CyberSec Research

We propose a stochastic branching particle-based method for solving nonlinear non-conservative advection-diffusion-reaction equations. The method splits the evolution into an advection-diffusion step, based on a linearized Kolmogorov forward equation and approximated by stochastic particle transport, and a reaction step implemented through a branching birth-death process that provides a consistent temporal discretization of the underlying reaction dynamics. This construction yields a mesh-free, nonnegativity-preserving scheme that naturally accommodates non-conservative systems and remains robust in the presence of singularities or blow-up. We validate the method on two representative two-dimensional systems: the Allen-Cahn equation and the Keller-Segel chemotaxis model. In both cases, the present method accurately captures nonlinear behaviors such as phase separation and aggregation, and achieves reliable performance without the need for adaptive mesh refinement.

This study investigates into the adsorption sensing capabilities of single-walled (5,5) boron nitride nanotubes (BNNTs) towards environmental pollutant gas molecules, including CH2, SO2, NH3, H2Se, CO2 and CS2. Employing a linear combination of atomic orbital density functional theory (DFT) and spin-polarized generalized gradient approximation (GGA), the investigation reveals the nanotube's robust adsorption behavior without compromising its structural integrity. Thermodynamic and chemical parameters, such as adsorption energy, HOMO-LUMO gap, vertical ionization energy, and vertical electron affinity, highlight the (5,5) BNNTs' potential as efficient absorbents for pollutant molecules. Infrared spectroscopy confirms the formation of distinct BNNT-gas complexes. These findings underscore the promising application of BN nanotubes as absorbents for common gaseous pollutants, essential for developing sensors to enhance indoor air quality.

We present a first--principles density functional theory (DFT) study of transition metal (TM = Ti, Cr, Mn, Fe, Co, Ni) functionalized two--dimensional polyaramid (2DPA) to explore their structural, electronic, and magnetic properties. Mechanical parameters, such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and Pugh ratio, together with phonon dispersion, confirm the mechanical and dynamic stability of all doped systems. Electronic structure analysis shows strong binding of Co, Cr, Fe, Ni, and Ti with formation energies between --1.15 eV and --2.96 eV, while Mn binds more weakly (--0.67 eV). TM doping introduces new electronic states that reduce the band gap, with Fe-doped 2DPA exhibiting the lowest value of 0.26 eV. The systems display predominantly ferromagnetic ordering, with magnetic moments of 1.14 {\mu}B (Co), 3.57 {\mu}B (Cr), 2.26 {\mu}B (Fe), 4.19 {\mu}B (Mn), and 1.62 {\mu}B (Ti). These results demonstrate that TM--doped 2DPA possesses tunable magnetic and electronic characteristics, highlighting its potential for spintronic applications.

Numerical simulations of reactive hypersonic flow under thermodynamic and chemical non-equilibrium conditions are presented for the Mars Pathfinder capsule. An 8-species chemical model is employed to simulate Mars' atmosphere. Park's two-temperature model is used to account for the thermal non-equilibrium phenomena. The present work analyzes the impact of different values of the weight factors used in Park's model, aiming to broaden the understanding of the weight factors influence. The code used to simulate the flows solves the Navier-Stokes equations modified to account for reacting gas mixtures. The findings are depicted in terms of the Mach number and temperature modes along the stagnation streamline in a region close to the shock wave. The present analysis also includes results regarding the stagnation point convective heat flux. The results indicate that varying the weight factors yields negligible differences in the shock wave position and stagnation point convective heat flux. The changes in the weight factors cause variations in the maximum temperature mode values in the non-equilibrium region. The results presented are in good agreement with experimental data present in the literature. The present work indicates that Park's two-temperature model weight factors can substantially affect the temperature mode distributions in the flow non-equilibrium region.

Achieving an optimal biomechanical environment within bone scaffolds is critical for promoting tissue regeneration, particularly in load-bearing anatomical sites where rigid fixation can induce stress shielding and compromise healing. Functionally graded (FG) scaffolds, which incorporate controlled variations in porosity or material properties, have attracted significant attention as a strategy to mitigate stress shielding by promoting more favourable load transfer. In this study, the effects of porosity gradient magnitude (i.e., max-to-min ratio of porosity), gradient resolution, scaffold material properties, and fixation plate rigidity on the distribution of mechanical stimuli within FG scaffolds were systematically investigated. Finite element analyses (FEA) were conducted on a femoral segmental defect model stabilised with a bone plate, and multiple porosity gradient strategies were compared against a corresponding uniform scaffold composed of body-centred cubic (BCC) unit cells. Scaffolds composed of titanium alloy (Ti-6Al-4V), bioactive glass (45S5 Bio-glass), and polylactic acid (PLA) were evaluated to capture a range of material stiffnesses. Introducing porosity gradients consistently enhanced the mean octahedral shear strain within the scaffold, particularly in regions adjacent to the fixation plate affected by stress shielding. The magnitude of mechanical stimulus improvement increased with both greater porosity gradient magnitudes and higher gradient resolution. These improvements were more pronounced in stiffer materials, such as Ti-6Al-4V, emphasising the critical interplay between scaffold material properties and architectural design. These findings highlight the importance of tailoring both porosity profiles and material selection to optimise scaffold mechanics for bone regeneration.

The wave operator model provides a framework for modeling wave propagation by encoding material parameter distributions into matrix-form operators. This paper extends this framework from lossless to lossy media. We present a derivation of the wave operator solution for the electric field in dissipative environments, which can be decomposed into a closed-form propagation term and a non-closed-form dissipation term. Based on an analysis of the dominant exponential decay within the propagation term, an attenuation compensation strategy is proposed to restore the attenuated data to an approximate lossless state. The performance of this compensation strategy is analyzed and validated through numerical experiments, establishing the theoretical foundation for reduced order model (ROM)-based techniques in lossy media.

Using particle-resolved molecular-dynamics simulations, we compute the phase diagram for soft repulsive spherocylinders confined on the surface of a sphere. While crystal (K), smectic (Sm), and isotropic (I) phases exhibit a stability region for any aspect ratio of the spherocylinders, a nematic phase emerges only beyond a critical aspect ratio lying between 6.0 and 7.0. As required by the topology of the confining sphere, the ordered phases exhibit a total orientational defect charge of +2. In detail, the crystal and smectic phases exhibit two +1 defects at the poles, whereas the nematic phase features four +1/2 defects which are connected along a great circle. For aspect ratios above the critical value, lowering the packing fraction drives a sequence of transitions: the crystal melts into a smectic phase, which then transforms into a nematic through the splitting of the +1 defects into pairs of +1/2 defects that progressively move apart, thereby increasing their angular separation. Eventually, at very low densities, orientational fluctuations stabilize an isotropic phase. Our simulations data can be experimentally verified in Pickering emulsions and are relevant to understand the morphogenesis in epithelial tissues.

We investigate the evolution of red supergiant (RSG) progenitors of core-collapse (CC) supernovae (SNe) with initial masses between $12-20~M_\odot$ focusing on the effects of enhanced mass loss due to pulsation-driven instabilities in their envelopes and subsequent dynamical ejections during advanced stages of nuclear burning. Using time-dependent mass loss from detailed MESA stellar evolution models, including a parameterized prescription for pulsation-driven superwinds and time-averaged mass loss rates attributed to resulting shock-induced ejections, we construct the circumstellar medium (CSM) before the SN explosion. We calculate resulting CSM density profiles and column densities considering the acceleration of the stellar wind. Our models produce episodes of enhanced mass loss $10^{-4}-10^{-2}~M_\odot~\rm{yr}^{-1}$ in the last centuries-decades before explosion forming dense CSM ($>10^{-15}~\rm{gcm}^{-3}$ at distances $<10^{15}$ cm) -- consistent with those inferred from multi-wavelength observations of Type II SNe such as SN~2023ixf and SN~2020ywx.

We show that both temporal and spatial symmetry breaking in canonical K-type transition arise as organized hydrodynamic structures rather than stochastic fluctuations. Before the skin-friction maximum, the flow is fully described by a periodic, spanwise symmetric, harmonic response to the Tollmien-Schlichting wave, forming a spatially compact coherent structure that produces hairpin packets. This fundamental harmonic response may visually resemble turbulence, but remains fully periodic and delimits the exact extent of the deterministic regime. A distinct regime change occurs after this point; a hierarchy of new (quasi-)periodic and aperiodic space-time structures emerges, followed shortly by anti-symmetric structures that develop similarly despite no anti-symmetric inputs, marking the onset of aperiodicity and spanwise asymmetry. We identify these structures as symmetry-decomposed spectral and space-time proper orthogonal modes that resolve the full progression from deterministic to broadband dynamics. The key insight is that laminar-turbulent transition can be viewed as a sequence of symmetry breaking events, each driven by energetically dominant, space-time coherent modes that gradually turn an initially harmonic flow into broadband turbulence.

This article introduces a new 3D magnetohydrodynamic (MHD) equilibrium solver, based on the concept of admissible variations of B, p that allows for magnetic relaxation of a magnetic field in a perturbed/non-minimum energy state to a lower energy state. We describe the mathematical theory behind this method, including ensuring certain bounds on the magnetic energy, and the differential geometry behind transforming to and from a logical domain and physical domain. Our code is designed to address a number of traditional challenges to 3D MHD equilibrium solvers, e.g. exactly enforcing physical constraints such as divergence-free magnetic field, exhibiting high levels of numerical convergence, dealing with complex geometries, and modeling stochastic field lines or chaotic behavior. By using differentiable Python, our numerical method comes with the additional benefits of computational efficiency on modern computing architectures, high code accessibility, and differentiability at each step. The proposed magnetic relaxation solver is robustly benchmarked and tested with standard examples, including solving 2D toroidal equilibria at high-beta, and a rotating ellipse stellarator. Future work will address the integration of this code for 3D equilibrium optimization for modeling magnetic islands and chaos in stellarator fusion devices.

Accurately describing the ground state of strongly correlated systems is essential for understanding their emergent properties. Neural Network Backflow (NNBF) is a powerful variational ansatz that enhances mean-field wave functions by introducing configuration-dependent modifications to single-particle orbitals. Although NNBF is theoretically universal in the limit of large networks, we find that practical gains saturate with increasing network size. Instead, significant improvements can be achieved by using a multi-determinant ansatz. We explore efficient ways to generate these multi-determinant expansions without increasing the number of variational parameters. In particular, we study single-step Lanczos and symmetry projection techniques, benchmarking their performance against diffusion Monte Carlo and NNBF applied to alternative mean fields. Benchmarking on a doped periodic square Hubbard model near optimal doping, we find that a Lanczos step, diffusion Monte Carlo, and projection onto a symmetry sector all give similar improvements achieving state-of-the-art energies at minimal cost. By further optimizing the projected symmetrized states directly, we gain significantly in energy. Using this technique we report the lowest variational energies for this Hamiltonian on $4\times 16$ and $4 \times 8$ lattices as well as accurate variance extrapolated energies. We also show the evolution of spin, charge, and pair correlation functions as the quality of the variational ansatz improves.

Ferroelectric materials are a class of dielectrics that exhibit spontaneous polarization which can be reversed under an external electric field. The emergence of ferroelectric order in incipient ferroelectrics is a topic of considerable interest from both fundamental and applied perspectives. Among the various strategies explored, strain engineering has been proven to be a powerful method for tuning ferroelectric polarization in materials. In the case of KTaO3, first principles calculations have suggested that strain can drive a ferroelectric phase transition. In this study, we investigate the impact of in-plane uniaxial and biaxial strain, ranging from 0% to 1%, on pristine KTaO3 to explore its potential for ferroelectricity induction via inversion symmetry breaking. By integrating density functional theory calculations with the stochastic self-consistent harmonic approximation assisted by on the fly machine learned force field, we obtain accurate structural information and dynamical properties under varying strain conditions while incorporating higher-order anharmonic effects. Employing the Berry phase method, we obtained the ferroelectric polarization of the strained structures over the entire temperature range up to 300 K. Our findings provide valuable insights into the role of strain in stabilizing ferroelectricity in KTaO3, offering guidance for future experimental and theoretical studies on strain-engineered ferroelectric materials.

We construct a generative network for Monte-Carlo sampling in lattice field theories and beyond, for which the learning of layerwise propagation is done and optimised independently on each layer. The architecture uses physics-informed renormalisation group flows that provide access to the layerwise propagation step from one layer to the next in terms of a simple first order partial differential equation for the respective renormalisation group kernel through a given layer. Thus, it transforms the generative task into that of solving once the set of independent and linear differential equations for the kernels of the transformation. As these equations are analytically known, the kernels can be refined iteratively. This allows us to structurally tackle out-of-domain problems generally encountered in generative models and opens the path to further optimisation. We illustrate the practical feasibility of the architecture within simulations in scalar field theories.

We develop an accelerated algorithm for computing an approximate eigenvalue decomposition of bistochastic normalized kernel matrices. Our approach constructs a low rank approximation of the original kernel matrix by the pivoted partial Cholesky algorithm and uses it to compute an approximate decomposition of its bistochastic normalization without requiring the formation of the full kernel matrix. The cost of the proposed algorithm depends linearly on the size of the employed training dataset and quadratically on the rank of the low rank approximation, offering a significant cost reduction compared to the naive approach. We apply the proposed algorithm to the kernel based extraction of spatiotemporal patterns from chaotic dynamics, demonstrating its accuracy while also comparing it with an alternative algorithm consisting of subsampling and Nystroem extension.

High-energy laser facilities such as PHELIX at GSI require excellent beam pointing stability for reproducibility and relative independence for future experiments. Beam pointing stability has been traditionally achieved using simple proportional-integral-derivative (PID) control which removes the problem of slow drift, but is limited because of the time delay in knowing the diagnosis and the inertia in the mechanical system associated with mirrors. In this work, we introduce a predictive control strategy where the forecasting of beam pointing errors is performed by a patch-based multilayer perceptron (Patch-MLP) designed to capture local temporal patterns for more robust short-term jitter prediction. The subsequent conversion of these predicted errors into correction signals is handled by a PID controller. The neural network has been trained on diagnostic time-series data to predict beam pointing error. Using the feed-forward controller compensates for system delays. Simulations with a correction mirror placed upstream of the PHELIX pre-amplifier bridge confirm that the predictive control scheme reduces residual jitter compared to conventional PID control. Over a 10-hour dataset the controller maintained stable performance without drift, while standard pointing metrics showed consistent improvements of the order of 10 to 20 percent. The predictive controller operates without drift, and therefore may improve reproducibility and operational efficiency in high energy, low repetition rate laser experiment conditions.

The detailed simulation of extensive air showers, produced by primary cosmic rays interacting in the atmosphere, is a task that is traditionally undertaken by means of Monte Carlo methods. These processes are computationally intensive, accounting for a major fraction of the computational resources used in the large-scale simulations required by current and future experiments in the field of astroparticle physics. In this work, we present a novel approach based on Generative Adversarial Networks (GANs) to accelerate air shower simulations. We developed and trained a GAN on a dataset of high-energy proton-induced air showers generated with \texttt{CORSIKA}; our model reproduces key distributions of secondary particles, such as energy spectra and spatial distributions at ground level of muons. Once the model has been trained, which takes approximately 74 hours, the generation real time per shower is reduced by a factor of $10^4$ with respect to the full \texttt{CORSIKA} simulation, leading to a substantial decrease in both computational time and energy consumption.

The bound electron-hole pairs known as excitons govern the optical properties of insulating solids. While their behavior in equilibrium is well-understood theoretically, the nonequilibrium regime at high excitation densities-where phenomena like electron-hole liquids emerge - is less explored. This thesis presents a first-principles study of excitons in two-dimensional materials. We use the GW approximation and the Bethe-Salpeter equation to investigate their properties from equilibrium to nonequilibrium conditions. We first demonstrate how increasing photo-excited carrier density leads to a redshift-blueshift crossover of excitons. We then show that electron-phonon interactions critically modify optical spectra and exciton lifetimes at finite temperatures. Finally, we unify these effects to demonstrate the formation of an electron-hole liquid phase above a critical carrier density and below a critical temperature. Our work identifies how enhanced Coulomb interactions in two dimensions can stabilize this phase at significantly higher temperatures, proposing promising material candidates for observing these collective states.

In this study, the capabilities of the Physics-Informed Neural Network (PINN) method are investigated for three major tasks: modeling, simulation, and optimization in the context of the heat conduction problem. In the modeling phase, the governing equation of heat transfer by conduction is reconstructed through equation discovery using fractional-order derivatives, enabling the identification of the fractional derivative order that best describes the physical behavior. In the simulation phase, the thermal conductivity is treated as a physical parameter, and a parametric simulation is performed to analyze its influence on the temperature field. In the optimization phase, the focus is placed on the inverse problem, where the goal is to infer unknown physical properties from observed data. The effectiveness of the PINN approach is evaluated across these three fundamental engineering problem types and compared against conventional numerical methods. The results demonstrate that although PINNs may not yet outperform traditional numerical solvers in terms of speed and accuracy for forward problems, they offer a powerful and flexible framework for parametric simulation, optimization, and equation discovery, making them highly valuable for inverse and data-driven modeling applications.