Entire Regime Research Articles

The Realization Rule as a Legal Standard

The realization “rule” in tax law is better characterized as a legal standard. This characterization matters after the Supreme Court’s decision in Moore v. United States, which sets the stage for future courts to decide that the Constitution mandates realization—an identifiable event before accrued income is reportable by taxpayers. The stakes of a constitutional realization requirement are underappreciated. Because current statutory law embeds realization as a background principle, a constitutional realization requirement would operate as a taxpayer-initiated antiabuse doctrine—a sword that taxpayers could use selectively to invalidate parts of the Internal Revenue Code and Treasury Regulations. This novel constitutional tool has adverse, and underappreciated, implications for the U.S. tax system’s structure and complexity. Through the lens of the longstanding academic literature on legal rules and standards, the dangers of a constitutional realization requirement extend beyond top-down risks to individual Internal Revenue Code provisions or, as the Moore majority posited, entire taxing regimes. Instead, a constitutional realization requirement threatens to erode federal income tax law from the bottom up, through incremental public and private challenges to the fundamental mechanics of taxation. Realization and nonrealization permeate business entity taxation in deeply technical ways. In these areas, a constitutional realization requirement may facilitate aggressive private planning, undermine the law’s coherence, and dampen reform efforts. Even Moore’s whisper of a constitutional realization requirement ventures into poorly charted territory, with potentially detrimental consequences that may prove difficult to unwind. Moreover, a constitutional realization requirement portends increased complexity in tax law. Government-asserted antiabuse doctrines constrain complexity by allowing lawmakers to write simpler rules that cover high-frequency transactions. Low-frequency transactions, including those that reflect inappropriate tax planning, are addressed through (and discouraged by) open-ended standards in the enforcement process. As a taxpayer-initiated antiabuse doctrine, a constitutional realization requirement would have the reverse effect, increasing complexity by increasing the frequency of tax-planned transactions, encouraging more costly government responses to taxpayer abuse, and changing the dynamics of enforcement. The resulting complexity would be systemic—and could increase over time.

Legislation Development in Vietnam: Is the criminal law becoming more humane?

After four decades since the present of the first “modern” Criminal code of Vietnam in 1985, Vietnamese lawmakers have reached many remarkable milestones in terms of criminal justice policy and legislation. The paper shall discuss and clarify 02 main hypotheses. Firstly, there are 05 criteria to evaluate the clemency of the Vietnamese criminal law, including: 1) The proportion between the number of very serious, extremely serious crimes and total number of crimes; 2) Severity of the punishments in the 2015 Criminal Code; 3) The number of provisions on exemption from serving sentences, reduction of sentence duration and conviction expungement; 4) The number of provisions on penalty decisions in favor of the offenders; 5) The proportion between the decriminalized crimes and criminalized conducts in the criminal code. Secondly, based on analyzing these criteria, the paper shall prove that Vietnamese criminal law is becoming more humane. The achieved developments come from several reasons. The main one is that the entire political regime of Vietnam, with the key role of Communist Party, participated in the reformation process of the criminal law.

Universal Properties of the Evolution of the Universe in Modified Loop Quantum Cosmology

In this paper, we systematically study the evolution of the Universe within the framework of a modified loop quantum cosmological model (mLQC-I) using various inflationary potentials, including chaotic, Starobinsky, generalized Starobinsky, polynomials of the first and second kinds, generalized T-models and natural inflation. In all these models, the big bang singularity is replaced by a quantum bounce, and the evolution of the Universe, both before and after the bounce, is universal and weakly dependent on the inflationary potentials, as long as the evolution is dominated by the kinetic energy of the inflaton at the bounce. In particular, the pre-bounce evolution can be universally divided into three different phases: pre-bouncing, pre-transition, and pre-de Sitter. The pre-bouncing phase occurs immediately before the quantum bounce, during which the evolution of the Universe is dominated by the kinetic energy of the inflaton. Thus, the equation of state of the inflaton is about one, w(ϕ)≃1. Soon, the inflation potential takes over, so w(ϕ) rapidly falls from one to negative one. This pre-transition phase is very short and quickly turns into the pre-de Sitter phase, whereby the effective cosmological constant of Planck size takes over and dominates the rest of the contracting phase. Throughout the entire pre-bounce regime, the evolution of both the expansion factor and the inflaton can be approximated by universal analytical solutions, independent of the specific inflation potentials.

Wrinkling of differentially growing bilayers with similar film and substrate moduli

Growth-induced surface wrinkling in constrained bilayers comprising a thin film attached to a thick substrate is a canonical model for understanding pattern formation in many biological systems. While the bilayer model has received much prior attention, the nonlinear behaviour for arrangements with similar film and substrate properties, or substrate growth that outpaces film growth, remains poorly understood. This paper therefore focuses on these cases in which the substrate’s elasticity dominates surface wrinkling. By combining analytical modelling and finite element simulations incorporating advanced path-following techniques, we characterise critical wrinkling states and explore the initial and advanced post-buckling behaviour for a wide range of film-to-substrate modulus and growth rate ratios. It is shown that the classical leading-order asymptotic expression for the critical strain is not of sufficient accuracy for film-to-substrate modulus ratios below 50, and higher order correction terms are presented. Leveraging a weakly nonlinear analytical model, we introduce a phase diagram categorising stable and unstable post-buckling regimes. Advanced path-following simulations are employed to unveil the evolution of wrinkling patterns, from initial sinusoidal instabilities to complex formations involving period doubling, quadrupling, and eventual surface creasing. These comprehensive phase diagrams, parameterised by film-to-substrate modulus and growth rate ratios, provide new insights into the rich dynamics of surface wrinkling. Finally, we demonstrate the existence of multi-stability in the advanced post-buckling regimes for bilayers experiencing substrate-dominated growth. This work contributes to the understanding of the mechanics underlying pattern formation in growing bilayers over the entire parameter regime, with potential implications for explaining biological morphogenesis and informing the development of novel diagnostic tools and artificial flexible electronic skins.

Emergent Ferroelectric Nematic and Heliconical Ferroelectric Nematic States in an Achiral "Straight" Polar Rod Mesogen.

Ferroelectric nematic liquid crystals (NFLCs) are distinguished by their remarkable polarization characteristics and diverse physical phenomena, sparking significant interest and excitement within the scientific community. To date, over 150 NFLC molecules are developed; however, there are no reports regarding straight linear polar molecules with a parallel alignment of the permanent dipole moment and the molecular axis. The straight polar mesogen nBOE exhibits an enantiotropic NF phase with a wide temperature window (up to 100 K) despite having a longer alkyl chain (up to n = 6) than the critical alkyl chain length of conventional models. Interestingly, nBOE with a medium-length alkyl chain displays an exotic phase sequence of NF-HCNF-SmXF during the elimination of positional displacement among adjacent molecules. Furthermore, the reflective color modulation of the HCNFLC over the entire VIS-NIR spectral regime by ultralow E-field (up to 0.14V µm-1) is demonstrated.

Long range order for three-dimensional random field Ising model throughout the entire low temperature regime

Long range order for three-dimensional random field Ising model throughout the entire low temperature regime

Compact modeling of short-channel effects in back-gated 2D negative capacitance (NC) FETs

The negative capacitance field-effect transistor with 2D channel material (2D NC-FET) holds significant promise for low-power applications owing to its remarkable resilience against short-channel effects (SCEs) and favorable noise characteristics. In this study, we establish a compact current–voltage (I–V) model for short-channel back-gated 2D NC-FETs with metal-ferroelectric-metal–insulator–semiconductor structure by self-consistently solving the two-dimensional Poisson, drift–diffusion and Landau–Khalatnikov equations. The proposed model is valid and continuous throughout the entire operating regime, including the fully-depleted region, partly-depleted region, and accumulation region. Furthermore, we derive analytical equations for the threshold voltage ( VTH ) and subthreshold swing ( SS ) of back-gated 2D NC-FETs based on the developed I–V model. Lastly, we elucidate the influence mechanisms of various device parameters and voltage bias on the subthreshold characteristics of short-channel back-gated 2D NC-FETs using the proposed I–V model in conjunction with analytical expressions of VTH and SS . Our findings reveal that back-gated 2D NC-FETs shows unconventional degradation behavior in VTH and SS, resulting from the competition between traditional SCEs and novel negative capacitance effects.

Global sampling of Feynman's diagrams through normalizing flow

Normalizing flows (NF) are powerful generative models with increasing applications in augmenting Monte Carlo algorithms due to their high flexibility and expressiveness. In this work we explore the integration of NF in the diagrammatic Monte Carlo (DMC) method, presenting an architecture designed to sample the intricate multidimensional space of Feynman's diagrams through dimensionality reduction. By decoupling the sampling of diagram order and interaction times, the flow focuses on one interaction at a time. This enables one to construct a general diagram by employing the same unsupervised model iteratively, dressing a zero-order diagram with interactions determined by the previously sampled order. The resulting NF-augmented DMC method is tested on the widely used single-site Holstein polaron model in the entire electron-phonon coupling regime. The obtained data show that the model accurately reproduces the diagram distribution by reducing sample correlation and observables' statistical error, constituting the first example of global sampling strategy for connected Feynman's diagrams in the DMC method. Published by the American Physical Society 2024

Fluctuations of the free energy in p-spin SK models on two scales

20 years ago, Bovier, Kurkova, and Löwe (Ann Probab 30(2):605–651, 2002) proved a central limit theorem (CLT) for the fluctuations of the free energy in the p-spin version of the Sherrington–Kirkpatrick model of spin glasses at high temperatures. In this paper we improve their results in two ways. First, we extend the range of temperatures to cover the entire regime where the quenched and annealed free energies are known to coincide. Second, we identify the main source of the fluctuations as a purely coupling dependent term, and we show a further CLT for the deviation of the free energy around this random object.

Study of implicit CFD modeling of riblets on wind turbine airfoil in transitional flow

The study introduces a novel hybrid boundary condition, derived from existing literature, crafted for predicting the impact of riblets on airfoils in transitional flow. In contrast to models tailored for fully turbulent flow, the hybrid approach successfully captures the operational dynamics of riblets, as demonstrated through meticulous testing. The boundary condition integrates slip length and a modified specific dissipation rate (ω) boundary to encompass the entire riblet regime. Adjusting the model to match measured drag behavior enables predictions of riblet effects at higher Reynolds numbers pertinent to wind turbine blades. Validation reveals the model’s proficiency in capturing the order of magnitude in drag reduction and aligns the change in drag in the correct direction for diverse riblet heights, yet highlights discrepancies in replicating absolute drag reduction values, particularly at smaller angles of attack. This underscores the imperative for further refinement and tuning, necessitating additional experimental data at higher Reynolds numbers and across various angles of attack to ensure the model’s robust applicability across a broader spectrum of conditions.

Weak Harnack inequality for doubly non-linear equations of slow diffusion type

We consider non-negative weak super-solutions u:ΩT→R≥0 to the doubly non-linear equation∂t(|u|q−1u)−divA(x,t,u,Du)=0inΩT=Ω×(0,T], where Ω is an bounded open set in RN for N≥2, T>0 and q is a non-negative parameter. Furthermore, the vector field A satisfies standard p-growth assumptions for some p>1. The main novelty of this paper is that we establish the weak Harnack inequality in the entire slow diffusion regime p−q−1>0. Additionally, we only require that the weak super-solution u is located in the function spaceCloc0([0,T];Llocq+1(Ω))∩Llocp(0,T;Wloc1,p(Ω)).

Magnetic phases of XY model with three-spin terms: interplay of topology and entanglement

Magnetic and topological properties along with quantum correlations in terms of several entanglement measures have been investigated for an antiferromagnetic (AFM) spin-1/2 XY model in the presence of transverse magnetic field and XZX−YZY type of three-spin interactions. Symmetries of the spin Hamiltonian have been identified. Under the Jordan–Wigner transformation, the spin Hamiltonian converted into spinless superconducting model with nearest neighbor (NN) hopping and Cooper pairing terms in addition to next NN Cooper pairing potential. Long range AFM order has been studied in terms of staggered spin–spin correlation functions, while the topological orders have been characterized by winding numbers. Magnetic and topological phase diagrams have been prepared. Faithful coexistence of magnetic and topological superconducting phases is found in the entire parameter regime. Boundaries of various quantum phases have been marked and positions of bicritical points have been identified.

Technical note: Two-component electrical-conductivity-based hydrograph separation employing an exponential mixing model (EXPECT) provides reliable high-temporal-resolution young water fraction estimates in three small Swiss catchments

Abstract. The young water fraction represents the portion of water molecules in a stream that have entered the catchment relatively recently, typically within 2–3 months. It can be reliably estimated in spatially heterogeneous and nonstationary catchments from the amplitude ratio of seasonal isotope (δ18O or δ2H) cycles of stream water and precipitation, respectively. Past studies have found that young water fractions increase with discharge (Q), thus reflecting the higher direct runoff under wetter catchment conditions. The rate of increase in the young water fraction with increasing Q, defined as the discharge sensitivity of the young water fraction (Sd*), can be useful for describing and comparing catchments' hydrological behaviour. However, the existing method for estimating Sd*, which only uses biweekly isotope data, can return highly uncertain and unreliable Sd* when stream water isotope data are sparse and do not capture the entire flow regime. Indeed, the information provided by isotope data depends on when the respective sample was taken. Accordingly, the low sampling frequency results in information gaps that could potentially be filled by using additional tracers sampled at a higher temporal resolution. By utilizing high-temporal-resolution and cost-effective electrical conductivity (EC) measurements, along with information obtainable from seasonal isotope cycles in stream water and precipitation, we develop a new method that can estimate the young water fraction at the same resolution as EC and Q measurements. These high-resolution estimates allow for improvements in the estimates of the Sd*. Our so-called EXPECT (Electrical-Conductivity-based hydrograph separaTion employing an EXPonential mixing model) method is built upon the following three key assumptions: We construct a mixing relationship consisting of an exponential decay of stream water EC with increasing young water fraction. This has been obtained based on the relationship between flow-specific young water fractions and EC. We assume that the two-component EC-based hydrograph separation technique, using the above-mentioned exponential mixing model, can be used for a time-source partitioning of stream water into young (transit times < 2–3 months) and old (transit times > 2–3 months) water. We assume that the EC value of the young water endmember (ECyw) is lower than that of the old water endmember (ECow). Selecting reliable values from measurements of ECyw and ECow to perform this unconventional EC-based hydrograph separation is challenging, but the combination of information derived from the two tracers allows for the estimation of endmembers' values. The two endmembers have been calibrated by constraining the unweighted and flow-weighted average young water fractions obtained with the EC-based hydrograph separation to be equal to the corresponding quantities derived from the seasonal isotope cycles. We test the EXPECT method in three small experimental catchments in the Swiss Alptal Valley using two different temporal resolutions of Q and EC data: sampling resolution (i.e. we only consider Q and EC measurements during dates of isotope sampling) and daily resolution. The EXPECT method has provided reliable young water fraction estimates at both temporal resolutions, from which a more accurate discharge sensitivity of the young water fraction (SdEXP) could be determined compared with the existing approach. Also, the method provided new information on ECyw and ECow, yielding calibrated values that fall outside the range of measured EC values. This suggests that stream water is always a mixture of young and old water, even under very high or very low wetness conditions. The calibrated endmembers revealed a good agreement with both endmembers obtained from an independent method and EC measurements from groundwater wells. For proper use of the EXPECT method, we have highlighted the limitations of EC as a tracer, identified certain catchment characteristics that may constrain the reliability of the current method and provided recommendations about its adaptation for future applications in catchments other than those investigated in this study.

Platelet-Rich Plasma Injections in Chronic Lateral Ankle Instability: A Case Series.

The platelet-rich plasma (PRP) approach may be an effective treatment for joint and cartilage pathologies. However, the rationale for its effectiveness on joint instability is limited. This study aimed to assess the safety and effectiveness of PRP injections in patients with chronic lateral ankle instability (CLAI). This retrospective study was performed at a single-center outpatient clinic between January 2015 and February 2023 and included pre-intervention assessment and short-term follow-up. Patients were excluded if they had received previous surgical treatment or had constitutional hyperlaxity, systemic diseases, or grade II or III osteoarthritis. The clinical and functional evaluation consisted of the Karlsson score, the Cumberland Ankle Instability Tool (CAIT), Good's grading system, the patient's subjective satisfaction level, and the time required to return to exercise. The entire PRP therapy regime consisted of three PRP administrations at 7-day intervals and follow-up appointments. PRP was administered both intraarticularly and into talofibular ligaments. A total of 47 consecutive patients with CLAI were included, 11 were female (23.4%), with a mean age at intervention of 31.19 ± 9.74 years. A statistically significant improvement was found in the CAIT and Karlsson scores at 3 months (27.74 ± 1.68 and 96.45 ± 4.28, respectively) relative to the pre-intervention status (10.26 ± 4.33 and 42.26 ± 14.9, respectively, p < 0.000). The mean follow-up of patients with CLAI was 17.94 ± 3.25 weeks. This study represents successful short-term functional and clinical outcomes in patients with CLAI after PRP treatment, with no adverse effects. It demonstrates the feasibility of a randomized controlled trial to further assess this therapy.

Subcritical Gaussian multiplicative chaos in the Wiener space: construction, moments and volume decay

We construct and study properties of an infinite dimensional analog of Kahane’s theory of Gaussian multiplicative chaos (Kahane in Ann Sci Math Quebec 9(2):105-150, 1985). Namely, if HT(ω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_T(\\omega )$$\\end{document} is a random field defined w.r.t. space-time white noise B˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{B}$$\\end{document} and integrated w.r.t. Brownian paths in d≥3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$d\\ge 3$$\\end{document}, we consider the renormalized exponential μγ,T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _{\\gamma ,T}$$\\end{document}, weighted w.r.t. the Wiener measure P0(dω)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {P}_0(\ extrm{d}\\omega )$$\\end{document}. We construct the almost sure limit μγ=limT→∞μγ,T\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _\\gamma = \\lim _{T\\rightarrow \\infty } \\mu _{\\gamma ,T}$$\\end{document} in the entire weak disorder (subcritical) regime and call it subcritical GMC on the Wiener space. We show that μγ{ω:limT→∞HT(ω)T(ϕ⋆ϕ)(0)≠γ}=0almostsurely,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\begin{aligned} \\mu _\\gamma \\Big \\{\\omega : \\lim _{T\\rightarrow \\infty } \\frac{H_T(\\omega )}{T(\\phi \\star \\phi )(0)} \ e \\gamma \\Big \\}=0 \\qquad \ ext{ almost } \ ext{ surely, } \\end{aligned}$$\\end{document}meaning that μγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _\\gamma $$\\end{document} is supported almost surely only on γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}-thick paths, and consequently, the normalized version is singular w.r.t. the Wiener measure. We then characterize uniquely the limit μγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _\\gamma $$\\end{document} w.r.t. the mollification scheme ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} in the sense of Shamov (J Funct Anal 270:3224–3261, 2016) – we show that the law of B˙\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\dot{B}$$\\end{document} under the random rooted measure Qμγ(dB˙dω)=μγ(dω,B˙)P(dB˙)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb Q_{\\mu _\\gamma }(\ extrm{d}\\dot{B}\ extrm{d}\\omega )= \\mu _\\gamma (\ extrm{d}\\omega ,\\dot{B})P(\ extrm{d}\\dot{B})$$\\end{document} is the same as the law of the distribution f↦B˙(f)+γ∫0∞∫Rdf(s,y)ϕ(ωs-y)dsdy\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\mapsto \\dot{B}(f)+ \\gamma \\int _0^\\infty \\int _{\\mathbb {R}^d} f(s,y) \\phi (\\omega _s-y) \ extrm{d}s \ extrm{d}y$$\\end{document} under P⊗P0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P \\otimes \\mathbb {P}_0$$\\end{document}. We then determine the fractal properties of the measure around γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}-thick paths: -C2≤lim infε↓0ε2logμ^γ(‖ω‖<ε)≤lim supε↓0supηε2logμ^γ(‖ω-η‖<ε)≤-C1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-C_2 \\le \\liminf _{\\varepsilon \\downarrow 0} \\varepsilon ^2 \\log {\\widehat{\\mu }}_\\gamma (\\Vert \\omega \\Vert< \\varepsilon ) \\le \\limsup _{\\varepsilon \\downarrow 0}\\sup _\\eta \\varepsilon ^2 \\log {\\widehat{\\mu }}_\\gamma (\\Vert \\omega -\\eta \\Vert < \\varepsilon ) \\le -C_1$$\\end{document} w.r.t a weighted norm ‖·‖\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Vert \\cdot \\Vert $$\\end{document}. Here C1>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_1>0$$\\end{document} and C2<∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_2<\\infty $$\\end{document} are the uniform upper (resp. pointwise lower) Hölder exponents which are explicit in the entire weak disorder regime. Moreover, they converge to the scaling exponent of the Wiener measure as the disorder approaches zero. Finally, we establish negative and Lp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L^p$$\\end{document} (p>1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p>1$$\\end{document}) moments for the total mass of μγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu _\\gamma $$\\end{document} in the weak disorder regime.

Free convection in a differentially heated square cavity filled with low-Prandtl-number materials: Numerical studies using transition shear stress transport model

Computing the flow field under free convection in a cavity becomes particularly challenging for low-Prandtl-number (Pr) fluids typically encountered for liquid metals. The objective of the present study is to investigate the natural convection process in a differentially heated square cavity employing the transition shear stress transport (SST) model for the Prandtl number Pr∈[0.001,0.1] and the Rayleigh number Ra∈[104,1010]. The mean flow field is visualized through streamlines, isotherms, non-dimensional velocity, and temperature profiles, turbulence intensity, contours of intermittency (γ) times, the production of turbulent kinetic energy (Pκ), and distribution of skin friction coefficient and the Nusselt number (Nu). The transition SST model can capture the mean flow field and thermal transport over the entire parametric regime successfully. An average Nusselt number (Nu¯) on the hot wall is found to scale with a certain power (n) of the Boussinesq number (Bo), the product of Ra and Pr. The value of n is 0.18 for Ra up to 106 and 0.25 for higher Ra.

Brexit – the EU membership crisis that wasn’t?

This introduction to the special issue recalls the alarm raised in EU capitals and Brussels after the UK’s in-out referendum delivered a Leave vote in June 2016. The fear was of a domino effect and the further fragmentation of an already divided EU. Seven years later, it is clear that there was rapid attrition of Eurosceptic triumphalism, and the EU-27 showed remarkable unity. This required a sustained collective effort to contain a membership crisis and maintain the EU polity. Yet, the issue contributors challenge the notion that the alarm was unfounded and explain why this counter-factual did not materialise, even though potential for future membership crises of different sorts was revealed. Theoretically, this supports an understanding of the EU as a polity that is fragile, yet able to assert porous borders, exercise authority over a diverse membership, and mobilise a modicum of loyalty when the entire integration regime is under threat.

A variant of improved discrete velocity method for efficient simulation of flows in entire Knudsen number regimes

In this paper, a variant of the improved discrete velocity method (VIDVM) is proposed for flows in the whole Knudsen number regimes. This method retains the advantage of the improved discrete velocity method (IDVM), which calculates numerical fluxes through a self-adaptive strategy by combining the microscopic reconstruction and the macroscopic reconstruction. Like the IDVM, the microscopic reconstruction for VIDVM is also based on the collisionless Boltzmann solver. However, different from IDVM, the macroscopic reconstruction for VIDVM is established on the Euler solver instead of the Navier–Stokes solver. Considering that the Euler solver merely computes the inviscid fluxes while the Navier–Stokes solver additionally calculates the viscous fluxes, the present method could be more efficient than IDVM. To validate the accuracy and efficiency of the present scheme, some benchmark cases from the continuum regime to the free molecular regime are conducted. Results reveal that the present scheme can predict the flow as well as IDVM, but the present solver is more efficient than IDVM.

Can Geometric Parameters Enable Direct Prediction of Non‐Fickian Transport in Rock Fractures Across Diverse Flow Regimes?

AbstractAnomalous solute migrations in fractured rocks are governed by geometric characteristics and flow regimes. Although existing inverse models can describe this behavior, the underlying physics for quantifying key transport coefficients remains largely unexplored. Here, we investigate the quantitative impacts of geometric heterogeneity and flow regimes on solute transport in rock fractures. We conduct numerical experiments to simulate water flow and conservative solute transport in 3D fractures with varying geometric features and Reynolds numbers. Our results show that the non‐Fickian transport is prevalent across the entire flow regime, with Darcy flows attributed to geometric heterogeneity and non‐Darcian flows influenced by additional eddy zones. We employ the mobile‐immobile (MIM) domain model and continuous time random walk (CTRW) model to inversely model simulated breakthrough curves. Inverse analyses demonstrate that both models effectively characterize anomalous transport behaviors. The fitted transport coefficients of the MIM model exhibit stronger quantitative relationships with aperture and roughness parameters, as well as Reynolds number, compared to the CTRW model. By incorporating parameterized transport coefficients, we propose physics‐ and statistics‐based models to directly predict anomalous transport behaviors under different flow regimes. These prediction models accurately reproduce solute transport processes of all simulated cases with acceptable errors. The feasibility of directly predicting solute transport under varying flow regimes using geometric information is thus validated. Our study not only supports the study of substance migration based on geometric structure features, but also serves as a foundation for investigating geological activities based on substance migration information.

Control of Reverse Flow over Cantilevered Swept Blades Using Passive Camber Morphing

High-speed rotorcraft experience a region of reversed flow over the retreating blade at high advance ratios. This reverse flow region results in multiple unfavorable effects, including negative lift, increased drag, and a large pitching moment impulse. The effect of the sweep angle on a rotor blade in reverse flow was explored, and it was demonstrated that the introduction of a trailing edge reflex camber could mitigate the adverse effects seen in this regime. A cantilevered, finite-span NACA 63-218 blade was examined at a Reynolds number Rec=2.38×105 both with and without a 10° trailing edge reflex camber. Three blades were tested: one with 20° forward sweep, one with 20° backward sweep, and one with no sweep. The experiments consisted of load measurements across a range of angles of attack, as well as volumetric flowfield measurements using stereoscopic particle image velocimetry on the two swept models at 10° angle of attack in reverse flow. The flowfields exhibited a highly three-dimensional separation bubble that existed on the blades in both backward and forward sweep conditions. Cambering of the trailing edge led to almost complete flow attachment on the backward swept model and a significant reduction in separation over the forward swept model. Cambering also led to a large reduction in drag in the entire reverse flow regime in both swept and unswept conditions. A large reduction in pitching moment and a smaller reduction in negative lift were also observed at moderate angles of attack.