Search Results (13)

The present study evaluates the optical and colorimetric properties of Polylactic acid (PLA)-based films blended with Poly(3-hydroxybutyrate) (PHB) and Poly(butylene succinate) (PBS) and impregnated with mango leaf extract (MLE) using supercritical solvent impregnation (SSI) under different operating conditions (pressure: 10–30 MPa; temperature: 35–55 °C). Additionally, the relationship between impregnation load (IL) and color properties, as well as the release kinetics of the impregnated compounds, was investigated. The incorporation of PHB and PBS into the PLA matrix prior to impregnation led to a slight increase in the b* parameter (from 1.64 to 2.61), indicating a tendency toward yellowish tones. After SSI, all films exhibited noticeable color changes, with a shift toward yellowish-green hues and a decrease in lightness, regardless of processing conditions. Statistical analysis confirmed that polymer composition and its interaction with pressure and temperature significantly affected color properties (p-value < 0.001). The addition of PHB and PBS, as well as MLE impregnation, enhanced UV-barrier properties, while also modifying film transparency and opacity. In particular, PLA-PBS films showed higher opacity (more than 20 times) and lower transparency compared to neat PLA. These films also exhibited the highest IL values (2.41–4.75 mg MLE/100 mg polymer). Multivariate regression analysis demonstrated a strong correlation between CIELAB parameters (L*, a*, and b*) and IL (R² > 85%, p-value < 0.001). Release studies in a food simulant showed partial release profiles, well described by Peleg’s model (R² > 0.90). Furthermore, Korsmeyer–Peppas model fitting yielded diffusion exponents (n < 0.5), indicating quasi-Fickian diffusion mechanisms governing the release process. Full article

A recently proposed tensor–scalar extension of gravity coupled to extended Aharonov–Bohm electrodynamics admits one-variable traveling reductions in which a longitudinal electromagnetic scalar mode $S={\partial }_{\mu }{A}^{\mu }$ couples nonlinearly to gravitational scalars. In the weak-field regime outside sources, a one-dimensional traveling ansatz depending on $\xi =x-vt$ reduces the field equations to a coupled autonomous ODE system. The mathematical core of the reduction is a singular Newton-type equation whose classical mechanics counterpart is known; the novelty here lies in its derivation from the scalar–tensor/Aharonov–Bohm field system, in the physically motivated normalization of the traveling-wave families, and in the resulting phase–space interpretation for source-generated pulse selection. We provide a systematic classification of all admissible initial data and of the corresponding maximal solutions, distinguishing repulsive/attractive regimes and subcritical/critical/supercritical behaviors through a normalized parameter map. In particular, attractive branches may reach the singularity in finite time with a universal collision exponent $2/3$, while escaping branches exhibit asymptotically uniform motion with a computable logarithmic correction. Finally, we construct a numerical atlas of representative trajectories and validate the computations by cross-checking direct time integration against numerical inversion of the implicit quadrature, together with energy-defect diagnostics. Full article

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

Since the beginning of the 21st century, the supercritical carbon dioxide (sCO₂) Brayton cycle has emerged as a hot topic of research in the energy field. Among its key components, the sCO₂ compressor has received significant attention. In particular, axial-flow sCO₂ compressors are increasingly being investigated as power systems advance toward high power scaling. This paper reviews global research progress in this field. As for performance characteristics, currently, sCO₂ axial-flow compressors are mostly designed with large mass flow rates (>100 kg/s), near-critical inlet conditions, multistage configurations with relatively low stage pressure ratios (1.1–1.2), and high isentropic efficiencies (87–93%). As for internal flow characteristics, although similarity laws remain applicable to sCO₂ turbomachinery, the flow dynamics are strongly influenced by abrupt variations in thermophysical properties (e.g., viscosities, sound speeds, and isentropic exponents). High Reynolds numbers reduce frictional losses and enhance flow stability against separation but increase sensitivity to wall roughness. The locally reduced sound speed may induce shock waves and choke, while drastic variation in the isentropic exponent makes the multistage matching difficult and disperses normalized performance curves. Additionally, the quantitative impact of a near-critical phase change remains insufficiently understood. As for the experimental investigation, so far, it has been publicly shown that only the University of Notre Dame has conducted an axial-flow compressor experimental test, for the first stage of a 10 MW sCO₂ multistage axial-flow compressor. Although the measured efficiency is higher than that of all known sCO₂ centrifugal compressors, the inlet conditions evidently deviate from the critical point, limiting the applicability of the results to sCO₂ power cycles. As for design and optimization, conventional design methodologies for axial-flow compressors require adaptations to incorporate real-gas property correction models, re-evaluations of maximum diffusion (e.g., the DF parameter) for sCO₂ applications, and the intensification of structural constraints due to the high pressure and density of sCO₂. In conclusion, further research should focus on two aspects. The first is to carry out more fundamental cascade experiments and numerical simulations to reveal the complex mechanisms for the near-critical, transonic, and two-phase flow within the sCO₂ axial-flow compressor. The second is to develop loss models and design a space suitable for sCO₂ multistage axial-flow compressors, thus improving the design tools for high-efficiency and wide-margin sCO₂ axial-flow compressors. Full article

This paper focuses on the study of a class of fractional $p\&q$-Laplacian problems with unbalanced growth, which includes vanishing potential and a supercritical growth exponent. By employing the mountain pass theorem alongside the Truncation method, penalization method, and Moser iteration method, the main result establishes the existence of a nontrivial solution under conditions of low perturbations of supercritical nonlinearity. Furthermore, we derive $L^{\infty }\left({\mathbb{R}}^N\right)$ estimates and the interior Hölder regularity of weak solutions in the context of supercritical growth. Full article

In this article, we consider the following fractional $(p,q)$-Laplacian problem ${(-\Delta )}_p^{s_1}u+{(-\Delta )}_q^{s_2}u+{V\left(x\right)\left(\right|u|}^{p-2}u+{\left|u\right|}^{q-2}{u)=f\left(u\right)+\lambda |u|}^{r-2}u,$ where $x\in {\mathbb{R}}^N$, ${(-\Delta )}_p^{s_1}$ is the fractional p-Laplacian operator (${(-\Delta )}_q^{s_2}$ is similar), $0<s_1<s_2<1<p<q<\frac{N}{s_2}$, $q_{s_2}^{*}=\frac{Nq}{N-s_{2}q}$, $r\ge q_{s_2}^{*}$, f is a $C^1$ real function and V is a coercive function. By using variational methods, we prove that the above problem admits a sign-changing solution if $\lambda >0$ is small. 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

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

This paper is about the dynamical evolution of a family of chaotic jerk systems, which have different attractors for varying values of parameter a. By using Hopf bifurcation analysis, bifurcation diagrams, Lyapunov exponents, and cross sections, both self-excited and hidden attractors are explored. The self-exited chaotic attractors are found via a supercritical Hopf bifurcation and period-doubling cascades to chaos. The hidden chaotic attractors (related to a subcritical Hopf bifurcation, and with a unique stable equilibrium) are also found via period-doubling cascades to chaos. A circuit implementation is presented for the hidden chaotic attractor. The methods used in this paper will help understand and predict the chaotic dynamics of quadratic jerk systems. Full article

Brain dynamics show a rich spatiotemporal behavior whose stability is neither ordered nor chaotic, indicating that neural networks operate at intermediate stability regimes including critical dynamics represented by a negative power-law distribution of avalanche sizes with exponent $\alpha =-1.5$. However, it is unknown which stability regimen allows global and local information transmission with reduced metabolic costs, which are measured in terms of synaptic potentials and action potentials. In this work, using a hierarchical neuron model with rich-club organization, we measure the average number of action potentials required to activate n different neurons (avalanche size). Besides, we develop a mathematical formula to represent the metabolic synaptic potential cost. We develop simulations variating the synaptic amplitude, synaptic time course (ms), and hub excitatory/inhibitory ratio. We compare different dynamic regimes in terms of avalanche sizes vs. metabolic cost. We also implement the dynamic model in a Drosophila and Erdos–Renyi networks to computer dynamics and metabolic costs. The results show that the synaptic amplitude and time course play a key role in information propagation. They can drive the system from subcritical to supercritical regimes. The later result promotes the coexistence of critical regimes with a wide range of excitation/inhibition hub ratios. Moreover, subcritical or silent regimes minimize metabolic cost for local avalanche sizes, whereas critical and intermediate stability regimes show the best compromise between information propagation and reduced metabolic consumption, also minimizing metabolic cost for a wide range of avalanche sizes. Full article

The healthcare resources supply network design for resilience is an effective way to deal with uncertainty disruption. In this article we propose a model of supply network self-organization evolution, and establish self-organized criticality as a cause of cascade failure. Our main purpose is to keep the system in a resilient range, i.e., critical state. A network structural design with smaller degree distribution exponent can achieve better absorptive capacity at macro level. An interactive rule design with extremal optimization has better adaptive capacity at micro level. Using macro statistic and indicator micro performance indicator, we demonstrate that our design can slow the development to a supercritical state and can improve the resilience of the supply network. Full article

The influence of temperature and strain rate on the hot tensile properties of 0Cr18AlSi ferritic stainless steel, a potential structural material in the ultra-supercritical generation industry, was investigated at temperatures ranging from 873 to 1123 K and strain rates of 1.7 × 10⁻⁴–1.7 × 10⁻² s⁻¹. The microstructural evolution linked to the hot deformation mechanism was characterized by electron backscatter diffraction (EBSD). At the same strain rate, the yield strength and ultimate tensile strength decrease rapidly from 873 K to 1023 K and then gradually to 1123 K. Meanwhile, both yield strength and ultimate tensile strength increase with the increase in strain rate. At high temperatures and low strain rates, the prolonged necking deformation can be observed, which determines the ductility of the steel to some extent. The maximum elongation is obtained at 1023 K for the strain rates of 1.7 × 10⁻³ and 1.7 × 10⁻² s⁻¹, while this temperature is postponed to 1073 K once decreasing the strain rate to 1.7 × 10⁻⁴ s⁻¹. Dynamic recovery (DRV) and continuous dynamic recrystallization (CDRX) are found to be the main softening mechanisms during the hot tensile deformation. With the increase of temperature and the decrease of strain rate (i.e., 1123 K and 1.7 × 10⁻⁴ s⁻¹), the sub-grain coalescence becomes the main mode of CDRX that evolved from the sub-grain rotation. The gradual decrease in strength above 1023 K is related to the limited increase of dynamic recrystallization and the sufficient DRV. The area around the new small recrystallized grains on the coarse grain boundaries provides the nucleation site for cavity, which generally results in a reduction in ductility. Constitutive analysis shows that the stress exponent and the deformation activation energy are 5.9 and 355 kJ·mol⁻¹ respectively, indicating that the dominant deformation mechanism is the dislocations motion controlled by climb. This work makes a deeply understanding of the hot deformation behavior and its mechanism of the Al-bearing ferritic stainless steel and thus provides a basal design consideration for its extensive application. Full article

Supersonic ejectors are used extensively in all kind of applications: compression of refrigerants in cooling systems, pumping of volatile fluids or in vacuum generation. In vacuum generation, also known as zero-secondary flow, the ejector has a transient behaviour. In this paper, a numerical and experimental research of a supersonic compressible air nozzle is performed in order to investigate and to simulate its behaviour. The CFD toolbox OpenFOAM 6 was used, with two density-based solvers: explicit solver rhoCentralFoam, which implements Kurganov Central-upwind schemes, and implicit solver HiSA, which implements the AUSM+up upwind scheme. The behaviour of the transient evacuation ranges between adiabatic polytropic exponent at the beginning of the process and isothermal at the end. A model for the computation of the transient polytropic exponent is proposed. During the evacuation, two regimes are encountered in the second nozzle. In the supercritic regime, the secondary is choked and sonic flow is reached. In the subcritic regime, the secondary flow is subsonic. The final agreement is good with the two different solvers, although simulation tends to slightly overestimate flow rate for large values region. Full article