diffusion models

Decision-Making in Augmented Reality: A Drift Diffusion Analysis of the Effects of Visualization and Hardware

Augmented Reality (AR) is increasingly applied in real-world contexts that requires users to interpret visual information and make rapid decisions. However, little is known about how different AR visualization formats and hardware configurations influence underlying perceptual decision processes. This study addresses how AR-specific technical characteristics affect decision processes in a random-dot motion discrimination task, in which participants discriminate the coherent motion direction of a proportion of dots embedded in random noise, under multiple AR conditions and a real-world baseline condition. Behavioral data were analyzed using the drift-diffusion model to estimate latent decision parameters such as evidence accumulation and decision caution. The results show significant differences between AR configurations, indicating that visualization design and hardware characteristics likely affect the efficiency of evidence processing.

Electromagnetism, Photon Dynamics, Gravitational Tensor Mapping, Quantum Dynamics, and Cosmological Expansion in the LOEANE Informational Framework

This paper presents a complete derivation of fundamental physical phenomena from a discrete, self-updating informational substrate known as the Linearity of Existence and Non-Existence (LOEANE) framework. By replacing background continuous spacetime and externally imposed gauge groups with a relational architecture, the model demonstrates how standard macroscopic limits emerge naturally and cleanly. The core mathematics are driven by two primitive substrate fields: the scalar collapse-depth field \(\delta(x)\) and the internal periodic refresh-cycle phase \(\theta(x)\), which is governed by a fundamental four-stroke operator identity (\(F^4 = I\)). Key derivations detailed within this work include: Emergent Electrodynamics: Constructing the \(U(1)\) gauge group structure and Maxwellian field tensors directly from phase gradients coupled to collapse-depth variations. Photon Dynamics: Modeling a massless photon as a self-equilibrating, idempotent null cycle (\(P = ENEN\)) pinned to critical collapse-depth boundaries. Gravitational Tensor Mapping: Mapping second-order collapse-depth Hessians directly to the Einstein curvature tensor (\(G_{\mu \nu }\)) and deriving the emergent gravitational constant (\(G\)). Quantum Sector: Demonstrating how complexified collapse-depth oscillations simulate Schrödinger-like diffusion and relativistic Klein–Gordon wave dynamics. Expansion Cosmology: Deriving cosmological scale acceleration and vacuum energy limits from large-scale variations in the substrate network, offering an alternative origin for dark energy. Ultimately, these subsystems are tied together into a single total variational action, yielding a comprehensive set of unified LOEANE field equations that remain free from traditional ultraviolet divergences, singularities, and ontological incompatibilities.

Euclidean Self-Return: Complex Metric Rotation, Vacuum Fluctuations, Quantum Diffusion, and Cosmogenesis

We develop Euclidean self-return as a geometric and deterministic mechanism for vacuum fluctuations, quantum diffusion, and rare cosmogenic formation. The construction begins with a complex signature angle through which a Lorentzian metric rotates around the degeneracy of the corresponding real metric path, reaches the exact Euclidean section, and returns to a Lorentzian section without losing invertibility. A positive Hermitian metric-speed norm defines Euclidean inertia, while conserved or retardedly stabilized phase momentum produces persistent oriented winding. Within the declared one-normal metric sector, a common Euclidean calibration and common constitutive law imply pointwise universality of the rotation energy, asymptotic winding rate, and local fluctuation spectrum, without requiring identical local phases or histories. Projection of the deterministic parent dynamics yields resolved drift, memory, and an orthogonal history force. Contact-Anosov mixing, a quadratic thermodynamic scaling, and a Ford–Kac–Mazur response model produce a finite effective noise kernel and the inverse-mass diffusion law \[ D_{\rm q}(m)=\frac{\mathcal A_*}{2m}. \] After the empirical identification \(\mathcal A_*=\hbar\), time-symmetric diffusion recovers the Bohm quantum potential and the uncertainty scale \(\Delta x\,\Delta p_{\rm fl}\geq\hbar/2\). The rotating projection has zero phase mean but nonzero quadratic mean; deterministic dephasing converts this persistent oscillatory activity into a strictly positive Green–Kubo coefficient. The same framework supports three compatible cosmogonic regimes: stationary rare nucleation, formation during nonstationary high-energy parent relaxation, and a conserved phase-domain branch. In the third branch, ordinary integrable mixing is first shown to erase macroscopic phase averages. A nonlinear conserved phase field then supplies metastable zero bias, two oppositely oriented locked states, exact global signed-charge conservation, and rare domain nucleation. Spatially heterogeneous retention barriers create hotspots in which multiple same-sign remnants have enhanced conditional probability. A positive pair-capture kernel and an open Skyrme locking basin give a conditional positive probability for universe-forming collisions, while opposite topological charge remains in distant domains or the diffuse background. Cosmological expansion is interpreted as dilution of matter on a fixed mother space rather than expansion of the mother metric. Collision recoil and rotation-generated topological stress yield a positive material virial, whereas dense matter screens the transmission of this stress into relative material motion. An explicit density-dressed propagator gives \(S(\rho)=(1+\alpha\rho)^{-2}\), so dilution progressively unmasks the washing channel. Finally, a linear response identity transfers the inhomogeneous formation-stress spectrum into a nonnegative late-time density spectrum, providing a mathematical route from early rotational stress to voids and large-scale material structure. Astronomical identification remains an empirical test of the completed model. ### Keywords **Euclidean self-return; complex metric rotation; Euclidean inertia; vacuum fluctuations; deterministic homogenization; quantum diffusion; topological stress; phase-domain nucleation; matter screening; cosmogenesis; cosmic voids; Skyrme topology**

Model, decoder, and feature data for Cross-cue reconstruction of perceived 3D object structure from human visual cortex

OverviewThis item contains model-related data used in the following paper:"Cross-cue reconstruction of perceived 3D object structure from human visual cortex." In preparation.The data include trained point-cloud autoencoder parameters, DNN latent features extracted from model-input point-cloud representations, and trained fMRI-to-feature decoders used in the reconstruction pipeline. AtlasNet is the primary autoencoder used for the main analyses, and a diffusion-based point-cloud autoencoder is included as a complementary model used for robustness checks.Source materials noteThis item distributes model parameters, DNN feature arrays, and fMRI-to-feature decoder parameters.Some files in this item were trained from, extracted from, or otherwise derived from point-cloud representations associated with third-party 3D object resources, including ShapeNet and 3D Warehouse resources used in the study. Accordingly, reuse of these files in relation to the underlying 3D object resources may be subject to the ShapeNet Terms of Use, the 3D Warehouse Terms of Use, and any applicable rights retained by the original model developers or other rights holders. Users are responsible for ensuring that their use of these files complies with all applicable terms and rights.The item-level license displayed by Figshare does not supersede or replace the terms and restrictions associated with the underlying third-party 3D model resources. It should not be interpreted as granting unrestricted reuse of these files for purposes that would require rights to the underlying third-party 3D object resources.Before using, redistributing, modifying, extracting, or otherwise reusing these files or their contents in relation to the underlying 3D object resources, please consult the applicable terms of use, including those of ShapeNet and 3D Warehouse.ContentsThe archives included in this item are as follows:Pretrained DNN model weightsdnn-weights-atlasnet.zip: trained AtlasNet autoencoder parameters.dnn-weights-diffusion-point-cloud-autoencoder.zip: trained diffusion-based point-cloud autoencoder parameters.True DNN featuresfeature-train-3d-natural-objects.zip: DNN latent features for the natural-object training set.feature-test-3d-natural-objects.zip: DNN latent features for the natural-object test set.feature-test-3d-artificial-objects.zip: DNN latent features for the artificial-object test set.Each archive includes features from both AtlasNet and the diffusion-based point-cloud autoencoder.Trained feature decodersdecoder-train-3d-natural-objects.zip: trained fMRI-to-feature decoders for the five subjects and visual ROIs.These decoders were trained on fMRI responses to 2D rendered images of the training natural objects and are used to predict DNN latent features from fMRI responses.Relationship to other items in the collectionThe model-input point-cloud representations used to extract the true DNN features are provided in the natural-object and artificial-object stimulus data items. The corresponding fMRI responses are provided in the fMRI response data item. The trained feature decoders in this item are used with those fMRI responses to generate decoded DNN features, which are then passed to the point-cloud autoencoder generators for 3D reconstruction. Reconstruction videos are provided in the natural-object and artificial-object reconstruction video items.CitationPlease cite the following when using this item:Figshare Collection: 10.6084/m9.figshare.c.8508462Associated paper: "Cross-cue reconstruction of perceived 3D object structure from human visual cortex." In preparation.ShapeNet: Chang, A. X., Funkhouser, T., Guibas, L., Hanrahan, P., Huang, Q., Li, Z., Savarese, S., Savva, M., Song, S., Su, H., Xiao, J., Yi, L., & Yu, F. (2015). ShapeNet: An Information-Rich 3D Model Repository. arXiv. https://doi.org/10.48550/ARXIV.1512.030123D Warehouse: https://3dwarehouse.sketchup.com/AtlasNet: Groueix, T., Fisher, M., Kim, V. G., Russell, B. C., & Aubry, M. (2018). AtlasNet: A Papier-Mache Approach to Learning 3D Surface Generation. CVPR.Diffusion probabilistic model for 3D point clouds: Luo, S., & Hu, W. (2021). Diffusion Probabilistic Models for 3D Point Cloud Generation. CVPR.

What drives innovation and imitation in decentralized energy technologies? Evidence from distributed solar PV in Brazil

Hybrid Integral Transform Solution of a Nonlinear Core-Flooding Model with Capillary Pressure and End Effects

Abstract Oil-water displacement in coreflooding experiments is governed by a nonlinear convection-diffusion equation derived from the extended Buckley-Leverett formulation that accounts for capillary pressure effects. When realistic constitutive relations are combined with nonlinear capillary end-effect boundary conditions, such as those proposed by Chang and Yortsos, the problem becomes significantly more challenging due to the strong coupling between saturation and capillary pressure gradients at the inlet and outlet boundaries. In this work, a hybrid numerical-analytical solution based on the Generalized Integral Transform Technique (GITT) is developed for the one-dimensional immiscible displacement problem, incorporating the nonlinear Chang-Yortsos boundary conditions into the mathematical formulation. The governing partial differential equation is integral transformed with just a simple filter to make the boundary conditions homogeneous and reduced to a coupled system of nonlinear ordinary differential equations in modal space via eigenfunction expansion. Nonlinear diffusion and boundary flux contributions are preserved explicitly through the application of Green´s second identity, thereby maintaining the physical structure of capillary end effects. Validation against a literature benchmark core-flood case demonstrates excellent agreement and rapid spectral convergence. The resulting reduced-order framework provides an accurate and computationally efficient tool for forward simulation of unsteady-state coreflooding experiments.

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion

Abstract The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

The Quantized Cage: Unified Physics from One Algebraic Identity

Summary The Quantized Cage is a single self-contained monograph of 3558 pages that derives the Standard Model of particle physics, general relativity in Christoffel form, the principal cosmological parameters and a unified account of catalogued physical mysteries from one algebraic identity, $[\widehat{\Xi},\widehat{H}]=\widehat{I}$, in which the sub-diagonal operator $\widehat{H}$ annihilates modes and the super-diagonal operator $\widehat{\Xi}$ creates them on a semi-infinite sequence space. The framework, called $\Omega$, treats nature as a discrete countable lattice whose universal interaction metric is the Gram matrix of the weighted basis $\phi_k(x)=(k{+}1)x^k$ on the unit interval, $\mathcal{W}_{m,n}=(m{+}1)(n{+}1)/(m{+}n{+}1)$. Continuous spacetime, the Klein–Gordon equation, the Einstein field equations and ordinary quantum mechanics arise as the image of this discrete structure under explicit Hermite–Gaussian and Bargmann–Fock isomorphisms, both of which preserve the operator roles and realize the canonical ladder relation through an anti-homomorphism. Throughout, the framework works in row-vector convention and replaces postulates with theorems whose proofs are independently checkable, where possible through captioned Python listings that are extracted from the manuscript and run verbatim. Main findings Single-identity derivation. The Standard Model gauge content, the three generations, the fermion and gauge boson mass hierarchy and the Einstein–Hilbert action are derived from the commutator alone, with no adjustable parameters. The Prime Mass Equation. $M(p)=M_0\sqrt{p^2-p^{-2}}$, with the single derived scale $M_0=m_e\alpha^{-1}\approx70$ MeV, sends every prime to a hadron mass. From the pion up to the $\Upsilon$ the formula reproduces the observed spectrum to sub-percent accuracy without fitting. Written over a common denominator the equation is also an integer statement: the numerator $p^4-1$ is divisible by $240$ for every prime $p>5$, sharply, and the only exceptions are $p=2,3,5$, which are precisely the primes dividing $240$. The divisibility is a fact about the modulus rather than about primes, holding for every integer coprime to $30$, composites included, and it cancels from every ratio the theory can measure. A positivity theorem, and the gap it does not close. The framework supplies a strict-positivity statement about the stiffness operator on a gauge-invariant subspace, reached by four arguments that agree on the value $M_0\sqrt{2^2-2^{-2}}$, which is the Prime Mass Equation at its smallest prime and lands within half a percent of the pion. That value is not the Yang–Mills mass gap. Pure Yang–Mills contains no pions; the pion requires quarks, while the Yang–Mills gap is the lightest glueball, an order of magnitude heavier. Nor are the four arguments independent: they reach one number, and in each the non-Abelian input is a Lie-algebra relation inserted as a hypothesis, with no action, no functional integral and no Hamiltonian whose spectrum is at issue. Reflection positivity is likewise a Gramian statement: Osterwalder–Schrader positivity is a condition on Schwinger functions, and this work constructs none, so the axiom is not established. The Schwartz isomorphism $\Phi:\ell^2(\mathbb{N}^3)\to L^2(\mathbb{R}^3)$ *is* constructed and unitary; what its codomain lacks is a time argument, so the missing step is second quantization rather than the state map. Both stand as open problems. Geometry from algebra. Under the Hermite–Gaussian isomorphism the stiffness operator becomes the Klein–Gordon operator with Lorentzian signature, forcing four dimensions, the Minkowski metric, the Einstein field equations and the geodesic equation as algebraic identities rather than variational ansätze. A cage-regularized Schwarzschild metric with a nonsingular de Sitter core reproduces Mercury's perihelion advance, and a single closure-defect theorem shows that one piece of rotation-number arithmetic governs relativistic precession, orbital resonance, the Pythagorean comma and the Mandelbrot internal-bulb angle. Curvature, and the limit of the algebraic route. The antisymmetrized Gramian square $R_{mnpq}=\mathcal{W}_{mp}\mathcal{W}_{nq}-\mathcal{W}_{mq}\mathcal{W}_{np}$ is proved to satisfy every algebraic Riemann symmetry, including the first Bianchi identity, from symmetry of $\mathcal{W}$ alone. Its reach is bounded just as sharply: the square has identically vanishing Weyl tensor and sectional curvature exactly $1$ on every plane, so it realizes the conformally flat class and nothing outside it, six components of the $n^2(n^2-1)/12$ that a general curvature carries. No pure-Weyl observable, which includes tidal stretching in vacuum, gravitational radiation and the Schwarzschild exterior, may be computed from the square. This is a rule about where one tool applies and not a claim about the theory, because the framework reaches curvature by a second and independent route, the commutator $R_{ij}=[\nabla_i,\nabla_j]$, whose Weyl sector nothing here constrains. The bound also supplies a usable check: on the conformally flat sector, which contains every Friedmann geometry, the square is exact rather than approximate, so any discrepancy there is an arithmetic error and cannot be charged to a finite cutoff. Mixing matrices and cosmology. The PMNS and CKM matrices are obtained as truncated Maclaurin expansions across structurally asymmetric modes, reproducing all three lepton mixing angles and the Wolfenstein hierarchy to sub-percent accuracy. The boundary projection yields the Casimir energy, the GMOR pion relation, the chiral anomaly and the cosmological constant, addressing the vacuum catastrophe geometrically. A consolidated comparison with string and M-theory records where the frameworks part company: four spacetime dimensions are forced rather than compactified, the Gramian is unique rather than one point in a landscape, positivity on the critical line excludes tachyons and ghosts, and fermions arise from a Möbius–Jordan–Wigner phase string rather than from supersymmetric partners. Each point of departure carries its own falsifiable signature. Atomic structure as torsion defects. Helium, including the singlet and triplet series, exchange splittings and autoionizing resonances, follows from diagonalizing a finite matrix whose every entry traces back to the two ladder operators and the Gramian, with the ground state converging to the Hylleraas value with no variational parameters. An $N$-electron extension delivers correlation energies from lithium through uranium. A universal differential-equation solver. Every linear differential equation is the left kernel of a polynomial in the ladder operators. Constant-coefficient equations factor into characteristic roots, the special-function equations carry an eigenvalue quantization that is the origin of discrete spectra and that runs on a single dial, one word whose middle coefficient selects Chebyshev, Legendre and the whole ultraspherical family and whose value is the spatial dimension, the construction lifts to partial differential equations through Kronecker directional derivatives, and nonlinearity is the Gramian product through the interaction operator, so that Navier–Stokes becomes a single algebraic condition on one descriptor. A deterministic non-Gaussian estimator. The same algebra yields the $\Omega$-Kalman filter: prediction is translation with diffusion as process noise, and the Bayesian update is the interaction product renormalized by the charge functional. It fuses arbitrary non-Gaussian and multimodal distributions in closed form, recovers the classical Kalman gain in the Gaussian limit, extends to vector states through the Kronecker descriptor, returns the model evidence as its normalizer, and forms a commutative monoid on the probability simplex. Distribution theory as an exact matrix calculus. The Dirac delta at the wall is the flat descriptor, one shift-subtract flattens it to the constant, and the delta at the origin is a different object wearing the same symbol, a column where the others are rows; what identifies either is the moment ladder rather than the coefficients. Fractional and integer powers of the delta acquire a clean Gelfand-triple grading, making point sources, their roots and their products tractable as explicit matrices. What this establishes is that products of finite-depth operators are always defined and can stand where distributional products cannot; it does not construct the distributional square of the delta, and no map back into distributions is claimed. Loop integrals, on the reader's own terms. A Feynman-parameter integral is evaluated inside the algebra as the top row sum of an inverse portrait, $\int_0^1\mathcal{F}^{-\lambda}=\sum_k[\mathcal{F}(\Xi)^{-\lambda}]_{0,k}$, exact in rational arithmetic at every truncation, with arbitrary complex $\lambda$ admitted because the multiplier is nilpotent under truncation and the binomial series terminates. Infrared divergence is the failure of the portrait's scalar part to be invertible. Integration by parts, the engine of every multi-loop reduction, is the framework's single commutator read through the boundary projection. The route converges exactly when the Symanzik polynomial has no zero in the closed unit disc, a condition strictly stronger than positivity on the interval. This is the framework's falsifiable interface with an established computational technology: the answers are already known to many digits. The reduction is an isomorphism, and the determinant is the Källén function. For the massive one-loop bubble family the three master integrals are proved to be a basis of the integration-by-parts quotient, and the change of basis to the twisted de Rham cohomology $H^1(X,\nabla)$ has determinant $\det C=\lambda(r_--r_+)/s=\pm\lambda\sqrt{\kappa}/(p^2 s)$, where $\kappa=(p^2-(m_1+m_2)^2)(p^2-(m_1-m_2)^2)$ is the Källén function and $s=\nu+\mu-1-2\lambda$.

Understanding online conversations through fractal dimension: a case study linking semantic and structural analysis of reddit posts on AI

Abstract Fractal dimension can measure the complexity of a branching structure. Botanical trees for example have more sparse branching in poor environments, and more complex branching in good environments. We hypothesize that the branching structures of online conversations can also use fractal dimension to measure sparse versus complex branching. To test this we measured the fractal dimension of Reddit posts about AI. Posts about purely technical content (e.g. distinctions between different algorithms) had lower fractal dimension than those about social controversies (job loss, racial bias, etc.), suggesting that the controversial conversations had more complex branching structures. A sentiment analysis revealed that social posts had more negative sentiment, consistent with characterizing them as more controversial. We also found that even within each category (social vs technical), higher fractal dimension was associated with more negative sentiment.The fractal model offers further insights when considering its analogous biological models. While it is common to use the metaphor of “conversation tree” we find that fractal metrics reveal a structure closer to Diffusion Limited Growth, found in bacteria colonies, fungi, and rhizomatic plant spread, where “sub-trees” can vary in fractal dimension from the parent. The fractal dimension of social controversy subtrees have a stronger coupling to that of the parent than do the technical subtrees, which has potential implications for the semantic process differences. Overall the application of fractal models to online conversations shows that it allows correlations between structural and semantic aspects, and offers a new way to illuminate the underlying characteristics.

Simulating open-channel flows and advective diffusion phenomena through SPH model

The present thesis treats Computational Fluid Dynamics based on particle\nmethods. The fully Lagrangian approach Smoothed Particle Hydrodynamics\n(SPH) is developed for two-phase flows. The model is extended to\nresearch fields of environmental hydraulic and open-channel flows. SPH is\na Lagrangian, meshless and particle model. It was born about 30 years ago\nto solve gas-dynamics problems in open space (Lucy, 1977 [1]; Gingold and\nMonaghan, 1977 [2]). For many years, the SPH method has been applied\nto problems in the astrophysical field, as documented in the review paper\nby Benz (1990) [3]. During the last decades, the SPH method has been increasingly\nmodified and extended to provide approximations to the partial\ndifference equations (PDEs) in a wide range of scientific and engineering\napplications particularly in the hydrodynamic field. Monaghan (1994) [4]\nwas the first to apply the SPH scheme to fluid-dynamics problems. After\nthat, the SPH approach has been successfully extended to multiphase flows\n(see e.g. Grenier et al., 2009 [5]) and fluid-structure interaction problems\n(see e.g. Colagrossi and Landrini, 2003 [6]). Following the SPH method,\nthe motion of a continuum medium is described using an interpolation\ntechnique which allows to approximate functions and differential operators\non an irregular distribution of points. In the standard SPH, where\na weakly compressible fluid is considered, the discretized continuity and\nmomentum equations are linked via a state equation.\nFirstly, an algorithm is developed to treat upstream/downstream boundary\nconditions for 2D open-channel flows in SPH context. For this purpose\ntwo suitable sets of particles (in/out-flow particles) are defined allowing\nthe enforcement of different upstream and downstream flow conditions.\nIn particular this permits to avoid generation of unphysical pressure\nshock waves due to a direct creation/deletion of fluid particles. As first\ntest case, the proposed algorithm is validated for a viscous laminar flow\nin open channel considering Reynolds numbers of order O(102). The obtained\nresults are compared with analytical ones in order to heuristically\ncheck the convergence of the numerical scheme. The simulations are performed\nfor a time interval long enough to reach steady state conditions.\nThe suitability of the in/out-flow algorithm has been highlighted comparing\nthe velocity field with the analytical Poiseuille solution. The second\ntest case deals with a hydraulic jump for which different upstream and\ndownstream conditions are needed. Several types of jumps, obtained varying\nthe flow Froude number, are investigated with particular reference\nto the location of the jump and the velocity field. Comparisons between\nthe numerical results and the classical theory of the hydraulic jump are\nprovided, showing good agreements.\nIn the second part of the thesis, the SPH model is applied to evaluate\nthe concentration field of pollutants in water. A Lagrangian formalism is\nformulated to solve the fickian diffusion equation considering pollutants\nwith the same density as the water. Furthermore, a SPH form of the advective\ndiffusion equation is also developed for pollutant-water, taking into\naccount the effects of molecular diffusion and natural advection induced\nvii\nby differences between the fluid densities. These equations are coupled\nwith the fluid mechanics equations. Attention is paid to the numerical\naspects involved in the solution procedure and to the optimization of the\nmodel parameters. Environmental engineering problems concerning diffusion\nand natural advection phenomena occur in the presence of a pollutant\nin still water. Numerical tests referring to a strip and a bubble of contaminant\nin a water tank with different initial concentration laws have been\ncarried out. The results obtained by the proposed SPH models are compared\nwith other available SPH formulations, showing an overall better\nagreement with standard analytical solutions in terms of spatial evolution\nof the concentration values. Capabilities and limits of the proposed SPH\nmodels to simulate advective diffusion phenomena for a wide range of\ndensity ratios are discussed.\nAs future perspectives, coupling the two aspects considered in this thesis,\nit will be developed a numerical code for the simulation of the concentration\nfield along a water stream by an intake of pollutants.\nviii

(Short Paper16) Super-Intercellular Synchronization and High Light Adaptation in 4-Cell Green Alga Tetrabaena: A Spatially Extended Quantum Computing Model via a 4-QPU Array

Tetrabaena socialis, a four-celled colonial green alga arranged in a planar square, exhibits hydrodynamically synchronized swimming despite each cell possessing autonomous flagella. Furthermore, unlike related species that execute phototactic avoidance migrations under intense light stress, T. socialis adopts a distinct survival strategy by remaining in place and synchronously activating photoprotective and antioxidant defense metabolic pathways across all cells. In this paper, we formulate the four-cell architecture of Tetrabaena as the minimal multi-qubit quantum array composed of four spatially coupled local QPUs. Mediated by 31 P nuclear spin memories in Posner molecules and quantum correlations across cellular junctions, we elucidate the physical mechanism by which the four cells function as a “single quantum system,” executing non-local in-phase synchronization and metabolic optimization independent of classical molecular diffusion or membrane potential propagation delays.

(Short Paper16) Super-Intercellular Synchronization and High Light Adaptation in 4-Cell Green Alga Tetrabaena: A Spatially Extended Quantum Computing Model via a 4-QPU Array

Tetrabaena socialis, a four-celled colonial green alga arranged in a planar square, exhibits hydrodynamically synchronized swimming despite each cell possessing autonomous flagella. Furthermore, unlike related species that execute phototactic avoidance migrations under intense light stress, T. socialis adopts a distinct survival strategy by remaining in place and synchronously activating photoprotective and antioxidant defense metabolic pathways across all cells. In this paper, we formulate the four-cell architecture of Tetrabaena as the minimal multi-qubit quantum array composed of four spatially coupled local QPUs. Mediated by 31 P nuclear spin memories in Posner molecules and quantum correlations across cellular junctions, we elucidate the physical mechanism by which the four cells function as a “single quantum system,” executing non-local in-phase synchronization and metabolic optimization independent of classical molecular diffusion or membrane potential propagation delays.