Search Results (54)

This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Pohozaev identities, and prove the existence of radial, decreasing ground states, while showing nonexistence in the $L^2$-critical case. For $L^2$-supercritical exponents, we identify parameter regimes where ground states exist, characterized by a negative Lagrange multiplier. The analysis combines variational methods, scaling techniques, and the careful study of fibering maps to address challenges posed by competing nonlinearities and nonlocal interactions. Full article

This paper investigates the existence and uniqueness of local and global solutions to the incompressible three-dimensional Navier–Stokes equations within the framework of homogeneous Lei–Lin–Gevrey spaces ${\mathcal{X}}_{a,\gamma }^{\rho }({\mathbb{R}}^3)$, where $\rho \in [-1,0),a>0$, and $\gamma \in (0,1)$. These function spaces combine the critical scaling structure of the Lei–Lin spaces with the exponential regularity of Gevrey classes, thereby enabling a refined treatment of analytic regularity and frequency localization. The main results are obtained under the assumption of small initial data in the critical Lei–Lin space ${\mathcal{X}}^{\rho }({\mathbb{R}}^3)$, extending previous works and improving regularity thresholds. In particular, we establish that for suitable initial data, the Navier–Stokes system admits unique solutions globally in time. The influence of the Gevrey parameter $\gamma$ on the high-frequency behavior of solutions is also discussed. This work contributes to a deeper understanding of regularity and decay properties in critical and supercritical regimes. Full article

The valorization of by-products in the olive sector has increasingly become the focus of business and research in the context of biorefineries. This work evaluates the recovery of bioactive compounds from olive leaves and their subsequent incorporation into poly(L-lactic- acid-co-caprolactone) (PLCL) filaments through supercritical impregnation. Obtaining an olive leaf extract (OLE) using enhanced solvent extraction at a high pressure (ESE with CO₂/ethanol 1:1 v/v) resulted in higher yields and concentrations of bioactives with high antioxidant and anti-inflammatory activity. No significant differences were found between the extracts obtained with different water regimes (irrigated and dry land). The supercritical impregnation of PLCL filaments showed that a low depressurization rate is essential to avoid material deformation, while the impregnation pressure and temperature influenced the OLE loading and antioxidant activity of the filaments. In vitro release studies showed the prolonged release of active compounds over 90 days, and the kinetics best fit the Korsmeyer–Peppas model, suggesting a diffusion mechanism. These results validate supercritical impregnation as a promising strategy for the development of OLE-active PLCL filaments with potential for biomedical applications requiring sustained therapeutic release. Full article

The automotive industry is a key driver of global economic growth. However, traditional management approaches, relying on statistical tools and continuous improvement methodologies from the 1990s, lack the agility needed to address today’s complex challenges. This study proposes the Agile Viable Model (AVM), which integrates Viable System Model (VSM), Soft Systems Methodology (SSM), and Agile Methodologies to enhance responsiveness, resilience, and strategic decision-making in quality management. Applied to the Problem Resolution Process in Quality Control, the study identified low network connectivity, confirming that the system operates under a Supercritical Regime, limiting efficiency. Analyst involved and his leader emerged as critical nodes, with 68% of interactions being conflictual, revealing the need for improved communication and collaboration. To address these challenges, agile tools such as virtual boards, product logs, and daily meetings were integrated, optimizing process flexibility. CATWOE analysis facilitated the development of conceptual models aligned with organizational objectives. The Problem Resolution Process is vital both pre- and post-sale, influencing customer satisfaction and warranty costs. Strengthening connectivity and collaboration will lead to faster problem resolution, reduced costs, and enhanced reputation. The AVM offers a structured yet adaptive solution, improving operational efficiency and decision-making in automotive quality management. Full article

Transitory states and supercritical regimes in channel junctions have been challenging to model using 1D models, and it has been common to resort to 2D models to locally solve networks of channels. In this paper, we present a methodology based on the Junction Riemann Problem that manages to include supercritical solutions by making use of suitable limiting coefficients. The method is compared against a pure 2D model in a series of test cases with challenging geometries that include transitory flow conditions. The results show that the method hereby presented is robust across all regimes and is able to capture the main features of wave propagation along a network of channels. Full article

Gravel coverage on slopes influences overland flow and soil erosion. However, the effect of different gravel sizes on the soil erosion process remains underexplored. In this study, a runoff scour test was performed to examine the effects of gravel coverage on the hydrodynamic characteristics of slope runoff and sediment transport capacity (T_c). The slope gradient varied from 18% to 84%, the unit flow discharge ranged from 0.27 × 10⁻³ to 1.11 × 10⁻³ m² s⁻¹, and gravel coverage was adjusted from 0% to 90%. The results reveal that water depth, shear stress, and stream power increased with gravel coverage. However, once coverage exceeded 20%, flow velocity and unit stream power decreased and stabilized. As gravel coverage increased, the hydraulic regimes transitioned from laminar to turbulent flow and shifted from supercritical to subcritical. Consequently, T_c first increased and then decreased with the increase in gravel coverage, reaching a peak at 20% coverage (1.66 kg m⁻¹ s⁻¹). Moreover, the degree of coverage indirectly influenced T_c through grain shear stress. The new equations, based on the Box–Lucas function, incorporated slope, grain shear stress, and flow velocity, thereby effectively simulating T_c for runoff on gravel-covered slopes (R² = 0.94, NSE = 0.94). These findings provide a basis for modeling soil erosion on gravel-covered slopes. Full article

Hydraulic jump is a phenomenon that occurs in open channels with a sudden and rapid transition of the flow regime from supercritical to subcritical. One of the common approaches in controlling the energy dissipation of hydraulic jumps aims to expand the section of the stilling basin with the development of T-jumps. However, T-jumps without additional baffle and terminal elements are unacceptable for thorough energy dissipation. Therefore, this study investigates the main characteristics of T-jumps in an abruptly expanding channel and in the presence of bed water jets and sinusoidal roughness elements. Such complex configurations are hardly found in the literature. Inflow Froude numbers from 6.2 to 10.85, five relative jet flow rates from 0.10 to 0.27, and three rough beds with roughness wave slopes from 0.33 to 0.60 were selected. Experimental results revealed that increasing the bed corrugation would decrease the length of the jump, the length of the roller, and the sequent depth ratio. The same results were found in presence of bed water jets and sinusoidal roughness elements, but the T-jump would appear to be better stabilized. In fact, it was also observed that increasing the relative flow rate of the jet had a significant effect in controlling the T-jump and reducing its relative length. The simultaneous presence of bed water jets and sinusoidal roughness elements decreased the relative length of the T-jump by about 81% and the tailwater depth by about 42% in comparison with the classic hydraulic jumps on smooth beds. Full article

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid. Full article

The problem of submerged body motion in a frozen channel is considered. The fluid in the channel is assumed to be inviscid and incompressible. Fluid flow is the potential. The ice cover has non-uniform compression along the principal coordinates. The damping of hydroelastic waves generated by the motion of submerged body is modeled by taking into account porosity of ice. The submerged body is modeled as a dipole, the potential of which is determined using mirror images from the channel walls. The main problem of the submerged body motion at constant speed along the central line of the channel is considered. Two subproblems are addressed: comparison of damping effects of the porosity and viscosity of ice and investigation of effects of symmetrically variable ice thickness relative to the central line of the channel. It was found that the most important compressive stress is the stress in the direction of the motion of the submerged body. The speed of the body, which was subcritical for uncompressed ice, may become critical or supercritical. Compressive stresses perpendicular to the direction of motion do not qualitatively change the character of the ice response. These stresses, in combination with compressive stresses along the direction of motion, strengthen the effect of the latter, making the transition from subcritical to supercritical regime faster. Full article

To study the behavior of a bubble clusters in cavitation devices, a numerical study of the dynamics of bubbles in a compressible liquid was performed, taking into account interfacial heat and mass transfer. The influence of regime and system parameters on the intensity of cavitation processes is considered. Physical and chemical transformations during the cavitation treatment of liquids are caused not only by the action of shock waves and emitted pressure pulses but also by extreme thermal effects. At the stage of extreme compression of the bubble, the vapor inside the bubble and the liquid in its vicinity transform into the state of a supercritical fluid. The presented model analyzes the nature of microflows in the interbubble space and carries out a quantitative calculation of the local values of the parameters of the velocity and pressure fields. Full article

To understand how the temporal non-locality («memory») properties of a process affect its critical regimes, the power-law compound and time-fractional Poisson process is presented as a universal hereditary model of criticality. Seismicity is considered as an application of the theory of criticality. On the basis of the proposed hereditarian criticality model, the critical regimes of seismicity are investigated. It is shown that the seismic process has the property of «memory» (non-locality over time) and statistical time-dependence of events. With a decrease in the fractional exponent of the Poisson process, the relaxation slows down, which can be associated with the hardening of the medium and the accumulation of elastic energy. Delayed relaxation is accompanied by an abnormal increase in fluctuations, which is caused by the non-local correlations of random events over time. According to the found criticality indices, the seismic process is in subcritical regimes for the zero and first moments and in supercritical regimes for the second statistical moment of events’ reoccurrence frequencies distribution. The supercritical regimes indicate the instability of the deformation changes that can go into a non-stationary regime of a seismic process. Full article

The aim of this study is to explore the insights of the information-theoretic definition of similarity for a multitude of flow systems with wave propagation. This provides dimensionless groups of the form ${\Pi }_{info}=U/c$, where U is a characteristic flow velocity and c is a signal velocity or wave celerity, to distinguish different information-theoretic flow regimes. Traditionally, dimensionless groups in science and engineering are defined by geometric similarity, based on ratios of length scales; kinematic similarity, based on ratios of velocities or accelerations; and dynamic similarity, based on ratios of forces. In Part I, an additional category of entropic similarity was proposed based on ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes. In this Part II, the information-theoretic definition is applied to a number of flow systems with wave phenomena, including acoustic waves, blast waves, pressure waves, surface or internal gravity waves, capillary waves, inertial waves and electromagnetic waves. These are used to define the appropriate Mach, Euler, Froude, Rossby or other dimensionless number(s)—including new groups for internal gravity, inertial and electromagnetic waves—to classify their flow regimes. For flows with wave dispersion, the coexistence of different celerities for individual waves and wave groups—each with a distinct information-theoretic group—is shown to imply the existence of more than two information-theoretic flow regimes, including for some acoustic wave systems (subsonic/mesosonic/supersonic flow) and most systems with gravity, capillary or inertial waves (subcritical/mesocritical/supercritical flow). For electromagnetic wave systems, the additional vacuum celerity implies the existence of four regimes (subluminal/mesoluminal/transluminal/superluminal flow). In addition, entropic analyses are shown to provide a more complete understanding of frictional behavior and sharp transitions in compressible and open channel flows, as well as the transport of entropy by electromagnetic radiation. The analyses significantly extend the applications of entropic similarity for the analysis of flow systems with wave propagation. Full article

The results of a theoretical study on Benjamin–Ono (BO) soliton evolution are presented in a simple model of a two-layer ocean with a shear flow and viscosity. The upper layer is assumed to move with a constant speed relative to the lower layer with a tangential discontinuity in the flow profile. It is shown that in the long-wave approximation, such a model can be appropriate. If the flow is supercritical, i.e., its speed (U) exceeds the speed of long linear waves ($c_1$), then BO solitons experience “explosive-type” enhancement due to viscosity, such that their amplitudes increase to infinity in a finite time. In the subcritical regime, when $U<c_1$, BO solitons experience very slow decay due to viscosity. Soliton amplitude decays with time as $A\sim t^{-1/2}$ or $A\sim t^{-1/3}$, depending on whether both layers are weakly viscous (the former case) or only the lower layer is viscous (the latter case). Estimates of "explosion time" are presented for real oceanic parameters. Full article

The remarkable yield performance of super hybrid rice has played a crucial role in ensuring global food security. However, there is a scarcity of studies investigating the contribution of radiation use efficiency (RUE) to hybrid rice yields under different nitrogen and potassium treatments. In this three-year field experiment, we aimed to evaluate the impact of two hybrid rice varieties (Y-liangyou 900: YLY900 and Quanyouhuazhan: QYHZ) under varying nitrogen regimes (N₉₀: 90 kg N ha⁻¹, N₁₂₀: 120 kg N ha⁻¹, N₁₈₀: 180 kg N ha⁻¹) and potassium regimes (K₁₂₀: 120 kg K₂O ha⁻¹, K₁₆₀: 160 kg K₂O ha⁻¹, K₂₁₀: 210 kg K₂O ha⁻¹) on grain yield and its physiological determinants, including RUE, intercepted photosynthetically active radiation (IPAR), aboveground biomass production, and harvest index (HI). Our results revealed that both rice varieties exhibited significantly higher yields when coupled with nitrogen and potassium fertilization. Compared to the N₉₀ × K₁₂₀ treatment, the N₁₂₀ × K₁₆₀ and N₁₈₀ × K₂₁₀ combinations resulted in substantial increases in grain yield (12.0% and 21.1%, respectively) and RUE (11.9% and 21.4%, respectively). The YLY900 variety showed notable yield improvement due to enhanced aboveground biomass production resulting from increased IPAR and RUE. In contrast, the QYHZ variety’s aboveground biomass accumulation was primarily influenced by RUE rather than IPAR, resulting in higher RUE and grain yields of 9.2% and 5.3%, respectively, compared to YLY900. Importantly, fertilization led to significant increases in yield, biomass, and RUE, while HI remained relatively constant. Both varieties demonstrated a positive relationship between grain yield and IPAR and RUE. Multiple regression analysis indicated that increasing RUE was the primary driver of yield improvement in hybrid rice varieties. By promoting sustainable agriculture and enhancing fertilizer management, elevating nitrogen and potassium levels from a low base would synergistically enhance rice yield and RUE, emphasizing the critical importance of RUE in hybrid rice productivity compared to HI. Full article

We present a thorough numerical analysis of the relaxational dynamics of the Sherrington–Kirkpatrick spherical model with an additive non-disordered perturbation for large but finite sizes N. In the thermodynamic limit and at low temperatures, the perturbation is responsible for a phase transition from a spin glass to a ferromagnetic phase. We show that finite-size effects induce the appearance of a distinctive slow regime in the relaxation dynamics, the extension of which depends on the size of the system and also on the strength of the non-disordered perturbation. The long time dynamics are characterized by the two largest eigenvalues of a spike random matrix which defines the model, and particularly by the statistics concerning the gap between them. We characterize the finite-size statistics of the two largest eigenvalues of the spike random matrices in the different regimes, sub-critical, critical, and super-critical, confirming some known results and anticipating others, even in the less studied critical regime. We also numerically characterize the finite-size statistics of the gap, which we hope may encourage analytical work which is lacking. Finally, we compute the finite-size scaling of the long time relaxation of the energy, showing the existence of power laws with exponents that depend on the strength of the non-disordered perturbation in a way that is governed by the finite-size statistics of the gap. Full article