A Recursive Algorithm for Order Cycle-time that Minimizes Logistics Cost

A firm's logistics cost, including shipping and inventory-carrying, is a substantial percentage of its sales. Nevertheless, typical inventory-control methods ignore or insufficiently represent the shipping cost. This paper describes a recursive algorithm that determines the reorder cycle-time that minimizes total logistics cost. It allows for a realistic accounting of shipping cost, which is modelled here as a function of shipping distance and weight. The algorithm uses a relaxation procedure to identify a suitable initial approximation to the optimal order cycle-time and then, through a series of recursive steps, moves to the optimal result. We demonstrate the algorithm with a single item, with a group of items that share a common order cycle, and with multi-items when item demands are random variables. Experience with this algorithm indicates that it converges to the optimal result in a very few steps.     

Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Kryoskopische Bestimmung der Aktivitätskoeffizienten von Nichtelektrolytmischungen

Zusammenfassung Es wurde eine Methode entwickelt, welche die Aufnahme von Schmelzkurven von binären Nichtelektrolytmischungen mit einer Genauigkeit von 0,001° (und dementsprechend von etwa 0,00001 im Molenbruch) gestattet. Die Bestimmung der Schmelzpunkte erfolgte an Hand von Erwärmungskurven, die bei konstanter Wärmezufuhr mit einem Thermistor aufgenommen wurden.Die Methode wurde auf die Systeme 1,2,4-Trichlorbenzol-(1)-n-Hexan und Anilin-(1)-Cyclohexan angewendet und sollte hier der Überprüfung und Ergänzung der Daten dienen, die früher aus Dampfdruckmessungen¹ und Messungen der Löslichkeitskurve² abgeleitet wurden. Die Übereinstimmung mit den früheren Resultaten ist bei dem System Trichlorbenzol-Hexan ausgezeichnet, bei dem System Anilin-Cyclohexan annehmbar. Die nun genauer zu bestimmenden lnf ₁/x ₂ ² -Kurven (f _i Aktivitätskoeffizient,x _i Molenbruch der Komponentei) zeigen bei dem Übergang von verdünnter zu konzentrierterer Lösung eine plötzliche Änderung, als ob mit Erhöhung der Konzentration der Komponente 2 eine plötzliche Änderung der molekularen Struktur der Lösung einherginge. Dieser Befund steht zwar mit früheren Beobachtungen^1,2 in qualitativer Übereinstimmung, konnte aber bisher nicht so scharf formuliert werden.Mit 11 AbbildungenAuszugsweise vorgetragen auf der Chemiedozententagung der Chemischen Gesellschaft der Deutschen Demokratischen Republik in Halle (Saale) 24.–26. Juni 1959.     

Static-lattice theory of crystalline HCN.: II. Elastic and piezoelectric properties

An effective dipole potential is used to calculate the elastic and piezoelectric coefficients for a static-lattice model of tetragonal HCN, using the generalized thermodynamic theory of internal strain. The model is unstable with respect to molecular rotation away from the tetragonal axis, owing to the use of a point effective dipole. An improved potential would represent the molecule as a set of polarizable point dipoles. Isotropic pressures makes HCN expand along the tetragonal axis as it contracts perpendicular to the axis, because of strong elastic cross-linking. The piezoelectric stress coefficient for shear strain is dominated by the contribution from molecular rotation. Both physical and thermodynamic coefficients are calculated; the differences between the coefficients, which arise from the permanent polarization in HCN, are especially marked in the strain coefficient.     

Calculation of Birefringence Changes in Anthracene and Phenanthrene Crystals

Birefringence changes due to thermal expansion have been calculated for anthracene and phenanthrene. The method assumes that the effective molecular polarizability calculated at room temperature is constant in the molecular axis system for small changes of molecular orientation and separation. For anthracene, the calculations reproduce the observed birefringence change quantitatively. For phenanthrene, two thirds of the observed change is due to thermal expansion, the rest to structural alterations at the 70°C phase transition; transition to a Pa structure is ruled out. Birefringence calculations could be used to test other high-temperature structures for phenanthrene which might be suggested by lattice-energy calculations.     

Electrostatic energy of vacancy formation in crystals of polar molecules

An exact expression is derived for the electrostatic energy of a crystal of polar polarizable molecules containing an unrelaxed vacancy. The energy exceeds twice the electrostatic binding energy per molecule L by a polarization energy term, when changes in dielectric response due to the vacancy are ignored. The electrostatic energy of a molecule at a crystal surface is estimated from surface and bulk polarization energy measurements. It can be as high as 1.5 L. making the electrostatic energy of vacancy formation significantly less than L. the value for non-polarizable molecules. This may help to explain anomalous results for certain plastic crystals.     

Biomimetic postcapillary expansions for enhancing rare blood cell separation on a microfluidic chip

Blood cells naturally auto-segregate in postcapillary venules, with the erythrocytes (red blood cells, RBCs) aggregating near the axis of flow and the nucleated cells (NCs)--which include leukocytes, progenitor cells and, in cancer patients, circulating tumor cells--marginating toward the vessel wall. We have used this principle to design a microfluidic device that extracts nucleated cells (NCs) from whole blood. Fabricated using polydimethylsiloxane (PDMS) soft lithography, the biomimetic cell extraction device consists of rectangular microchannels that are 20-400 μm wide, 11 μm deep and up to 2 cm long. The key design feature is the use of repeated expansions/contractions of triangular geometry mimicking postcapillary venules, which enhance margination and optimize the extraction. The device operates on unprocessed whole blood and is able to extract 94 ± 4.5% of NCs with 45.75 ± 2.5-fold enrichment in concentration at a rate of 5 nl s(-1). The device eliminates the need to preprocess blood via centrifugation or RBC lysis, and is ready to be implemented as the initial stage of lab-on-a-chip devices that require enriched nucleated cells. The potential downstream applications are numerous, encompassing all preclinical and clinical assays that operate on enriched NC populations and include on-chip flow cytometry (A. Y. Fu et al., Anal. Chem., 2002, 74, 2451-2457; A. Y. Fu et al., Nat. Biotechnol., 1999, 17, 1109-1111), genetic analyses (M. M. Wang et al., Nat. Biotechnol., 2005, 23, 83-87; L. C. Waters et al., Anal. Chem., 1998, 70, 5172-5176) and circulating tumor cell extraction (S. Nagrath et al., Nature, 2007, 450, 1235-1241; S. L. Stott et al., Proc. Natl. Acad. Sci. U. S. A., 2010, 18392-18397; H. K. Lin et al., Clin. Cancer Res., 2010, 16, 5011-5018).     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Unified theory of the dielectric properties and lattice vibrational intensities of the HCN crystal

The effective polarizability of the HCN molecule in its two crystal phases is calculated from the mean crystal dielectric constant and molecular- orbital dipole moment calculations, using lattice dipole sums for molecules treated as one, two and three points. The axial polarizability agrees with the gas-phase value, but the transverse polarizability from each calculation is roughly twice the gas-phase value. The lattice infrared absorption intensities and LO-TO splitting are calculated; the three-point treatment with the crystal-phase polarizability yields agreement with experiment. The lattice Raman intensities are also calculated; they depend markedly on the choice of polarizability. The results illustrate how several properties can be calculated within one model. Some inconsistencies for HCN may be attributable to the effects of hydrogen bonding, but could be resolved by dielectric tensor, refractive index, or lattice Raman intensity measurements.