Abstract: Motivated and inspired by Truesdell's seminal article [``Two measures of vorticity," Journal of Rational Mechanics and Analysis {\bf 2}, 173--217 (1953)], recently the present author has introduced the turbulence kinematical vorticity number $\widetilde{\cal V}_{K}$ to measure the mean rotationality of turbulence [``On the classical Bradshaw--Richardson number: Its generalized form, properties, and application in turbulence," Physics of Fluids {\bf 30}, 125110 (2018)]. In this work, first, within the general framework of the Cauchy equation of motion, we derive the general equation of motion for the turbulence kinematical vorticity number $\widetilde{\cal V}_{K}$ in turbulent flows of incompressible non-Newtonian fluids, which depicts the underlying dynamical character of $\widetilde{\cal V}_{K}$ and in laminar flows reduces to the general equation of motion for the kinematical vorticity number---the Truesdell number ${\cal V}_{K}$. Second, we obtain an inequality which places the relevant dynamical restriction upon the mean Cauchy stress tensor, the Reynolds stress tensor, and the mean body force density vector in the ensemble-averaged Cauchy equation of motion for turbulence modelling. Moreover, we derive the general Reynolds stress transport equation for turbulence modelling of incompressible non-Newtonian fluids based on Cauchy's laws of motion, which includes as a special case the classical Reynolds stress transport equation for an incompressible Newtonian fluid derived from the Navier--Stokes equation.

Abstract: We propose a two-level theory that connects a Lin-equation-based dynamical coarse-graining of the turbulence cascade with an information-theoretic selection principle in logarithmic wavenumber space, thereby placing the dissipation-range spectral shape on a verifiable logical chain rather than an ad hoc fit. In the first (dynamical) stage, an autonomous conservative Fokker–Planck description is formulated for the normalized density and probability current; assuming sufficient boundary decay and a strictly positive effective diffusion, we prove that the sign-reversed KL divergence is a Lyapunov functional, yielding a rigorous H-theorem and fixing the arrow of time in scale space. In the second (selection) stage, the dissipation range is posed as a stationary boundary-value problem for an open system by introducing a killing term for an unnormalized scale density. WKB (Liouville–Green) analysis constrains the admissible tail class to a stretched-exponential form and links the tail exponent to the high-wavenumber scaling of the effective diffusion. To eliminate arbitrariness, the exponential prefactor is fixed by dissipation-rate consistency, and the remaining degree of freedom is identified via one-dimensional KL minimization (Hyper-MaxEnt) against a globally constructed reference distribution. The resulting exponent range is validated against high-resolution DNS spectra reported in the literature.

Abstract: Boiling crises are a complex stochastic process that is influenced by the physical phenomena of heat transfer and evaporation, as well as the shape and roughness of the boiling surface. When calculating the critical heat fluxes corresponding to the point of the first boiling crisis, it is important to know the numerical density of the formed bubbles per unit surface and volume. Most models consider only non-interacting bubbles. This greatly reduces their predictive accuracy. An analysis of the video footage of bubble boiling near the point of the first boiling crisis allows us to conclude that this is a typical picture for a continuum off-lattice problem of percolation theory. The main idea of the work is to consider the point of the first boiling crisis as the percolation threshold for a three-dimensional problem. This threshold describes the transition from finite size inclusions (single bubbles and small groups of weakly interacting bubbles) to a percolation structure in which there is a macroscopic irregular bubble, the size of which is comparable to the size of the entire system. This hypothesis allows us to make estimates for the concentration of bubbles at the boiling point and to obtain estimates for critical heat fluxes at this point. The fundamental difference between the proposed approach and previous attempts to apply percolation theory to the description of boiling crisis is the consideration of a three-dimensional problem in liquid volume, rather than a two-dimensional problem onto a hot boiling surface. It is shown for the first time that the proportionality constant in Kutateladze-Zuber equation coincides with the percolation threshold for a three-dimensional continuum percolation problem on overlapping ellipsoids.

Abstract: Recently, Figueroa et al. demonstrated that steady streaming can be generated by the oscillatory motion of a floating magnet driven by electromagnetic forcing in a shallow electrolytic layer. They also found that the rotation direction of the resulting steady vortices is opposite to that of classical streaming flows. In this work, we present a theoretical and experimental investigation of the fluid–structure interaction between a freely moving wall and an oscillatory flow. Our objective is to elucidate the coupling mechanism between the fluid and the oscillating body that gives rise to reverse streaming and to apply this analysis to the case of a freely moving wavy wall. The flow is analyzed theoretically and an analytical solution is obtained using a perturbation method. Experimental results based on Particle Image Velocimetry are also presented, where an oscillatory flow generated by an electromagnetic force in an electrolyte layer drives a wavy wall floating on the surface. The results confirm the occurrence of reverse streaming and demonstrate that the flow dynamics depend on the density ratio between the freely moving solid and the fluid. The analytical solution qualitatively captures the behavior observed in the experiments.

Abstract: A full-factorial 3⁴ (81-run) design-of-experiment using a high-fidelity SOLPS-ITER surrogate model demonstrates that deliberate injection of 1–5 μm lithium or beryllium dust from the mid-plane scrape-off layer reduces ITER divertor peak heat flux by 78–94%, raises divertor radiation fraction above 85%, and suppresses ELM energy release by > 90% while maintaining core contamination well below 10⁻⁵ — performance unattainable by any gaseous seeding scenario. Model validation using full SOLPS-ITER confirms predictive stability within the optimal region. Controlled low-Z dust injection thus emerges as a programmable power exhaust actuator with unprecedented performance, warranting pilot-scale experimental investigation in ITER and DEMO-class reactors.

Abstract: Building upon the recently proposed Topological Model of Spatial Connectivity, we develop a covariant formulation of Maxwell’s equations in an anisotropic geometric background defined by the local connectivity tensor G_ij(x,t). Within this framework, the antisymmetric part of G_ij represents a fundamental twist of spatial connectivity, while the symmetric part encodes local curvature. Variations of G_ij rescale the effective Planck length Lp = l* sqrt(G_ij(x,t) n^i n^j) and consequently modify the local propagation constant c_eff ∝ Lp^-2/3. We derive explicit 3+1 equations for the electromagnetic field in such anisotropic geometry, showing that local Lorentz invariance is preserved while direction-dependent permittivity and permeability naturally arise. Localized deformations of G_ij—interpreted as topological connectivity defects—generate nonlinear drifts of the form δv ∼ ∇c_eff / c_eff, which advect and suppress small-scale plasma fluctuations. This provides a purely geometric route to plasma stabilization without external confinement or power input. This version of the manuscript is currently under review at Physics of Plasmas (AIP). Minor differences may appear in the final published version.

Abstract: Large magnetic fields, either imposed externally or produced spontaneously, are often present in laser-driven high-energy-density systems. In addition to changing plasma conditions, magnetic fields also directly modify laser-plasma interactions (LPI) by changing participating waves and their nonlonear interactions. In this paper, we use two-dimensional particle-in-cell (PIC) simulations to investigate how magnetic fields directly affect crossbeam energy transfer (CBET) from a pump to a seed laser beam, when the transfer is mediated by the ion-acoustic wave (IAW) quasimode. Our simulations are performed in the parameter space where CBET is the dominant process, and in a linear regime where pump depletion, distribution function evolution, and secondary instabilities are insignificant. We use a Fourier filter to separate out the seed signal, and project the seed fields to two electromagnetic eigenmodes, which become nondegenerate in magnetized plasmas. By comparing the seed energy before CBET occurs and after CBET reaches quasi-steady state, we extract CBET energy gains of both eigenmodes for lasers that are initially linearly polarized. Our simulations reveal that starting from a few MG fields, the two eigenmodes have different gains, and magnetization alters how the gains depend on laser detuning. The overall gain decreases with magnetization when the laser polarizations are initially parallel, while a nonzero gain becomes allowed when the laser polarizations are initially orthogonal. These findings qualitatively agree with theoretical expectations.

Abstract: Simplifying the representation of a dynamical system allows us to identify its genuine degrees of freedom and, consequently, the types of instabilities it can exhibit. In this work, we extend earlier variational analysis of classical non-barotropic flows to the more general relativistic non-barotropic case. Specifically, we present a new Eulerian variational formulation for relativistic non-barotropic flows, based on six functions.

Abstract: As devices and systems shrink in size, understanding heat transfer at the mesoscopic scale becomes increasingly critical for the design of efficient thermal management strategies. This study investigates convective heat transfer in concentric cylinders, a geometry which is relevant to small-scale technologies. Finite elements simulation are used to examine the influence of geometry and temperature on effective thermal conductivity, and on a parameter introduced as the apparent thermal transfer coefficient. It is found that the effective thermal conductivity goes above unity for inner and outer radii at the millimeter scale, which is smaller than that predicted by previous analytical studies. This deviation is attributed to the fact that finite element simulations capture the behavior of temperature boundary layers more accurately at small scales than analytical models. These insights aid in identifying conditions in which convection can be ignored, significantly simplifying thermal simulations. This work also reveals that at mesoscales, the ratio between outer and inner radius for which a cylinder can be considered free-standing, is much larger than at the macroscale. This highlights the importance of taking the surrounding surfaces into consideration when performing experiments on the heat transfer properties of mesoscale cylinders such as wires.

Abstract: This study systematically investigates the effect of hydrogen flow rate (100, 200, 300, and 400 sccm) on the properties of DC53 steel during a 4-hour plasma nitriding process conducted at 400 °C in an asymmetric bipolar pulsed reactor. A comprehensive characterization approach was employed. X-ray diffraction (XRD) was used to identify the phase composition, revealing the formation of a compound layer consisting of ε-Fe_2-3N (identified by its (100), (101), and (102) planes) and γ'-Fe₄N (identified by its (220) plane). Mechanical properties were assessed using Vickers microhardness for surface measurements and nanoindentation for depth profiling. Glow discharge optical emission spectroscopy (GD-OES) provided elemental depth analysis, while a ball-on-disk tribometer evaluated the tribological performance. The optimal treatment was achieved at a hydrogen flow rate of 200 sccm. This condition yielded a peak surface hardness of 1121.5 ± 69.2 HV_0.2. GD-OES analysis directly correlated this mechanical enhancement to a high surface nitrogen content of approximately 8.5% and an effective diffusion depth of about 50 µm.

Abstract: A novel analytical solution to the incompressible Navier-Stokes equations for arbitrary flow geometries and Cauchy data is introduced to establish a mathematical theory of turbulence through a direct attack on the Millennium Problem from first principles. All nine advective terms are left fully nonlinear. The velocity field is first separated into rotational and irrotational parts in a Helmholtz decomposition. The irrotational velocity is found by assembling standard vector calculus identities in potential flow while Leray projections are used to carefully handle irrotational and rotational velocity Cauchy data. The rotational velocity derivation is begun by taking the curl of the momentum equations twice, effectively replacing pressure with a Poisson integral of Cauchy data and the forcing terms with incompressibility preventing vorticity entanglement. The resultant pseudo-depressurized momentum equations are addressed by a heavily generalized integral transformation similar to the Cole-Hopf transformation, which captures all nine nonlinear terms in a coupled yet solvable triquadratic algebraic system in the velocity components whose coefficients satisfy heat equations. When said system is solved for the rotational velocity in terms of quartic polynomial roots, the root cause of turbulence is identified as multiplicity collapse of quartic root pairs. Cauchy data is reconciled between the heat equations and velocity components using the method of characteristics. The irrotational and rotational velocities are substituted into the Helmholtz decomposition and its Leray projections, finally resulting in velocity closure. Pressure is recovered when the velocity field is substituted into the standard pressure-Poisson equation. Existence, uniqueness, differentiability class, and kinetic boundedness are analyzed in the Millennium Problem context. Practical implementation is expected to shift CFD paradigms since HPC jobs requiring days would require mere minutes.

Abstract: Artificial intelligence (AI) continues to face fundamental mathematical challenges such as optimization in high-dimensional nonconvex landscapes, generalization under uncertainty, lack of interpretability, and sharp phase transitions in learning dynamics. Similar unresolved problems appear in physics and engineering---for example in turbulence, nuclear fusion, neural information processing, and extreme events \cite{riemann_turb_chaos, riemann_ml_zeros}. We propose that the universal approximation property of the Riemann zeta function offers a unified mathematical framework for these phenomena \cite{voronin1975universality, Bagchi1981}. In particular, we introduce the zeta-derived potential \[ S(\Re s, \Im s) = \bigl|\zeta(s)\bigr| - \ln\bigl|\zeta(s)\bigr| - 1, \] where $s = \Re s + i \Im s$, which generates a family of self-consistent measures reproducing canonical physical distributions such as Boltzmann, Planck, and Kolmogorov spectra \cite{riemann_zeta_f_turb, riemann_hyperlog_turb}. By incorporating the zeros of the zeta function, we develop a zero-aware reparameterization framework that improves optimization, accelerates convergence, and provides a principled turbulence closure mechanism \cite{riemann_ce_opt, riemann_mhd_turb}. This approach creates a bridge between data, dynamics, and statistical measures while preserving analytical properties of $\zeta(s)$ and basic conservation laws. As a result, it offers a single coherent structure for understanding AI optimization, turbulence modeling, and critical transitions in complex systems.

Abstract: We analyze thrust production in a single-fluid magnetohydrodynamic (MHD) thruster with aligned flow and magnetic field. Starting from the momentum equation with an anisotropic conductivity tensor, we show that axial thrust is governed by the competition between the imposed axial electric field and the motional electric field generated by the flow across a radial magnetic field. In a coaxial Hall-type geometry, this yields a simple design rule: thrust increases when the motional field exceeds the axial bias. We clarify the role of cross-helicity (a measure of flow–field alignment) versus the motional term in Ohm’s law. A validation plan is outlined, combining finite-volume MHD simulations with laboratory measurements (PIV, Hall probes, thrust stand). The framework identifies practical levers—velocity–field alignment, magnetic topology that enhances the radial field, and control of the off-diagonal conductivity—for efficient MHD propulsion.

Abstract: We present the Transition Theory’s Electromagnetic Storm (TTEMS), a novel theoretical framework for modeling self-organized electromagnetic phenomena within structured environments. TTEMS integrates the principles of Transition Theory (TT)—originally developed for cosmological evolution—with Fibonacci-based scaling laws and logarithmic spiral symmetries. In this framework, electric and magnetic field intensities emerge from a central electromagnetic void and grow nonlinearly with distance, following Fibonacci-modulated trajectories. This self-similar, radially expanding distribution offers a mathematically elegant and physically plausible departure from conventional linear or exponential field formulations. Beyond its conceptual innovation, TTEMS demonstrates potential for practical implementation through meta-materials, Fibonacci-spaced coil systems, plasma confinement chambers, and phase-locked emitter arrays. The model not only provides new insights into the organization of complex electromagnetic fields but also suggests avenues for advanced applications in structured light, plasma physics, energy transfer, and communication systems. By embedding natural growth constants into electromagnetic theory, TTEMS bridges mathematical aesthetics with physical applicability, positioning itself as a pioneering framework for exploring next-generation self-organized field dynamics.

Abstract: Plasma medicine is a field of research that focuses on the sterilization of bacteria, wounds and cancer treatment, tissue regeneration and other biomedical applications using plasma. Dielectric barrier discharge microplasma was used for biomedical applications such as sterilization of bacteria and skin treatment for transdermal drug delivery. In this research we have investigated the feasibility of microplasma use for blood coagulation. Blood from a dog and a cat was treated with microplasma and after the treatment the blood coagulation effect was observed. By comparison, the blood treated only with air flow did not coagulate after the same treatment time as for microplasma treatment. Microplasma electrodes were energized using a negative pulse voltage power supply and environmental air was used as discharge gas. An increase in the blood coagulation effect was observed with the increase of treatment time, discharge voltage and frequency. The blood coagulation process is attributed to the reactive oxygen and nitrogen species generated by microplasma. This research showed promising results that suggest the potential of using microplasma treatment as a tool for blood coagulation. Furthermore, the microplasma's suitability for portability and integration indicates the potential for developing a compact device tailored for use by first responders.

Abstract: Turbulent flow in neutral fluids and fusion plasmas is known to have many commonalities, one example being the application of energy and enstrophy cascades. In this review, we discuss a novel cyclic process which may also be common to both fluids and plasmas: This includes exact coherent states (or magnetic islands), Reynolds stress-driven (zonal) flows and internal interface layers (or internal transport barriers). We briefly review the current understanding of internal interface layers in fluids and discuss open questions and possible research directions to pursue. The main objective of our review is to create awareness of the shared mechanism to motivate further interdisciplinary research in this field, both by the fluid mechanics and plasma physics communities.

Abstract: The paper presents experimental results for a modified pulsed plasma thruster (PPT) with solid propellant, using a coaxial anode-cathode design. Graphite from pencil leads served as propellant, and a tungsten trigger electrode was tested to reduce carbonization effects. Experiments were performed in a vacuum chamber at 0.001 Pa, employing diagnostics such as discharge current/voltage recording, power measurement, ballistic pendulum, time-of-flight (TOF) method, and a Faraday cup. Current and voltage waveforms matched an oscillatory RLC circuit with variable plasma channel resistance. Key discharge parameters were measured, including current pulse duration/amplitude and plasma channel formation/decay dynamics. Impulse bit values, obtained with a ballistic pendulum, reached up to 8.5 μN·s. Increasing trigger capacitor capacitance reduced thrust due to unstable “pre-plasma” formation and partial pre-discharge energy loss. Using TOF and Faraday cup diagnostics, plasma front velocity, ion current amplitude, current density, and ion concentration were determined. Tungsten electrodes produced lower charged particle concentrations than graphite but offered better adhesion resistance, minimal carbonization, and stable long-term performance. The findings support optimizing trigger electrode materials and PPT operating modes to extend lifetime and stabilize thrust output.

Abstract: This paper introduces and computationally analyzes a modified version of the Hala attractor as a chaotic system designed to bridge the gap between dissipative and Hamiltonian dynamics. The model incorporates a tunable dissipation parameter, δ, and an external periodic forcing term to simulate resonance in physical plasma systems. Through numerical simulations and a detailed analysis of Lyapunov exponents and phase space trajectories, it was demonstrated that the system's chaoticity and dissipative properties can be independently controlled. It is shown that the system can transition from a non-chaotic, dissipative state to a chaotic, non-dissipative (Hamiltonian-like) state. This novel approach provides a framework for modeling phenomena in plasma physics, such as wave-particle interactions and collective behavior, where the degree of chaos is not an inherent property but a controllable variable. The findings validate the utility of tunable chaotic systems for advanced applications in engineered chaotic processes.

Abstract: This paper presents a comprehensive investigation into the deterministic chaotic behavior of a quiescent physical plasma system, bridging empirical observation with a new theoretical framework. We first revisit an experimental analysis of Langmuir probe current-voltage (I-V) traces, where a quadratic fit of the electron saturation region revealed a discrete recurrence relation. The resulting bifurcation diagram unequivocally demonstrates a period-doubling cascade leading to a chaotic regime, providing strong empirical evidence for nonlinear dynamics inherent in the plasma-probe interaction. To model this observed behavior, we introduce the Hala attractor, a low-dimensional dynamical system inspired by the Lorenz equations but modified with a self-regulating feedback mechanism. We demonstrate the Hala attractor’s ability to model two key phenomena: a spatial transition from chaos at the magnetically confined plasma boundaries to a stable state in the quiescent bulk, and a temporal transition to chaos induced by the active perturbation of a diagnostic probe. The model’s simulation results, including a bifurcation from a stable fixed point to a chaotic attractor and the emergence of hysteresis in simulated I-V curves, quantitatively validate the Langmuir probe's experimental findings. By unifying these empirical and theoretical approaches, we establish that chaos in this system is not a fixed, intrinsic property but a dynamic, tunable state dependent on both spatial location and the influence of external measurement. This work provides a powerful, unified framework for interpreting experimental data and reinforces the value of applying chaos theory to understand complex plasma phenomena.

Abstract: Microfluidic methods are an important tool for studying the microrheology of blood and the mechanical properties of blood cells - erythrocytes, leukocytes and platelets. In patients with diabetes, hypertension, obesity, sickle cell anemia, and cerebrovascular or peripheral vascular diseases, hemorheological alterations are commonly observed. These include increased blood viscosity and red blood cell (RBC) aggregation, along with reduced RBC deformability. Such disturbances significantly contribute to impaired microcirculation and microvascular perfusion. In blood vessels, abnormal hemorheological parameters can elevate resistance to blood flow, exert greater mechanical stress on the endothelial wall, and lead to microvascular complications. Among these parameters, erythrocyte deformability is a potential biomarker for diseases including diabetes, malaria, and cancer. This review highlights recent advances in microfluidic technologies for in vitro assays of RBC deformability and aggregation, as well as leukocyte aggregation and adhesion. It summarises the core principles of microfluidic platforms and the experimental findings related to hemodynamic parameters. The advantages and limitations of each technique are discussed, and future directions for improving these devices are explored. Additionally, some aspects of modeling the microrheological properties of blood cells are considered. Overall, the described microfluidic systems represent promising tools for investigating erythrocyte mechanics and leukocyte behaviour.