Search Results (18)

Non-linear least squares (NLS) methods are commonly used for quantitative magnetic resonance imaging (MRI), especially for multi-exponential T1ρ mapping, which provides precise parameter estimation for different relaxation models in tissues, such as mono-exponential (ME), bi-exponential (BE), and stretched-exponential (SE) models. However, NLS may suffer from problems like sensitivity to initial guesses, slow convergence speed, and high computational cost. While deep learning (DL)-based T1ρ fitting methods offer faster alternatives, they often face challenges such as noise sensitivity and reliance on NLS-generated reference data for training. To address these limitations of both approaches, we propose the HDNLS, a hybrid model for fast multi-component parameter mapping, particularly targeted for T1ρ mapping in the knee joint. HDNLS combines voxel-wise DL, trained with synthetic data, with a few iterations of NLS to accelerate the fitting process, thus eliminating the need for reference MRI data for training. Due to the inverse-problem nature of the parameter mapping, certain parameters in a specific model may be more sensitive to noise, such as the short component in the BE model. To address this, the number of NLS iterations in HDNLS can act as a regularization, stabilizing the estimation to obtain meaningful solutions. Thus, in this work, we conducted a comprehensive analysis of the impact of NLS iterations on HDNLS performance and proposed four variants that balance estimation accuracy and computational speed. These variants are Ultrafast-NLS, Superfast-HDNLS, HDNLS, and Relaxed-HDNLS. These methods allow users to select a suitable configuration based on their specific speed and performance requirements. Among these, HDNLS emerges as the optimal trade-off between performance and fitting time. Extensive experiments on synthetic data demonstrate that HDNLS achieves comparable performance to NLS and regularized-NLS (RNLS) with a minimum of a 13-fold improvement in speed. HDNLS is just a little slower than DL-based methods; however, it significantly improves estimation quality, offering a solution for T1ρ fitting that is fast and reliable. Full article

The behavior of polyzwitterions, constituted by dipole-like zwitterionic monomers, is significantly different from that of uniformly charged polyelectrolytes. The origin of this difference lies in the intrinsic capacity of polyzwitterions to self-associate intramolecularly and associate with interpenetrating chains driven by dominant dipolar interactions. Earlier attempts to treat polyzwitterions implicitly assume that the dipoles of zwitterion monomers are randomly oriented. At ambient temperatures, the dipolar zwitterion monomers can readily align with each other generating quadrupoles and other multipoles and thus generating heterogeneous structures even in homogeneous solutions. Towards an attempt to understand the role of such dipolar associations, we present a mean field theory of solutions of polyzwitterions. Generally, we delineate a high-temperature regime where the zwitterion dipoles are randomly oriented from a low-temperature regime where quadrupole formation is significantly prevalent. We present closed-form formulas for: (1) Coil-globule transition in the low-temperature regime, the anti-polyelectrolyte effect of chain expansion upon addition of low molar mass salt, and chain relaxation times in dilute solutions. (2) Spontaneous formation of a mesomorphic state at the borderline between the high-temperature and low-temperature regimes and its characteristics. A universal law is presented for the radius of gyration of the microgel, as a proportionality to one-sixth power of the polymer concentration. (3) Swelling equilibrium of chemically cross-linked polyzwitterion gels in both the high temperature and low-temperature regimes. Addressing the hierarchical internal dynamics of polyzwitterion gels, we present a general stretched exponential law for the time-correlation function of gel displacement vector, that can be measured in dynamic light scattering experiments. The present theory is of direct experimental relevance and additional theoretical developments to all polyzwitterion systems, and generally to biological macromolecular systems such as intrinsically disordered proteins. Full article

Thermoplastic polymers exhibit relatively limited surface energies and this results in poor adhesion when bonded to other materials. Plasma surface modification offers the potential to overcome this challenge through the functionalisation of the polymer surfaces. In this study, three polymers of differing hydrophobicity (HDPE, PA12, and PA6) were subjected to a novel, atmospheric, μPlasma surface treatment technique, and its effectiveness at increasing the surface energies was evaluated via measurement of the contact angle. To characterise the physical and chemical changes following μPlasma surface modification, the surface morphology was observed using atomic force microscopy (AFM), and the functionalisation of the surface was evaluated using infrared spectroscopy. Immediately after treatment, the contact angle decreased by 47.3° (HDPE), 42.6° (PA12), and 50.1° (PA6), but the effect was not permanent in that there was a pronounced relaxation or ageing phenomenon in operation. The ageing process over five hours was modelled using a modified stretched exponential function Kohlrausch–Williams–Watts (KWW) model, and it was found that the ageing rate was dependent on the hydrophilicity of polymers, with polyamides ageing more rapidly than polyethylene. Full article

In a previous investigation, the authors proposed nitrogen as a possible candidate for exploiting the donor spin in silicon quantum devices. This system is characterized by a ground state deeper than the other group V impurities in silicon, offering less stringent requirements on the device temperature necessary to access the unionized state. The nitrogen donor is slightly displaced from the substitutional site, and upon heating, the system undergoes a motional transition. In the present article, we show the results from our investigation on the spin–relaxation times in ^natSi and ²⁸Si substrates and discuss the motional effects on relaxation. The stretched exponential relaxation observed is interpreted as a distribution of spin–lattice relaxation times, whose origin is also discussed. This information greatly contributes to the assessment of a nitrogen-doped silicon system as a potential candidate for quantum devices working at temperatures higher than those required for other group V donors in silicon. Full article

Different viscoelastic models and characteristics are commonly used to describe, analyze, compare and improve the mechanical properties of polymers. A time-dependent linear relaxation modulus next to frequency-domain storage and loss moduli are the basic rheological material functions of polymers. The exponential Maxwell model and the exponential stretched Kohlrausch–Williams–Watts model are, probably, the most known linear rheological models of polymers. There are different identification methods for such models, some of which are dedicated to specific models, while others are general in nature. However, the identification result, i.e., the best model, always depends on the specific experimental data on the basis of which it was determined. When the rheological stress relaxation test is performed, the data are composed of the sampling instants used in the test and on the measurements of the relaxation modulus of the real material. To build a relaxation modulus model that does not depend on sampling instants is a fundamental concern. The problem of weighted least-squares approximation of the real relaxation modulus is discussed when only the noise-corrupted time-measurements of the relaxation modulus are accessible for identification. A wide class of models, that are continuous, differentiable and Lipschitz with respect to parameters, is considered for the relaxation modulus approximation. The main results concern the models that are selected asymptotically as the number of measurements tends to infinity. It is shown that even when the true relaxation modulus description is completely unknown, the approximate optimal model parameters can be derived from the measurement data that are obtained for sampling instants that are selected randomly due to the appropriate randomization introduced whenever certain conditions regarding the adopted class of models are satisfied. It is shown that the most commonly used stress relaxation models, the Maxwell and Kohlrausch–Williams–Watts models, satisfy these conditions. Since the practical problems of the identification of relaxation modulus models are usually ill posed, Tikhonov regularization is applied to guarantee the stability of the regularized solutions. The approximate optimal model is a strongly consistent estimate of the regularized model that is optimal in the sense of the deterministic integral weighted square error. An identification algorithm leading to the best regularized model is presented. The stochastic-type convergence analysis is conducted for noise-corrupted relaxation modulus measurements, and the exponential convergence rate is proved. Numerical studies for different models of the relaxation modulus used in the polymer rheology are presented for the material described by a bimodal Gauss-like relaxation spectrum. Numerical studies have shown that if appropriate randomization is introduced in the selection of sampling instants, then optimal regularized models of the relaxation modulus being asymptotically independent of these time instants can be recovered from the stress relaxation experiment data. The robustness of the identification algorithm to measurement noises was demonstrated both by analytical and numerical analyses. Full article

We study the low-temperature (T = 4.7 K) emission dynamics of a thin film of methylammonium lead bromide (MAPbBr${}_3$), prepared via the anti-solvent method. Using intensity-dependent (over 5 decades) hyperspectral microscopy under quasi-resonant (532 nm) continuous wave excitation, we revealed spatial inhomogeneities in the thin film emission. This was drastically different at the band-edge (∼550 nm, sharp peaks) than in the emission tail (∼568 nm, continuum of emission). We are able to observe regions of the film at the micrometer scale where emission is dominated by excitons, in between regions of trap emission. Varying the density of absorbed photons by the MAPbBr${}_3$ thin films, two-color fluorescence lifetime imaging microscopy unraveled the emission dynamics: a fast, resolution-limited (∼200 ps) monoexponential tangled with a stretched exponential decay. We associate the first to the relaxation of excitons and the latter to trap emission dynamics. The obtained stretching exponents can be interpreted as the result of a two-dimensional electron diffusion process: Förster resonant transfer mechanism. Furthermore, the non-vanishing fast monoexponential component even in the tail of the MAPbBr${}_3$ emission indicates the subsistence of localized excitons. Finally, we estimate the density of traps in MAPbBr${}_3$ thin films prepared using the anti-solvent method at n∼10${}^{17}$ cm${}^{-3}$. Full article

We have investigated the ultrasonically induced birefringence traces of aqueous solutions of dexamethasone disodium phosphate, a derivative of hydrocortisone (cortisol). The stationary birefringence and the transient built-up and decay relaxation processes were studied as a function of solution concentration, ultrasound frequency and intensity, as well as a function of temperature. The results were analyzed in view of structural peculiarities of the system in an effort to gain further insights into the molecular relaxation dynamics and the proposed self-association process occurring in the system. The detected ultrasonically induced birefringence relaxation is motivated by the rotational diffusion of dexamethasone disodium phosphate aggregates due to self-association depending on the solution concentration. The observed relaxation mechanism is directly linked to the hydrodynamic size of the acoustic field-induced self-assembly. The systematic analysis of the transient birefringence signals caused by the applied ultrasonic field allowed us to evaluate the interplay between permanent and induced dipoles with changing concentration, temperature, and ultrasound properties. The birefringence traces are adequately fitted with a stretched exponential law indicating the polydispersive nature of the self-aggregated molecular structures. The obtained results are described in the light of recent studies performed on this system. Full article

Spin-crossover solids have been studied for many years for their promising applications as optical switches and reversible high-density memories for information storage. This study reports the effect of random metal dilution on the thermal and structural properties of a spin-crossover single crystal. The analysis is performed on a 2D rectangular lattice using an electro-elastic model. The lattice is made of sites that can switch thermally between the low-spin and high-spin states, accompanied by local volume changes. The model is solved by Monte Carlo simulations, running on the spin states and atomic positions of this compressible 2D lattice. A detailed analysis of metal dilution on the magneto-structural properties allows us to address the following issues: (i) at low dilution rates, the transition is of the first order; (ii) increasing the concentration of dopant results in a decrease in cooperativity and leads to gradual transformations above a threshold concentration, while incomplete spin transitions are obtained for big dopant sizes. The effects of the metal dilution on the spatiotemporal aspects of the spin transition along the thermal transition and on the low-temperature relaxation of the photo-induced metastable high-spin states are also studied. Significant changes in the organization of the spin states are observed for the thermal transition, where the single-domain nucleation caused by the long-range elastic interactions is replaced by a multi-droplet nucleation. As to the issue of the relaxation curves: their shape transforms from a sigmoidal shape, characteristic of strong cooperative systems, into stretched exponentials for high dilution rates, which is the signature of a disordered system. Full article

The spin-lattice relaxation rate (T₁⁻¹) of lipid spin labels obtained from saturation recovery EPR measurements in deoxygenated membranes depends primarily on the rate of the rotational diffusion of the nitroxide moiety within the lipid bilayer. It has been shown that T₁⁻¹ also can be used as a qualitative convenient measure of membrane fluidity that reflects local membrane dynamics; however, the relation between T₁⁻¹ and rotational diffusion coefficients was not provided. In this study, using data previously presented for continuous wave and saturation recovery EPR measurements of phospholipid analog spin labels, one-palmitoyl-2-(n-doxylstearoyl)phosphatidylcholine in 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine/cholesterol membranes, we show that measured T₁⁻¹ values are linear functions of rotational diffusion of spin labels. Thus, these linear relationships can be used to transfer T₁⁻¹ values into spin label rotational rates as a precise description of membrane fluidity. This linearity is independent through the wide range of conditions including lipid environment, depth in membrane, local hydrophobicity, and the anisotropy of rotational motion. Transferring the spin-lattice relaxation rates into the rotational diffusion coefficients makes the results obtained from saturation recovery EPR spin labeling easy to understand and readily comparable with other membrane fluidity data. Full article

Single pulse, solid-state ²⁹Si nuclear magnetic resonance (NMR) spectroscopy offers an additional method of characterisation of opal-A and opal-CT through spin-lattice (T₁) relaxometry. Opal T₁ relaxation is characterised by stretched exponential (Weibull) function represented by scale (speed of relaxation) and shape (form of the curve) parameters. Relaxation is at least an order of magnitude faster than for silica glass and quartz, with Q₃ (silanol) usually faster than Q₄ (fully substituted silicates). 95% relaxation (Q₄) is achieved for some Australian seam opals after 50 s though other samples of opal-AG may take 4000 s, while some figures for opal-AN are over 10,000 s. Enhancement is probably mostly due to the presence of water/silanol though the presence of paramagnetic metal ions and molecular motion may also contribute. Shape factors for opal-AG (0.5) and opal-AN (0.7) are significantly different, consistent with varying water and silanol environments, possibly reflecting differences in formation conditions. Opal-CT samples show a trend of shape factors from 0.45 to 0.75 correlated to relaxation rate. Peak position, scale and shape parameter, and Q₃ to Q₄ ratios offer further differentiating feature to separate opal-AG and opal-AN from other forms of opaline silica. T₁ relaxation measurement may have a role for provenance verification. In addition, definitively determined Q₃/Q₄ ratios are in the range 0.1 to 0.4 for opal-AG but considerably lower for opal-AN and opal-CT. Full article

Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are obtained according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadband dielectric spectroscopy. Both sets of data are usually fitted by time or frequency dependent functions which, in turn, may be analytically transformed among themselves using the Laplace transform. This leads to the question on comparability of results obtained using just mentioned experimental procedures. If we would like to do that in the time domain we have to go beyond widely accepted Kohlrausch–Williams–Watts approximation and become acquainted with description using the Mittag–Leffler functions. To convince the reader that the latter is not difficult to understand we propose to look at the problem from the point of view of objects which appear in the stochastic processes approach to relaxation. These are the characteristic exponents which are read out from the standard non-Debye frequency dependent patterns. Characteristic functions appear to be expressed in terms of elementary functions whose asymptotics is simple. This opens new possibility to compare behavior of functions used to describe non-Debye relaxations. It turnes out that the use of Mittag-Leffler function proves very convenient for such a comparison. Full article

In this article, the boundary layer flow of a viscous nanofluid induced by an exponentially stretching surface embedded in a permeable medium with the Cattaneo–Christov heat flux model (CCHFM) is scrutinized. We took three distinct kinds of nanoparticles, such as alumina (Al₂O₃), titania (TiO₂) and copper (Cu) with pure water as the base fluid. The features of the heat transfer mechanism, as well as the influence of the relaxation parameter on the present viscous nanofluid flow are discussed here thoroughly. The thermal stratification is taken in this phenomenon. First of all, the problem is simplified mathematically by utilizing feasible similarity transformations and then solved analytically through the OHAM (optimal homotopy analysis method) to get accurate analytical solutions. The change in temperature distribution and axial velocity for the selected values of the specific parameters has been graphically portrayed in figures. An important fact is observed when the thermal relaxation parameter (TRP) is increased progressively. Graphically, it is found that an intensification in this parameter results in the exhaustion of the fluid temperature together with an enhancement in the heat transfer rate. A comparative discussion is also done over the Fourier’s law and Cattaneo–Christov model of heat. Full article

A mathematical model comprising Darcy Forchheimer effects on the 3D nanofluid flow with engine oil as a base fluid containing suspended carbon nanotubes (CNTs) is envisioned. The CNTs are of both types i.e., multi-wall carbon nanotubes (MWCNTs) and single-walled carbon nanotubes (SWCNTs). The flow is initiated by an exponentially stretched surface. The impacts of Cattaneo–Christov heat flux along with velocity and thermal slip conditions are key factors in the novelty of the defined model. The boundary layer notion is designed to convert the compact form of equations into the component shape. Appropriate transformations lead to differential equations with high nonlinearity. The final non-dimensional system is solved numerically by a “MATLAB” function known as bvp4c. For both CNTs, different graphical sketches are drawn to present the influence of arising parameters versus related profiles. The outcomes show that higher slip parameter boosts the axial velocity, whereas fluid temperature lowers for a sturdier relaxation parameter. Full article

In the last decade, nanoparticles have provided numerous challenges in the field of science. The nanoparticles suspended in various base fluids can transform the flow of fluids and heat transfer characteristics. In this research work, the mathematical model is offered to present the 3D magnetohydrodynamics Darcy–Forchheimer couple stress nanofluid flow over an exponentially stretching sheet. Joule heating and viscous dissipation impacts are also discussed in this mathematical model. To examine the relaxation properties, the proposed model of Cattaneo–Christov is supposed. For the first time, the influence of temperature exponent is scrutinized via this research article. The designed system of partial differential equations (PDE’s) is transformed to set of ordinary differential equations (ODE’s) by using similarity transformations. The problem is solved analytically via homotopy analysis technique. Effects of dimensionless couple stress, magnetic field, ratio of rates, porosity, and coefficient of inertia parameters on the fluid flow in x- and y-directions have been examined in this work. The augmented ratio of rates parameter upsurges the velocity profile in the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, and couple stress parameter diminishes the velocity field along the x-direction. The augmented magnetic field, porosity parameter, coefficient of inertia, ratio of rates parameter, and couple stress parameter reduces the velocity field along the y-axis. The influences of time relaxation, Prandtl number, and temperature exponent on temperature profile are also discussed. Additionally, the influences of thermophoresis parameter, Schmidt number, Brownian motion parameter, and temperature exponent on fluid concentration are explained in this work. For engineering interests, the impacts of parameters on skin friction and Nusselt number are accessible through tables. Full article

Gels are amorphous solids whose macroscopic viscoelastic response derives from constraints in the material that serve to localize the constituent molecules or particles about their average positions in space. These constraints may either be local in nature, as in chemical cross-linking and direct physical associations, or non-local, as in case of topological “entanglement” interactions between highly extended fiber or sheet structures in the fluid. Either of these interactions, or both combined, can lead to “gelation” or “amorphous solidification”. While gels are often considered to be inherently non-equilibrium materials, and correspondingly termed “soft glassy matter”, this is not generally the case. For example, the formation of vulcanized rubbers by cross-linking macromolecules can be exactly described as a second order phase transition from an equilibrium fluid to an equilibrium solid state, and amorphous solidification also arises in diverse physical gels in which molecular and particle localization occurs predominantly through transient molecuar associations, or even topological interactions. As equilibrium, or near equilibrium systems, such gels can be expected to exhibit universal linear and non-linear viscoelastic properties, especially near the “critical” conditions at which the gel state first emerges. In particular, a power-law viscoelastic response is frequently observed in gel materials near their “gelation” or “amorphous solidification” transition. Another basic property of physical gels of both theoretical and practical interest is their response to large stresses at constant shear rate or under a fixed macrocopic strain. In particular, these materials are often quite sensitive to applied stresses that can cause the self-assembled structure to progressively break down under flow or deformation. This disintegration of gel structure can lead to “yield” of the gel material, i.e., a fluidization transition, followed by shear thinning of the resulting heterogeneous “jelly-like” fluid. When the stress is removed, however, the material can relax back to its former equilibrium gel state, i.e., gel rejuvenation. In constrast, a non-equilibrium material will simply change its form and properties in a way that depends on processing history. Physical gels are thus unique self-healing materials in which the existence of equilibrium ensures their eventual recovery. The existence of equilibrium also has implications for the nature of both the linear and non-linear rheological response of gel materials, and the present paper explores this phenomenon based on simple scaling arguments of the kind frequently used in describing phase transitions and the properties of polymer solutions. Full article