Effect of rotation in magneto-thermoelastic transversely isotropic hollow cylinder with three-phase-lag model

This article deals with the various heat source responses in a transversely isotropic hollow cylinder under the purview of three-phase-lag (TPL) generalized thermoelasticity theory. In presence of magnetic field and due to the rotating behavior of the cylinder, the governing equations are redefined for generalized thermoelasticity with thermal time delay. In order to obtain the stress, displacement and temperature field, the field functions are expressed in terms of modified Bessel functions in Laplace transformed domain. When the outer radius of hollow cylinder tends to infinity, the corresponding results are discussed. Finally an appropriate Laplace transform inversion technique is adopted.     

Analyticity of resonances and eigenvalues and spectral properties of the massless Spin–Boson model

We extend the method of Pizzo multiscale analysis for resonances introduced in [5] in order to infer analytic properties of resonances and eigenvalues (and their eigenprojections) as well as estimates for the localization of the spectrum of dilated Hamiltonians and norm-bounds for the corresponding resolvent operators, in neighborhoods of resonances and eigenvalues. We apply our method to the massless Spin–Boson model assuming a slight infrared regularization. We prove that the resonance and the ground-state eigenvalue (and their eigenprojections) are analytic with respect to the dilation parameter and the coupling constant. Moreover, we prove that the spectrum of the dilated Spin–Boson Hamiltonian in the neighborhood of the resonance and the ground-state eigenvalue is localized in two cones in the complex plane with vertices at the location of the resonance and the ground-state eigenvalue, respectively. Additionally, we provide norm-estimates for the resolvent of the dilated Spin–Boson Hamiltonian near the resonance and the ground-state eigenvalue. The topic of analyticity of eigenvalues and resonances has let to several studies and advances in the past. However, to the best of our knowledge, this is the first time that it is addressed from the perspective of Pizzo multiscale analysis. Once the multiscale analysis is set up our method gives easy access to analyticity: Essentially, it amounts to proving it for isolated eigenvalues only and use that uniform limits of analytic functions are analytic. The type of spectral and resolvent estimates that we prove are needed to control the time evolution including the scattering regime. The latter will be demonstrated in a forthcoming publication. The introduced multiscale method to study spectral and resolvent estimates follows its own inductive scheme and is independent (and different) from the method we apply to construct resonances.     

The Cauchy problem for a spin-liquid model in three space dimensions

In this paper, we study the Cauchy problem for magnetic fluid of spin-liquid type with Mermin-Ho relation in the three-dimensional space and prove global existence and uniqueness of solutions. The proof is based on the equivalence relation between smooth solutions of the spin-liquid model and the systems of Schrödinger equations with Abelian gauge field. The Sobolev spaces with fractional derivatives are also used in our estimates.     

Mathematical Modeling of Nylon 6/6,6 Copolymerization in Batch Reactor: Investigating Recipes without Water and with Cyclic Dimer

A model is used to simulate batch copolymerization of caprolactam with hexamethylene diamine (HMD) and adipic acid (ADA) to produce nylon 6/6,6. Four different recipes are considered: a recipe containing caprolactam and an aqueous solution of HMD and ADA, a recipe containing caprolactam and dry HMD/ADA salt, and two recipes with a portion of the caprolactam replaced by nylon 6 cyclic dimer (CD). Consuming CD would be advantageous because CD is an undesirable side product from nylon 6 production. Simulation results lead to three important findings: (i) operation using dry salt rather than aqueous salt solution leads to higher degree of polymerization, (ii) substantial quantities of CD can be consumed to produce nylon 6/6,6 copolymer, and (iii) including water in the recipe is beneficial for achieving improved consumption of CD. The results of this study will be helpful in designing experiments aimed at improving industrial nylon 6/6,6 copolymerization processes.     

Salen–Mg-doped NH2–MIL-101(Cr) for effective CO2 adsorption under ambient conditions

A novel metal-doped metal–organic framework (MOF) was developed by incorporating salen–Mg into NH₂–MIL-101(Cr) structure under ambient conditions. The Schiff base complex was successfully prepared by condensing salicylaldehyde with a free amino group and then coordinating metal ions. Such a structure can endow the sample with higher CO₂ adsorption performance. At 0°C and 1 bar, the salen–Mg-modified sample achieves the maximum adsorption capacity of 2.18 mmol g⁻¹ for CO₂, which was 5.8% higher than the pristine salen–MOF under the same conditions. Notably, the Freundlich model indicates that the CO₂ adsorption process of all samples conforms to reversible adsorption. However, the correlation coefficients (R²) of the Mg-doped sample are lower than that of the pristine sample. Besides, the CO₂/N₂ adsorption selectivity and isosteric heat also show a similar trend. These results indicate that the salen–Mg can enhance the interaction between the material and CO₂ molecules.     

Homogenization of Periodically Heterogeneous Thin Beams

Consider an elastic thin three-dimensional body made of a periodic distribution of elastic inclusions. When both the thickness of the beam and the size of the heterogeneities tend simultaneously to zero the authors obtain three different one-dimensional models of beam depending upon the limit of the ratio of these two small parameters.     

Self-assembly mechanism of PEG-b-PCL and PEG-b-PBO-b-PCL amphiphilic copolymer micelles in aqueous solution from coarse grain modeling

We followed the self-assembly of high-molecular weight MePEG- b -PCL (poly(methyl ethylene glycol)-block-poly(ε-caprolactone)) diblock and MePEG- b -PBO- b -PCL (poly(methyl ethylene glycol)-block-poly(1,2-butylene oxide)-block-poly(ε-caprolactone)) into micelles using molecular dynamics simulation with a coarse grain (CG) force field based on quantum mechanics (CGq FF). The triblock polymer included a short poly(1,2-butylene oxide) (PBO) at the hydrophilic-hydrophobic interface of these systems. Keeping the hydrophilic length fixed (MePEG₄₅), we considered 250 chains in which the hydrophobic length changed from PCL₄₄ or PBO₆- b -PCL₄₃ to PCL₆₂ or PBO₉- b -PCL₆₁. The polymers were solvated in explicit water for 2 μs of simulations at 310.15 K. We found that the longer diblock system undergoes a morphological transition from an intermediate rod-like micelle to a prolate-sphere, while the micelle formed from the longer triblock system is a stable rod-like micelle. The two shorter diblock and triblock systems show similar self-assembly processes, both resulting in slightly prolate-spheres. The dynamics of the self-assembly is quantified in terms of chain radius of gyration, shape anisotropy, and hydration of the micelle cores. The final micelle structures are analyzed in terms of the local density components. We conclude that the CG model accurately describes the molecular mechanisms of self-assembly and the equilibrium micellar structures of hydrophilic and hydrophobic chains, including the quantity of solvent trapped inside the micellar core.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐。然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM方法仅以回波幅值作为成像指标,忽略了Lamb波与损伤的相互作用,故而不能通过损伤表面的物理参数增强成像质量。针对这两个问题,本文首先在时域TFM基础上发展了频域TFM,在计算中纳入频散关系以规避频散的影响;其次以包含明确的损伤特征参数--反射率为成像指标,结合频域TFM方法建立损伤逆散射模型,以实现对损伤的准确成像。仿真和实验结果表明:频域逆散射TFM成像方法能够实现对铝板结构中的损伤检测,在工程实践中具有应用价值。     

An asymptotic Reissner–Mindlin plate model

A mathematical study via variational convergence of a periodic distribution of classical linearly elastic thin plates softly abutted together shows that it is not necessary to use a different continuum model nor to make constitutive symmetry hypothesis as starting points to deduce the Reissner–Mindlin plate model.     

Optical and static dielectric study of a terminally fluorinated liquid crystalline compound

Optical and static dielectric studies on a terminally fluorinated liquid crystalline compound have been carried out. Measurements of temperature variation of refractive indices of the compound are done by using thin prism method. A four-parameter model is validated by fitting the experimentally measured values of refractive indices, birefringence and average refractive indices of the compound with the theoretical ones. Refractive index and density data are utilized for determination of orientational order parameter. The temperature variation of dielectric permittivities of the compound are measured by a LCR meter.