Search Results (145)

Liquid sulfur exhibits the famous $\lambda$-transition at T = 432 K, changing from a liquid mainly consisting of eight-membered rings into a liquid with chains of different lengths. This transition is accompanied by an increase in viscosity that reaches four orders of magnitude. We present a neutron-scattering study conducted throughout the transition to elucidate the slow relaxation dynamics. The data are analyzed within the frequency domain and, after Fourier transformation, in the time domain as well. The relaxation dynamics between 1 ps and 140 ps deviate strongly from simple exponential decay and can be accurately described as stretched exponential decay. The relaxation times demonstrate a change to faster dynamics above the transition at a wave vector corresponding to nearest-neighbor distances. At smaller wave vectors, however, and hence greater length scales, the relaxation times increase with an increasing temperature, evidencing a significant change in dynamics. The Q-dependence of the relaxation rate above the $\lambda$-transition agrees with predictions for polymer melt dynamics. The relaxation dynamics at these length scales are dominated by chain-like structures, and the observed polymer-like dynamics might be the microscopic origin of the increase in viscosity. Full article

Biological muscles generate tension from the combined contribution of the passive elastic recoil and the actively controlled contractile mechanisms. Understanding and replicating these passive and active tensions is necessary and beneficial for designing soft robotic actuators that emulate muscle-like behavior. In the current work, the aim is to develop a mathematical framework for modeling both the passive and active tensions in a biological muscle as functions of muscle length and contraction velocity. We will describe the passive tension by a nonlinear monotonically increasing function of length with threshold behavior in order to capture the experimentally observed stiffening occurring in stretched biological muscles. We will model the active tension using the superposition of Gaussian functions that relate bell-shaped tension-length with a flat plateau over the optimal length of the sarcomere. The parameters of this Gaussian representation of the active tension-length relation are determined from formulating a least-squares optimization problem, such that a Characteristic (indicator) function is approximated globally over the optimal length range of the sarcomere by summation of some Gaussian functions. The closed-form formulations for the required integrals are derived using the integral of the product of two Gaussian functions over ${\mathbb{R}}^n$ as well as the error function which enables efficient parameter identification. We will also propose a symmetric tension–velocity relation that distinguishes three phases of concentric, eccentric and isometric contractions, and is parametrized directly by measurable quantities of isometric tension and maximum shortening velocity. The passive and active tensions are finally combined into a unified comprehensive tension model in which the exponentially modeled passive tension is added up to the active contribution, formulated as the product of the activation level, a normalized length-dependent factor and a normalized velocity-dependent factor. The resulting model reproduces canonical tension-length and tension-velocity relations and provides an analytically tractable comprehensive tension model that can be embedded in the dynamics of soft and continuum robot actuators inspired by biological muscles. Full article

We propose a two-level theory that connects Lin-equation-based dynamical coarse-graining of the turbulence cascade with an information-theoretic selection principle in logarithmic wavenumber space. This framework places the dissipation-range spectral shape on a verifiable logical basis rather than on ad hoc fitting. At the first (dynamical) level, we formulate an autonomous conservative Fokker–Planck equation for the normalized density and probability current. Under sufficient boundary decay and a strictly positive effective diffusion, the sign-reversed Kullback–Leibler divergence is shown to be a Lyapunov functional, yielding a rigorous H-theorem and fixing the arrow of time in scale space. At the second (selection) level, the dissipation range is treated as a stationary boundary-value problem for an open system by introducing a killing term for an unnormalized scale density. A WKB (Liouville–Green) analysis restricts the admissible tail to a stretched-exponential form and links the tail exponent to the high-wavenumber scaling of the effective diffusion. The exponential prefactor is fixed by dissipation-rate consistency, and the remaining degree of freedom is determined by one-dimensional Kullback–Leibler minimization (Hyper-MaxEnt) against a globally constructed reference distribution. The resulting exponent range is validated against the high-resolution DNS spectra reported in the literature. Full article

We establish precise exponential tail estimates for lacunary trigonometric sums of the form $f_N\left(x\right)={\sum }_{k=1}^N{c}_k\cos \left(2\pi n_{k}x\right)$, under the Hadamard gap condition. Using cumulant expansions and moment-generating function techniques, we obtain non-asymptotic upper bounds for the tail probabilities, including third-order corrections that refine the classical central limit theorem estimates. Furthermore, several examples illustrate these bounds for various choices of coefficients, highlighting the transition from subgaussian to stretched-exponential tail behavior. Full article

The polar oxide Lithium Niobate Tantalate is probed using time-resolved luminescence spectroscopy with the goal of revealing an initial structural insight into the solid solution by analyzing the spectral properties and dynamics of radiatively decaying self-localization phenomena. A blue-green luminescence band can be induced by ultraviolet nanosecond laser pulses with a temperature-dependent intensity and spectral width, pointing to the radiative decay of optically generated self-trapped excitons as its origin, i.e., electron–hole pairs with strong coupling to either the NbO₆- or TaO₆-octahedra. The luminescence decay takes place in the microsecond time range and deviates significantly from a single exponential behavior, so the determined lifetime constants of up to ≈70 μs and stretching factors (1/3–1/5) are validated in more detail using alternative evaluation methods. We discuss our findings, considering the interplay of radiative and non-radiative decay channels, the transition from self-trapped to free excitons, and the presence of a structural disorder of the oxygen octahedra in the solid solutions. Overall, our results suggest self-trapped excitons as local probes for an initial structural elucidation and provide essential information about further experimental and theoretical studies on the atomic structure of Lithium Niobate Tantalate, but also for improving the crystal quality in the framework of applications in photonics and quantum optics. Full article

Drug delivery from cylindrical tablets of arbitrary dimensions is discussed here, using the analytical solution of diffusion equation. Utilizing dimensionless quantities, we show that the release profiles are determined by a unique parameter, represented by the aspect ratio of the cylindrical formulation. Fractional release curves are presented for different values of the aspect ratio, covering a range of many orders of magnitude. The corresponding release profiles lie in between the two opposite limits of release from thin slabs and two-dimensional radial release, pertinent to the cases of thin and long cylinders, respectively. In a quest for a part of the delivery process closer to a zero-order release, the release rate is calculated, which is found to exhibit the typical behavior of purely diffusional release systems. Two simple fitting formulae, containing two parameters each, are considered to approximate the infinite series of the exact solution: The stretched exponential (Weibull) function and a recently suggested expression interpolating between the correct time dependencies at the initial and final stages of the process. The latter provides a better fitting in all cases. The variation of the fitting parameters with the aspect ratio of the device is presented for both fitting functions. We also calculate the characteristic release time, which is found to correspond to an amount of fractional release between 64% and around 68% depending on the cylindrical aspect ratio. We discuss how the last quantities can be used to estimate the drug diffusion coefficient from experimental release profiles and apply these ideas to published drug delivery data. Full article

In this study, bio-based polyurethanes (PUs) were synthesized using renewable polyols derived from sunflower seed oil, aiming to develop flexible yet robust polymeric films and scaffolds. Given their composition and favorable physico-chemical properties, these materials may represent promising candidates for the design and development of advanced biomedical systems. Two distinct oil polyols were prepared via glycerol transesterification (GM) and epoxidation (EPO) with hydrogen peroxide/glacial acetic acid, respectively. These polyols, in combination with poly(tetramethylene ether) glycol (PTMEG) and/or poly(ethylene glycol) (PEG), served as diol components in a one-step reaction with 1,6-hexamethylene diisocyanate (HDI). The structure of the polyol precursors was thoroughly characterized by MALDI-TOF MS and NMR spectroscopy, confirming successful functionalization. The resulting PU films exhibited excellent flexibility (885%) and mechanical properties (23 MPa), as evaluated by ATR-FTIR, Tensile test, DSC, DMA and SEM methods. The crosslink density of the order of 10⁻³ also contributes to the development of outstanding mechanical properties. Stress relaxation experiments were described using a stretched exponential (Kohlrausch–Williams–Watts) model to capture the viscoelastic behavior of the materials. In addition, stress vs. relative elongation curves revealing strain-hardening behavior were also analyzed and modeled mathematically to better describe the mechanical response under deformation. Furthermore, salt leaching techniques were employed to fabricate porous scaffolds. This work highlights the versatility of vegetable oil-based feedstocks in producing functional polyurethanes with tunable mechanical properties for applied polymer systems. Full article

Tuning structural heterogeneity in metallic glasses is key to improving their mechanical performance. Here we examine how carbon micro-alloying modulates the relaxation dynamics and creep of Fe-based amorphous ribbons. Increasing carbon content lowers the crystallization temperature, amplifies β-relaxation, and reduces hardness, consistent with enhanced atomic mobility. Nanoindentation creep, fitted with a stretched-exponential model, shows a decreasing exponent with carbon addition, indicating broader relaxation–time distributions and stronger dynamic heterogeneity. Nanoscale force-mapping further reveals a larger fraction of liquid-like regions and pronounced viscoelastic heterogeneity in carbon-rich samples. These changes facilitate the activation of shear-transformation zones and promote room-temperature creep flow. Together, the results establish a direct link between structural heterogeneity, relaxation processes, and mechanical response, providing guidance for the design of ductile metallic glasses. Full article

Using the results of numerical simulations and solar observations, this study shows that the transition from deterministic chaos to hard turbulence in the magnetic field generated by the emerging small-scale, near-surface (within the Sun’s outer 5–10% convection zone) solar MHD dynamos occurs through a randomization process. This randomization process has been described using the concept of distributed chaos, and the main parameter of distributed chaos $\beta$ has been employed to quantify the degree of randomization (the wavenumber spectrum characterising distributed chaos has a stretched exponential form $E\left(k\right)\propto exp-{(k/k_{\beta })}^{\beta }$). The dissipative (Loitsianskii and Birkhoff–Saffman integrals) and ideal (magnetic helicity) magnetohydrodynamic invariants govern the randomization process and determine the degree of randomization $0<\beta \le 1$ at various stages of the emerging MHD dynamos, directly or through Kolmogorov–Iroshnikov phenomenology (the magnetoinertial range of scales as a precursor of hard turbulence). Despite the considerable differences in the scales and physical parameters, the results of numerical simulations are in quantitative agreement with solar observations (magnetograms) within this framework. The Hall magnetohydrodynamic dynamo is also briefly discussed in this context. Full article

We analyze long-range dependence (LRD) for word time series, understood as a slower than exponential decay of the two-point Shannon mutual information. We achieve this by examining the decay of the cosine correlation, a proxy object defined in terms of the cosine similarity between word2vec embeddings of two words, computed by an analogy to the Pearson correlation. By the Pinsker inequality, the squared cosine correlation between two random vectors lower bounds the mutual information between them. Using the Standardized Project Gutenberg Corpus, we find that the cosine correlation between word2vec embeddings exhibits a readily visible stretched exponential decay for lags roughly up to 1000 words, thus corroborating the presence of LRD. By contrast, for the Human vs. LLM Text Corpus entailing texts generated by large language models, there is no systematic signal of LRD. Our findings may support the need for novel memory-rich architectures in large language models that exceed not only hidden Markov models but also Transformers. Full article

In this study, we investigate the impact of rising time on alternating current (AC) stress-induced degradation in amorphous indium–tin–gallium–zinc oxide (a-ITGZO) TFTs through both experiments and simulations. When AC bias stresses with rising and falling times (t_r-f) of 400 ns, 200 ns, and 100 ns were applied to the a-ITGZO TFTs, the threshold voltage (V_TH) shifted positively by 0.97 V, 2.68 V, and 2.83 V, respectively. These experimental results align with a stretched exponential model, which attributes the V_TH to electron trapping in bulk dielectric states or at interface traps. The simulation results further validate the stretched exponential model by illustrating the potential distribution across the dielectric and channel layers as a function of t_r-f and the density of states in the a-ITGZO TFT. Full article

This study presents an analytical solution to examine the mechanical behavior of an incompressible, functionally graded hyperelastic cylinder under combined extension and torsion. The exp-exp strain energy density function characterizes the hyperelastic material, with parameters varying exponentially along the radial direction. To validate the solution, finite element simulations using a custom UHYPER in ABAQUS are performed. The analytical and numerical results show strong agreement across different stretch and twist levels. The stress distribution and maximum stress are significantly influenced by the exponential parameter governing material gradients. Unlike axial stretch, torsion induces a more intricate longitudinal stress distribution, with large twisting producing two extrema that shift toward the cylinder’s center and outer surface. Longitudinal stress primarily governs von Mises stress and strain energy density variations across the radial direction. A critical axial stretch is identified, below which torsion-induced axial force transitions to compression, elongating the cylinder during twisting. Beyond this stretch, the axial force shifts from tensile to compressive with increasing twist, causing initial shortening before further elongation. Full article

This work develops a unified size-dependent shear deformation theory (SDSDT) to analyze the free vibration behavior of a functionally graded (FG) magneto-electro-elastic (MEE) microplate under fully simply supported conditions, open- or closed-circuit surface conditions, biaxial compression, magnetic and electric potentials, and uniform temperature changes based on consistent couple stress theory (CCST). The FG-MEE microplate is composed of BaTiO₃ (a piezoelectric material) and CoFe₂O₄ (a magnetostrictive material). Various CCST-based SDSDTs, considering couple stress and thickness stretching effects, can be reproduced by employing a generalized shape function that characterizes shear deformation distributions along the thickness direction within the unified SDSDT. These CCST-based SDSDTs encompass the size-dependent classical plate theory (CPT), first-order shear deformation theory (SDT), Reddy’s refined SDT, exponential SDT, sinusoidal SDT, and hyperbolic SDT. The unified SDSDT is validated by comparing its solutions with relevant three-dimensional solutions available in the literature. After validation and comparison studies, we conduct a parametric study, whose results indicate that the effects of thickness stretching, material length-scale parameter, inhomogeneity index, and length-to-thickness ratio, as well as the magnitude of biaxial compressive forces, electric potential, magnetic potential, and uniform temperature changes significantly impact the microplate’s natural frequency. Full article

In an era where social media shapes public opinion, understanding information spreading is key to grasping its broader impact. This paper explores the intricacies of information diffusion on Twitter, emphasizing the significant influence of content saturation on user engagement and retweet behaviors. We introduce a diffusion model that quantifies the likelihood of retweeting relative to the number of accounts a user follows. Our findings reveal a significant negative correlation where users following many accounts are less likely to retweet, suggesting a saturation effect in which exposure to information overload reduces engagement. We validate our model through simulations, demonstrating its ability to replicate real-world retweet network characteristics, including diffusion size and structural properties. Additionally, we explore this saturation effect on the temporal behavior of retweets, revealing that retweet intervals follow a stretched exponential distribution, which better captures the gradual decline in engagement over time. Our results underscore the competitive nature of information diffusion in social networks, where tweets have short lifespans and are quickly replaced by new information. This study contributes to a deeper understanding of content propagation mechanisms, offering a model with broad applicability across contexts, and highlights the importance of information overload in structural and temporal social media dynamics. Full article

Compared to natural and shale gas, studies on predicting production specific to coalbed methane (CBM) are still relatively limited, and mainly use decline curve methods such as Arps, Stretched Exponential Decline Model, and Duong’s model. In recent years, machine learning (ML) methods applied to CBM production prediction have focused on the significant data characteristics of production, achieving more accurate predictions. However, throughout the application process, these models require a large amount of data for training and can only achieve accurate forecasts over a short period, such as 30 days. This study constructs a hybrid ML model by integrating a long short-term memory (LSTM) network and Transformer architecture. The model is trained using the mean absolute error (MAE) loss function, optimized using the Adam optimizer, and finally evaluated using metrics such as MAE, root mean square error (RMSE), and R squared (R²) scores. The results show that the LSTM-Attention (LSTM-A) hybrid model based on small training datasets can accurately capture the CBM production trend and is superior to traditional methods and the LSTM model regarding prediction accuracy and effective prediction time interval. The methodologies established and the results obtained in this study are of great significance to accurately predict CBM production. It is also helpful to better understand the mechanisms of CBM production. Full article