Papers

Mars lacks a global intrinsic dipole magnetic field, but its interaction with the solar wind generates a global induced magnetosphere. Until now, most studies have relied on single-spacecraft measurements, which could not simultaneously capture upstream solar wind conditions and the induced magnetic fields, thereby limiting our understanding of the system. Here, we statistically re-examine the properties of Mars' induced magnetic field by incorporating, for the first time, real-time upstream solar wind conditions from the coordinated MAVEN and Tianwen-1 observations. Our results are show that both solar wind dynamic pressure and the interplanetary magnetic field (IMF) magnitude enhance the strength of the induced magnetic field, but they exert opposite effects on the compression ratio: higher dynamic pressure strengthens compression, while stronger IMF weakens it. The induced field is stronger under quasi-perpendicular IMF conditions compared with quasi-parallel IMF, reflecting a stronger mass-loading effect. We further investigate the clock angle departures of the induced fields. They remain relatively small in the magnetosheath near the bow shock, increase gradually toward the induced magnetosphere, and become significantly larger within the induced magnetosphere. In addition, clock angle departures are strongly enhanced under quasi-parallel IMF conditions. Their dependence on upstream drivers further shows that, within the magnetosheath, clock angle departures are minimized under low dynamic pressure, high IMF magnitude, and low Alfven Mach number conditions. These results may enhance our understanding of solar wind interaction with Mars, and highlight the critical role of multi-point observations.

This work proposes a data-driven explicit algebraic stress-based detached-eddy simulation (DES) method. Despite the widespread use of data-driven methods in model development for both Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES), their applications to DES remain limited. The challenge mainly lies in the absence of modelled stress data, the requirement for proper length scales in RANS and LES branches, and the maintenance of a reasonable switching behaviour. The data-driven DES method is constructed based on the algebraic stress equation. The control of RANS/LES switching is achieved through the eddy viscosity in the linear part of the modelled stress, under the $\ell^2-\omega$ DES framework. Three model coefficients associated with the pressure-strain terms and the LES length scale are represented by a neural network as functions of scalar invariants of velocity gradient. The neural network is trained using velocity data with the ensemble Kalman method, thereby circumventing the requirement for modelled stress data. Moreover, the baseline coefficient values are incorporated as additional reference data to ensure reasonable switching behaviour. The proposed approach is evaluated on two challenging turbulent flows, i.e., the secondary flow in a square duct and the separated flow over a bump. The trained model achieves significant improvements in predicting mean flow statistics compared to the baseline model. This is attributed to improved predictions of the modelled stress. The trained model also exhibits reasonable switching behaviour, enlarging the LES region to resolve more turbulent structures. Furthermore, the model shows satisfactory generalization capabilities for both cases in similar flow configurations.

Locally covariant algebraic quantum field theory (LCQFT) satisfies Einstein causality through microcausality and operational no-signalling, yet Bell-type correlations persist in entangled field states across spacelike regions. We demonstrate that this apparent tension reflects a fundamental covariance obstruction: no assignment of classical past variables can simultaneously be covariant under spacetime embeddings, screen off quantum correlations, and reproduce AQFT statistics. This obstruction is distinct from dynamical nonlocality or signalling violations. We formalize this as a no-go theorem in the category-theoretic framework of LCQFT, showing that Bell's notion of local causality – requiring factorization conditioned on a common past – is structurally incompatible with diffeomorphism covariance. The failure of Bell locality thus reflects not a breakdown of relativistic causality but the impossibility of embedding quantum correlations into a classical causal framework without introducing preferred foliations or non-covariant beables. This clarifies the conceptual status of nonlocality in relativistic quantum theory.

The 3$\omega$ method is widely used to measure the thermal conductivity and the specific heat of wires and thin films. These measurements are typically performed under high vacuum conditions, which justify the use of heat transfer models that exclude thermal losses to a surrounding fluid. Here, we study the effect of thermal conduction from a joule-heated wire to a surrounding gas on pressure-dependent 3$\omega$ measurements, and show how a one-dimensional (1D) heat-transfer model may be used to reliably determine the wire's thermal properties. We derive a full analytical solution of the 1D heat-transfer equation with finite heat-transfer coefficient $h$ and validate it experimentally using a 16-$\mu$m diameter platinum wire in air across pressures from $10^{-5}$ to $10^3$ mbar. We introduce a model for heat transfer between the wire and the surrounding gas based on kinetic gas theory that accurately describes the data across continuum to free-molecular gas regimes, with $h$ varying from near-zero in high vacuum to approximately 700 W/(m$^2\cdot$K) at atmospheric pressure. We show that use of a validated $h(p)$ model allows extracting both thermal conductivity $\kappa$ and volumetric heat capacity $\rho c_p$, whereas volumetric heat capacity can be extracted even without invoking a specific $h(p)$ model. Our approach facilitates the characterization of fine wires with moderate to low thermal conductivities and may enable accurate thermal measurements of suspended wires with diameters on the nanometer scale.

The habitat of microorganisms is typically complex and viscoelastic. A natural question arises: Do polymers in a suspension of active swimmers enhance chaotic motion or promote orientational order? We address this issue by performing lattice Boltzmann simulations of squirmer suspensions in polymer solutions. At intermediate swimmer volume fractions, comparing to the Newtonian counterpart, polymers enhance polarization by up to a factor of 26 for neutral squirmers and 5 for pullers, thereby notably increasing orientational order. This effect arises from hydrodynamic feedback mechanism: squirmers stretch and align polymers, which in turn reinforce swimmer orientation and enhance polarization via hydrodynamic and steric interactions. The mechanism is validated by a positive correlation between polarization and a defined polymer-swimmer alignment parameter. Our findings establish a framework for understanding collective motion in complex fluids and suggest strategies for controlling active systems via polymer-mediated interactions.

The Ekman boundary layer is a fundamental concept in fluid dynamics that describes fluid motion near boundaries affected by Earth's rotation. Most theoretical studies have simplified their analysis by assuming a planar boundary surface, resulting in limited exploration of structures with general smooth boundary conditions. Investigating the impact of boundary geometry in the Ekman boundary layer is essential, as initially suggested by J.L. Lions and further examined in Masmoudi's study [Comm. Pure Appl. Math. 53 (2000), 432-483] under small amplitude periodic boundary conditions. This paper clarifies how boundary geometry influences flow fields and characterizes its effects on near-boundary layer flow. We construct a class of multi-scale approximate solutions based on the boundary's geometric features and establish their convergence in the L^{\infty} framework. Our findings do not require a small-amplitude assumption, only an upper bound on the Gaussian curvature of the boundary surface. Notably, when the boundary is planar, our approach aligns with existing studies. Additionally, in the vanishing-viscosity limit, we derive a limiting-state system dependent on boundary geometric parameters. These contributions extend the theoretical understanding of boundary-layer interactions to general curved geometries and have possible applications in atmospheric, oceanic, and other geophysical flow contexts.

A fundamental open problem in the theory of the compressible Navier-Stokes equations is whether regular spherically symmetric flows can develop singularities, such as cavitation or implosion, in finite time. A formidable challenge lies in how the well-known coordinate singularity at the origin can be overcome to control the lower or upper bound of the density. In this paper, when the viscosity coefficients are degenerately density-dependent (as in the shallow water equations), we prove that, for general large spherically symmetric initial data with bounded positive density, solutions remain globally regular and cannot undergo cavitation or implosion in two and three spatial dimensions. Moreover, the far-field vacuum is allowed for the data under consideration here. Our results hold for all adiabatic exponents $\gamma\in(1,\infty)$ in two dimensions, and for physical adiabatic exponents $\gamma\in (1, 3)$ in three dimensions, without any restriction on the size of the initial data.

A central challenge in the study of complex systems is the quantification of emergence – understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work has proposed practical measures to detect emergence, these approaches tend to double-count the contribution of shared components, which substantially hinders their capability to effectively study large systems. In this work, we introduce a family of improved information-theoretic measures of emergence that iteratively correct for double-counted terms. Our approach is computationally efficient and provides a controllable trade-off between computational load and sensitivity, leading to more accurate and versatile estimates of emergence. The benefits of the proposed approach are demonstrated by successfully detecting emergence in both simulated and real-world data related to flocking behaviour.

Pricing multi-asset options via the Black-Scholes PDE is limited by the curse of dimensionality: classical full-grid solvers scale exponentially in the number of underlyings and are effectively restricted to three assets. Practitioners typically rely on Monte Carlo methods for computing complex instrument involving multiple correlated underlyings. We show that quantized tensor trains (QTT) turn the d-asset Black-Scholes PDE into a tractable high-dimensional problem on a personal computer. We construct QTT representations of the operator, payoffs, and boundary conditions with ranks that scale polynomially in d and polylogarithmically in the grid size, and build two solvers: a time-stepping algorithm for European and American options and a space-time algorithm for European options. We compute full-grid prices and Greeks for correlated basket and max-min options in three to five dimensions with high accuracy. The methods introduced can comfortably be pushed to full-grid solutions on 10-15 underlyings, with further algorithmic optimization and more compute power.

A new modelling approach shows how the Earth's hidden vibrations may drive global weather dynamics and atmospheric pressure variations, hinting that the planet's own beat could be imprinted on our climate. The atmospheric rotational patterns of the mean sea level pressure, in connection to the development of powerful storms, are shown to be caused by Earth's rotational elastic dynamics and earthquake-induced oscillations. These seismic excitations are discussed in relation to storm formation and the global atmospheric patterns of high-pressure regions.

Water adopts many different crystal structures in its solid form. These provide insight into potential structures of water even in its liquid phase, and they can be used to calibrate pair potentials used for simulation of water. In crowded biological environments, water may behave more like ice than bulk water. The different ice structures have different dielectric properties. This brief primer is intended to facilitate further research.

This thesis presents a physics-informed machine learning framework for solving the Floquet-Bloch eigenvalue problem associated with particles in two-dimensional periodic potentials, with a focus on honeycomb lattice geometry, due to its distinctive band topology featuring Dirac points and its relevance to materials such as graphene. By leveraging neural networks to learn complex Bloch functions and their associated eigenvalues (energies) simultaneously, we develop a mesh-free solver enforcing the governing Schrödinger equation, Bloch periodicity, and normalization constraints through a composite loss function without supervision. The model is trained over the Brillouin zone to recover band structures and Bloch modes, with numerical validation against traditional plane-wave expansion methods. We further explore transfer learning techniques to adapt the solver from nearly-free electron potentials to strongly varying potentials, demonstrating its ability to capture changes in band structure topology. This work contributes to the growing field of physics-informed machine learning for quantum eigenproblems, providing insights into the interplay between symmetry, band structure, and neural architectures.

One-dimensional NMR spectroscopy is one of the most widely used techniques for the characterization of organic compounds and natural products. For molecules with up to 36 non-hydrogen atoms, the number of possible structures has been estimated to range from $10^{20} - 10^{60}$. The task of determining the structure (formula and connectivity) of a molecule of this size using only its one-dimensional $^1$H and/or $^{13}$C NMR spectrum, i.e. de novo structure generation, thus appears completely intractable. Here we show how it is possible to achieve this task for systems with up to 40 non-hydrogen atoms across the full elemental coverage typically encountered in organic chemistry (C, N, O, H, P, S, Si, B, and the halogens) using a deep learning framework, thus covering a vast portion of the drug-like chemical space. Leveraging insights from natural language processing, we show that our transformer-based architecture predicts the correct molecule with 60.4% accuracy within the first 15 predictions using only the $^1$H and $^{13}$C NMR spectra, thus overcoming the combinatorial growth of the chemical space while also being extensible to experimental data via fine-tuning.

Winds in the atmospheric boundary layer (ABL) display a wide range of velocity profiles and turbulence properties that affect wind turbine wake dynamics. However, standard concurrent-precursor large eddy simulations (LES) often neglect phenomena such as mesoscale patterns, limiting the range and controllability of inflow parameters that can be studied. Here, we propose a synthetic inflow LES method with high inflow controllability to allow parameters such as shear, turbulence, and Coriolis effects to be varied independently, facilitating the efficient exploration of wake dynamics across the full range of conditions observed in the field. The synthetic inflow method faithfully reconstructs wake dynamics when compared with standard concurrent-precursor LES. We then run a suite of over 600 LES cases to investigate the ABL processes that most affect wake dynamics. We find that wake recovery strongly depends on inflow wind veer, especially at low turbulence intensities, due to the elongation of the skewed wake. Furthermore, we identify a novel scaling relation that collapses wake deflections and dynamics onto the combination of shear and veer. The suite of LES cases elucidates ABL regimes and wake dynamics where current and future wind turbines may operate, building toward improved wake modeling for wind farm design and control.

Water nanoconfinement is known to occur inside material void spaces, such as 2D confinement between surfaces, 1D confinement inside nanotubes, and variable-dimension confinement inside nanoporous materials. In the present work we investigate, through molecular dynamics simulations, the morphologies and self-diffusion coefficient of water channels that are nanoconfined in the void space between adjacent surfaces of nanotube bundles - an existing class of materials. In our simulations, we begin with water filling completely the void space, and then we progressively increase the inter-surface separation, maintaining the water content. We find that, as the inter-surface separation progresses, the dimensionality of the water channel decreases from 2D to 1D, the latter consisting of self-confined water channels along surface grooves. The morphologies and self-diffusion coefficients of these 1D water nanochannels are strongly dependent on the nature of the water-surface interaction and on the diameter of the nanotubes. Interestingly, as we decrease the nanotube diameter from 10 to 5 nm, the self-diffusion coefficients of the 1D channels increase by tenfold for hydrophilic surfaces and by sixfold for hydrophobic surfaces, surpassing, in both cases, the bulk water values. We also investigated the water channels at the interstitial voids of the bulk bundle material, finding 1D water channels that are similar to the surface ones.

We report suborbital in situ measurements of atmospheric thermodynamic variables and ionizing cosmic radiation obtained during a stratospheric balloon experiment conducted over the Mexican Plateau. The flight reached a maximum geometric altitude of 28.94 km above mean sea level, providing vertical sampling of the troposphere, tropopause, and lower stratosphere. Continuous temperature and pressure measurements acquired during ascent and descent were used to derive vertical profiles and to compute atmospheric density as a function of altitude under the hydrostatic approximation. The resulting thermal structure exhibits distinct lapse-rate regimes, allowing for a piecewise parametrization consistent with the International Standard Atmosphere (ISA) within the sampled altitude range. Simultaneous measurements of ionizing radiation show the expected altitude dependence of secondary cosmic-ray fluxes generated by atmospheric cascades, including the formation of a Regener-Pfotzer maximum. A peak ambient dose equivalent rate of 2.96 microGy h^{-1} was measured at an altitude of 18.64 km, consistent with mid-latitude stratospheric conditions. To the best of our knowledge, this experiment constitutes the first documented stratospheric balloon mission conducted in the State of Mexico to combine near-space atmospheric profiling with direct in situ measurements of ionizing cosmic radiation at altitudes approaching 30 km.

We investigate the shift caused by asymmetry of spectroscopic lineshape in atomic interferometers, which has not previously been discussed in the scientific literature. This asymmetry arises because laser field is frequency-chirped not only during the free-evolution intervals of atoms, but also during the Ramsey pulses. As a result, the effective detuning from the working atomic transition during the pulses also depends on the chirping rate, which, in turn, leads to the lineshape-asymmetry-caused shift (LACS). It is shown that this shift has an inverse cubic dependence of $\propto 1/T^3$ on the duration of the interval between the Ramsey pulses $T$, which markedly contrasts with the $\propto 1/T^2$ dependence typical in atomic interferometry. Therefore, the metrological importance of this shift substantially increases for compact atomic interferometers with a short baseline. For example, for interferometers-gravimeters using two-photon transitions in rubidium atoms, at $T\sim 1$~ms we estimate the LACS shift and its variations at the level of 0.1-1~mGal, while for $T\sim 100$~$\mu$s this can reach a value of 0.1-1~Gal.

Microscale additive manufacturing of reflective copper is becoming increasingly important for microelectronics and microcomputers, due to its excellent electrical and thermal conductivity. Yet, it remains challenging for state-of-the-art commercial metal 3D printers to achieve sub-100-micron manufacturing. Two aspects are sub-optimal using commercial laser powder bed fusion systems with infrared (IR) lasers (wavelength of 1060-1070 nm): (1) IR laser has a low absorption rate for Cu, which is energy-inefficient for manufacturing; (2) short wavelength lasers can potentially offer higher resolution processing due to the diffraction-limited processing. On the other hand, laser sintering or melting typically uses continuous wave (CW) lasers, which may reduce the manufacturing resolution due to a large heat-affected zone. Based on these facts, this study investigates the UV (wavelength of 355 nm) nanosecond (ns) laser sintering of Cu nanoparticles. Different laser processing parameters, as well as different nanoparticle packing densities, are studied. Our results show that a short-wavelength laser can reduce the required energy for sintering with decent morphology, and a densified nanoparticle powder bed favors continuous melting. We further show that sub-20 micron printing can be readily achieved with a UV ns laser. These findings provide new insights into short-wavelength laser-metal nanoparticle interactions, which may pave the way to achieve high-resolution micro and nano-scale additive manufacturing.

The Boussinesq approximation is a cornerstone of geophysical fluid dynamics, yet its thermodynamic and energetic underpinnings have remained ambiguous. In standard formulations, the links with the fully compressible Navier–Stokes equations are obscured, internal energy is only implicit, and the representation of diffusion and irreversibility remains ad hoc. Here we derive a new Boussinesq model in a fully traceable way from the two-component compressible Navier-Stokes equations, ensuring exact energy conservation and consistent thermodynamics. Assuming a linear equation of state, our model treats density as a proxy for specific volume, distinguishes in-situ and potential temperature explicitly, and incorporates diffusive fluxes that homogenise the correct thermodynamic potentials, ensuring consistent non-negative entropy production. The result clarifies the status of gravitational potential energy, resolves ambiguities surrounding salinity–entropy coupling, and retains the small terms carriers of key information about thermodynamics. Alongside this, we introduce an exact thermodynamically soundproof (TS) model whose weak diabatic divergence highlights the role of compressibility effects in stratified turbulence. Together, these models provide a transparent framework that reconciles classical approximations with compressible energetics, offering better-defined pathways for analysing stratified mixing, mixing efficiency, and the energy budgets of geophysical flows.

We discuss a simple three layer model of the tropical atmosphere. The rainfall variance of the model is dominated by a rainfall mode moving parallel to the equator having the approximate size and propagation speed of the Madden-Julian Oscillation (MJO). The origin of the convective aggregation in the model is the imposition of distinct length scales for the deep updraft and stratiform downdraft circulations. Subsidence induced by the deep updraft circulation suppresses convective instability on a scale of $\sim$ 1000 km, while ascent induced by the downdraft circulation promotes convective instability on a scale of $\sim$ 500 km. Within the MJO envelope, high rainfall rates are maintained both by increased column relative humidity, and increased variance in lower tropospheric vertical motion. Each of the three model layers has a prescribed target pressure thickness. Convective mass fluxes introduce a mass excess into grid cells where there is net detrainment, and a mass deficit into grid cells from which there is net entrainment. Horizontal transport in the model is based on export of mass from grid cells where there is an excess, and import of mass toward grid cells where there is a deficit. The resulting patterns of horizontal convergence and divergence generate vertical motions between model levels. The simulated MJO events propagate eastward when there is a slight preference for mass deficits in the boundary layer to be compensated by inward flow from the west. The forward propagation of the MJO is limited by the rate at which the downdraft circulation within the MJO is able to generate net upward motion and promote new convective activity in advance of the leading edge. We also offer some guidance on how convective parameterizations that are implemented in models with more realistic dynamical schemes might be designed to exhibit stronger MJO variance.

Life is commonly described as a self-organized, far-from-equilibrium process that maintains internal order by consuming free energy and exporting entropy. This thermodynamic view underlies diverse theoretical frameworks – from autopoiesis and relational biology to autocatalytic sets and hypercycles – yet dissipation is typically treated as a necessary consequence of living organization rather than as a property shaped by its internal dynamics. Here, through explicit calculations of biotic chemical reactions and empirical documentation, we show that living systems universally function as non-normal chemical accelerators. Their elevated entropy production emerges from the asymmetric and hierarchical architecture of their biochemical networks. We introduce a general conceptual and mathematical framework in which biological structuration is understood as a dynamical property. Characterized by asymmetric couplings and transient amplification despite asymptotic stability, non-normal dynamics are shown to naturally generate kinetic acceleration, enhanced energy throughput, and phase-transition-like reorganizations without classical bifurcations. In this view, biological organization is not merely compatible with dissipation but actively structured to amplify free-energy flux and entropy export. We support this perspective with empirical and theoretical evidence that biochemical networks generically give rise to intrinsically non-normal operators through non-reciprocal interactions and hierarchical design. This framework yields testable predictions for dissipation rates, robustness, and evolutionary design principles, and suggests a kinetic principle of evolution in which living systems preferentially construct increasingly non-normal reaction architectures, driving sustained amplification of chemical fluxes and entropy flow.

Incompressible flow solvers based on strong-form meshfree methods represent arbitrary geometries without the need for a global mesh system. However, their local evaluations make it difficult to satisfy incompressibility at the discrete level. Moreover, the collocated arrangement of velocity and pressure variables tends to induce a zero-energy mode, leading to decoupling between two variables. In projection-based approaches, a spatial discretization scheme based on a conventional node-based moving least-squares method for the pressure causes inconsistency between discrete operators on both sides of the Poisson equation. Thus, a solenoidal velocity field cannot be ensured numerically. In this study, a numerical method for the incompressible Navier-Stokes equations is developed by introducing a local primal-dual grid into the mesh-constrained discrete point method, enabling consistent discrete operators. The constructed virtual dual cell is defined solely from local node connectivity, and thus the method retains its meshfree nature. To consistently couple velocity and pressure variables under primal-dual arrangement, a numerical technique called time evolution converting, which evaluates interface quantities by considering the temporal evolution of flow, is used to update the velocity at cell interfaces. For numerical validation, a linear acoustic equation is solved to confirm the effectiveness of the staggered-variable arrangement based on the local primal-dual grid. Then, the incompressible Navier-Stokes equations are solved, and the proposed method is demonstrated to reduce the discrete velocity divergence to a level determined by the residual of the pressure Poisson equation, achieve the expected spatial convergence order, and accurately reproduce flow features over a wide range of Reynolds numbers.

We present a numerical study of several inequality measures across two kinetic wealth exchange models with extreme inequality features (namely the Banerjee model, and the Chakraborti or Yard Sale model) and two earthquake simulating models (namely the Chakrabarti Stinchcombe two fractal overlap model and the nonlinear dynamical Burridge Knopoff model). For each model we compute numerically the Lorenz function for the respective models wealth, overlap magnitude or avalanche distributions. We then estimate the variations of Gini (g), Pietra (p) and Kolkata (k) indices in these models with systematic variations of saving propensity (for the two wealth exchange models), with systematic variations of generation or block numbers (for the two earthquake simulating models). We find that for appropriate values of the respective model parameters, the inequality indices g and k in corresponding the distributions (of wealth or avalanche) show quantitatively similar behavior, namely g equal to k nearly equal to 0.86, which was identified earlier to correspond to the precursor point of criticality in self organized critical models (k equal to 0.80 corresponds to that for Pareto 80/20 law). The values of p/(2k-1) in all these (wealth exchange and earthquake) models remain a little above unity, as was predicted theoretically. These observations for the inequality indices g, k and p across the socio economic and geophysical models indicate the presence of unifying subtle features in the statistics of such disparate dynamical systems.

Computing spectral functions in large, non-periodic super-moiré systems remains an open problem due to the exceptionally large system size that must be considered. Here, we establish a tensor network methodology that allows computing momentum-resolved spectral functions of non-interacting and interacting super-moiré systems at an atomistic level. Our methodology relies on encoding an exponentially large tight-binding problem as an auxiliary quantum many-body problem, solved with a many-body kernel polynomial tensor network algorithm combined with a quantum Fourier transform tensor network. We demonstrate the method for one and two-dimensional super-moiré systems, including super-moiré with non-uniform strain, interactions treated at the mean-field level, and quasicrystalline super-moiré patterns. Furthermore, we demonstrate that our methodology allows us to compute momentum-resolved spectral functions restricted to selected regions of a super-moiré, enabling direct imaging of position-dependent electronic structure and minigaps in super-moiré systems with non-uniform strain. Our results establish a powerful methodology to compute momentum-resolved spectral functions in exceptionally large super-moiré systems, providing a tool to directly model quantum twisting microscope experiments in twisted van der Waals heterostructures.

Hybrid quantum-classical algorithms have begun to leverage quantum devices to efficiently represent many-electron wavefunctions, enabling early demonstrations of molecular simulations on real hardware. A key prerequisite for scalable quantum chemistry, however, is size consistency: the energy of non-interacting subsystems must scale linearly with system size. While many algorithms are theoretically size-consistent, noise on quantum devices may couple nominally independent subsystems and degrade this fundamental property. Here, we systematically evaluate size consistency on quantum hardware by simulating systems composed of increasing numbers of non-interacting H$_{2}$ molecules using optimally shallow unitary circuits. We find that molecular energies remain size-consistent within chemical accuracy for an estimated 118 and 71 H$_{2}$ subsystems for one- and two-qubit unitary designs, respectively, demonstrating that current quantum devices preserve size consistency over chemically relevant system sizes and supporting the feasibility of scalable, noise-resilient simulation of strongly correlated molecules and materials.

We investigate the transport behavior of tungsten impurities with finite inertia in drift-wave turbulence using the Hasegawa-Wakatani model. Unlike previous tracer-based models, our simulations reveal a transition to non-diffusive dynamics for a range of charge states. This novel mechanism offers a turbulence-driven route to core impurity accumulation. This finding underscores the nontrivial role of particle inertia in impurity dynamics and has strong implications for impurity control in future fusion devices.

Flow equation methods, more generally known as Similarity Renormalization Group (SRG) techniques, were developed to address multiscale problems where multiple length or energy scales contribute simultaneously. In this Thesis, we formulate the flow equation method within a wavelet-based framework and apply it to study scale (resolution) separation in a two-dimensional scalar field theory. We demonstrate that the flow systematically block-diagonalizes the Hamiltonian with respect to wavelet resolution, achieving improved truncation compared to earlier studies. Using a model of two real scalar fields coupled through a quadratic interaction, we show that the flow equations effectively suppress couplings between low- and high-resolution degrees of freedom. This provides a clear mechanism for isolating low-resolution physics and offers insight into the construction of effective Hamiltonians using a wavelet-based flow equation approac

Analysis of space-charge effects on electron emission typically makes some assumption of continuity and smoothness, whether this is continuity of charge as in the classical derivation of the Child-Langmuir current, or the mean-field approximation used in particle-in-cell simulations. However, when studying the physics of electron emission and propagation at the mesoscale it becomes necessary to consider the discrete nature of electronic charge to account for the space-charge effect of each individual point charge. In this paper we give an extensive analysis of some previous work on the distribution of electrons under space-charge limited conditions. We examine the spacing of electrons as they are emitted from a planar surface, We present simplified models for analysis of such conditions to derive scaling laws for emission and compare them to computer simulations.

Pressure-driven flow collapses when confined ($u\propto r^{2}$). Asymmetry rectifies surface activity (exchange or slip gradients) into axial flux at $\Delta P=0$ despite zero net exchange. Lorentz reciprocity yields a projection law: throughput is the inner product of source with a geometry kernel. Signatures include inverted “narrower-is-faster” scaling ($u\propto r^{-1}$), leading-order viscosity independence, length amplification ($Q\propto L$), and linear superposition, defining surface-induced flow as a pressure-free Stokes-transport mode from microfluidics to physiology.

Plasmons in atomically thin materials offer a compelling route to trigger nonlinear light-matter interactions through extreme optical confinement in the two-dimensional (2D) limit. However, optical nonlocality in plasmons is typically associated with losses in the linear response regime. Here, we show that nonlocal effects mediate strong plasmon-assisted optical nonlinearity in electrically reconfigurable 2D heterostructures. Using atomistic simulations that capture quantum finite-size and nonlocal effects in the nonlinear plasmonic response of graphene and phosphorene nanoribbon dimers, we reveal how symmetry and inter-ribbon coupling shape harmonic generation processes in perturbative and high-harmonic regimes. Independent tuning of geometry and carrier density in nanoribbon heterostructures is shown to induce inter-ribbon plasmon hybridization, impacting inversion symmetry governing even-ordered nonlinear processes like second-harmonic generation. These results reveal design principles for active and passive tuning of nonlinear plasmonic effects and enable selective enhancement of specific harmonic processes, establishing 2D heterostructures as a versatile platform for nonlinear nanophotonics.