Weak Limit Research Articles

Biocompatible ionic liquid self-assembled transdermal delivery system (P-M IL/AKE) for significantly improved skin photoaging and reduced wrinkles

Most peptide drugs have good biological activity and safety, but their stability and permeability are poor, limiting their applications in the field of local drug delivery. Snake venom peptide (AKE) is a tripeptide with good anti-wrinkle effects, but its weak esterophilicity, poor penetration, and low bioavailability limit its full anti-wrinkle potential. To address this issue, a bioactive ionic liquid (P-M IL) was prepared and an efficient self-assembled peptide drug delivery system was constructed through AKE loading, which increased the cumulative absorption of AKE in the skin by more than five-fold, resulting in good biocompatibility. Further, P-M IL/AKE can significantly increase collagen protein secretion by human fibroblasts, improved skin photoaging and reduce the areas and volume of wrinkle in the eye tail lines. In addition, for the first time, quantum chemical calculations, homology modeling, molecular docking and binding free energy calculations were used to analyze the structural stability of the system, construct the 3D model, explore the interaction mode and reveal the theoretical basis of anti-wrinkle effect. Therefore, this supramolecular self-assembled transdermal drug delivery system has potential advantages, providing a novel approach for the highly efficient and non-invasive delivery of peptide drugs.

Hexadecapole at the heart of nonlinear electromagnetic fields

In classical Maxwell’s electromagnetism, the monopole term of the electric field is proportional to r −2, while higher order multipole terms, sourced by anisotropic sources, fall-off faster. However, in nonlinear electromagnetism even a spherically symmetric field has multipole-like contributions. We prove that the leading subdominant term of the electric field, defined by nonlinear electromagnetic Lagrangian obeying Maxwellian weak field limit, in a static, spherically symmetric, asymptotically flat spacetime, is of the order O(r−6) as r→∞ . Moreover, using Lagrange inversion theorem and Faà di Bruno’s formula, we derive the series expansion of the electric field from the Taylor series of an analytic electromagnetic Lagrangian.

UNVEILING THE DYNAMICS OF DOMESTIC PRICES OF CACAO BEANS IN INDONESIA

This study is crucial for understanding the factors affecting cacao bean prices in Indonesia. Cacao is a vital commodity in the country's economy, and fluctuations in its price impact various stakeholders. By analyzing these factors, we can make informed decisions benefiting the government, industry, and cacao farmers. The purpose of this study is to analyze the domestic price of cacao beans in Indonesia. The dependent variable in this study is the domestic price of cacao in Indonesia, while the independent variables are volume of cacao bean exports, volume of cacao bean imports, global price of cacao beans, volume of domestic production of cacao beans, Rupiah to USD exchange rate, the federal reserve rate, Gross Domestic Product (GDP) annual growth rate of Indonesia, and export duties imposed on export of cacao beans. This research design utilizes time series data from 1996 to 2022 to analyze the factors influencing the domestic price of cacao beans in Indonesia. The results of the analysis show that the variables of the volume of cacao bean imports, the global price of cacao beans, Rupiah to USD exchange rate, and dummy variable for export duties imposed on export of cacao beans are significant affecting the domestic price of cacao. While volume of cacao bean exports, the federal reserve rate, volume of domestic production of cacao beans and GDP annual growth rate of Indonesia are not significant. The non-significance of volume of cacao bean exports, the federal reserve rate, volume of domestic production of cacao beans, and GDP annual growth rate could be caused by weak relationships, multicollinearity, data issues, or model specification limitations.

The gravitational lensing by rotating black holes in loop quantum gravity

In this paper, we explore gravitational lensing effects associated with rotating black holes within the framework of loop quantum gravity. Utilizing the Gauss-Bonnet theorem as extended by Ono et al., we compute the light deflection angle in the weak field limit for a lens that is finitely distanced from both the source and the observer. Our findings indicate that the weak deflection angle for rotating black holes in LQG is smaller than that observed for the classical Kerr black holes, albeit with minimal deviations. In the strong field limit, we determine the photon sphere radius, the light deflection angle, and lensing observables, including the image position θ∞, angular separation s, magnification rmag, and temporal delays among various relativistic images. By considering supermassive black holes, such as Sgr A* and M87*, within the LQG framework, we calculate these observables and investigate the influence of the quantum parameter Aλ on them, compared with the Kerr black hole outcomes. Our comparative analysis reveals that the image position θ∞ and separation s for Sgr A* consistently exceed those for M87*, whereas M87* exhibits considerably greater time delays than Sgr A*. These distinctions could be important in differentiating between rotating black holes in LQG and classical Kerr black holes in future astronomical observations.

A discontinuous Galerkin method for a coupled Stokes–Biot problem

The interaction between fluid and poroelastic structure is a complex problem that couples the Stokes equations with the Biot system. In this work, we rewrite the poroelastic equations using three fields (displacement, fluid pressure, and total pressure) to account for locking phenomenon in fluid–structure interaction and the oscillation of numerical solutions. Then, in order to solve the coupled system, we use the weighted discontinuous Galerkin finite element method for spatial discretization and propose a semi-discrete scheme. In addition, we propose a fully discrete scheme using the backward Euler’s method for temporal discretization. In the framework of the Galerkin approximation, the stability and errors of semi- and fully discrete schemes are analyzed using the theory of differential algebraic equations and weak compactness arguments. Through numerical experiments, we validate the theoretical rate of convergence, explain the behavior of the method in modeling the interaction between surface and groundwater hydrological systems, investigate the robustness of the method with respect to physical parameters, and simulate channel filtering. In particular, the numerical results are free of locking features, reducing non-physical numerical oscillations.

Asymptotic optimality of a class of controlled non-Markov processes

Motivated by applications in power systems and problems arising in simulation of large scale complex system optimizations, this work is concerned with controlled stochastic switching systems. The system of interest displays a multi-time scale structure. In contrast to the so-called singularly perturbed diffusions and multi-scale Markov decision processes, controlled non-Markov processes (also known as non-Markov decision processes) are treated. The novelty of our work is the treatment of the non-Markov controlled processes and the time-scale used. The fast and slow processes are coupled through a stochastic differential equation. Using averaging, it is first shown that the non-Markov switching process has a weak limit that is a Markov decision process. Then asymptotic optimal control of the non-Markov process is obtained by using the limit process.

Massive propagating modes of torsion

The dynamics of the torsion field is analyzed in the framework of the Covariant Canonical Gauge Theory of Gravity (CCGG), a De Donder–Weyl Hamiltonian formulation of gauge gravity. The action is quadratic in both, the torsion and the Riemann–Cartan tensor. Since the latter adds the derivative of torsion to the equations of motion, torsion is no longer identical to spin density, as in the Einstein–Cartan theory, but an additional propagating degree of freedom. As torsion turns out to be totally anti-symmetric, it can be parametrised via a single axial vector. It is shown in this paper that, in the weak torsion limit, the axial vector obeys a wave equation with an effective mass term which is partially dependent on the scalar curvature. The source of torsion is thereby given by the fermion axial current which is the net fermionic spin density of the system. Possible measurable effects and approaches to experimental analysis are addressed. For example, neutron star mergers could act as a dipoles or quadrupoles for torsional radiation, and an analysis of radiation of pulsars could lead to a detection of torsion wave background radiation.

Weakly compact sets in Orlicz–Bochner sequence spaces

AbstractIn this work, we give three kinds of criteria for weak sets in Orlicz–Bochner sequence spaces without constraints, conditions posited in each criterion are necessary and sufficient. As an application, we give criteria for weak sets in Orlicz sequence spaces. Well‐known conclusions are exhibited once more, such as Schur's theorem, Banach–Alaoglu's theorem, and the boundedly compact principle of finite dimension space. The results obtained show that the weak compactness may not be extrapolated straightforwardly from to , for example, .

Fixed points of nonexpansive operators and normal structure concerning s-Orlicz convex sets

The concept of normal structure for s-Orlicz convex sets (0<s≤1) is introduced and a class of nonexpansive operators in p-normed spaces (0<p≤1) are considered. By developing the ideas and methods related to convex sets, some new fixed point theorems for nonexpansive operators concerning s-Orlicz convex sets are proved: the weak compactness condition of sets is replaced by the coverage condition of operators.

The fluctuational transition mechanism of non-hyperbolic chaotic invariant sets

In order to reveal the general escape mechanism of non-hyperbolic chaotic invariant sets under both weak noise limit and finite noise intensity, the simplest example of Hénon map, which represents the stretching and folding of the phase space, is taken to study the escape mechanism under two kinds of global bifurcation: the fractal boundary crisis and the attractor contact crisis. In this paper, we revealed the general exit mechanism by analyzing the escape paths derived from the shooting method and Monte Carlo simulation. Finally, to further demonstrate universality, an example of high-dimensional differential dynamical system, namely the transient chaos Duffing oscillator, is examined, which underscores the main idea of this paper analyzing specific deterministic structures not only enhances the comprehensibility of the escape process, but also allows for predictions of general escape behavior under weak noise intensity.

Convergence of Fibonacci–Ishikawa iteration procedure for monotone asymptotically nonexpansive mappings

In uniformly convex Banach spaces, we study within this research Fibonacci–Ishikawa iteration for monotone asymptotically nonexpansive mappings. In addition to demonstrating strong convergence, we establish weak convergence result of the Fibonacci–Ishikawa sequence that generalizes many results in the literature. If the norm of the space is monotone, our consequent result demonstrates the convergence type to the weak limit of the sequence of minimizing sequence of a function. One of our results characterizes a family of Banach spaces that meet the weak Opial condition. Finally, using our iterative procedure, we approximate the solution of the Caputo-type nonlinear fractional differential equation.

General fractal dimensions of typical sets and measures

Consider (Y,ρ) as a complete metric space and S as the space of probability Borel measures on Y. Let dim‾BΨ,Φ(E) be the general upper box dimension of the set E⊂Y. We begin by proving that the general packing dimension of the typical compact set, in the sense of the Baire category, is at least inf⁡{dim‾BΨ,Φ(B(x,r))|x∈Y,r>0} where B(x,r) is the closed ball in Y with center at x and radii r>0. Next, we obtain some estimates of the general upper and lower box dimensions of typical measures in the sense of the Baire category. Finally, we demonstrate that if S is equipped with the weak topology and under some assumptions then the set of measures possessing the general upper and lower correlation dimension zero are residual. Furthermore, the general upper correlation dimension of typical measures (in the sense of the Baire category) is approximated through the general local lower and upper entropy dimensions of Y.

Production of the ΞN dibaryon as a weakly bound system in pp collisions

The ΞN interaction plays an important role in understanding the long-anticipated H dibaryon. Recent lattice QCD calculations verified the attractive nature of the ΞN interaction. On the other hand, whether it is strong enough to generate a bound state remains inconclusive. In this work, assuming it can generate a weakly bound state, we study the yields of the ΞN dibaryon for different binding energies in pp collisions at 7 TeV using the coalescence model and the transport model PACIAE. The yields are estimated first numerically and then analytically, adopting a Yukawa-type wave function. In particular, we find that in the weak binding limit, there exists a universal relation between the yield and the binding energy, valid for pp collisions. Published by the American Physical Society 2024

Deflection of light by a Reissner–Nordström black hole and Painlevé VI equation

We consider the bending angle of the trajectory of a photon incident from and deflected to infinity around a Reissner–Nordström black hole. We treat the bending angle as a function of the squared reciprocal of the impact parameter and the squared electric charge of the background normalized by the mass of the black hole. It is shown that the bending angle satisfies a system of two inhomogeneous linear partial differential equations with polynomial coefficients. This system can be understood as an isomonodromic deformation of the inhomogeneous Picard–Fuchs equation satisfied by the bending angle in the Schwarzschild spacetime, where the deformation parameter is identified as the background electric charge. Furthermore, the integrability condition for these equations is found to be a specific type of the Painlevé VI equation that allows an algebraic solution. We solve the differential equations both at the weak and strong deflection limits. In the weak deflection limit, the bending angle is expressed as a power series expansion in terms of the squared reciprocal of the impact parameter and we obtain the explicit full-order expression for the coefficients. In the strong deflection limit, we obtain the asymptotic form of the bending angle that consists of the divergent logarithmic term and the finite O(1) term supplemented by linear recurrence relations which enable us to straightforwardly derive higher order coefficients. In deriving these results, the isomonodromic property of the differential equations plays an important role. Lastly, we briefly discuss the applicability of our method to other types of spacetimes such as a spinning black hole.

Genetic mechanism and main controlling factors of high-quality clastic rock reservoirs in deep and ultradeep layers: A case study of Oligocene Linhe Formation in Linhe Depression, Hetao Basin, NW China

Based on new data from cores, drilling and logging, combined with extensive rock and mineral testing analysis, a systematic analysis is conducted on the characteristics, diagenesis types, genesis and controlling factors of deep to ultra-deep abnormally high porosity clastic rock reservoirs in the Oligocene Linhe Formation in the Hetao Basin. The reservoir space of the deep to ultra-deep clastic rock reservoirs in the Linhe Formation is mainly primary pores, and the coupling of three favorable diagenetic elements, namely the rock fabric with strong compaction resistance, weak thermal compaction diagenetic dynamic field, and diagenetic environment with weak fluid compaction-weak cementation, is conducive to the preservation of primary pores. The Linhe Formation clastic rocks have a superior preexisting material composition, with an average total content of 90% for quartz, feldspar, and rigid rock fragments, and strong resistance to compaction. The geothermal gradient in Linhe Depression in the range of (2.0–2.6) °C/100 m is low, and together with the burial history of long-term shallow burial and late rapid deep burial, it forms a weak thermal compaction diagenetic dynamic field environment. The diagenetic environment of the saline lake basin is characterized by weak fluid compaction. At the same time, the paleosalinity has zoning characteristics, and weak cementation in low salinity areas is conducive to the preservation of primary pores. The hydrodynamic conditions of sedimentation, salinity differentiation of ancient water in saline lake basins, and sand body thickness jointly control the distribution of high-quality reservoirs in the Linhe Formation.

A Variational Perspective on Auxetic Metamaterials of Checkerboard-Type

The main result of this work is a homogenization theorem via variational convergence for elastic materials with stiff checkerboard-type heterogeneities under the assumptions of physical growth and non-self-interpenetration. While the obtained energy estimates are rather standard, determining the effective deformation behavior, or in other words, characterizing the weak Sobolev limits of deformation maps whose gradients are locally close to rotations on the stiff components, is the challenging part. To this end, we establish an asymptotic rigidity result, showing that, under suitable scaling assumptions, the attainable macroscopic deformations are affine conformal contractions. This identifies the composite as a mechanical metamaterial with a negative Poisson’s ratio. Our proof strategy is to tackle first an idealized model with full rigidity on the stiff tiles to acquire insight into the mechanics of the model and then transfer the findings and methodology to the model with diverging elastic constants. The latter requires, in particular, a new quantitative geometric rigidity estimate for non-connected squares touching each other at their vertices and a tailored Poincaré type inequality for checkerboard structures.

Pore Structures and Evolution Model of Reservoirs in Different Secondary Structural Zones in the Eocene Shahejie Formation, Chezhen Sag, Bohai Bay Basin.

Although abundant unconventional oil resources have been discovered in conglomerate and sandstone reservoirs in rift basins, the mechanism of differential pore evolution in conglomerates and sandstone reservoirs within different secondary structural zones of rift basins is not yet clear. The pore structures of conglomerate and sandstone reservoirs in the distinct secondary structural zones in the Chezhen Sag were quantified in three dimensions using high-resolution microcomputed tomography (micro-CT). Thin section and scanning electron microscopy observations were used to investigate the differential evolution mechanisms of conglomerate and sandstone reservoirs. Micro-CT analysis of the pore structures of conglomerate and sandstone reservoirs revealed that sandstone reservoirs are superior to conglomerate reservoirs with regard to the pore number and pore connectivity and that sandstone reservoirs are more heterogeneous than conglomerate reservoirs. Triangles dominate the pore and pore throat geometries of sandstone and conglomerate reservoirs, while the sandstone reservoir pores are more regular than conglomerate reservoir pores. The depositional environment, mineral composition, and diagenetic intensity jointly control the quality of the reservoirs. Because of the lengthy transportation distance of their parent rocks, the compositional maturity and sorting behavior of sandstone reservoirs in depression and gentle slope zones are better than those of conglomerate reservoirs in steep slope zones, and thus sandstone reservoirs have a higher initial porosity than conglomerate reservoirs. The rapid compaction experienced by the conglomerate reservoirs in steep slope zones in their early stages creates a closed diagenetic environment, making it difficult to effectively improve reservoir porosity through dissolution. However, the widely developed microfractures in the reservoirs provide channels for fluid migration, promote the development of dissolution pores, and form a tight reservoir dominated by secondary pores. With weak compaction and an open diagenetic environment, the primary pores in sandstone reservoirs in the gentle slope zone are preserved in large quantities. Meanwhile, dissolution expands the secondary pores of the reservoir, resulting in a high-quality reservoir having both primary and secondary pores. In addition, an approach based on primary, secondary, and total porosity was proposed in the study to efficiently evaluate reservoir quality and identify reservoir evolution mechanisms.

Trees adjust nutrient acquisition strategies across tropical forest secondary succession.

Nutrient limitation may constrain the ability of recovering and mature tropical forests to serve as a carbon sink. However, it is unclear to what extent trees can utilize nutrient acquisition strategies - especially root phosphatase enzymes and mycorrhizal symbioses - to overcome low nutrient availability across secondary succession. Using a large-scale, full factorial nitrogen and phosphorus fertilization experiment of 76 plots along a secondary successional gradient in lowland wet tropical forests of Panama, we tested the extent to which root phosphatase enzyme activity and mycorrhizal colonization are flexible, and if investment shifts over succession, reflective of changing nutrient limitation. We also conducted a meta-analysis to test how tropical trees adjust these strategies in response to nutrient additions and across succession. We find that tropical trees are dynamic, adjusting investment in strategies - particularly root phosphatase - in response to changing nutrient conditions through succession. These changes reflect a shift from strong nitrogen to weak phosphorus limitation over succession. Our meta-analysis findings were consistent with our field study; we found more predictable responses of root phosphatase than mycorrhizal colonization to nutrient availability. Our findings suggest that nutrient acquisition strategies respond to nutrient availability and demand in tropical forests, likely critical for alleviating nutrient limitation.

Superconductivity in monolayer Janus titanium-sulfur hydride (TiSH) at ambient pressure

Janus two dimensional (2D) materials are new and novel materials. As they break out-of-plane symmetry, they possess several fascinating properties which can be applied in catalytic reactions and opto-electronics. Recent synthesis of MoSH and the prediction of phonon-mediated superconductivity have opened a new way to investigate the properties of hydrogenated Janus materials (Novoselov et al 2004 Science 306 666–9; Mehta et al 2023 Solid State Commun. 375 115347; Naik et al 2023 Comput. Theor. Chem. 1228 114278). In this work, we performed the density functional theory calculations to demonstrate that titanium sulfur hydride (TiSH) is dynamically stable and becomes phonon-mediated superconductor with the superconducting critical temperature, Tc = 9.24 K with the corresponding value of electron–phonon coupling constant, λ = 0.71, in the weak interaction limits, under ambient conditions. Eliashberg spectral function α2F(ω) was well converged for dense grid of q1 × q2 × q3 = 12 × 12 × 1 and nk1 × nk2 × nk3 = 140 × 140 × 1. The effect of smearing broadening was also considered for determining well converged value of Tc and λ. Figure (b) shows that after smearing broadening of 0.02 Ry, λ shows convergent values, and subsequent changes are as low as less that 5% of the peak value. Overall, our findings predicted a new member in the 2D Janus hydride family with possible applications in 2D nanomaterials and superconducting devices applications.

Neutron star cooling with lepton-flavor-violating axions

The cores of dense stars are a powerful laboratory for studying feebly coupled particles such as axions. Some of the strongest constraints on axionlike particles and their couplings to ordinary matter derive from considerations of stellar axion emission. In this work we study the radiation of axionlike particles from degenerate neutron star matter via a lepton-flavor-violating coupling that leads to muon-electron conversion when an axion is emitted. We calculate the axion emission rate per unit volume (emissivity) and by comparing with the rate of neutrino emission, we infer upper limits on the lepton-flavor-violating coupling that are at the level of |gaeμ|≲10−6. For the hotter environment of a supernova, such as SN 1987A, the axion emission rate is enhanced and the limit is stronger, at the level of |gaeμ|≲10−11, competitive with laboratory limits. Interestingly, our derivation of the axion emissivity reveals that axion emission via the lepton-flavor-violating coupling is suppressed relative to the familiar lepton-flavor-preserving channels by the square of the plasma temperature to muon mass ratio, which is responsible for the relatively weaker limits. Published by the American Physical Society 2024