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.

     

Influence of pressure and crystallization rate on the surface microhardness of high-density polyethylene

The indentation microhardnessMH of high-density polyethylene crystallized at different pressuresp and crystallization rates _c has been investigated. The results confirm thatMH is an increasing function of lamellar thickness and therefore of density. The rate of increase depends on the crystallization conditionsp and _c. Crystallization at high pressure leads toMH values considerably higher than those of samples prepared under atmospheric pressure. The results are discussed in terms of compressed amorphous regions contributing to an elastic release after removal of the indenter. For samples crystallized under different pressures the hardness value turns out to be nearly independent of the elastic modulusE. For samples crystallized at different rates _c there is a steady decrease of microhardness with increasing _c (decrease of lamellar thickness) but no simple relationship withE. With higher rates _c the appearance of strained tie molecules provokes a rapid increase ofE whileMH decreases further because the crystals become smaller.     

Superplastic deformation of strongly textured Ti-6Al-4V

Changes in microstructure and texture during superplastic deformation of strongly textured Ti-6Al-4V bar have been determined in order to establish the cause of stress and strain anisotropy. The effect of strain on the microstructure of the alloy was to cause a progressive break-up, due to grain-boundary sliding, of an initially directional microstructure containing contiguous-phase. The texture of the-phase, however, changed very little with superplastic strain but that of the-phase was randomized. Shape changes predicted by permitted deformation modes in the-phase did not correlate with the observed shape changes, whereas the observed anisotropy could be explained by the break-up of the contiguous-phase. A model to account for this anisotropy is described briefly, together with a typical microstructure which should exhibit isotropic superplastic deformation.     

The mechanism of continuous dissolution of the lamellar structure in aged Al 22 at% Zn alloy

The mechanism of continuous dissolution was studied using transmission electron microscopy, X-ray diffraction and hardness measurements. The metastable phase was identified in the first stage of dissolution nucleating at the - boundaries. Interface dislocations at the - boundaries forming a perpendicular net in the 110 directions were identified as of screw character and of Burgers vector b=1/2a 110. During dissolution a change of shape of precipitates occurs leading to their fragmentation and to a change of the direction of boundaries into 110 directions.     

Thermal Conductivity of the Accidental Degeneracy and Enlarged Symmetry Group Models for Superconducting UPt3

We present theoretical calculations of the thermal conductivity for the accidental degeneracy and enlarged symmetry group models that have been proposed to explain the phase diagram of UPt ₃ . The order parameters for these models possess point nodes or cross nodes, reflecting the broken symmetries of the ground state. These broken symmetries lead to robust predictions for the ratio of the low-temperature thermal conductivity for heat flow along the axis and in the basal plane. The anisotropy of the heat current response at low temperatures is determined by the phase space for scattering by impurities. The measured anisotropy ratio, _c/ _b, provides a strong constraint on theoretical models for the ground state order parameter. The accidental degeneracy and enlarged symmetry group models based on no spin-orbit coupling do not account for the thermal conductivity of UPt ₃. The models for the order parameter that fit the experimental data for the and directions of the heat current are the 2D E_1g and E _2u models, for which the order parameters possess line nodes in the ab-plane and point nodes along the axis, and the A_1gE _1g model of Zhitomirsky and Ueda. This model spontaneously breaks rotational symmetry in the ab-plane below T_c2 and predicts a large anisotropy for the ab-plane heat current.     

Ultrasonic study of the temperature and pressure dependences of the elastic properties of ceramic dimolybdenum carbide (α-Mo2C)

Pulse-echo overlap measurements of ultrasonic wave velocity have been used to determine the elastic stiffness moduli and related elastic properties of ceramic samples of dimolybdenum carbide (-Mo₂C) as functions of temperature in the range 130–295 K and hydrostatic pressure up to 0.2 GPa at room temperature. The temperature dependences of the shear elastic stiffness () and Young's modulus (E) show normal behaviour and can be approximated by a conventional model for vibrational anharmonicity. The longitudinal elastic stiffness (C _L) increases with decreasing temperature and shows a knee at about 200 K; the decrease in slope below the knee indicates longitudinal acoustic-mode softening. The adiabatic bulk modulus (B ^S) is also affected by the mode softening below 200 K. The values obtained for the acoustic Debye temperature (_D) for ceramic -Mo₂C agree well with the thermal Debye temperature determined previously from heat capacity measurements. The velocities of both the longitudinal and shear ultrasonic waves in ceramic -Mo₂C increase approximately linearly with pressure: both the long-wavelength longitudinal and shear acoustic modes stiffen under pressure. The values determined at room temperature for the hydrostatic-pressure derivative (/P) _P=0 of the shear stiffness is similar to those found for ceramic TiC and TaC; while (C _L/P) _P=0 and (B ^S/P) _P=0 have large values, possibly due to the defect microstructure of ceramic -Mo₂C.     

Large deformation theory of coupled thermoplasticity including kinematic hardening

Summary Thermoplasticity is a topic central to important applications such as metalforming, ballistics and welding. The current investigation introduces a thermoplastic constitutive model accommodating the difficult issues of finite strain and kinematic hardening. Two potential functions are used. One is interpreted as the Helmholtz free energy. Its reversible portion describes elastic behavior, while its irreversible portion describes kinematic hardening. The second potential function describes dissipative effects and arises directly from the entropy production inequality. It is shown that the dissipation potential can be interpreted as a yield function. With two simplifying assumptions, the formulation leads to a simple energy equation, which is used to derive a rate variational principle. Together with the Principle of Virtual Work in rate form, finite element equations governing coupled thermal and mechanical effects are presented. Using a uniqueness argument, an inequality is derived which is interpreted as a finite strain thermoplastic counterpart to the classical inequality for stability in the small. A simple example is introduced using a von Mises yield function with linear kinematic hardening, linear isotropic hardening and linear thermal softening.Symbols D rate of deformation tensor - d VEC(D) - F deformation gradient tensor - h heat generation per unit mass - L velocity gradient tensor - q heat flux vector - workless internal variable - Lagrangian strain - e VEC() - E quasi-Eulerian strain - entropy - internal energy per unit mass - Helmholtz free energy - Cauchy stress tensor - Truesdell stress flux tensor - t VEC() - yield function - First Piola Kirchhoff stress - Second Piola Kirchhoff stress - s VEC() - s ^* backstress, center of the yield surface - Kronecker product symbol - VEC vectorization operator - tr(.) trace - DEV deviator of a tensor - TEN22 Kronecker tensor operator     

Analytical Theory of DC SQUIDS Operating in the Presence of Thermal Fluctuations

A comprehensive analytical theory of symmetric DC SQUIDs is presented taking into account the effects of thermal fluctuations. The SQUID has a reduced inductance < 1/ where = 2LI_c/₀, L is the loop inductance, ₀ is the flux quantum, and I_c is the critical current of the identical Josephson junctions which are assumed to be overdamped. The analysis, based on the two dimensional Fokker–Planck equation, has been successfully performed in first order approximation with considered a small parameter. All important SQUID characteristics (circulating current, current-voltage curves, transfer function, and energy sensitivity) are obtained. In the limit 1( = 2k_BT/I_c0 is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature) the theory reproduces the results of numerical simulations performed for the case of small thermal fluctuations. It was found that for < 1 the SQUID energy sensitivity is optimum when is higher than 1/, i.e., outside the range for which the present analysis is valid. However, for 1 the energy sensitivity has a minimum at L = L_F , where L_F = ( ₀ /2) ²/k_B , and therefore, in this case, the optimal reduced DC SQUID inductance is _opt = 1/, i.e., within the range for which the present analysis is valid. In contrast to the case of an RF SQUID, for a DC SQUID the transfer function decreases not only with increasing L/L_F but also with increasing (as 1/). As a consequence, the energy sensitivity of a DC SQUID with < 1/ degrades more rapidly (as ⁴ ) with the increase of than that of an RF SQUID does (as ² ).     

The Ni3Al-Ni3Cr-Ni3Ru section of the Ni-Cr-Al-Ru system

An investigation is reported of the 75 at% nickel section of the Ni-Cr-Al-Ru system at 1523 and 1273 K. Constitutional data obtained by electron probe microanalysis, X-ray diffraction and microscopical examination are presented as partial isothermal sections. At 1523 K, the major part of the section consists of phase, while the aluminium-rich region contains a and+ region; the extent of the solid solution of chromium and ruthenium in totals ~ 4 at%. The ruthenium-rich corner of the section shows a two-phase region consisting of + ruthenium-rich solid solution. At 1273 K the,+ and + ruthenium regions increase in extent. The/ mismatch values in the equilibrated alloys studied lie in the range ~ –0.08 to –0.39%. Constitutional features of as-cast alloys are also reported.     

A superconducting vibrating reed applied to flux-line pinning. I. Theory

A theoretical treatment is given of a superconducting reed clamped at one end and performing flexural vibrations in a homogeneous longitudinal magnetic fieldB _a. When the flux lines are rigidly pinned the reed behaves like an ideal diamagnet whose bending distorts the external field. This generates a magnetic restoring force (line tension) B _a ² which is independent of the reed thicknessd, whereas the mechanical restoring force (stiffness) is d ³. Therefore, the resonance frequency /2 of a thin superconducting reed increases drastically when a fieldB _a is applied, or for a givenB _a, when the reed is cooled below its critical temperatureT _c. With decreasing pinning strength (characterized by Labusch's parameter ) the resonance frequency decreases, ²²– _pin ² where _pin ^{2 –1}, and an attenuation _v ^–2 occurs due to the viscous motion of flux lines. For larger vibration amplitudes an additional, amplitude-dependent damping _h ^–3 occurs due to the hysteretic losses caused by elastic instabilities during flux motion.On leave from Centro Atómico, Bariloche, Argentina.     

Die Herleitung von Schalengleichungen über ein erweitertes Variationsprinzip bei Berücksichtigung der Querschubverzerrungen

Ohne ZusammenfassungBezeichnungen L Bezugsgrößen für dimensionslose Koordinaten - L charakteristische Schalenabmessung - t Schalendicke - Schalenparameter - körperfeste, krummlinige, dimensionslose Koordinaten der Schalenmittelfläche - Dimensionslose Koordinate in Richtung der Schalennormalen - i, j,...=1,2,3 Indizierung des dreidimensionalen Euklidischen Raumes - ,,...=1,2 Indizierung des zweidimensionalen Riemannschen Raumes - (...), Partielle Differentiation nach der Koordinate - (...), Kovariante Differentiation für Tensorkomponenten des zweidimensionalen Raumes nach der Koordinate - (...)| Kovariante Differentiation für Tensorkomponenten des dreidimensionalen Raumes nach der Koordinate - Variationssymbol - a ,a ₃ Basisvektoren der Schalenmittelfläche - V Verschiebungsvektor - U ,U ₃ Verschiebungskomponenten des Schalenraumes - v ,w,w ,W Verschiebungskomponenten der Schalenmittelfläche - Verhältnis der Metriktensoren des Schalenraumes und der Schalenmittelfläche - _ik Verzerrungstensor des Raumes - _{(, )}, Symmetrische Verzerrungstensoren der Schalenmittelfläche - _{[, ]} Antimetrischer Term des Verzerrungsmaßes - ^, Spannungstensor - n ,m ,q Tensorkomponenten der Schnittgrößenvektoren - p ,p,c Tensorielle Lastkomponenten     

Magnetic field dependence of zero-sound attenuation close to the pair-breaking edge in3He-B due toJ=1−,J z =±1 collective modes

Our previous theory yielded for the Zeeman splitting of the imaginaryJ=1 collective mode in³He-B the result =2+0.25J _z ( is the effective Larmor frequency). In this paper we take into account the downward shift of the pair-breaking edge from 2 to 2₂– (₂ and ₁ are the longitudinal and transverse gap parameters). This leads to a complex Landé factor: the frequencies of theJ _z =±1 components become =2+0.39J _z , and the linewidths of these resonances become finite: =0.18. The coupling amplitudes of theJ _z =±1 components to density are found to be proportional to gap distortion, (₁–₂/(/)². Our results for the ultrasonic attenuation due to theJ _z =±1,J=1 modes are capable of explaining the field dependence of the attenuation close to the pair-breaking edge as observed by Dobbs, Saunders, et al. The observed peak is caused by theJ _z =–1 component: its height increases due to gap distortion as the field is increased, and the peak shifts downward in temperature and its width increases with the field due to the complex Landé factor. TheJ _z =+1 component gives rise to a corresponding dip relative to the continuum attenuation.     

Fracture stress difference of notched polycarbonate between atmospheric pressure and a hydrostatic pressure

Experimental data on fracture stress of polycarbonate (PC) with and without various artificial notches have been obtained at atmospheric pressure and a high hydrostatic pressure (400 MPa). The difference in fracture stress, _F, between both pressures was directly proportional to the intensity of pressure,P, and was inversely proportional to the stress concentration factor of the notch,K _n such that _F following the form of the Kaieda-Oguchi formula, _F. By using the combined stress concentration factor,K _nc, of superposed notch and craze, and by considering the change in elastic modulus due to pressure, the experimental data agreed with the modified Kaieda-Oguchi formula. The stress concentration factor of the craze was calculated by using the Dugdale model.     

Bounding-surface plasticity: Stress space versus strain space

Summary A bounding-surface plasticity model is formulated in stress space in a general enough manner to accommodate a considerable range of hardening mechanisms. Conditions are then established under which this formulation can be made equivalent to its strain-space analogue. Special cases of the hardening law are discussed next, followed by a new criterion to ensure nesting. Finally, correlations with experimental data are investigated.Notation (a) centre of the stress-space (strain-space) loading surface; i.e., backstress (backstrain) - ^* (a ^*) centre of the stress-space (strain-space) bounding surface - (a ) target toward which the centre of the stress-space (strain-space) loading surface moves under purely image-point hardening - (b) parameter to describe how close the loading surface is to nesting with the bounding surface in stress (strain) space; see (H10) - (c) elastic compliance (stiffness) tensor - (d) parameter to describe how close the stress (strain) lies to its image point on the bounding surface; see (H10) - (D) generalised plastic modulus (plastic compliance); see (1) - function expressing the dependence of the generalised plastic modulus on (plastic complianceD ond) - ^* (D ^*) analogue to (D) for the bounding surface - function expressing the dependence of ^* on (D ^* ond) - () strain (stress) - ' (') deviatoric strain (stress) - ^P ( ^R ) plastic strain (stress relaxation); see Fig. 1 - () image point on the bounding surface corresponding to the current strain (stress) - _iso (f _iso) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change of radius; i.e., fraction of isotropic hardening in the stress-space theory - _kin (f _kin) at the point of invoking consistency, the fraction of local loading-surface motion arising from a change in the backstress (backstrain); i.e., fraction of kinematic hardening in the stress-space theory - _nor (f _nor) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - _ima (f _ima) at the point of invoking consistency, the fraction of backstress (backstrain) motion directed toward the image stress (strain); i.e., the image-point fraction of the kinematic hardening in the stress-space theory - function relating _iso to , , and (f _iso tob,d, andl) - function relating _kin to , , and (f _kin onb,d, andl) - function relating _nor to , , and (f _nor onb,d, andl) - function relating _ima to , , and (f _ima onb,d, andl) - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change of radius - the fraction of outwardly normal bounding-surface motion at the Mróz image point which arises from a change in the centre - function relating _iso ^* to (f _iso ^* tod) - function relating _kin ^* to (f _kin ^* tod) - (l) parameter to describe the full extent of plastic loading up to the present, giving the arc length of plastic strain (stress relaxation) trajectory; see (H10) - function relating the direction for image-point translation of the loading surface to various other tensorial directions associated with the current state; see (H5). With 6 Figures     

The fracture energy of a glass fibre composite

The fracture energy of a glass fibre-polyester composite has been measured by work of fracture ( _f) measurements on bending beams, and by linear elastic fracture mechanics analyses ( _i) of the bending beams and edge-notched tensile plates. It was found that for the bend specimens _i< _f. The work of fracture, _f, displayed a strain rate dependence, but there was no such dependence of _i. It is postulated that _i is determined by a debonding mechanism while _f is the sum of a debonding mechanism plus a pull-out contribution. The edge-notched tensile plate experiments showed that _i obtained from thick plates was less than that obtained from side-grooved plates, and that in each case there was a dependence of _i on crack size.     

Thermodynamic properties of iron doped beta″-alumina by e.m.f. measurements with beta-alumina electrolytes

Thermodynamic studies of the non-stoichiometric iron doped beta-alumina (ID) phase were carried out by electrochemical measurements coupled with coulometric titration using the cell Na_liq/Li-alumina/ID. Hot pressing and glass sealing techniques were developed and employed to obtain a suitable and stable Li-alumina/ID interface. The equilibrium e.m.f. of the cell was determined as a function of sodium concentration over the temperature range 444 to 523 K. The range of sodium concentrations over which the ID phase is stable was also determined. The relative partial molar thermodynamic quantities of sodium, , , and in ID alumina as a function of sodium concentration were obtained from cell e.m.f. data.     

Nearly isochoric finite torsion of a compressible isotropic elastic circular cylinder

Summary Finite torsion of a circular bar of isotropic compressible hyperelastic material is considered. A procedure suggested by Truesdell is used to obtain solutions for a particular strain energy function although the method used is not restricted to this particular form. The procedure is applicable if the volume strain is small. Results for finite twist with the length prevented from changing and with the length allowed to change so that the resultant longitudinal force is zero are presented.

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Fast-isochore endliche Torsion eines kompressiblen, isotropen, elastischen Kreiszylinders

Zusammenfassung Betrachtet wird die endliche Verdrehung eines Stabes mit Kreisquerschnitt aus einem isotropen, kompressiblen, hyperelastischen Werkstoff. Eine von Truesdell vorgeschlagene Vorgangsweise wird zur Bestimmung der Lösungen, für eine spezielle Verzerrungsenergiefunktion, verwendet, obwohl die verwendete Methode nicht auf diese spezielle Form beschränkt ist. Diese Vorgangsweise ist anwendbar, sofern die Volumsverzerrung klein ist. Ergebnisse für die endliche Verdrehung werden angegeben, wobei entweder die Längenänderung unterbunden ist oder die Länge sich ändern kann, so daß die resultierende Längskraft verschwindet.

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Notation F deformation gradient tensor - B=FF ^T left Cauchy-Green tensor - I identity matrix - I ₁=trB first invariant ofB - I ₂=1/2[(trB)²–trB ²] second invariant ofB - I ₃=detB third invariant ofB - W strain energy per unit volume of unstrained stateB ₀ - gradient operator for stateB - u small displacement from stateB - H=u small displacement gradient based on stateB - T true stress tensor based on stateB - f body force vector - T additional stress - =T+T true stress for final configuration - elastic constant equivalent to shear modulus for small deformation - elastic constant equivalent to Poisson's ratio for small deformation - r, ,z cylindrical polar coordinates - _r , , _z , _z physical components of stress tensor for cylindrical polar coordinates With 3 Figures     

On the analysis of tunneling data for A15 superconductors

We examine the applicability of the standard McMillan inversion of Eliashberg's equations for superconductors with a nonconstant electronic density of statesN(). We do this usign simple models forN() and a realistically shapedN() taken from recent band structure work for Nb₃Sn. It turns out that peak structure inN() near _F may lead to gross errors in the derived Eliashberg function ²F() when the energy dependence ofN() is omitted in the inversion procedure. For Nb₃Sn, this leads to a 40% overestimate of when ²F() is evaluated via the standard McMillan program.