Academic literature on the topic '(order-)weakly compact operator'

AbstractWe study the duality problem for order weakly compact operators by giving sufficient and necessary conditions under which the order weak compactness of an operator implies the order weak compactness of its adjoint and conversely.

We give sufficient conditions for order-bounded convex operators to be generically differentiable (Gâteaux or Fréchet). When the range space is a countably order-complete Banach lattice, these conditions are also necessary. In particular, every order-bounded convex operator from an Asplund space into such a lattice is generically Fréchet differentiable, if and only if the lattice has weakly-compact order intervals, if and only if the lattice has strongly-exposed order intervals. Applications are given which indicate how such results relate to optimization theory.

This paper is devoted to the relationship between almost limited operators and weakly compact operators. We show that ifFis aσ-Dedekind complete Banach lattice, then every almost limited operatorT:E→Fis weakly compact if and only ifEis reflexive or the norm ofFis order continuous. Also, we show that ifEis aσ-Dedekind complete Banach lattice, then the square of every positive almost limited operatorT:E→Eis weakly compact if and only if the norm ofEis order continuous.

We establish the domination property and some lattice approximation properties for almost L-weakly and almost M-weakly compact operators. Then, we consider the linear span of positive almost L-weakly (resp., almost M-weakly) compact operators and give results about when they form a Banach lattice and have an order continuous norm.

Recall that a Banach space X has the Dunford-Pettis property if every weakly compact operator defined on X takes weakly compact sets into norm compact sets. Some valuable characterisations of Banach spaces with the Dunford-Pettis property are: X has the DPP if and only if for all Banach spaces Y, every weakly compact operator from X to Y sends weakly convergent sequences onto norm convergent sequences (i.e. it requires that weakly compact operators on X are completely continuous) and this is equivalent to “if (xn) and (x*n) are sequences in X and X* respectively and limn xn = 0 weakly and limn x*n = 0 weakly then limn x*n xn = 0". A striking application of the Dunford-Pettis property (as was observed by Grothendieck) is to prove that if X is a linear subspace of L() for some finite measure  and X is closed in some Lp() for 1 ≤ p < , then X is finite dimensional. The fact that the well known spaces L1() and C() have this property (as was proved by Dunford and Pettis) was a remarkable achievement in the early history of Banach spaces and was motivated by the study of integral equations and the hope to develop an understanding of linear operators on Lp() for p ≥ 1. In fact, it played an important role in proving that for each weakly compact operator T : L1()  L1() or T : C()  C(), the operator T2 is compact, a fact which is important from the point of view that there is a nice spectral theory for compact operators and operators whose squares are compact. There is an extensive literature involving the Dunford-Pettis property. Almost all the articles and books in our list of references contain some information about this property, but there are plenty more that could have been listed. The reader is for instance referred to [4], [5], [7], [8], [10], [17] and [24] for information on the role of the DPP in different areas of Banach space theory. In this dissertation, however, we are motivated by the two papers [7] and [8] to study alternative Dunford-Pettis properties, to introduce a scale of (new) alternative Dunford-Pettis properties, which we call DP*-properties of order p (briefly denoted by DP*P), and to consider characterisations of Banach spaces with these properties as well as applications thereof to polynomials and holomorphic functions on Banach spaces. In the paper [8] the class Cp(X, Y) of p-convergent operators from a Banach space X to a Banach space Y is introduced. Replacing the requirement that weakly compact operators on X should be completely continuous in the case of the DPP for X (as is mentioned above) by “weakly compact operators on X should be p-convergent", an alternative Dunford-Pettis property (called the Dunford-Pettis property of order p) is introduced. More precisely, if 1 ≤ p ≤ , a Banach space X is said to have DPPp if the inclusion W(X, Y)  Cp(X, Y) holds for all Banach spaces Y . Here W(X, Y) denotes the family of all weakly compact operators from X to Y. We now have a scale of “Dunford-Pettis like properties" in the sense that all Banach spaces have the DPP1, if p < q, then each Banach space with the DPPq also has the DPPp and the strongest property, namely the DPP1 coincides with the DPP. In the paper [7] the authors study a property on Banach spaces (called the DP*-property, or briey the DP*P) which is stronger than the DPP, in the sense that if a Banach space has this property then it also has DPP. We say X has the DP*P, when all weakly compact sets in X are limited, i.e. each sequence (x*n)  X * in the dual space of X which converges weak* to 0, also converges uniformly (to 0) on all weakly compact sets in X. It turns out that this property is equivalent to another property on Banach spaces which is introduced in [17] (and which is called the *-Dunford-Pettis property) as follows: We say a Banach space X has the *-Dunford-Pettis property if for all weakly null sequences (xn) in X and all weak* null sequences (x*n) in X*, we have x*n(xn) n 0. After a thorough study of the DP*P, including characterisations and examples of Banach spaces with the DP*P, the authors in [7] consider some applications to polynomials and analytic functions on Banach spaces. Following an extensive literature study and in depth research into the techniques of proof relevant to this research field, we are able to present a thorough discussion of the results in [7] and [8] as well as some selected (relevant) results from other papers (for instance, [2] and [17]). This we do in Chapter 2 of the dissertation. The starting point (in Section 2.1 of Chapter 2) is the introduction of the so called p-convergent operators, being those bounded linear operators T : X  Y which transform weakly p-summable sequences into norm-null sequences, as well as the so called weakly p-convergent sequences in Banach spaces, being those sequences (xn) in a Banach space X for which there exists an x  X such that the sequence (xn - x) is weakly p-summable. Using these concepts, we state and prove an important characterisation (from the paper [8]) of Banach spaces with DPPp. In Section 2.2 (of Chapter 2) we continue to report on the results of the paper [7], where the DP*P on Banach spaces is introduced. We focus on the characterisation of Banach spaces with DP*P, obtaining among others that a Banach space X has DP*P if and only if for all weakly null sequences (xn) in X and all weak* null sequences (x*n) in X*, we have x*n(xn) n 0. An important characterisation of the DP*P considered in this section is the fact that X has DP*P if and only if every T  L(X, c0) is completely continuous. This result proves to be of fundamental importance in the study of the DP*P and its application to results on polynomials and holomorphic functions on Banach spaces. To be able to report on the applications of the DP*P in the context of homogeneous polynomials and analytic functions on Banach spaces, we embark on a study of “Complex Analysis in Banach spaces" (mostly with the focus on homogeneous polynomials and analytic functions on Banach spaces). This we do in Chapter 3; the content of the chapter is mostly based on work in the books [23] and [14], but also on the work in some articles such as [15]. After we have discussed the relevant theory of complex analysis in Banach spaces in Chapter 3, we devote Chapter 4 to considering properties of polynomials and analytic functions on Banach spaces with DP*P. The discussion in Chapter 4 is based on the applications of DP*P in the paper [7]. Finally, in Chapter 5 of the dissertation, we contribute to the study of “Dunford-Pettis like properties" by introducing the Banach space property “DP*P of order p", or briefly the DP*Pp for Banach spaces. Using the concept “weakly p-convergent sequence in Banach spaces" as is defined in [8], we define weakly-p-compact sets in Banach spaces. Then a Banach space X is said to have the DP*-property of order p (for 1 ≤ p ≤ ) if all weakly-p-compact sets in X are limited. In short, we say X has DP*Pp. As in [8] (where the DPPp is introduced), we now have a scale of DP*P-like properties, in the sense that all Banach spaces have DP*P1 and if p < q and X has DP*Pq then it has DP*Pp. The strongest property DP*P coincides with DP*P. We prove characterisations of Banach spaces with DP*Pp, discuss some examples and then consider applications to polynomials and analytic functions on Banach spaces. Our results and techniques in this chapter depend very much on the results obtained in the previous three chapters, but now we have to find our own correct definitions and formulations of results within this new context. We do this with some success in Sections 5.1 and 5.2 of Chapter 5. Chapter 1 of this dissertation provides a wide range of concepts and results in Banach spaces and the theory of vector sequence spaces (some of them very deep results from books listed in the bibliography). These results are mostly well known, but they are scattered in the literature - they are discussed in Chapter 1 (some with proof, others without proof, depending on the importance of the arguments in the proofs for later use and depending on the detail with which the results are discussed elsewhere in the literature) with the intention to provide an exposition which is mostly self contained and which will be comfortably accessible for graduate students. The dissertation reflects the outcome of our investigation in which we set ourselves the following goals: 1. Obtain a thorough understanding of the Dunford-Pettis property and some related (both weaker and stronger) properties that have been studied in the literature. 2. Focusing on the work in the paper [8], understand the role played in the study of difierent classes of operators by a scale of properties on Banach spaces, called the DPPp, which are weaker than the DP-property and which are introduced in [8] by using the weakly p-summable sequences in X and weakly null sequences in X*. 3. Focusing on the work in the paper [7], investigate the DP*P for Banach spaces, which is the exact property to answer a question of Pelczynsky's regarding when every symmetric bilinear separately compact map X x X  c0 is completely continuous. 4. Based on the ideas intertwined in the work of the paper [8] in the study of a scale of DP-properties and the work in the paper [7], introduce the DP*Pp on Banach spaces and investigate their applications to spaces of operators and in the theory of polynomials and analytic mappings on Banach spaces. Thereby, not only extending the results in [7] to a larger family of Banach spaces, but also to find an answer to the question: “When will every symmetric bilinear separately compact map X x X  c0 be p-convergent?"<br>Thesis (M.Sc. (Mathematics))--North-West University, Potchefstroom Campus, 2012.

In this thesis we present an extensive characterization of weak* sequentially precompact subsets of the dual of a sequentially order complete M-space with an order unit. This central part of the thesis generalizes results due to H.H. Schaefer and X.D. Zhang showing that small weak* compact subsets of the dual of a space of bounded measurable real-valued functions (continuous real-valued functions on a compact quasi-Stonian space) are weakly compact. Moreover, while the proofs of Schaefer and Zhang use measure theoretical arguments, the arguments presented here are purely elementary and are based on the well-known result, that the space l1 has the Schur property. Finally some applications are given. For example, we investigate compact or sequentially precompact subsets, which consist of order-weakly compact operators, in the space of continuous linear operators defined on a sequentially order complete Riesz space with values in a Banach space provided with the strong operator topology: as an immediate consequence of the results, we can easily deduce extended versions of the Vitali-Hahn-Saks theorem for vector measures. For this we need a generalization of the Yosida-Hewitt decomposition theorem, which is proved here with other techniques like the factorization of an order-weakly compact operator through a Banach lattice with order continuous norm.

The thesis consists of four research papers. The first three deal with the Choquet theory of function spaces. In Chapter 1, a theory on products and projective limits of function spaces is developed. It is shown that the product of simplicial spaces is a simplicial space. The stability of the space of maximal measures under continuous affine mappings is studied in Chapter 2. The third chapter employs results from the previous chapters to construct an example of a function space where the abstract Dirichlet problem is not solvable for any class of Baire-n functions with $n\in N$. It is shown that such an example cannot be constructed via the space of harmonic functions. In the final chapter, the recently introduced class of sequentially Right Banach spaces is being investigated. Connections to other isomorphic properties of Banach spaces are established and several characterizations are given.

This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω‎ ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω‎, one can choose a natural local coordinate system y = κ‎(x) vanishing at y0 so that the quadratic form associated with the metric takes a special form. To conclude, the chapter turns to the Hadamard parametrix.

This Chapter considers the keystone rule, the non-frustration rule and its operation and effect in the context of hostile takeovers. The Chapter first explores the scope of the rule to determine what steps target boards can and cannot take when faced with a hostile offer. It considers the general meeting approval of frustrating action and explains why in practice such approvals are never seen. The Chapter then proceeds to consider the optimality of the rule. It considers first the roots of both the Panel’s and more general public support for the rule, arguing that commitment to the rule is a function not of the policy balance between the advantages and disadvantages of the rule but rather a function of broader and deep structural understanding of the balance of power in a UK company. It is a commitment whose genesis is historically contingent which should, if possible, be discounted in the policy assessment of the advantages and disadvantages of allowing target boards to defend against unwanted takeovers. The Chapter then proceeds to consider this policy balance in a UK context which involves, inter alia, a consideration of: the extent to which defences can be used to entrench a board which is subject to pro-shareholder UK company law; the extent to which the market for corporate control acts a governance mechanism; and modern fund management behaviour influenced by relative performance metrics which supports a claim that defences can be justified in order to protect ultimate shareholders from their fund managers, a nuance on the standard justification that defences protect shareholders from themselves. The Chapter concludes that the policy case for prohibiting takeover defences is weak, and moves to consider the reform options in light of the post-Cadbury and Kraft debate on this issue. The Chapter considers and supports both reform of the non-frustration rule (by abolishing the rule) and a higher acceptance threshold (which effectively enables shareholders who are interested in long term fundamental value to make the decision). But the Chapter rejects disenfranchisement of short-term shareholders and enhanced public interest test. The Chapter concludes that it is now time for the Panel to engage with the broader consequences of the rule and reform options.

The need for compact models for ICs is a well-recognized problem in electronics cooling simulations of systems containing multiple PCBs and many devices per board. The disparate length scales inherent in the problem and the necessity of resolving these size scales renders the computational problem intractable. Many resistance-capacitance (RC) network compact models have been proposed in the literature. We present a methodology to automatically construct both the topology and characteristics of the reduced-order or compact models of devices (primarily Integrated Circuit (IC) packages) for use in system-level simulations using the multigrid operator. The multigrid technique has been extensively used over the past 20 years to accelerate the solution of liner systems. In addition to automatically generating both the RC network topology and its values, the procedure is general enough to be applicable for complex IC device types like Multi-Chip Modules (MCMs), stack up dies, distributed sources on the die, DC-DC converters and devices such as hard disk drives.

Brand represents one of the most important assets of the company. Brand-managing activities are typically related to brand positioning and integration with marketing campaigns, and can involve complex decisions. The branding of an organization is indeed a dynamic system with many cause-effect relationships as well as intangible and heterogeneous variables. In order to assess the value of individual brands can be used various models developed worldwide, based on different input data and valuation methodologies. We assume that individual environment in which company operates and consumers’ perceptions in different countries influence the ability and usability of these models in other countries. Therefore, we applied chosen well-known brand value models on the set of Slovak companies and validated their assessment ability in specific condition of the Slovak Republic. This was provided by the critical comparison of calculated values with the official values of brands of these companies listed in the Slovak journal. Through this, we pointed out the importance of the development of unique brand value model, which will be constructed in the specific condition of individual countries and highlight the weak assessment ability of foreign models.

In order to solve complex problems in hydrodynamics, a new method is developed. This method aims at finding a good compromise between computational efficiency, accuracy, and easy handling of complex geometries. The chosen method is an Explicit Cartesian Finite Volume method for Hydrodynamics (ECFVH) based on a compressible (hyperbolic) solver, with an embedded method for interfaces and geometry handling. The explicit nature of the solver is obtained through a weakly-compressible approach chosen to simulate nearly-incompressible flows. The explicit cell-centered resolution allows for an efficient solving of very large simulations together with a straightforward handling of multi-physics. The use of an embedded Cartesian grid ensures accuracy and efficiency, but also implies the need for a specific treatment of complex solid geometries, such as the cut-cell method in the fixed or moving body frame. Robustness of the cut-cell method is ensured by specific procedures to circumvent small cell volume numerical errors. A characteristic flux method for solving the hyperbolic part of the Navier-Stokes equations is used for which upwinding is necessary, also introducing numerical viscosity. This numerical viscosity is evaluated before trying to model viscous and turbulent effects. In a first approach viscous effects are computed via a finite difference Laplacian operator introduced as a source term. This solver is validated on 2-D test cases and future improvements are discussed.

The long term management of a production asset raises several major issues among which rank the technical management of the plant, its economics and the fleet level perspective one has to adopt. Decision makers are therefore faced with the need to define long term policies (up to the end of asset operation) which take into account multiple criteria including safety (which is paramount) and performance. In this context, EDF “PWR Durability I &amp; II” research projects have consecutively been launched, since 2001, at EDF – Research &amp; Development in order to develop methods and tools for EDF fleet. The aim of this paper is: • to summarize and analyze the research work that has been performed by EDF – R&amp;D in the field of decision making for nuclear power plant maintenance and operation during the past seven year; • to highlight the strong and weak points of the developed methodology and tools and to identify the research work needed in order to ensure their use by EDF decision makers; • to introduce and illustrate our last development based on the use of an “adaptative” man/machine user interface in order to allows technical/strategic experts and decision makers to consult the useful pieces of knowledge in a context dependent way and, thus, facilitate the validation of the knowledge-base content and the analysis of the processed results. As a result, in this paper, we first remind the reader of the EDF overall methodology for asset management and its adaptations to plant-level life cycle management and to fleet-level component major replacement or capital investment management. We then focus on the three software tools that implement this methodology in order to allow decision makers, in several different contexts to define, evaluate and analyze long term plant operation and maintenance policies, major component replacement policies and capital investment strategies. We also show how the methodology and the software tools were used, from 2003 to 2007, on several pilot case studies. Examples of technical and economic results obtained for plant level pilot case study is quickly described as well as the kinds of conclusions one can draw from them in order to help decision makers evaluate and analyze long term asset management strategies or compare different plants. We then present the opinion of EDF’s decision makers about the developedmethodology and tools — and their use — and our understanding of their feedback. Lastly, we illustrate, using examples of technical and economic knowledge, data and results obtained from our previous pilot case studies, how the concept of an “adaptative” man/machine user interface could be used in order to facilitate the mastering of the methodology and tools’ complexity and to support decision makers’ evaluation and analysis of long term asset management strategies.

Abstract Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. We augment this controller with a direct adaptive controller that will maintain stability of the full closed loop system even when the fixed gain controller fails to do so. We prove that the transmission zeros of the combined system are the original open loop transmission zeros, and the point spectrum of the controller alone. Therefore, the combined plant plus controller is Almost Strictly Dissipative (ASD) if and only if the original open loop system is minimum phase, and the fixed gain controller alone is exponentially stable. This result is true whether the fixed gain controller is finite or infinite dimensional. In particular this guarantees that a controller for an infinite dimensional plant based on a reduced -order approximation can be stabilized by augmentation with direct adaptive control to mitigate risks. These results are illustrated by application to direct adaptive control of general linear diffusion systems on a Hilbert space that are described by self-adjoint operators with compact resolvent.

Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.

The performance of the vitrification process currently used in the La Hague commercial reprocessing plants has been continuously improved during more than ten years of operation. In parallel COGEMA (industrial Operator), the French Atomic Energy Commission (CEA) and SGN (respectively COGEMA’s R&amp;D provider and Engineering) have developed the cold crucible melter vitrification technology to obtain greater operating flexibility, increased plant availability and further reduction of secondary waste generated during operations. The cold crucible is a compact water-cooled melter in which the radioactive waste and the glass additives are melted by direct high frequency induction. The cooling of the melter produces a soldified glass layer that protects the melter’s inner wall from corrosion. Because the heat is transferred directly to the melt, high operating temperatures can be achieved with no impact on the melter itself. COGEMA plans to implement the cold crucible technology to vitrify high level liquid waste from reprocessed spent U-Mo-Sn-Al fuel (used in gas cooled reactor). The cold crucible was selected for the vitrification of this particularly hard-to-process waste stream because it could not be reasonably processed in the standard hot induction melters currently used at the La Hague vitrification facilities: the waste has a high molybdenum content which makes it very corrosive and also requires a special high temperature glass formulation to obtain sufficiently high waste loading factors (12% in molybednum). A special glass formulation has been developed by the CEA and has been qualified through lab and pilot testing to meet standard waste acceptance criteria for final disposal of the U-Mo waste. The process and the associated technologies have been also being qualified on a full-scale prototype at the CEA pilot facility in Marcoule. Engineering study has been integrated in parallel in order to take into account that the Cold Crucible should be installed remotely in one of the R7 vitrification cell. This paper will present the results obtained in the framework of these qualification programs.

Increased research into the chemistry, physics and material science of hydrogen cycling compounds has led to the rapid growth of solid-phase hydrogen-storage options. The operating conditions of these new options span a wide range: system temperature can be as low as 70K or over 600K, system pressure varies from less than 100kPa to 35MPa, and heat loads can be moderate or can be measured in megawatts. While the intense focus placed on storage materials has been appropriate, there is also a need for research in engineering, specifically in containment, heat transfer, and controls. The DOE’s recently proposed engineering center of expertise underscores the growing understanding that engineering research will play a role in the success of advanced hydrogen storage systems. Engineering a hydrogen system will minimally require containment of the storage media and control of the hydrogenation and dehydrogenation processes, but an elegant system design will compensate for the storage media’s weaker aspects and capitalize on its strengths. To achieve such a complete solution, the storage tank must be designed to work with the media, the vehicle packaging, the power-plant, and the power-plant’s control system. In some cases there are synergies available that increase the efficiency of both subsystems simultaneously. In addition, system designers will need to make the hard choices needed to convert a technically feasible concept into a commercially successful product. Materials cost, assembly cost, and end of life costs will all shape the final design of a viable hydrogen storage system. Once again there is a critical role for engineering research, in this case into lower cost and higher performance engineering materials. Each form of hydrogen storage has its own, unique, challenges and opportunities for the system designer. These differing requirements stem directly from the properties of the storage media. Aside from physical containment of compressed or liquefied hydrogen, most storage media can be assigned to one of four major categories, chemical storage, metal hydrides, complex hydrides, or physisorption. Specific needs of each technology are discussed below. Physisorption systems currently operate at 77K with very fast kinetics and good gravimetric capacity; and as such, special engineering challenges center on controlling heat transfer. Excellent MLVSI is available, its cost is high and it is not readily applied to complex shape in a mass manufacture setting. Additionally, while the heat of adsorption on most physisorbents is a relatively modest 6–10kJ/mol H2, this heat must be moved up a 200K gradient. Physisorpion systems are also challenged on density. Consequently, methods for reducing the cost of producing and assembling compact, high-quality insulation, tank design to minimize heat transfer while maintaining manufacturability, improved methods of heat transfer to and from the storage media, and controls to optimize filling are areas of profitable research. It may be noted that the first two areas would also contribute to improvement of liquid hydrogen tanks. Metal hydrides are currently nearest application in the form of high pressure metal hydride tanks because of their reduced volume relative to compressed gas tanks of the same capacity and pressure. These systems typically use simple pressure controls, and have enthalpies of roughly 20kJ/mol H2 and plateau pressures of at most a few MPa. During filling, temperatures must be high enough to ensure fast kinetics, but kept low enough that the thermodynamically set plateau pressure is well below the filling pressure. To accomplish this balance the heat transfer system must handle on the order of 300kW during the 5 minute fill of a 10kg tank. These systems are also challenged on mass and the cost of the media. High value areas for research include: heat transfer inside a 35MPa rated pressure vessel, light and strong tank construction materials with reduced cost, and metals or other materials that do not embrittle in the presence of high pressure hydrogen when operated below ∼400K. The latter two topics would also have a beneficial impact on compressed gas hydrogen storage systems, the current “system to beat”. Complex hydrides frequently have high hydrogen capacity but also an enthalpy of adsorption &gt;30kJ/mol H2, a hydrogen release temperature &gt;370K, and in many cases multiple steps of adsorption/desorption with slow kinetics in at least one of the steps. Most complex hydrides are thermal insulators in the hydrided form. From an engineering perspective, improved methods and designs for cost effective heat transfer to the storage media in a 5 to 10MPa vessel is of significant interest, as are materials that resist embrittlement at pressures below 10MPa and temperatures below 500K. Chemical hydrides produce heat when releasing hydrogen; in some systems this can be managed with air cooling of the reactor, but in other systems that may not be possible. In general, chemical hydrides must be removed from the vehicle and regenerated off-board. They are challenged on durability and recycling energy. Engineering research of interest in these systems centers around maintaining the spent fuel in a state suitable for rapid removal while minimizing system mass, and on developing highly efficient recycling plant designs that make the most of heat from exothermic steps. While the designs of each category of storage tank will differ with the material properties, two common engineering research thrusts stand out, heat transfer and structural materials. In addition, control strategies are important to all advanced storage systems, though they will vary significantly from system to system. Chemical systems need controls primarily to match hydrogen supply to power-plant demand, including shut down. High pressure metal hydride systems will need control during filling to maintain an appropriately low plateau pressure. Complex hydrides will need control for optimal filling and release of hydrogen from materials with multi-step reactions. Even the relatively simple compressed-gas tanks require control strategies during refill. Heat transfer systems will modulate performance and directly impact cost. While issues such as thermal conductivity may not be as great as anticipated, the heat transfer system still impacts gravimetric efficiency, volumetric efficiency and cost. These are three key factors to commercial viability, so any research that improves performance or reduces cost is important. Recent work in the DOE FreedomCAR program indicates that some 14% of the system mass may be attributed to heat transfer in complex hydride systems. If this system is made to withstand 100 bar at 450K the material cost will be a meaningful portion of the total tank cost. Improvements to the basic shell and tube structures that can reduce the total mass of heat transfer equipment while maintaining good global and local temperature control are needed. Reducing the mass and cost of the materials of construction would also benefit all systems. Much has been made of the need to reduce the cost of carbon fiber in compressed tanks and new processes are being investigated. Further progress is likely to benefit any composite tank, not just compressed gas tanks. In a like fashion, all tanks have metal parts. Today those parts are made from expensive alloys, such as A286. If other structural materials could be proven suitable for tank construction there would be a direct cost benefit to all tank systems. Finally there is a need to match the system to the storage material and the power-plant. Recent work has shown there are strong effects of material properties on system performance, not only because of the material, but also because the material properties drive the tank design to be more or less efficient. Filling of a hydride tank provides an excellent example. A five minute or less fill time is desirable. Hydrogen will be supplied as a gas, perhaps at a fixed pressure and temperature. The kinetics of the hydride will dictate how fast hydrogen can be absorbed, and the thermodynamics will determine if hydrogen can be absorbed at all; both properties are temperature dependent. The temperature will depend on how fast heat is generated by absorption and how fast heat can be added or removed by the system. If the design system and material properties are not both well suited to this filling scenario the actual amount of hydrogen stored could be significantly less than the capacity of the system. Controls may play an important role as well, by altering the coolant temperature and flow, and the gas temperature and pressure, a better fill is likely. Similar strategies have already been demonstrated for compressed gas systems. Matching system capabilities to power-plant needs is also important. Supplying the demanded fuel in transients and start up are obvious requirements that both the tank system and material must be design to meet. But there are opportunities too. If the power-plant heat can be used to release hydrogen, then the efficiency of vehicle increases greatly. This efficiency comes not only from preventing hydrogen losses from supplying heat to the media, but also from the power-plant cooling that occurs. To reap this benefit, it will be important to have elegant control strategies that avoid unwanted feedback between the power-plant and the fuel system. Hydrogen fueled vehicles are making tremendous strides, as can be seen by the number and increasing market readiness of vehicles in technology validation programs. Research that improves the effectiveness and reduces the costs of heat transfer systems, tank construction materials, and control systems will play a key role in preparing advanced hydrogen storage systems to be a part of this transportation revolution.