A dynamic programming approach to the formulation and solution of finite element equations

A method for formulating and algorithmically solving the equations of finite element problems is presented. The method starts with a parametric partition of the domain in juxtaposed strips that permits sweeping the whole region by a sequential addition (or removal) of adjacent strips. The solution of the difference equations constructed over that grid proceeds along with the addition removal of strips in a manner resembling the transfer matrix approach, except that different rules of composition that lead to numerically stable algorithms are used for the stiffness matrices of the strips. Dynamic programming and invariant imbedding ideas underlie the construction of such rules of composition. Among other features of interest, the present methodology provides to some extent the analyst's control over the type and quantity of data to be computed. In particular, the one-sweep method presented in Section 9, with no apparent counterpart in standard methods, appears to be very efficient insofar as time and storage is concerned. The paper ends with the presentation of a numerical example

DROMO formulation for planar motions: Solution to the Tsien Problem

The two-body problem subject to a constant radial thrust is analyzed as a planar motion. The description of the problem is performed in terms of three perturbation methods: DROMO and two others due to Deprit. All of them rely on Hansen?s ideal frame concept. An explicit, analytic, closed-form solution is obtained for this problem when the initial orbit is circular (Tsien problem), based on the DROMO special perturbation method, and expressed in terms of elliptic integral functions. The analytical solution to the Tsien problem is later used as a reference to test the numerical performance of various orbit propagation methods, including DROMO and Deprit methods, as well as Cowell and Kustaanheimo?Stiefel methods.

Singularities in DROMO formulation. Analysis of deep flybys

The singularities in Dromo are characterized in this paper, both from an analytical and a numerical perspective. When the angular momentum vanishes, Dromo may encounter a singularity in the evolution equations. The cancellation of the angular momentum occurs in very speci?c situations and may be caused by the action of strong perturbations. The gravitational attraction of a perturbing planet may lead to rapid changes in the angular momentum of the particle. In practice, this situation may be encountered during deep planetocentric ?ybys. The performance of Dromo is evaluated in di?erent scenarios. First, Dromo is validated for integrating the orbit of Near Earth Asteroids. Resulting errors are of the order of the diameter of the asteroid. Second, a set of theoretical ?ybys are designed for analyzing the performance of the formulation in the vicinity of the singularity. New sets of Dromo variables are proposed in order to minimize the dependency of Dromo on the angular momentum. A slower time scale is introduced, leading to a more stable description of the ?yby phase. Improvements in the overall performance of the algorithm are observed when integrating orbits close to the singularity.

The elliptic rendezvous problem in DROMO formulation

The extension of DROMO formulation to relative motion is evaluated. The orbit of the follower spacecraft can be constructed through differences on the elements defining the orbit of the leader spacecraft. Assuming that the differences are small, the problemis linearized. Typical linearized solutions to relativemotion determine the relative state of the follower spacecraft at a certain time step. Because of the form of DROMO formulation, the performance of a frozen-anomaly transformation is explored. In this case, the relative state is computed for a certain value of the anomaly, equal for leader and follower. Since the time for leader and follower do not coincide, the implicit time delay needs to be corrected to recover the physical sense of the solution. When determining the relative orbit, numerical testing shows significant error reductions compared to previous linearized solutions.

The problem of the spreading of a liquid film along a solid surface: A new mathematical formulation

A new mathematical model is proposed for the spreading of a liquid film on a solid surface. The model is based on the standard lubrication approximation for gently sloping films (with the no-slip condition for the fluid at the solid surface) in the major part of the film where it is not too thin. In the remaining and relatively small regions near the contact lines it is assumed that the so-called autonomy principle holds—i.e., given the material components, the external conditions, and the velocity of the contact lines along the surface, the behavior of the fluid is identical for all films. The resulting mathematical model is formulated as a free boundary problem for the classical fourth-order equation for the film thickness. A class of self-similar solutions to this free boundary problem is considered.

Continuous amperometric monitoring of glucose in a brittle diabetic chimpanzee with a miniature subcutaneous electrode

The performance of an amperometric biosensor, consisting of a subcutaneously implanted miniature (0.29 mm diameter, 5 × 10−4 cm2 mass transporting area), 90 s 10–90% rise/decay time glucose electrode, and an on-the-skin electrocardiogram Ag/AgCl electrode was tested in an unconstrained, naturally diabetic, brittle, type I, insulin-dependent chimpanzee. The chimpanzee was trained to wear on her wrist a small electronic package and to present her heel for capillary blood samples. In five sets of measurements, averaging 5 h each, 82 capillary blood samples were assayed, their concentrations ranging from 35 to 400 mg/dl. The current readings were translated to blood glucose concentration by assaying, at t = 1 h, one blood sample for each implanted sensor. The rms error in the correlation between the sensor-measured glucose concentration and that in capillary blood was 17.2%, 4.9% above the intrinsic 12.3% rms error of the Accu-Chek II reference, through which the illness of the chimpanzee was routinely managed. Linear regression analysis of the data points taken at t>1 h yielded the relationship (Accu-Chek) = 0.98 × (implanted sensor) + 4.2 mg/dl, r2 = 0.94. The capillary blood and the subcutaneous glucose concentrations were statistically indistinguishable when the rate of change was less than 1 mg/(dl⋅min). However, when the rate of decline exceeded 1.8 mg/(dl⋅min) after insulin injection, the subcutaneous glucose concentration was transiently higher.

Role of tumor–host interactions in interstitial diffusion of macromolecules: Cranial vs. subcutaneous tumors

The large size of many novel therapeutics impairs their transport through the tumor extracellular matrix and thus limits their therapeutic effectiveness. We propose that extracellular matrix composition, structure, and distribution determine the transport properties in tumors. Furthermore, because the characteristics of the extracellular matrix largely depend on the tumor–host interactions, we postulate that diffusion of macromolecules will vary with tumor type as well as anatomical location. Diffusion coefficients of macromolecules and liposomes in tumors growing in cranial windows (CWs) and dorsal chambers (DCs) were measured by fluorescence recovery after photobleaching. For the same tumor types, diffusion of large molecules was significantly faster in CW than in DC tumors. The greater diffusional hindrance in DC tumors was correlated with higher levels of collagen type I and its organization into fibrils. For molecules with diameters comparable to the interfibrillar space the diffusion was 5- to 10-fold slower in DC than in CW tumors. The slower diffusion in DC tumors was associated with a higher density of host stromal cells that synthesize and organize collagen type I. Our results point to the necessity of developing site-specific drug carriers to improve the delivery of molecular medicine to solid tumors.

Subcutaneous vaccination with irradiated, cytokine-producing tumor cells stimulates CD8+ cell-mediated immunity against tumors located in the "immunologically privileged" central nervous system.

Vaccination with cytokine-producing tumor cells generates potent immune responses against tumors outside the central nervous system (CNS). The CNS, however, is a barrier to allograft and xenograft rejection, and established tumors within the CNS have failed to respond to other forms of systemic immunotherapy. To determine what barriers the "immunologically privileged" CNS would pose to cytokine-assisted tumor vaccines and what cytokines would be most efficacious against tumors within the CNS, we irradiated B16 murine melanoma cells producing murine interleukin 2 (IL-2), IL-3, IL-4, IL-6, gamma-interferon, or granulocyte-macrophage colony stimulating factor (GM-CSF) and used these cells as subcutaneous vaccines against tumors within the brain. Under conditions where untransfected B16 cells had no effect, cells producing IL-3, IL-6, or GM-CSF increased the survival of mice challenged with viable B16 cells in the brain. Vaccination with B16 cells producing IL-4 or gamma-interferon had no effect, and vaccination with B16 cells producing IL-2 decreased survival time. GM-CSF-producing vaccines were also able to increase survival in mice with pre-established tumors. The response elicited by GM-CSF-producing vaccines was found to be specific to tumor type and to be abrogated by depletion of CD8+ cells. Unlike the immunity generated against subcutaneous tumors by GM-CSF, however, the effector responses generated against tumors in the CNS were not dependent on CD4+ cells. These data suggest that cytokine-producing tumor cells are very potent stimulators of immunity against tumors within the CNS, but effector responses in the CNS may be different from those obtained against subcutaneous tumors.

Protection of nonobese diabetic mice from diabetes by intranasal or subcutaneous administration of insulin peptide B-(9-23).

The observation that overt type I diabetes is often preceded by the appearance of insulin autoantibodies and the reports that prophylactic administration of insulin to biobreeding diabetes-prone (BB-DP) rats, nonobese diabetic (NOD) mice, and human subjects results in protection from diabetes suggest that an immune response to insulin is involved in the process of beta cell destruction. We have recently reported that islet-infiltrating cells isolated from NOD mice are enriched for insulin-specific T cells, that insulin-specific T cell clones are capable of adoptive transfer of diabetes, and that epitopes present on residues 9-23 of the B chain appear to be dominant in this spontaneous response. In the experiments described in this report, the epitope specificity of 312 independently isolated insulin-specific T cell clones was determined and B-(9-23) was found to be dominant, with 93% of the clones exhibiting specificity toward this peptide and the remainder to an epitope on residues 7-21 of the A chain. On the basis of these observations, the effect of either subcutaneous or intranasal administration of B-(9-23) on the incidence of diabetes in NOD mice was determined. The results presented here indicate that both subcutaneous and intranasal administration of B-(9-23) resulted in a marked delay in the onset and a decrease in the incidence of diabetes relative to mice given the control peptide, tetanus toxin-(830-843). This protective effect is associated with reduced T-cell proliferative response to B-(9-23) in B-(9-23)-treated mice.

Evaluation of the pathogenicity of multiple isolates of Beauveria bassiana (Hypocreales: Clavicipitaceae) on Rhynchophorus ferrugineus (Coleoptera: Dryophthoridae) for the assessment of a solid formulation under simulated field conditions

A solid state formulation of Beauveria bassiana (Balsamo) Vuillemin has been developed for biological control of the Red Palm Weevil (RPW), Rhynchophorus ferrugineus (Olivier, 1790). Two kinds of bioassays (dry conidia and dipping) using 10 isolates from several coleopterans in Mediterranean environments, identified 2 RPW derived isolates (193 and 203) as most pathogenic to RPW larvae and adults (zero survival within first 4–5 d for dry conidia, and 14 and 23 d for dipping bioassays). Isolate 203 (5.1 × 108 ± 1.9 × 108 conidia g-1) was formulated with fragmented date seed into solid granules and tested in palms infested with RPW under semi-field conditions in Feb, Apr/May and Jun of both 2007 and 2008. Beauveria bassiana significantly reduced RPW adult survival with respect to controls in May 2007 and in the Apr/Jun 2008 experiments. Total RPW adult mortality was achieved within 30 days for all B. bassiana treatments, and was associated with increasing numbers of insects with signs of mycosis in 2008 experiments. Beauveria bassiana formulation reduced RPW multiplication in artificially infested palms compared to controls, and a positive correlation between numbers of larvae and time post-infestation was recorded. The suppression of RPW adult populations by B. bassiana persisted for at least 3 months under semi-field conditions. The Beauveria bassiana solid formulation, which induces great adult mortality and persistence in the field, could be applied as a preventive as well as a curative treatment for the integrated management of RPW.

Ceramic formulation and processing design for plutonium disposition

The focus of this research programme is to develop a single phase ceramic wasteform for waste PuO2 that is unsuitable for fuel manufacture. A suite of synthetic mineral systems have been considered including titanate, zirconate, phosphate and silicate based matrices. Although a wealth of information on plutonium disposition in some of the systems exists in the literature, the data is not always directly comparable which hinders comparison between different ceramic hosts. The crux of this research has been to compile a database of information on the proposed hosts to allow impartial comparison of the relative merits of each system. © 2009 Materials Research Society.

Joint development and value capture in Los Angeles : local policy formulation /

"DOT-I-83-23."

Alcohol Safety Action Projects evaluation of operations: data, tables of results, and formulation. Volume 4.

Mode of access: Internet.