Implicit and Implicit–Explicit Strong Stability Preserving Runge–Kutta Methods with High Linear Order

Strong stability preserving (SSP) time discretizations preserve the monotonicity properties satisfied by the spatial discretization when coupled with the first order forward Euler, under a certain time-step restriction. The search for high order strong stability preserving time-stepping methods with high order and large allowable time-step has been an active area of research. It is known that implicit SSP Runge–Kutta methods exist only up to sixth order; however, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and we can find implicit SSP Runge–Kutta methods of any linear order. In the current work we find implicit SSP Runge–Kutta methods with high linear order \(p_{lin} \le 9\) and nonlinear orders \(p=2,3,4\), that are optimal in terms of allowable SSP time-step. Next, we formulate a novel optimization problem for implicit–explicit (IMEX) SSP Runge–Kutta methods and find optimized IMEX SSP Runge–Kutta pairs that have high linear order \(p_{lin} \le 7\) and nonlinear orders up to \(p=4\). We also find implicit methods with large linear stability regions that pair with known explicit SSP Runge–Kutta methods. These methods are then tested on sample problems to demonstrate the sharpness of the SSP coefficient and the typical behavior of these methods on test problems.     

Creep and relaxation of cement paste caused by stress‐induced dissolution of hydrated solid components

The creep and relaxation of cement paste caused by dissolving solid hydration products is evaluated in this work. According to the second law of thermodynamics, dissolution or precipitation of solid constituents may be altered by the change in stress/strain fields inside cement paste via alteration of the stress power or strain energy. Thus, it is hypothesized that stress‐induced dissolution can affect the overall creep/relaxation behavior of cement composites. A novel, fully coupled thermodynamic, mechanical, and microstructural model (TM²) that uses the finite element method was developed to predict the time‐evolving properties of cement paste under prescribed strains and to test the hypothesis. In the model, the strain energy was incorporated to accurately predict the effect of stress and strain fields on cement microstructure change. From the simulation results, depending on the stress/strain levels and the choice of the domain (over which the thermodynamic equilibrium is enforced), stress‐induced dissolution of solid constituents can lead to significant creep/relaxation.     

Multi‐Material Tissue Engineering Scaffold with Hierarchical Pore Architecture

Multi‐material polymer scaffolds with multiscale pore architectures are characterized and tested with vascular and heart cells as part of a platform for replacing damaged heart muscle. Vascular and muscle scaffolds are constructed from a new material, poly(limonene thioether) (PLT32i), which meets the design criteria of slow biodegradability, elastomeric mechanical properties, and facile processing. The vascular–parenchymal interface is a poly(glycerol sebacate) (PGS) porous membrane that meets different criteria of rapid biodegradability, high oxygen permeance, and high porosity. A hierarchical architecture of primary (macroscale) and secondary (microscale) pores is created by casting the PLT32i prepolymer onto sintered spheres of poly(methyl methacrylate) (PMMA) within precisely patterned molds followed by photocuring, de‐molding, and leaching out the PMMA. Prefabricated polymer templates are cellularized, assembled, and perfused in order to engineer spatially organized, contractile heart tissue. Structural and functional analyses show that the primary pores guide heart cell alignment and enable robust perfusion while the secondary pores increase heart cell retention and reduce polymer volume fraction.     

Contrast enhancement for in vivo visible reflectance imaging of tissue oxygenation

Results are presented illustrating a straightforward algorithm to be used for real-time monitoring of oxygenation levels in blood cells and tissue based on the visible spectrum of hemoglobin. Absorbance images obtained from the visible reflection of white light through separate red and blue bandpass filters recorded by monochrome charge-coupled devices (CCDs) are combined to create enhanced images that suggest a quantitative correlation between the degree of oxygenated and deoxygenated hemoglobin in red blood cells. The filter bandpass regions are chosen specifically to mimic the color response of commercial 3-CCD cameras, representative of detectors with which the operating room laparoscopic tower systems are equipped. Adaptation of this filter approach is demonstrated for laparoscopic donor nephrectomies in which images are analyzed in terms of real-time in vivo monitoring of tissue oxygenation.     

Multiscale Modeling for Food Drying: State of the Art

Plant‐based food materials are mostly porous in nature and heterogeneous in structure with huge diversity in cellular orientation. Different cellular environments of plant‐based food materials, such as intercellular, intracellular, and cell wall environments, hold different proportions of water with different characteristics. Due to this structural heterogeneity, it is very difficult to understand the drying process and associated morphological changes during drying. Transport processes and morphological changes that take place during drying are mainly governed by the characteristics of and the changes in the cells. Therefore, to predict the actual heat and mass transfer process that occurs in the drying process and associated morphological changes, development of multiscale modeling is crucial. Multiscale modeling is a powerful approach with the ability to incorporate this cellular structural heterogeneity with microscale heat and mass transfer during drying. However, due to the huge complexity involved in developing such a model for plant‐based food materials, the studies regarding this issue are very limited. Therefore, we aim in this article to develop a critical conceptual understanding of multiscale modeling frameworks for heterogeneous food materials through an extensive literature review. We present a critical review on the multiscale model formulation and solution techniques with their spatial and temporal coupling options. Food structure, scale definition, and the current status of multiscale modeling are also presented, along with other key factors that are critical to understanding and developing an accurate multiscale framework. We conclude by presenting the main challenges for developing an accurate multiscale modeling framework for food drying.     

3D nanofluidic channels shaped by electron-beam-induced etching

In-plane nanofluidic channels with 3D topography are fabricated. Nanochannel masters are written by electron beam lithography in SU-8 resist and shaped by electron-beam-induced etching (EBIE) with water as the precursor gas. Nanofunnel replicas cast from unmodified and EBIE-modified masters show that the funnel tip dimensions decrease from a 150-nm depth and 80-nm width to a 70-nm depth and 40-nm width.     

Super-resolved spatial light interference microscopy

We report a scheme to achieve resolution beyond the diffraction limit in spatial light interference microscopy (SLIM). By adding a grating to the optical path, the structured illumination technique can be used to improve the resolution by a factor of 2. We show that a direct application of the structured illumination technique, however, has proved to be unsuccessful. Through two crucial modifications, namely, one to the pupil plane of the objective and the other to the demodulation procedure, faithful phase information of the object is recovered and the resolution is improved by a factor of 2.     

In situ growth of silver nanoparticles in porous membranes for surface-enhanced raman scattering

We demonstrate the in situ growth of silver nanoparticles in porous alumina membranes (PAMs) for use as a surface-enhanced Raman scattering (SERS) detection substrate. This fabrication method is simple, cost-effective, and fast, while providing control over the size of silver nanoparticles through the entire length of the cylindrical nanopores with uniform particle density inside the pores unachievable by the traditional infiltration technique. The in situ growth of silver nanoparticles was conducted from electroless-deposited nanoscale seeds on the interior of the PAM and resulted in the formation of numerous hot spots, which facilitated significantly higher SERS enhancement for these substrates compared with previously reported porous substrates.