A variational approach for continuous supply chain networks

We consider a continuous supply chain network consisting of buffering queues and processors first proposed by [D. Armbruster, P. Degond, and C. Ringhofer, SIAM J. Appl. Math., 66 (2006), pp. 896–920] and subsequently analyzed by [D. Armbruster, P. Degond, and C. Ringhofer, Bull. Inst. Math. Acad. Sin. (N.S.), 2 (2007), pp. 433–460] and [D. Armbruster, C. De Beer, M. Fre- itag, T. Jagalski, and C. Ringhofer, Phys. A, 363 (2006), pp. 104–114]. A model was proposed for such a network by [S. G ̈ottlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559] using a system of coupling ordinary differential equations and partial differential equations. In this article, we propose an alternative approach based on a variational method to formulate the network dynamics. We also derive, based on the variational method, a computational algorithm that guarantees numerical stability, allows for rigorous error estimates, and facilitates efficient computations. A class of network flow optimization problems are formulated as mixed integer programs (MIPs). The proposed numerical algorithm and the corresponding MIP are compared theoretically and numerically with existing ones [A. Fu ̈genschuh, S. Go ̈ttlich, M. Herty, A. Klar, and A. Martin, SIAM J. Sci. Comput., 30 (2008), pp. 1490–1507; S. Go ̈ttlich, M. Herty, and A. Klar, Commun. Math. Sci., 3 (2005), pp. 545–559], which demonstrates the modeling and computational advantages of the variational approach

Effect of pyridoxine treatment of a homocystinuric patient on the urinary excretion of some sulfur-containing amino acids

The effect of pyridoxine treatment of a homocystinuric patient on the urinary excretion of some sulfur-containing amino acids was studied and the following results were obtained. As a result of pyridoxine treatment, urinary homocystine decreased to a fairly great extent, and its unusual metabolites S.(3-hydroxy-3-carboxyn- propylthio) homocysteine (HCPTHC) and S-C8-carboxyethylthio homocysteine (j3-CETHC) increased to some extent. But its oxidation product (homocysteic acid) showed a tendency to decrease slightly. Urinary methionine and cystine increased to some extent, but cysteinehomocysteine mixed disulfide showed no remarkable change.</p

Theory of optimum shapes in free-surface flows. Part 1. Optimum profile of sprayless planing surface

This paper attempts to determine the optimum profile of a two-dimensional plate that produces the maximum hydrodynamic lift while planing on a water surface, under the condition of no spray formation and no gravitational effect, the latter assumption serving as a good approximation for operations at large Froude numbers. The lift of the sprayless planing surface is maximized under the isoperimetric constraints of fixed chord length and fixed wetted arc-length of the plate. Consideration of the extremization yields, as the Euler equation, a pair of coupled nonlinear singular integral equations of the Cauchy type. These equations are subsequently linearized to facilitate further analysis. The analytical solution of the linearized problem has a branch-type singularity, in both pressure and flow angle, at the two ends of plate. In a special limit, this singularity changes its type, emerging into a logarithmic one, which is the weakest type possible. Guided by this analytic solution of the linearized problem, approximate solutions have been calculated for the nonlinear problem using the Rayleigh-Ritz method and the numerical results compared with the linearized theory

Wall Effects in Cavity Flows and their Correction Rules

The wall effects in cavity flows have been long recognized to be more important and more difficult to determine than those in single-phase, nonseparated flows. Earlier theoretical investigations of this problem have been limited largely to simple body forms in plane flows, based on some commonly used cavity-flow models, such as the Riabouchinsky, the reentrant jet, or the linearized flow model, to represent a finite cavity. Although not meant to be exhaustive, references may be made to Cisotti (1922), Birkhoff, Plesset and Simmons (1950, 1952), Gurevich (1953), Cohen et al. (1957, 1958), and Fabula (1964). The wall effects in axisymmetric flows with a finite cavity has been evaluated numerically by Brennen (1969) for a disk and a sphere. Some intricate features of the wall effects have been noted in experimental studies by Morgan (1966) and Dobay (1967). Also, an empirical method for correcting the wall effect has been proposed by Meijer (1967). The presence of lateral flow boundaries in a closed water tunnel introduces the following physical effects: (i) First, in dealing with the part of irrotational flow outside the viscous region, these flow boundaries will impose a condition on the flow direction at the rigid tunnel walls. This "streamline-blocking" effect will produce extraneous forces and modifications of cavity shape. (ii) The boundary layer built up at the tunnel walls may effectively reduce the tunnel cross-sectional area, and generate a longitudinal pressure gradient in the working section, giving rise to an additional drag force known as the "horizontal buoyancy." (iii) The lateral constraint of tunnel walls results in a higher velocity outside the boundary layer, and hence a greater skin friction at the wetted body surface. (iv) The lateral constraint also affects the spreading of the viscous wake behind the cavity, an effect known as the "wake-blocking." (v) It may modify the location of the "smooth detachment" of cavity boundary from a continuously curved body. In the present paper, the aforementioned effect (i) will be investigated for the pure-drag flows so that this primary effect can be clarified first. Two cavity flow models, namely, the Riabouchinsky and the open-wake (the latter has been attributed, independently, to Joukowsky, Roshko, and Eppler) models, are adopted for detailed examination. The asymptotic representations of these theoretical solutions, with the wall effect treated as a small correction to the unbounded-flow limit, have yielded two different wall-correction rules, both of which can be applied very effectively in practice. It is of interest to note that the most critical range for comparison of these results lies in the case when the cavitating body is slender, rather than blunt ones, and when the cavity is short, instead of very long ones in the nearly choked-flow state. Only in this critical range do these flow models deviate significantly from each other, thereby permitting a refined differentiation and a critical examination of the accuracy of these flow models in representing physical flows. A series of experiments carefully planned for this purpose has provided conclusive evidences, which seem to be beyond possible experimental uncertainties, that the Riabouchinsky model gives a very satisfactory agreement with the experimental results, and is superior to other models, even in the most critical range when the wall effects are especially significant and the differences between these theoretical flow models become noticeably large. These outstanding features are effectively demonstrated by the relatively simple case of a symmetric wedge held in a non-lifting flow within a closed tunnel, which we discuss in the sequel

Cavity-flow wall effects and correction rules

This paper is intended to evaluate the wall effects in the pure-drag case of plane cavity flow past an arbitrary body held in a closed tunnel, and to establish an accurate correction rule. The three theoretical models in common use, namely, the open-wake, Riabouchinsky and re-entrant-jet models, are employed to provide solutions in the form of some functional equations. From these theoretical solutions several different rules for the correction of wall effects are derived for symmetric wedges. These simple correction rules are found to be accurate, as compared with their corresponding exact numerical solutions, for all wedge angles and for small to moderate 'tunnel-spacing ratio' (the ratio of body frontal width to tunnel spacing). According to these correction rules, conversion of a drag coefficient, measured experimentally in a closed tunnel, to the corresponding unbounded flow case requires only the data of the conventional cavitation number and the tunnel-spacing ratio if based on the open-wake model, though using the Riabouchinsky model it requires an additional measurement of the minimum pressure along the tunnel wall. The numerical results for symmetric wedges show that the wall effects invariably result in a lower drag coefficient than in an unbounded flow at the same cavitation number, and that this percentage drag reduction increases with decreasing wedge angle and/or with decreasing tunnel spacing relative to the body frontal width. This indicates that the wall effects are generally more significant for thinner bodies in cavity flows, and they become exceedingly small for sufficiently blunt bodies. Physical explanations for these remarkable features of cavity-flow wall effects are sought; they are supported by the present experimental investigation of the pressure distribution on the wetted body surface as the flow parameters are varied. It is also found that the theoretical drag coefficient based on the Riabouchinsky model is smaller than that predicted by the open-wake model, all the flow parameters being equal, except when the flow approaches the choked state (with the cavity becoming infinitely long in a closed tunnel), which is the limiting case common to all theoretical models. This difference between the two flow models becomes especially pronounced for smaller wedge angles, shorter cavities, and with tunnel walls farther apart. In order to gauge the degree of accuracy of these theoretical models in approximating the real flows, and to ascertain the validity of the correction rules, a series of definitive experiments was carefully designed to complement the theory, and then carried out in a high-speed water tunnel. The measurements on a series of fully cavitating wedges at zero incidence suggest that, of the theoretical models, that due to Riabouchinsky is superior throughout the range tested. The accuracy of the correction rule based on that model has also been firmly established. Although the experimental investigation has been limited to symmetric wedges only, this correction rule (equations (85), (86) of the text) is expected to possess a general validity, at least for symmetric bodies without too large curvatures, since the geometry of the body profile is only implicitly involved in the correction formula. This experimental study is perhaps one of a very few with the particular objective of scrutinizing various theoretical cavity-flow models

Relativistic Mean-Field and Beyond Approaches for Deformed Hypernuclei

We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the $\Lambda$ hyperon with orbital angular momentum $\ell=0$ (or $\ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate that there is generally a large configuration mixing between the two components $[^{A-1}Z (I^+) \otimes \Lambda p_{1/2}]^J$ and $[^{A-1}Z (I\pm2 ^+) \otimes \Lambda p_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight increases as the collective correlation of nuclear core becomes stronger. Finally, we show how the energies of hypernuclear low-lying states are sensitive to parameters in the effective $N \Lambda$ interaction, the uncertainty of which has a large impact on the predicted maximal mass of neutron stars.Comment: 12 pages, 7 figures. A plenary talk given at the 13th International Conference on Hypernuclear and Strange Particle Physics, June 24-29, 2018, Portsmouth, V

Disappearance of nuclear deformation in hypernuclei: a perspective from a beyond-mean-field study

The previous mean-field calculation [Myaing Thi Win and K. Hagino, Phys. Rev. C{\bf 78}, 054311 (2008)] has shown that the oblate deformation in $^{28,30,32}$Si disappears when a $\Lambda$ particle is added to these nuclei. We here investigate this phenomenon by taking into account the effects beyond the mean-field approximation. To this end, we employ the microscopic particle-rotor model based on the covariant density functional theory. We show that the deformation of $^{30}$Si does not completely disappear, even though it is somewhat reduced, after a $\Lambda$ particle is added if the beyond-mean-field effect is taken into account. We also discuss the impurity effect of $\Lambda$ particle on the electric quadrupole transition, and show that an addition of a $\Lambda$ particle leads to a reduction in the $B(E2)$ value, as a consequence of the reduction in the deformation parameter.Comment: 6 pages, 5 figures. The version to appear in Phys. Rev.