transform, the dynamical structure factor. Due to the role of spatial correlations in scattering, these quantities underpin neutron and X-ray scattering and atomic Bragg spectroscopy. This approach is broadly applicable, providing access to correlation functions between any pair of observables amenable to weak measurement, thereby going beyond the capabilities of conventional strong measurements. We further isolate the role of quantum backaction through Aharonov's post-selection-based quantum weak values.

We investigate the generation of standing waves in the model provided by the inhomogeneous telegraph equation under different forcing conditions. We show that sustained standing waves arise only for a specific forcing that is spatially distributed, continuous, and resonant.

We explore the role of intrinsic structural properties of hypergraphs in governing group-driven social dynamics with social reinforcement. First, we analyze simplicial contagion dynamics on random hypergraphs in which the level of hyperedge nestedness is systematically controlled. By developing the facet-based approximate master equation (FAME) method, we demonstrate that hyperedge nestedness induces a non-monotonic change in the outbreak threshold for simplicial contagion, displaying the lowest threshold at an intermediate level of hyperedge nestedness due to competition between simple and higher-order contagion processes. Next, we formulate the group-driven voter model (GVM) and investigate the consensus time for the GVM on hypergraphs with N nodes. Focusing on a representative case of the GVM, we show that the consensus time scales logarithmically with the system size as A ln N, where the prefactor A displays the fastest consensus formation at an intermediate level of social reinforcement due to competition between group-constraint and nonlinearity factors. Taken together, our results highlight the importance of competing effects arising from higher-order interactions in shaping optimality in group-driven social dynamical processes.

We demonstrate robust programmable state preparation in small Vertical Cavity Surface Emitting Laser (VCSEL) arrays with optical feedback using transient optical injection in the form of Gaussian pulses. In Lang-Kobayashi-type models of delay-coupled two- and three-laser arrays, multistability gives rise to coexisting synchronized and symmetry-broken equilibrium branches. We show that short injection pulses applied to one or more lasers can steer the system from free-running operation to any stable equilibrium branch in the absence of noise by appropriate choice of pulse detuning and amplitude, after which the selected state persists without continued forcing. With correlated noise, injection steering remains effective, but branches with small basins of attraction are effectively destabilized by noise. These results validate pulsed injection as a practical mechanism for attractor selection in multistable VCSEL arrays and point to a feasible route toward experimental realization of programmable collective-state control.

The special unitary group SU(2) plays a fundamental role in the description of symmetries in quantum mechanics, theoretical physics, and spherical signal processing. In this paper, we address the computational challenges of performing spectral analysis on this non-abelian compact Lie group. We present the Fourier Transform (FT) on SU(2) and develop a Fast Fourier Transform (FFT) algorithm inspired by the classical Cooley-Tukey divide-and-conquer scheme. Our approach efficiently discretizes the group using Euler angles, applying a two-dimensional FFT on the angular variables and exploiting the recursive properties of Jacobi polynomials. We provide an analysis of the computational complexity, demonstrating that our FFT-based method significantly outperforms the direct computation of the FT. This algorithm serves as a foundational tool for understanding the implementation of the FFT on SU(2), a key component in numerical simulations and advanced data analysis for high-performance computing applications on curved manifolds and quantum systems.

This manuscript introduces a novel method to assess tissue oxygen concentration via the quantum entanglement (QE) of photons originating from positronium which is produced within the patient's body during positron emission tomography. We also investigate the possibility of assessing hypoxia by simultaneously detecting positronium lifetime and the positronium decay rate ratio. We introduce two distinct quantum sensing approaches. Method 1 utilizes the correlation between oxygen concentration and ortho-positronium (o-Ps) decay rates, relying on the simultaneous measurement of the mean o-Ps lifetime ($\tau_{\mathrm{oPs}}$) and the $3\gamma$-to-$2\gamma$ annihilation rate ratio of o-Ps ($R_{\mathrm{oPs-3\gamma/2\gamma}}$). Method 2 introduces a novel hypothesis: that the degree of QE is sensitive to the relative contribution of annihilation mechanisms (pick-off vs. conversion), which in turn depends on oxygen concentration. We derive a formula for partial pressure of oxygen ($p\mathrm{O}_2$) as a function of $R_{\mathrm{oPs-3\gamma/2\gamma}}$ and $\tau_{\mathrm{oPs}}$ and estimate the measurement accuracy required for these parameters - and for the degree of QE - to sense in-vivo oxygen pressure in the range between hypoxic and physoxic conditions. Theoretical models and quantitative estimates for $R_{\mathrm{oPs-3\gamma/2\gamma}}$, $\tau_{\mathrm{oPs}}$ and for the degree of QE ($C_{\mathrm{QE}}$ ) as a function of $p\mathrm{O}_2$ are provided for water, isopropanol, cyclohexane, isooctane, and adipose tissue. In particular, applying the formulas derived under the working hypothesis that in pick-off process the photons are not entangled, we estimated that for $p\mathrm{O}_2 = 0$, the degree of quantum entanglement $C_{\mathrm{QE}}$ is equal to 0.890 for adipose, 0.886 for isopropanol, 0.867 for water, 0.818 for cyclohexane, and 0.784 for isooctane.

We develop a framework for superposition in relativistic gravity within Extended Relativity (ER), a Lorentz-covariant theory formulated in flat spacetime. In this approach, gravitational fields are described by deviations from the Minkowski metric associated with individual sources, and multi-source configurations are constructed through a superposition principle linear in the source parameters. The resulting metric preserves Lorentz covariance and reproduces the standard classical tests of General Relativity in the appropriate limits. We derive the explicit form of the superposed field for multiple moving sources and analyze its properties in both near and far zones. The formalism provides a consistent and physically transparent description of interacting gravitational sources and forms the basis for applications to relativistic dynamics and gravitational radiation.

We introduce a relativistic action that provides a unified and physically meaningful description of particle dynamics in external fields. The proposed action is constructed to be Lorentz covariant and reduces to the standard classical action in the appropriate limit. It incorporates gravitational and electromagnetic interactions within a single framework and leads to equations of motion consistent with known physical laws. The formulation offers a new perspective on relativistic dynamics and suggests a pathway toward unification of fundamental interactions.

The footprints of residential segregation have long been documented, yet the role of urban form as both medium and manifestation of segregation remains under-specified. We investigate whether the configuration of the built fabric may encode residential segregation in its spatial structure, hypothesising that built-form entropy (BFE) regimes are associated with the spatial distribution of income groups and their local clustering in non-linear ways. We examine this by quantifying BFE through a Shannon-based measure computed from building footprints, characterising income-based distributions using the Gini index and Moran's I, and placing both on a common spatial footing through a regular tessellation. Applying this framework to Sao Paulo, Latin America's largest city, we find non-linear relationships between BFE, income, and segregation: income levels and residential clustering increase toward both extremes of the entropy spectrum, with a stronger rise at the high-entropy end. This asymmetry suggests that high-entropy urban forms are associated with distinct spatial processes of segregation, including elite enclaving and incremental development in lower-income settlements, while low-entropy forms reflect more selective occupation shaped by planning and market filtering. Overall, the findings suggest that built form is more than a neutral backdrop, functioning as both affordance and signal of segregation.

Air lubrication regimes were studied using simultaneous drag force measurements and multi-plane imaging to characterize the regimes and identify the governing mechanisms of drag reduction. A bubbly, transitional, and air layer regime are identified over a large range of freestream velocities ($U_{\infty}$), air flow rates ($Q_{air}$), and Froude-depth numbers ($Fr_d$). For the lowest $U_{\infty}$, drag reduction lags significantly behind the non-wetted area coverage at all cases and no simple correlation exists. Within the bubbly regime, a drag increase is found for low $U_{\infty}$ with large, slow-moving bubbles forming a single layer over the plate height. For higher velocities, bubbles become smaller and disperse vertically, while the drag starts decreasing. For higher $Q_{air}$, irrespective of $U_{\infty}$, air patches start to form (transitional regime) and drag monotonically decreases, with the onset of the air layer regime at 60% drag reduction. A new scaling of the associated critical $Q_{air}$ is proposed, combining the air exit velocity, the liquid velocity close to the air layer and $Fr_d$. For a further increase of $Q_{air}$ and low $U_{\infty}$, a thicker and smoother air layer is formed with even lower drag; for higher $U_{\infty}$, marginal differences are observed. The air layer morphology is significantly altered however, depending on $Fr_d$: for $Fr_d>0.7$, it is unbounded, extending beyond the current test section length, and for subcritical conditions (deep water regime, $Fr_d<0.61$) a closure is formed and the air layer transitions to a cavity of a specific length.

Flat optics is now judged by more than a strong simulation or a single laboratory demonstration. To reach release, a device must survive a chain of handoffs: requirements, model selection, verification, layout release, fabrication, calibrated validation, packaging, and qualification. Diffractive optics brings mature routes for beam shaping and compact wavefront control, while meta-optics expands the design space through wavelength-scale control of phase, amplitude, and polarization. In both families, projects often slow down not because the optical function is impossible, but because the evidence required at each handoff is incomplete, poorly documented, or mismatched to the next decision. This tutorial organizes that problem into a stage-gate workflow, a set of compact technical checks, worked device examples, an artifact-based skills map, and an educational translation into workforce models, course deliverables, and assessment logic. The emphasis is practical: reduce avoidable redesign loops, make performance claims auditable, and clarify what students, instructors, and employers should be able to produce, review, and approve. The broader aim is to make the path from flat-optics concept to qualified hardware easier to understand, easier to teach, and easier to repeat.