Mathematical modeling of local gradient processes in inertial thermomechanical systems

Conclusions Using methods of thermodynamics of nonequilibrium processes and of mechanics of a continuous medium, a model is constructed of a third body, making it possible to describe mutually related physicomechanical fields with account of their gradients. It has been shown that inclusion of the gradient of the chemical potential field takes into account the features of the fields considered in the near-surface region of the body. Based on the determination of the chemical potential, thermodynamic stability criteria have been formulated.We provided the thermodynamic justification of generalized thermomechanics. It is based on determining the energy of motion in the phase space of the momenta of motion, and makes it possible to describe the increments in the internal energy and in the energy of motion within the same approximations.Institute of Applied Mechanical and Mathematical Problems, Ukrainian Academy of Sciences, L'vov. Translated from Prikladnaya Mekhanika, Vol. 28, No. 12, pp. 3–23, December, 1992.     

Assessing and predicting changes in vegetation cover associated with military land use activities using field monitoring data at Fort Hood, Texas

We assessed short-term impacts of changes in military training load on vegetative cover at Fort Hood, TX. From 1989 to 1995, permanent field transects were monitored for vegetative cover and land use disturbance using standard army monitoring methods [Land Condition Trend Analysis (LCTA)]. Land use intensity (training load) was quantified and used to develop a model to predict future vegetation cover values. We found that standard Army monitoring methods detected changes in installation resources associated with changes in training load. Increased training loads were associated with increased measures of disturbance, decreased ground cover, and decreased aerial vegetative cover. We found that the spatial pattern of disturbance and vegetation cover remained relatively constant over the study period despite large variations in overall training load. Our model used the consistency in spatial cover patterns over time and the strong relationship between training load and vegetation cover to predict the impact of future training loads on vegetation.     

Robust multigrid preconditioners for the high‐contrast biharmonic plate equation

We study the high‐contrast biharmonic plate equation with Hsieh–Clough–Tocher discretization. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by Aksoylu et al. (Comput. Vis. Sci. 2008; 11 :319–331). By extending the devised singular perturbation analysis from linear finite element discretization to the above discretization, we prove and numerically demonstrate the robustness of the preconditioner. Therefore, we accomplish a desirable preconditioning design goal by using the same family of preconditioners to solve the elliptic family of PDEs with varying discretizations. We also present a strategy on how to generalize the proposed preconditioner to cover high‐contrast elliptic PDEs of order 2k, k>2. Moreover, we prove a fundamental qualitative property of the solution to the high‐contrast biharmonic plate equation. Namely, the solution over the highly bending island becomes a linear polynomial asymptotically. The effectiveness of our preconditioner is largely due to the integration of this qualitative understanding of the underlying PDE into its construction. Copyright © 2010 John Wiley & Sons, Ltd.     

Interaction between green tea extract and 99mTc-pertechnetate on in vivo distribution

People drink various types of tea without knowing the side effects of biological and chemical contents and radiopharmaceutical interactions. In current study, it is aimed to evaluate the effects of green tea extract in different extraction solvents on the radiolabeling of the blood constituents with ^99mTc and on the biodistribution of radiopharmaceutical sodium pertechnetate (Na^99mTcO₄) in male Wistar Albino rats. The extraction of green tea was performed in different solvents. Biodistribution studies were performed on male rats which were treated via gavage with green tea extract in different extraction solvents or saline (0.9 % NaCl) as a control group for 7 days. The radiolabeling of blood constituents performed incubating with SnCl₂ and ^99mTc. According to experimental results, radiolabeling blood components with ^99mTc were not modified in the usage of the different extraction solvents for green tea extraction, but a significant alteration (P < 0.05) of biodistribution of Na^99mTcO₄ was observed after treatment with green tea extract in distilled water. Although there is no considerable effect on radiolabeling of blood components, there is an outstanding change on the biodistribution studies especially with green tea extract in distilled water. The identified change monitored in this study may cause to reduce the risk of misdiagnosis and/or avoid the repetition of the examinations in nuclear medicine.     

Nonlinear forced vibrations of an initially-deformed electrically-conducting layer in a magnetic field

Institute of Applied Problems of Mechanics and Mathematics, Academy of Sciences of the Ukrainian SSR, Lvov. Translated from Prikladnaya Mekhanika, Vol. 25, No. 4, pp. 82–88, April, 1989.     

Mechanical instability of amorphous polymeric networks: Asymmetric deformation under symmetric biaxial tension

Asymmetric deformation of a symmetrically loaded rubber sheet was observed, many years ago, by Treloar in his experiments on natural rubber. The problem has recently been studied by Kearsley, and the possibility of asymmetric deformations in an equi-biaxial state of force is predicted by the use of phenomenological constitutive relations. In the present study, the problem is analyzed in relation to the molecular constitution of rubber networks. It is shown that mechanical instability in symmetrically loaded networks may be possible only for limited choices of molecular parameters such as junction functionality, degree of crosslinking, and the degree of swelling during crosslinking and during deformation. Stability of multiple valued deformations is discussed by thermodynamic considerations of the elastic potential.     

Vibration-vibration energy transfer in gaseous HBr

The vibration-vibration energy transfer of HBr gas initially excited to the first vibrational state has been observed. Collisional pumping to the V = 2 level is measured by monitoring the fluorescence of the 2−1 transition. The rate constant for the process: HBr(V=0) + HBr(V=2) → 2HBr(V=1) is found to be 1.4×10⁵ sec⁻¹ torr⁻¹.     

Two point problems and analyticity of solutions of abstract parabolic equations

Fort ∈ [a, b], letA(t) be the unbounded operator inH ^0,p (G) associated with an elliptic-boundary value problem that satisfies Agmon’s conditions on the rays λ=±iτ, τ ≥0. Existence and uniqueness results are obtained for weak and strict solutions of two-point problems of the type (du/dt)−A(t) u(t) =f(t),E ₁(α)u (α)=u _α,E ₂ (β)u (β)=u _β. Here [α, β) χ- [a, b],E ₁ (α) andE ₂ (β) are spectral projections associated withA(α) andA(β) respectively, andA(α)E ₁ (α) and =A (β)E ₂ (β) are infinitesimal generators of analytic semigroups. WhenA(t) andf(t) are analytic in a convex, complex neighborhoodO of [a, b] we show that for someθ _i ,i=1,2, any solution ofdu/dt =A(t)u (t)=f(t) in [a, b] is analytic and satisfies the above equation in the setO∩{t; t ≠ a, t ≠ b, | arg (t −a) | <θ ₁, | arg (b −t) |θ ₂}. Research partially supported by N. N. F. grant at Brandeis University.