Physical Sciences

Abstract: Reijtenbagh, Tummers and Westerweel [Phys. Rev. Lett. 130, 174001 (2023)] measured the instantaneous drag on plates accelerated normal to their own plane, reported \(\hat F_a=C_a\rho A\sqrt{\nu aV_a}\) with \(C_a\simeq291\) independent of acceleration and velocity, and rationalized it with a history force built on the one-dimensional Stokes first problem. We solve the correct model problem---an unsteady Hiemenz layer whose strain rate grows linearly in time---using the similarity transformation of Sun [Phys. Fluids 36, 083616 (2024)]. The two-dimensional boundary-layer equation collapses to a single equation in $(\eta,\tau)$ whose coefficients are independent of the streamwise coordinate; its leading-order solution is exact and is a Kummer function of the second kind. The transformation identifies the experimental dimensionless time with the diffusion time, \(\tau=2t^{*}\), and an exact geometric identity returns the empirical law with the same coefficient \(2/\sqrt\pi\), generalized to arbitrary velocity programs as a Basset memory integral. The resulting force is smaller than the measurement by a factor that we show factorizes exactly into the ratio \(h/\delta=\sqrt{a^{*}\mathrm{Re}_h}\) of plate size to diffusion length and a residual factor of two: the boundary layer accelerates fluid over \(\sqrt{\nu t}\) where the plate accelerates it over \(h\). We then test the empirical law against the published data. Digitizing the reported coefficient for all runs shows that \(C_a\) is not constant but rises as \(V_a^{0.36\,[0.28,0.45]}\), excluding the assumed \(\nu^{1/2}\) scaling at about seven standard deviations. Frame-by-frame analysis of the supplemental video shows that \( F_D \approx \rho \, l_a \, \frac{d(\Gamma b_v)}{dt} \) to within $10\%$ throughout the acceleration, with no fitted parameter. The unsteady force on a starting plate is therefore vortical, and a single experiment---repeating a few runs at elevated viscosity---would settle the exponent.

Abstract: We construct the similarity structure of unsteady compressible two-fluid (Hall) plasma boundary layers with separate ion and electron temperatures. Combining the unsteady Howarth–Dorodnitsyn reduction of Stewartson \( [Q.~J.~Mech.~Appl.~Math.~\textbf{4}, 182 (1951)] \) with the diffusion-time similarity ansatz of Sun \( [Phys.~Fluids ~ \textbf{36}, 083616 (2024)] \), we obtain a closed system in \( (\eta,\tau) \) for the reduced stream function, flux function, out-of-plane field and velocity, and two temperatures. Three structural results organise the problem. First, the Hall transport operator is invariant under the Dorodnitsyn map: because the Hall coefficient \( \lambda=1/\mu_0 ne \) scales as the local temperature while the in-plane magnetic derivative \( B_\bot\!\cdot\!\nabla \) transforms with the inverse weight, the two cancel exactly, and the Hall term—together with the magnetic force per unit mass—takes precisely its incompressible form. The pressure gradient does not; it acquires the familiar factor \( \omega=T/T_r \). Second, variable density restores the electron-pressure (Biermann) term, which vanishes identically at constant density. We show it can never enter the in-plane flux equation, and that within a similarity solution at uniform pressure it still vanishes because all thermodynamic gradients are parallel; it survives only through the streamwise pressure gradient, where it reduces to the source \( \theta_{e,\eta}/2M^2 \) and generates a second, independent quadrupole. This Biermann quadrupole dominates the Hall quadrupole below \( M\simeq0.73 \) and exceeds it twelvefold at \( M^2=0.05 \). Third, exact Hall similarity requires a layer of constant thickness (\( m=1 \)) while exact compressible similarity requires constant edge Mach number (\( m=0 \)); the two are disjoint, so no exactly similar compressible two-fluid layer exists. The admissible families are a strongly heated stagnation-type layer, exact to all orders in \( \varepsilon_H \), and a compressible flat plate, exact in the thermodynamics and self-similar through \( O(\varepsilon_H) \), whose Hall subsystem remains a first-order pair with \( f\mapsto\omega f \). Further results: the change of type of the unsteady system is purely kinematic, both equations carrying \( 1-2\tau f_\eta, so \tau_{\rm crit}=1/2 \) independently of field strength, Mach number and wall condition; the Alfvénic degeneracy is not displaced by compressibility, because \( \omega\to1 \) at the layer edge where the transition is decided; an aligned frozen-in field destroys the Mach independence of the transformed flat-plate skin friction, by \( 38\% \) at \( M^2=0.7, M_e^2=16 \); a hot wall expels tangential flux, the wall field falling by a factor of \( 4.6 \) between \( M_e^2=0 \) and \( 16 \); and expansion cooling drives the electron temperature below its free-stream value when equipartition is weak. Numerical solutions reproduce Hiemenz, Blasius–Dorodnitsyn and the compressible recovery factor to six figures, and confirm the predicted \( O(\varepsilon_H^2) \) back-reaction over a sixteenfold range in \( \varepsilon_H \).

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. We propose that the universality of the Riemann zeta function provides a unified mathematical foundation for these phenomena. In particular, we introduce the zeta-derived potential S (Re, Im) \( = |\zeta(\Re + i\,\Im)| - \ln|\zeta(\Re + i\,\Im)| - 1, \) which generates a family of self-consistent measures reproducing canonical physical distributions such as Boltzmann, Planck and Kolmogorov spectra. 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. 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 modelling and critical transitions in complex systems.

Abstract: The notion of a vortex is fundamental in fluid dynamics, where it broadly refers to rotary fluid mo-tions of various forms. Yet a precise, universal definition has remained elusive. Two fundamental challenges persist in the existing definitions of a vortex. The first is the gap between the analytic perspective that adopts a framework of motion decomposition and the synthetic perspective that em-phasizes the geometric patterns of the composite motion. The second is the gap between precisely defined local measures of rotation and intuitive large-scale descriptions of vortices. The author devel-ops a geometric theory of smooth tangent vector fields on oriented closed surfaces that bridges the an-alytic and synthetic perspectives, and provides a nonlocal definition of a vortex core. Working within the frameworks of the irreducible symmetric-antisymmetric decomposition (iSAD), eigenvalue de-composition (EVD) and Helmholtz-Hodge decomposition (HHD), the author proves two principal results concerning these vortex cores. First, all streamlines therein wind in the same direction, indi-cating a nonlocal rotary motion in the entire vortex core. Second, each vortex core can have at most one axis (center or focus). The theory is illustrated with examples on spheres and tori of various cur-vature, demonstrating how geometry and topology influence the shape of vortex cores. The results are purely mathematical and extend naturally to open surfaces, offering a rigorous foundation for vortex identification across disciplines.

Abstract: This work presents an operational definition of angular time τ as an independent dimension within the angular displacement spacetime framework φ(τ) [1], Two complementary lines of evidence are provided. First, a zero-parameter turbulent scaling law, derived solely from the intrinsic 2π periodicity of , reproduces all high-precision DNS data up to order p=9 with relative errors below 0.3%—offering indirect empirical support for the physical reality of the τ dimension [2,3]. Second, a binary crucial experiment under the zero-area limit (r=0) is proposed: at the rotation center, where both special and general relativity predict zero frequency shift, the φ(τ) framework predicts a non-zero shift proportional to ω2. This clean, geometry-based test provides a direct falsification pathway. The work does not negate relativity but proposes a supplementary geometric framework for rotational dynamics, with experimentally testable consequences.

Abstract:

We construct from first principles the complete similarity structure of unsteady incompressible two-fluid (Hall) plasma boundary layers with separate ion and electron temperatures, and analyse the resulting states in full. We first establish four exact degeneracies of the planar problem that constrain any admissible formulation: the Hall force cancels identically from the total momentum equation; the electron-pressure (Biermann) term vanishes identically from the induction equation at constant density; if the out-of-plane field \(B_z\) is set to zero the Hall term drops out of the in-plane flux equation altogether, so that a strictly planar "Hall boundary layer" is indistinguishable from resistive magnetohydrodynamics; and the \(B_z\) magnetic pressure cancels exactly from streamwise momentum. The minimal consistent description is therefore a four-field system in (\(\psi, B_Z, \mu_\perp, \mu_Z\)) coupled to two temperatures. Reducing this system under the two-parameter similarity map \(\eta=y/\delta(x)\), \(\tau=\nu t/\delta^{2}(x)\), we prove an exhaustive classification theorem: exact similarity of the full two-fluid problem requires \(\delta'(x)=0\), which admits precisely two nondegenerate families—a stagnation-type layer with \(U_e\propto x\), exactly self-similar to all orders in the Hall parameter \(\varepsilon_H=Md_i/\delta\), and a degenerate Rayleigh layer—while the Blasius-type growing layer is self-similar exactly through first order in \(\varepsilon_H\) and breaks similarity only at \(O(\varepsilon_H^{2})\). The obstruction is intrinsic: \(d_i\) is an absolute length while \(\delta\) grows, so Hall physics in a growing layer is a leading-edge phenomenon confined to \(x\lesssim x_H\) with \(x_H/d_i=\tfrac12M^{2}\mathrm{Re}_{d_i}\). We derive the reduced systems, their boundary conditions, and a set of von K\'arm\'an integral relations in full detail; obtain the asymptotic hierarchy in \(\varepsilon_H\); and identify the dispersive whistler scale \(d_i/\delta=\varepsilon_H/M\). Numerical solutions of the steady boundary-value problem and of the unsteady initial-value problem—the latter requiring implicit integration because the Hall coupling is a stiff fourth-order whistler operator—confirm every structural prediction, including an exact identity between the viscous and magnetic displacement thicknesses. A linear stability analysis shows the similarity states to be stable, with a leading eigenvalue that reproduces the measured relaxation rate to 0.6%, equals -1 exactly in the field-free limit for all \(P_m\) (a mode we identify analytically), vanishes linearly at the Alfvénic point as -1.36(1-\(M^{2}\)), and becomes complex near \(\varepsilon_H\simeq0.4\), so that relaxation turns oscillatory under the whistler coupling. We close by mapping the accessible regime onto laboratory and space plasmas using Braginskii transport, and by stating plainly where the collisional description fails.

Abstract: Steady compressible magnetohydrodynamic (MHD) boundary layers have been studied since the work of Rossow [32], Bleviss [3] and Bush [5]. What has not been developed is their unsteady similarity structure. This paper supplies it, by combining the Howarth--Dorodnitsyn transformation with the diffusion-time similarity ansatz of Sun [37], and in doing so uncovers a control mechanism that the steady literature did not isolate. Taking the applied field normal to the wall, B \( = B_0(x)\hat{e}_y \), makes the current solenoidal identically in two dimensions, so no auxiliary electrostatic problem arises. The external circuit is characterised by the classical load factor \( k = -E_z/(UB_0) \) [29,38]. The reduction yields a coupled pair of equations in \( (\eta,\tau) \) for the reduced stream function f and reduced total enthalpy g, governed by \( (a,b,c;\Theta,\mathrm{Pr},N,k) \) with \( N=\sigma B_0^2\delta^2/(C\mu_r) \) a squared Hartmann number. Our central structural result is that the load factor cancels identically from the momentum equation once the outer pressure field is treated consistently, and survives only in the enthalpy equation, where the combined Lorentz work and Joule dissipation reduce exactly to J\( \cdot\boldsymbol{E} \) \( =\sigma B_{0}^{2}kU\left(kU-u\right) \). The momentum source is \( N\omega(1-f_\eta) \) for every k; the enthalpy source is \( NE\,\omega\,k(k-f_\eta) \). Three consequences follow. (i) The linear Crocco integral survives the field only at k=0, where the classical \( g\equiv1 \) holds exactly despite an arbitrarily strong field, and at k=1, where it holds only for the cooled wall \( T_w/T_e = 2-\Theta \); for all other k no linear enthalpy--velocity relation exists. (ii) Because \( k(k-f_\eta) \) changes sign at \( f_\eta = k \), a boundary layer operating in generator mode extracts enthalpy near its outer edge. (iii) Consequently the load factor is a thermal-control parameter: sweeping k moves the adiabatic recovery factor from r=0.336 (a 44%reduction in adiabatic wall temperature relative to the field-free value at M_e=4, N=4) through r=1 near \( k_*\simeq0.61 \) and on to thermal runaway, with an optimum cooling load factor \( k_{\rm opt}\simeq0.26 \) that is almost independent of N and is predicted analytically by \( k=f_\eta/2 \). The unsteady analysis gives three further results. The change of type of the reduced system is purely kinematic: both equations carry the same factor \( 1-c\tau f_\eta \), so \( \tau_{\rm crit}=1/c \) is independent of N, k, Mach number, Prandtl number and wall condition, while the thermal mode diverges beyond it a factor 1/Pr faster — confirmed by a \( 10^{44} \) disparity in computed divergences. Exact constancy of the compressibility parameter \( \Theta \) requires \( m=0 \) whereas unconditional well-posedness requires \( m\ge1 \), so the two are mutually exclusive. And for Pr=1 we derive and verify to seven digits the identity \( r = 2f_{\eta\eta}(0)Q-1 \) with \( Q=\int_{0}^{\infty}\exp\left[-\int_{0}^{\eta}f\right]d\eta \). Global solutions in the Williams--Rhyne chart connect the impulsive-start Rayleigh state to the steady state through the region forward marching cannot enter, and confirm that neither field nor compressibility is felt at the impulsive start.

Abstract: The diffusion-time similarity transformation introduced by Sun [Phys. Fluids 36, 083616 (2024)] reduces the two-dimensional unsteady boundary layer equations to a single partial differential equation in the two variables η = y/δ(x) and τ = νt/δ²(x). We extend the reduction to an electrically conducting fluid at low magnetic Reynolds number and show that the reduced problem changes type. Grouping the time-derivative terms reveals that the coefficient of the highest mixed derivative is 1 − Λ with Λ = cτf_η, so that a frozen-coefficient analysis gives the growth rate λ = −k²/(1 − Λ): marching forwards in the diffusion time is parabolic only where Λ < 1 and backward-parabolic beyond. For a power-law outer stream U = Cx^m we find Λ = (1 − m)ut/x, so the threshold coincides with the Stewartson starting-front criterion t = x/u for a flat plate. Integrating the constancy conditions rather than postulating a profile shows that the admissible flows comprise exactly three families—power-law, exponential and uniform—the exponential one being missed by the usual ansatz. Constancy of the magnetic interaction parameter is a separate condition, B₀δ = const, so a uniform applied field is admissible only where the layer does not grow—that is, only at a stagnation point. The reduction is unconditionally well posed for m ≥ 1 and, for m < 1, must be integrated backwards in τ beyond τ = 1/c, which corresponds to marching downstream. A second-order implicit scheme confirms the threshold sharply: for c = 2 the wall shear is grid-converged to six figures up to τ = 0.45 on four successive meshes and diverges non-monotonically in the mesh beyond τ = 0.5. We further derive the two-term strong-field expansion f_ηη(0) ≃ M^1/2 + (a/12 + 2b/3)M^−1/2 for the magnetic interaction parameter M, which reproduces published spectral benchmarks to eight significant figures and fixes the prefactor of the √M friction law at unity.

Abstract: The thermal boundary layer on a flat plate is almost always computed by inserting the steady Blasius velocity field into a time-dependent energy equation, so that the temperature evolves along trajectories that do not. The inconsistency has been unavoidable: no exact solution of the two-dimensional unsteady laminar boundary layer was available until Sun [16] obtained one in terms of Kummer functions, using the diffusion time \(\tau=\nu t/\delta^{2}(x)\) as a similarity variable. We solve the corresponding thermal problem. The similarity transformation applied to the energy equation yields \[ \theta_{\tau}-\alpha f\theta_{\eta}+\gamma\tau(f_{\tau}\theta_{\eta} -f_{\eta}\theta_{\tau})=Pr^{-1}\theta_{\eta\eta}+Ec\,f_{\eta\eta}^{2}, \] the terms in \(\eta f_{\eta}\theta_{\eta}\) cancelling identically; the system closes only for a flat plate. Sun's solution, given through six auxiliary functions, collapses to three Kummer-\(U\) expressions and is invariant under the group generated by \(X=(\eta\tau+2)\partial_{\eta}+2\tau^{2}\partial_{\tau}\), with \(Xf=\tau f-\eta\). On group-invariant temperature fields the convective operator loses all dependence on the velocity field, and the energy equation reduces exactly to \[ \Theta''+2Pr\,\omega\Theta'+Pr\,Ec\,[F'(\omega)]^{2}=0 \] with \(\omega=(3\eta\tau+2)/2\sqrt{3}\tau^{3/2}\). Hence \[ \theta=\operatorname{erfc}(\sqrt{Pr}\,\omega)+Pr\,Ec\,\Phi(\omega), \] together with closed forms for the Nusselt number, a recovery factor \(r=2Pr\,P_{\infty}\), a Reynolds analogy factor \(0.7132Pr^{-1/2}\) and a thickness ratio \(1.0910Pr^{-1/2}\) exact at all $Pr$. Both fields satisfy the governing equations to below \(10^{-17}\). Boundary conditions are met to \(O(\tau^{-1})\), inherited from the parent solution.

Abstract: Partially averaged Navier–Stokes (PANS) has evolved over the past two decades from a conventional RANS–DNS bridging model into a scale-resolving simulation framework with controllable turbulence resolution. By introducing the unresolved fractions of turbulent kinetic energy and dissipation, fk and fε, PANS regulates the partition between modeled and resolved turbulence. However, the turbulence resolution achieved in practical simulations is not solely determined by the prescribed parameters, but also depends on the interaction among turbulence closure, grid resolution, numerical dissipation, and physical modeling. This review summarizes the theoretical foundations, resolution-control strategies, and engineering applications of PANS, with particular emphasis on the consistency between prescribed and realized turbulence resolution. The formulation of partially averaged governing equations, closure transformations, scale relationships, and the limiting behaviors toward RANS and DNS are first discussed. Recent developments in variable-resolution formulations, commutation-error treatment, scale-supplying variables, near-wall resolution approaches, dissipation-resolution control, and variable-density extensions are subsequently reviewed. Applications to canonical turbulence, separated flows, rotating machinery, marine hydrodynamics, cavitation, heat transfer, combustion, and compressible flows are assessed in terms of turbulence statistics, coherent structures, spectral characteristics, and engineering prediction capability. Existing studies demonstrate that PANS can recover energetic unsteadiness suppressed by RANS and improve predictions of complex flows when sufficient numerical resolution and appropriate physical closures are provided. Nevertheless, reducing fk does not necessarily guarantee improved accuracy, as the prescribed resolution must be consistent with grid resolution, time-step selection, numerical schemes, boundary treatments, and multiphysics models. Future developments of PANS will focus on reliable resolution estimation, conservative variable-resolution strategies, consistent multiphysics scale closures, and systematic verification and validation procedures to establish quantitative relationships among prescribed resolution, numerical realization, and predictive accuracy.

Abstract: Atmospheric-pressure plasma optical emission spectroscopy (OES) is a promising technique for rapid, and label-free characterization of particulate materials because of its ability to generate material-dependent optical emission signatures under ambient conditions. In this work, an enhanced plasma-induced ionization fluorescence spectroscopy (PIFS) platform based on an open atmospheric-pressure discharge configuration is presented for the characterization of representative organic and inorganic particulate materials. The PIFS system uses two porous nickel electrodes separated by a dielectric (glass) spacer to generate a stable DC plasma discharge while simultaneously providing a large effective discharge nanotextured surface for plasma-particle interactions. Unlike our previously reported PIFS platforms, the porous-electrode architecture enhances plasma stability and promotes localized electrostatic particle accumulation, thereby improving plasma-particle interactions and measurement reproducibility. Optical emission generated during particle excitation was collected using a fiber-optic probe coupled to an Ocean Insight QE Pro spectrometer with approximately 1 nm spectral resolution. Representative organic materials, consisting of bee pollen, cellulose, and lactate, together with inorganic materials such as rust particles (iron oxide), sodium chloride, and blowing dust, were investigated at particle loadings of 1, 3, and 6 mg. The measured spectra revealed distinct emission fingerprints over the visible and near-infrared spectral regions. Bee pollen and iron oxide showed the largest spectral modifications, whereas cellulose, sodium chloride, and blowing dust produced comparatively smaller perturbations of the plasma emission profile. Quantitative comparison of characteristic emission wavelengths at 590, 660, 775, and 950 nm further indicated that each material possesses a unique normalized intensity distribution suitable for spectral discrimination. Analysis of the influence of particle loading showed increasing emission intensity for bee pollen, relatively stable responses for cellulose, lactate, and sodium chloride, and a decreasing response for blowing dust, due to particle deposition, optical attenuation and insulation of electrode surfaces. The proposed experimental platform provides a simple, reproducible, and cost-effective approach for plasma-based particulate characterization and demonstrates considerable potential for environmental monitoring, aerosol identification, and industrial process diagnostics.

Abstract: The main aim in this paper is to present a temperature-dependent version of the Englert-Schwinger functional, within the quantum statistical model, for computing the finite temperature equation of state of electrons in plasmas. Schwinger and co-workers originally derived the functional for the case of isolated atoms at zero temperature, and applied it to compute the electronic properties. After deriving the extension to finite temperatures, a new algorithm is developed to solve the finite temperature Englert-Schwinger model. With the introduction of corrections to the density of strongly bound electrons, the model automatically takes into account the effects of these electrons in all the thermodynamic properties. Furthermore, the approach reduces the order of the nonlinear differential equation to two, in lieu of four in the quantum statistical model. Thus, at much less computing efforts, the model would be useful in high-energy-density physics applications of equation of state theory. Numerical results obtained for Cu and Al are compared with those of the original quantum statistical model. Good agreement is found for pressure and energy of electrons. The Appendix provides a derivation of the stationary property of the finite temperature free energy functional, and details of the new algorithm.

Abstract: We examine energetic electron distributions in the region of the diffuse aurora using a two-dimensional bi-Maxwellian model, applied to electron flux data at a single geomagnetic equator (L = 6.5). Electron flux is analyzed as a function of energy and pitch angle and transformed into velocity space to reconstruct the distribution function. An unweighted log-space least-squares fit of the bi-Maxwellian model to the reconstructed distribution yields a reduced residual measure of χ2 v = 1.000053, a mean absolute residual of |∆log10 f| = 0.0469 dex, an anisotropy factor, AT = 0.9886±0.0016, and no statistically significant bulk drift. These results show that, at this location, the bi-Maxwellian model reproduces the observed velocity-space structure with good quantitative accuracy and reveals a quasi-isotropic, near-equilibrium electron population.

Abstract: In the grand narrative of mathematical physics, a profound gap separates microscopic particle dynam- ics and macroscopic continuum mechanics. Hilbert’s sixth problem aims to construct the axiomatic foundation of macroscopic physical laws starting from atomism; this is not only a pursuit of mathemat- ical rigor but also an ultimate inquiry into the essential laws of the physical world. This paper provides an in-depth analysis of two milestone works in this field: the rigorous derivation of fluid equations by Deng, Hani, and Ma [1] and the constructive decomposition of kinetic equations by Chang Liu and Kun Xu [2]. The former establishes the inevitability of macroscopic laws by rigorously proving long-time convergence from hard-sphere systems to fluid equations through the introduction of a "Molecular Cutting Algorithm." The latter constructs a unified equation system traversing the entire Knudsen spectrum by introducing physical constraints under finite parameters via a "Local Dynamical Horizon." In particular, the work by Liu and Xu provides intermediate equation sets from the BGK model to the Navier-Stokes equations that vary continuously with scale, creatively solving the immense challenge of "how to establish control equations at designated scales" in multi-scale engineering calculations. This paper systematically compares these two distinct but highly complementary research paradigms from four dimensions: the height of mathematical analysis, the depth of physical modeling, the breadth of computational methods, and the width of application prospects.

Abstract: The main objective of this study is to obtain the average parameters of gas-discharge plasma when controlling the steady position of the bow shock wave (BSW) using the combined action of a gas discharge initiated by a current from an external source and a magnetic field near the frontal surface of the model. The studies were carried out using both experimental and numerical methods in xenon and air. A comparison of the numerical and experimental dependences of the relative distance of the steady BSW from the model on the discharge power showed good agreement. Based on the conducted flow modeling, taking into account the dependence of the adiabatic index on the degree of ionization and the degree of nonequilibrium, and using the Burm's theory, gas-discharge plasma characteristics were obtained, such as the degree of ionization and the degree of nonequilibrium, the electron density and the electron temperature in the absence and presence of a magnetic field. By this way an integrated experimental-computational system was formed in which the measured characteristics of the discharge and BSW, as well as the numerically obtained averaged plasma parameters in the impact zone, are combined with the Burm's theory to clarify the thermodynamic state of the medium and determine the corresponding characteristics of the gas-discharge plasma. The obtained results can be used to develop control systems for high-speed flows that take into account the influence of plasma parameters and the electric and magnetic fields.

Abstract: Dynamic stall and its control using synthetic jets are investigated for a sinusoidally pitching NACA 0018 airfoil at a chord-based Reynolds number of 40000, a reduced pitch frequency of 0.112, and two pitching amplitudes. An array of ten circular-orifice actuators is installed near the leading edge to examine the effects of low- and high-frequency burst-modulated forcing. Particle image velocimetry (PIV) is employed to measure phase-locked velocity fields along the airfoil centerline, while hot-wire anemometry is used to characterize wake frequency spectra. The baseline pitching cases exhibit complex vortex dynamics, with a wide range of coherent structures and vortex formation processes occurring over the entire airfoil surface. The formation and detachment of a leading-edge vortex (LEV) are identified as the primary features of dynamic stall across all cases. Both low- and high-frequency forcing are found to delay the onset of static and dynamic stall, although their influence on the boundary layer transition differs. The actuator placement near the leading edge is shown to be a critical parameter governing control effectiveness. Furthermore, the disparity between the forcing and pitching frequencies introduces additional unsteady vortex interactions associated with rapid variations in the adverse pressure gradient, which are unique to the dynamically stalling flow.

Abstract: The development of steady-state advanced operation modes with high fusion gain (Q) is a primary objective of magnetic confinement fusion research. The advancement of high-temperature superconducting (HTS) magnet technology has introduced a new development path using devices like SPARC. This path contrasts with the conventional low-temperature superconducting (LTS) approach represented by devices such as BEST. This study utilizes the fast integrated modeling code METIS to compare the physical conditions required for an HTS-based (SPARC-like) and LTS-based (BEST-like) devices to achieve an energy gain of Q≈5. Furthermore, we simulated the achievable fusion power for both devices under an identical set of core physics parameters to isolate the effect of magnetic field strength. Simulation results show that at a similar Q≈5, the HTS device, leverages its high magnetic field to require significantly lower auxiliary heating power (approximately 50%-60% less). Additionally, it operates at a lower Greenwald density fraction (fGW≈0.37) than the LTS device (fGW≈0.87). This directly validates the strong dependence of the fusion triple product on magnetic field strength (∝B3). Under identical high-density ("BEST-like") parameters, the HTS device achieves much higher fusion power but faces a drastically increased L-H transition power threshold. This increase may force operation in L-mode. Crucially, even in L-mode, the high-field HTS device can still achieve Q>5 via high-density operation.

Abstract: This paper aims to reveal the systematic unification of dimensional analysis with scaling Lie group invariants and Lie algebra representation theory, proving that its essence is the symmetry reduction of physical laws under the scaling group (stretching group). By introducing the theory of Lie groups and their Lie algebras, we reinterpret dimensionless numbers as absolute invariants under group action, and the dimensional matrix as the representation matrix of the Lie algebra. On this basis, we demonstrate in detail how to solve the invariant equations via infinitesimal generators, and through the rigorous solution of two classic physics examples. We elucidate that the Lie group method can not only naturally derive the Buckingham \(\Pi\) theorem but also reveal deep structural insights into the orthogonal decoupling between physical quantities.

Abstract: The multi-scale self-similarity and intermittency in incompressible turbulence fundamentally stem from scaling symmetry and its breaking. Using Lie group and infinitesimal generator theory, this paper algebraically reconstructs the Kolmogorov K41 and She-Leveque (SL) scaling laws as an equivalent mapping of existing phenomenological models rather than a first-principles derivation. We show that K41 corresponds to the invariance (zero eigenvalue) of energy flux under the scaling generator, yielding a strictly linear character, whereas anomalous scaling reflects symmetry breaking. Furthermore, SL's hierarchical recursion is demonstrated to be equivalent to an eigenvalue difference equation of the prolonged generator acting on the hierarchy. This difference eigenvalue quantifies the hierarchy's ``nonlinear sensitivity'' to scale variations---akin to weight differences in representation theory---characterizing the degree of symmetry breaking. By solving this recursion with the geometric boundary conditions of 3D vortex tubes, the SL formula is reconstructed. Our framework reveals K41 as the flat spacetime of the turbulent mean field, and SL as the curved spacetime induced by vortex singularities, with Lie algebra providing the elegant mathematical language for this transition.

Abstract: This paper develops a thermo-acoustic continuation framework for physically admissible compressible Navier–Stokes–Fourier evolution. The analysis is formulated under the assumptions of positivity of density and temperature, entropy admissibility, free-energy dissipation, finite acoustic propagation, strict hyperbolicity, uniformly subsonic evolution, constitutive smoothness, and a finite-energy weak solution framework. The admissibility conditions are treated as the physical regime of the theory. The central objective is to determine whether thermo-acoustic dissipative structure suppresses scale-critical concentration compatible with singularity formation. A localized entropy concentration quantity is introduced using the entropy-production density generated by viscous deformation and thermal diffusion. The analysis establishes localized thermo-acoustic coercivity, derives nonlinear subcriticality estimates for transport, thermal, acoustic, pressure, coefficient, and commutator remainders, and obtains higher thermo-acoustic integrability through compactness and Meyers-type arguments. Campanato iteration then yields oscillation decay, localized Hölder regularization, and thermo-acoustic ε-regularity. Within the admissible thermo-acoustic regime, persistent scale-critical concentration is excluded. Consequently, admissible thermo-acoustic evolution admits continuation beyond finite admissible evolution intervals. The continuation mechanism is generated by entropy production, thermal diffusion, free-energy dissipation, and finite-speed acoustic redistribution.The paper also studies incompressible projection of the thermo-acoustic system. Using projection fibers and conditional disintegration theory, it is shown that the entropy-generating thermo-acoustic structure is not generally reconstructible from incompressible projected variables alone. The analysis identifies a structural difference between admissible thermo-acoustic compressible evolution and mechanically projected incompressible evolution.The paper does not prove unconditional global regularity for arbitrary compressible Navier–Stokes–Fourier solutions, unconditional propagation of thermo-acoustic admissibility, or regularity or singularity formation for incompressible Navier–Stokes evolution. The continuation result is conditional on persistence of the admissible thermo-acoustic regime.