Breakdown theory of a granular bed by the flow of a continuum

The article discusses the statement of problems of local breakdown of a granular bed under the action of a stream filtering through it, and a general method of their approximate analysis is suggested. The simplest examples are examined.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 3, pp. 433–442, September, 1979.     

Atomistic-based continuum constitutive relation for microtubules: elastic modulus prediction

Mechanical behavior of cells is primarily governed by the cytoskeleton (CSK), a remarkable system of filaments consisting of microtubules, actin filaments and intermediate filaments. This system defines the shape and bulk mechanical properties of the cell. In order to understand how the CSK network influences the mechanical behavior of living cells from a theoretical perspective, the mechanical properties of an individual CSK filament must first be properly described. Existing atomistic simulation methods have computational size limitations; conversely, conventional continuum mechanics lack fundamental nanoscale information. Here a new simulation method is developed that bridges the gap between these two simulation regimes using an atomistic-based continuum constitutive relation for microtubules based on the interatomic potential for proteins and specific atomic structures. This theory is used to predict the elastic modulus of microtubules, which agrees with the range of experimentally measured values without any parameter fitting. The proposed method is applicable to other biopolymers if the subunits are bonded through noncovalent bonds.     

Empirical relation for the activation energy of diffusion in elemental substances

By examining the reported data on the self-diffusion in metals, inert-gas crystals, and silicon and the diffusion of impurities in silicon and silver, it is shown that the activation energy of diffusion can be related to the entropy of melting of the diffuser and the melting point of the host material     

Examining the physical foundation of continuum theories from the viewpoint of phonon dispersion relation

An overview of crystal types and their interatomic force models are given and the basic feature of the dynamics of atoms in crystal is introduced. Elastic waves described by classical continuum theory, phonon dispersion relations by micromorphic theory, micropolar theory, couple stress theories and nonlocal theory are calculated and presented. The physical foundation and the applicability are examined from the viewpoint of phonon dispersion relation. Two physical examples, including the apparent change of material constants at different length scales and the macroscopic phenomenon of piezoelectricity are discussed.     

A study on the effect of selected process parameters in a jet diffusion flame for Pt nanoparticle formation

Pt is used in many catalytic applications from three-way catalysts to fuel cells. Particle size and morphology are key parameters that influence the electrocatalytic activity. Flame synthesis is an efficient and continuous manufacturing route capable of producing Pt nanoparticles with desirable catalytic properties. In order to understand the effect of the forced oxidant, solvent composition, and quench rate on nanoparticle formation, a systematic study of process parameters using Pt was undertaken. Reactive spray deposition technology was used as the synthesis platform. In order to obtain a tight control of the Pt size, it was found that the fuel must contain a sufficient enthalpy of combustion and appropriate propane content. The fuel must be mixed adequately to form a turbulent diffusion flame and must create conditions where unwanted Pt coarsening cannot occur. From this study, the conditions that favor this morphology require an O₂ flow rate setting of 6.89 L/min or higher, a propane content of 20 wt%, and no quenching. Electrochemical data show decreasing electrochemical surface area (75–36 m²/g_Pt), increasing mass activity (120–610 mA/mg_Pt), and increasing specific activity (150–1350 \( \upmu {\text{A}}/ {\text{cm}}^{2} {_{\text{Pt}}} \)) with increasing oxidant flow.     

The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes

In this paper, the constitutive relations of nonlocal elasticity theory are presented for application in the analysis of carbon nanotubes (CNTs) when modelled as Euler-Bernoulli beams, Timoshenko beams or as cylindrical shells. In particular, the shear stress and strain relation for the nonlocal Timoshenko beam theory is discussed in great detail due to a misconception by some researchers that the nonlocal effect should appear in this constitutive relation. Different theories for proposing the value of the small scale parameter are also introduced and a recommendation for the value from the standpoint of wave propagation of CNTs is given.     

A view of the relation between the continuum theory of lattice defects and non-euclidean geometry in the linear approximation

A view is presented of the relation between the continuum theory of defects in crystals and the mathematical theory of non-metric, non-Riemannian geometry. Both theories are treated in the linear approximation. The lattice defects consist of disclinations, dislocations, and extra-matter, which are identified with the following three important tensors from non-Euclidean geometry: the Riemann-Christoffel curvature tensor, the Cartan torsion tensor and the non-metric Q-tensor. The correspondence between the two theories is established by finding a relation between the coefficients of linear connection of non-Euclidean geometry and the elastic strain, bend-twist, and quasi-plastic strain of defect theory. The definitions of the important tensors from non-Euclidean geometry then generally correspond to the field equations of defect theory. The identities for the curvature tensor generally correspond to the continuity equations of defect theory. The relation to the conventional formulation of defect theory is pointed out. Two examples are given to illustrate the concepts of the paper. One example is related to the deformations associated with constant dislocation distribution and the other to the deformations of a constant disclination distribution.     

Luminescent nanoparticle probes for bioimaging

Bioimaging with luminescent nanoparticle probes have recently attracted widespread interest in biology and medicine. In comparison with commonly used organic dyes, luminescent nanoparticles are better in terms of photostability and sensitivity. These optical features of nanoparticle probes are critical for real time tracking and monitoring of biological events in the cellular level, which may not be accomplished using regular fluorescent dyes. Nanoparticle probes are also shown highly suitable for immunoassay and other diagnostic and therapeutic applications. In this article, we describe a variety of optical nanoparticle probes such as quantum dots, metal nanoparticles, dye-doped nanoparticles etc. for bioimaging applications.     

Mathematical homogenization theory for electroactive continuum

Two‐scale continuum equations are derived for heterogeneous continua with full nonlinear electromechanical coupling using nonlinear mathematical homogenization theory. The resulting coarse‐scale electromechanical continuum equations are free of coarse‐scale constitutive equations. The unit cell (or representative volume element) is subjected to the overall mechanical and electric field extracted from the solution of the coarse‐scale problem and is solved for arbitrary constitutive equations of fine‐scale constituents. The proposed method can be applied to analyze the behavior of electroactive materials with heterogeneous fine‐scale structure and can pave the way forward for designing advanced electroactive materials and devices. Copyright © 2012 John Wiley & Sons, Ltd.     

Boltzmann schemes for continuum gas dynamics

Many problems arising in the aerodynamic design of aerospace vehicles require the numerical solution of the Euler equations of gas dynamics. These are nonlinear partial differential equations admitting weak solutions such as shock waves and constructing robust numerical schemes for these equations is a challenging task. A new line of research called Boltzmann or kinetic schemes discussed in the present paper exploits the connection between the Boltzmann equation of the kinetic theory of gases and the Euler equations for inviscid compressible flows. Because of this connection, a suitable moment of a numerical scheme for the Boltzmann equation yields a numerical scheme for the Euler equations. This idea called the “moment method strategy” turns out to be an extremely rich methodology for developing robust numerical schemes for the Euler equations. The richness is demonstrated by developing a variety of kinetic schemes such as kinetic numerical method, kinetic flux vector splitting method, thermal velocity based splitting, multidirectional upwind method and least squares weak upwind scheme. A 3-D time-marching Euler code calledbheema based on the kinetic flux vector splitting method and its variants involving equilibrium chemistry have been developed for computing hypersonic reentry flows. The results obtained from the codebheema demonstrate the robustness and the utility of the kinetic flux vector splitting method as a design tool in aerodynamics. The work presented in this paper is based on the research work done by several graduate students at our laboratory and collaborators from research and development organizations within the country.     

Finite element solution for the continuum traffic equilibrium problems

In this paper, we consider a city with a highly compact Central Business District (CBD), and the commuters’ destinations from the CBD are dispersed over the whole city. The street network is approximated as a continuum and commuters’ movements in the city are measured by the flow intensity, and the local travel cost depends on the location and the traffic flow intensity. We extend the continuum user equilibrium problem to deal with the case of variable demand, in which the traffic demand from any destination in the city to the CBD is assumed to be a function of both the destination location and the total travel cost to the CBD. An equivalent mathematical model is formulated and proved to satisfy the user equilibrium conditions, which is then solved by a finite element solution algorithm. Numerical examples are given to illustrate the effectiveness of the proposed method. © 1998 John Wiley & Sons, Ltd.     

A fiber-bundle model for the continuum deformation of brittle material

The deformation of brittle material is primarily accompanied by micro-cracking and faulting. However, it has often been found that continuum fluid models, usually based on a non-Newtonian viscosity, are applicable. To explain this rheology, we use a fiber-bundle model, which is a model of damage mechanics. In our analyses, yield stress was introduced. Above this stress, we hypothesize that the fibers begin to fail and a failed fiber is replaced by a new fiber. This replacement is analogous to a micro-crack or an earthquake and its iteration is analogous to stick–slip motion. Below the yield stress, we assume that no fiber failure occurs, and the material behaves elastically. We show that deformation above yield stress under a constant strain rate for a sufficient amount of time can be modeled as an equation similar to that used for non-Newtonian viscous flow. We expand our rheological model to treat viscoelasticity and consider a stress relaxation problem. The solution can be used to understand aftershock temporal decay following an earthquake. Our results provide justification for the use of a non-Newtonian viscous flow to model the continuum deformation of brittle materials.     

Clotrimazole nanoparticle gel for mucosal administration

In this study a formulation suitable to be applied on oral and/or vaginal mucosa has been developed for the treatment of fungal infections.The aim of the research is a comparison between clotrimazole (CLO) containing semisolid formulations based on monoolein aqueous dispersion (MAD) or nanostructured lipid carrier (NLC). MAD and NLC have been characterized in terms of morphology and dimensional distribution by cryogenic Transmission Electron Microscopy (cryo-TEM) and Photon Correlation Spectroscopy (PCS). CLO was encapsulated with high entrapment efficiency both in MAD and in NLC, according to Sedimentation Field Flow Fractionation (SdFFF) combined with HPLC. CLO recovery in MAD and NLC has been investigated by time.In order to obtain formulations with suitable viscosity for mucosal application, MAD was diluted with a carbomer gel, while NLC was directly viscosized by the addition of poloxamer 407 in the dispersion. The rheological properties of MAD and NLC after viscosizing have been investigated.Franz cell has been employed to study CLO diffusion from the different vehicles, evidencing diffusion rates from MAD and NLC superimposable to that obtained using Canesten^®.An anticandidal activity study demonstrated that both CLO-MAD and CLO-NLC were more active against Candida albicans with respect to the pure drug.     

Harnessing the collective properties of nanoparticle ensembles for cancer theranostics

Individual inorganic nanoparticles （NPs） have been widely used in the fields of drug delivery, cancer imaging and therapy. There are still many hurdles that limit the performance of individual NPs for these applications. The utilization of highly ordered NP ensembles opens a door to resolve these problems, as a result of their new or advanced collective properties. The assembled NPs show several advantages over individual NP-based systems, such as improved cell internalization and tumor targeting, enhanced multimodality imaging capability, superior combination therapy arising from synergistic effects, possible complete clearance from the whole body by degradation of assemblies into original small NP building blocks, and so on. In this review, we discuss the potential of utilizing assembled NP ensembles for cancer imaging and treatment by taking plasmonic vesicular assemblies of Au NPs as an example. We first summarize the recent developments in the self-assembly of plasmonic vesicular structures of NPs from amphiphilic polymer-tethered NP building blocks. We further review the utilization of plasmonic vesicles of NPs for cancer imaging （e.g. multi-photon induced luminescence, photothermal, and photoacoustic imaging）, and cancer therapy （e.g., photothermal therapy, and chemotherapy）. Finally, we outline current challenges and our perspectives along this line.     

A continuum theory for two phase media

Summary A continuum theory of a two phase solid-fluid media is formulated. The basic balance laws for the solid phase as well as for the fluid phase are presented. Based on thermodynamical consideration a set of constitutive equations are derived and the basic equations of motions of the distributed solid and fluid continua are obtained and discussed. It is shown that the theory contains as its special cases, Mohr-Coulomb criterion of limiting equilibrium of granular materials, Saffman theory of dusty gas, as well as Darcy's law of flow through porous media. It is then concluded that the present theory covers the full spectrum of two phase solid-fluid media from low porosity granular media with Darcy's law of fluid motion to low and high concentration two phase flows such as dusty gas and blood flow.