The impact of sorting strategies on automated sortation system performance

In this paper, we develop an analytical model of an order sortation system used in automated distribution centers. In such systems, groups of orders are delivered to a recirculating conveyor system where they are sorted into shipping lanes for final preparation and loaded onto waiting trucks. We develop a model of the sorting process, which incorporates the stochastic elements of these systems, to determine the relative merits of two common categories of sorting strategies found in industry: fixed priority schemes and the next available rule. Fixed priority schemes include such popular rules as “sort the largest (or smallest) orders first”. We show that in systems with little lane blocking, a rule which assigns the next available order to a shipping lane will outperform any fixed priority scheme in terms of sorting time and system throughput while in systems with significant lane blocking, the sorting rule has little impact.     

Systematic derivation of contour integration formulae for laplace and elastostatic gradient BIE's

A complete set of contour integrands is derived for the primary BIE's of elastostatics and potential flow. Because of surface-independent properties of vector potentials, these apply to nonplanar surfaces and can be differentiated at the fixed point, producing contour integrands for both the so-called hypersingular and Cauchy singular parts of the gradient BIE. The results are applicable to far field, near field and on surface cases. Numerical examples demonstrate exact agreement with surface quadrature, and contour plots are given showing variation of the hypersingular integrands in on surface cases.     

Phase relationships in Si3N4-AIN-MxOy systems and their implications for sialon fabrication

Phase relationships in Si₃N₄-AIN-M_xO_y systems involving -sialon, where M represents lithium, magnesium, calcium, yttrium, neodymium, samarium, gadolinium, dysprosium, erbium and ytterbium are outlined. Their implications for the formation and fabrication of single-phase -sialon and two-phase : sialon ceramics are discussed.     

Analysis of Rheological Equations Involving More Than One Fractional Parameters by the Use of the Simplest Mechanical Systems Based on These Equations

The behaviour of rheological models containing more than onefractional derivative or fractional operator of fractional orders areinvestigated. All rheological models discussed can be separated intothree groups depending on magnitudes of the value_*/_* (where_* and _* are the orders ofsenior fractional derivatives of stress and strain, respectively): themodels are thermodynamically admissible only when_*/_* = 1 (the first group),thermodynamically compatible only for_*/_* 1 (the secondgroup) and, finally, thermodynamically well-conditioned both at_*/_* 1 and_*/_* > 1 (the third group).It is shown that, under nonstationary excitations, thebehaviour of the simplest mechanical systems (mechanical oscillators,finite and semi-infinite viscoelastic rods), based on the consideredrheological models, may be different (from the point of view ofthermodynamics) from that of the underlying rheological models. Thus,under impulse excitations, the mechanical models based on rheologicalmodels of the first and second groups become thermodynamicallyadmissible not only at_*/_* = 1 but alsowhen _*/_* < 1(mechanical models of group I), but mechanical models based onrheological models of the third group remain thermodynamicallywell-conditioned at the same magnitudes of rheological parameters as thecorresponding rheological models do (mechanical models of group II). Asthis takes place, group I mechanical models possess diffusion-wavefeatures, that is at_*/_*=1 the stress waves ina semi-infinite rod propagate at a finite speed, and the roots ofcharacteristic equations (for nonstationary vibrations of a mechanicaloscillator or a rod of finite length) as functions of the relaxation orretardation times, behave in a way similar to the characteristicequation roots of rheological models possessing instantaneous elasticity(models of the Maxwell type). When_*/_*<1, the stress wavesin a semi-infinite rod propagate instantaneously at infinitely largespeeds, and the roots of characteristic equations (under nonstationaryvibrations of a mechanical oscillator or a rod of finite length) asfunctions of relaxation times behave in a way similar to thecharacteristic equation roots of rheological models lackinginstantaneous elasticity (models of the Kelvin–Voigt type).Mechanical models from group II possess pure wave or pure diffusionfeatures at all magnitudes of_*/_*.     

A frequency distribution function derived from a stochastic model considering human behaviors and its comparison with an empirical bibliometric distribution

Simon's stochastic model is extended to take both selective and random factors in human behaviors into consideration. The resulting distribution function is of non-steadystate type and approaches the Poisson distribution at the random limit while the Yule (or Zipf) distribution at the selective limit. A comparison of the theoretical distribution with an observed one for classification items indexed in a bibliorgraphic database is made. The results give some insights into statistical features of a class in which the total number of elements is fixed.     

The effect of Ag additions on the microstructure of aluminium–lithium alloys

Minor quantities of Ag have been added to Al–Li–Cu–Mg–Zr alloys. Their microstructure has been studied by means of optical metallography, transmission electron microscopy and X-ray diffraction. In the high Li, low Cu:Mg ratio alloys the main phases found were , , S and T1, while fewer T2 and Al7Cu2Fe precipitates were also observed. The addition of up to 0.5 wt% Ag diminishes the and T1 precipitates size. This is attributed to a small increase of Li solubility in the matrix. In the low Li, high Cu:Mg ratio alloy the addition of 0.2 wt% Ag resulted in the precipitation of phase simultaneously with , , S and T1 phases. Due to the low Li concentration an unusual growth of the / precipitates at the expense of the precipitates was also observed. © 1998 Kluwer Academic Publishers     

Negatively isotone optimal policies for random walk type Markov decision processes

Summary This paper considers a random walk type Markov decision process in which the state spaceI is an integer subset of IR ^m , and the action spaceK is independent ofi I. The natural order, overI, and a quasi order,, overK, is assumed, together with aconditional convexity assumption on the returns {r _i ^k }, and certain other assumptions about these rewards and the transition probabilities in relationship to the orders and.A negatively isotone policy is one for whichi i(i))(i) (i.e.(i) (i) or(i) i)). It is shown that, under specified conditions, a negatively isotone optimal policy exists. Some consideration is given to computational implications in particular relationship to Howard's policy space method.

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Zusammenfassung Wir betrachten einen Markovschen Entscheidungsprozeß vom random walk Typ. Der ZustandsraumI sei eine Teilmenge des IR^m, wobeii I ganzzahlige Komponenten habe. Die MengeK der zulässigen Aktionen ini I sei unabhängig voni I. Sei die natürliche Ordnung aufI und sei eine Quasiordnung aufK. Die Erträge {r _i ^k }seienbedingt konvex, darüberhinaus seien weitere Voraussetzungen über diese Erträge und die Übergangswahrscheinlichkeiten in Bezug auf die Ordnungen und erfüllt. Eine Politik heißt negativ isoton, falls ausi i folgti(i) (d. h.(i) (i) oder(i)(i)). Wir zeigen, daß unter gewissen Voraussetzungen einenegativ isotone optimale Politik existiert: Auch diskutieren wir einige Folgerungen für die Numerik, insbesondere hinsichtlich Howards Politikiteration.

     

The Possibility of Reproducing the Units of Complex Permittivity at High Frequencies

The results of theoretical investigations of the reproduction of the units of the components of complex permittivity and by a method based on the use of the wave properties of a coaxial line are presented. The errors in reproducing and are analyzed.     

Elevated temperature deformation behaviour of multi-phase Ni-20 at % Al-30 at % Fe and its constituent phases

The mechanical behaviour of the multi-phase ( + /) alloy Ni-20 at % Al-30 at % Fe and alloys similar to its constituent and / phases, Ni-30 at % Al-20 at % Fe and Ni-12 at % Al-40 at % Fe, respectively, were investigated. When tested in tension at 300 K, the alloys exhibited 20%, 2% and 28% elongation, respectively. At elevated test temperatures (700, 900 and 1100 K), the multi-phase alloy exhibited increased ductility, reaching an elongation in excess of 70% at 1100 K without necking or fracture. Similarly, the alloy demonstrated increased ductility with increasing test temperatures. In contrast, the / alloy showed greatly reduced ductility with increasing temperature and was quite brittle both at 900 and 1100 K. Thus, whilst at room temperature the / phase improved the ductility of the + / aggregate, at elevated temperatures the phase alleviated the brittleness of the / phase, thereby preventing any embrittlement of the multi-phase alloy over the temperature range 300–1100 K. Also, whilst the phase improved the room-temperature strength of the multi-phase alloy, at elevated temperatures where the phase is known to be weak, the / phase improved the strength of the multi-phase alloy up to 900 K, beyond which the strength deteriorated due to disordering and lack of anomalous strengthening in the / component.     

The morphology of α′ martensite in a two-phase (α+γ) Fe-Cr-Ni stainless steel

Both lath-shaped and martensites are induced by tensile deformation within of a two-phase ( + ) Fe-Cr-Ni stainless steel, forms from the through the at an intersection of two crystals. These are observed both when is surrounded by and when borders . The amount of strain at which both and nucleate, increases with test temperatures in the range –196 to 50° C. Adjacent laths are either twin-related, or 5, 9, 15 or 19° off the twin relationship, as found by analysing electron diffraction patterns.     

Localized single-particle excitations and the density of states for superconducting composites

The problem of localized single-particle excitations and the density of states (DOS) for an inhomogeneous system consisting of a spherical superconductor (with radius a and order parameter ₁) embedded in another superconductor (order parameter ₂) of infinite size is considered. With the assumption of constant values of ₁ and ₂, the Bogoliubov equations are solved for general values of l (the orbital angular momentum quantum number). For a fixed value of ₁/₂ and different values of ₂/E _F, the dependence of the excitation energy (l=0)/₂ on the particle sizek _F a is shown (k _F is the Fermi wave vector andE _F is the Fermi energy). Fork _F a=300, 450, and 800 and a fixed value of ₂/E _F, the variations in the DOS by changing ₁/₂ are also shown.     

Signal rise time of the magnetic bolometer

We present measurements of the temperature dependent signal rise time _S and discuss a model for calculating _S(T). The bolometer consists of a paramagnetic sample and an absorber. The lattice is heated up by absorbing - particles, and the relaxation of the magnetization is measured with a SQUID. With decreasing temperatures _S first increases as ₁1/T, but then decreases strongly. At 30 mK it is reduced by orders of magnitude compared with ₁. This result is in agreement with a theoretical model which takes into account the heat capacities of the lattice, the resonant phonons, the spins, and thermal resistances between these capacities. Under the condition of the bottleneck effect _S is found to be proportional to T³. At low temperatures the lowest values of _S of 2 ms may already be limited by the Kapitza resistance. These are the first measurements of the spin-lattice relaxation times with the energy being transferred from the lattice to the spins.     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De     

The neural net of neural network research

In this paper we discuss the limits and potentials of bibliometric mapping based on a specific co-word analysis. The subject area is neural network research. Our approach is a simulation of expert assessment by offering the reader a narrative of the field which can be used as background information when reading the bibliometric maps. The central issue in the applicability of bibliometric maps is whether these maps may supply additional intelligence to users. In other words, whether such a bibliometric tool has an epistemological value, in the sense that it ecriches existing knowledge by supplying unexpected relations between specific pieces of knowledge (synthetic value) or by supplying unexpected problems (creative value). We argue that sophisticated bibliometric mapping techniques are indeed valuable for open new avenues to study science as a self-organizing system in the form of a neural network like structure of which the bibliometric map is a first-order aproximation. In that sense, this paper deals with the neural net of neural network research as our bibliometric techniques in fact mimic a connectionistic approach.     

Phase relationship between β′- and O′-sialon at 1623 K

-sialon whiskers and co-products of synthesis, such as -sialon powders and O-sialon powders, were annealed at 1623 K for 8 h in a closed graphite reaction tube under 1 atm nitrogen. Phase stabilities, Si/Al ratios, and crystallographic features were investigated. The O-sialon phase, which formed in the early stage of synthesis when oxygen partial pressure was relatively high, became less stable in the present annealing condition and decomposed. The majority of released aluminium and possibly oxygen from the decomposed O-powder was incorporated into -sialon whiskers with little change in its lattice parameters, when the -sialon whiskers were included in annealing. The aluminium contents were always lower in the -whiskers than in the powders even after increasing its aluminium content during 8 h annealing. The lattice parameters of both -whiskers and powders increased with increasing aluminium content and became closer after annealing. The lattice parameters of -whiskers remained the same before and after annealing despite the increased aluminium content, while the lattice parameters of -powders decreased despite its aluminium content remaining unchanged. The lattice parameters of O-sialon increased with increasing aluminium content, and the increase in thea direction is the largest when compared with other parameters.     

Solution of thermal conductivity problems with boundary condition of the third kind and arbitrary coordinate and time dependence of the biot number

An analytical solution of the thermal conductivity problem with boundary conditions of the third kind and arbitrary coordinate and time dependence of the Biot number is found in the form of a converging series of quadratures.Notation , z dimensionless coordinates - dimensionless temperature - Q dimensionless volume heat-liberation density per unit time - Fo=/² Fourier number - Bi₁(, Fo)=(, Fo) · / Biot number - thermal diffusivity coefficient - plate thickness - time - (, Fo) heat-liberation coefficient - thermal conductivity coefficient - i summation index - Jo zero order Bessel function of the first kind Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 41, No. 3, pp. 536–540, September, 1981.     

Structure and Magnetism of the Composite Crystal Ca0.824CuO2

We have studied the magnetic state from a viewpoint of crystallographic features of the 1-D chain compound Ca_0.824CuO₂. A possible spin-hole arrangement in the magnetically coexisting state was determined by analyzing the local structural distortion in the CuO₂ chain by means of a modulated-crystal-structure analysis. The essential periodic sequence expected is (: up- and down-spin, : hole), which can be regarded as a kind of spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain.     

Cohesive crack models for semi-brittle materials derived from localization of damage coupled to plasticity

Based on discontinuous displacement approximation of the continuum and shear band kinematics, two cohesive crack models are derived within the constitutive framework of coupled damage and plasticity. The models employ the Rankine fracture criterion, and the model parameters are determined from a uniaxial tension test (mode I cracking). Bifurcation analysis is used in order to diagnose critical directions along which the crack will gradually develop and propagate. These directions depend on the actual stress state and are kept fixed after fracture has initiated, whereby a fixed crack model is obtained. A discrete crack strategy is employed at the finite element implementation in the sense that interfaces (that represent the cohesive crack) are introduced along inter-element boundaries. This implementation strategy calls for gradual realignment of the mesh as a key feature of the algorithm. Numerical results from the analysis of mixed mode fracture in a notched concrete plate are presented.     

Fabrication of β- and β′′-Al2O3 tubes by pressureless powder packing forming and salt infiltration

A new forming method, pressureless powder packing (PLPP), was studied to fabricate the - and -Al2O3 tubes. Alkali sources were infiltrated into the pores of -Al2O3 tube preforms that had been prepared by the PLPP forming method. The composition for the synthesis of -Al2O3 phase was Na2O · 0. 138Li2 · 4.4Al2O3. The -Al2O3 fraction of calcined and sintered bodies was increased with the increase of calcination temperature, and phase formation was largely affected by the type of starting -Al2O3. Large particle size and narrow size distribution of fused -Al2O3 resulted in uniform green microstructure that enhanced the homogeneity of alkali salts after infiltration, which was very important for the -Al2O3 formation. Sintered microstructure was uniform in all specimens but further development was required for density improvement.     

The age hardening effect in Ti-6 Al-4 V due to ω and α precipitation in the β grains

The structure at room temperature of a quenched TA6V titanium alloy has been investigated. This structure is + or + according to the treatment temperature; it is always metastable. During ageing the grains decomposed by the reaction + + +; this decomposition was accompanied by a large increase of the 0.2% yield stress. No structural modification was observed in. The and phase of TA6V were separately investigated in the form of single-phase alloys. The hardness of was insensitive to ageing, while was considerably hardened by and; we deduced that the strengthening of the minor phase during ageing is mainly responsible for the hardening of TA6V.