A peridynamic theory for linear elastic shells

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one geometric dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states yield the necessary force and deformation vectors governing the motion of the shell. By incorporating a shear correction factor, the formulation also accommodates analysis of shells that have higher thickness. In order to attain this, a consistent second order approximation to the complementary energy density is considered and incorporated in peridynamics via constitutive correspondence. Unlike the uncoupled constitution for thin shells, a consequence of a first order approximation, constitutive relations for thick shells are fully coupled in that surface wryness influences the in-plane stress resultants and surface strain the moments. Our proposal on the peridynamic shell theory is numerically assessed against simulations on static deformation of spherical and cylindrical shells, that of flat plates and quasi-static fracture propagation in a cylindrical shell. (C) 2016 Elsevier Ltd. All rights reserved.

Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

Una teoría general para la enseñanza del derecho civil : una propuesta para el Bicentenario

Resumen: El presente trabajo propone elementos para una reformulación de la enseñanza del Derecho Civil en la Argentina del Bicentenario. Parte del análisis del estado actual de la enseñanza en esta rama jurídica, con especial referencia a sus etapas históricas. Considera luego lo que se denomina “el modelo del cententario”, con particular atención a la influencia de la modernidad ilustrada y la cultura del Código. Evalúa luego la cuestión a partir de la tensión entre modernidad ilustrada y posmodernidad, proponiendo una alternativa al modelo de enseñanza surgido de la posmodernidad. Como hipótesis de trabajo propone una lectura de la denominada cultura jurídica desde los principios del derecho, y aportar así una alternativa desde la perspectiva del realismo jurídico clásico.

Cómo recibir a Merleau-Ponty en la “theory of time” : una polémica

Resumen: El presente trabajo busca clarificar (en polémica con el abordaje de Stephen Priest) el auténtico sentido del “subjetivismo” merleaupontyano con respecto al tiempo, según el cual solo existe tiempo como correlato de una subjetividad situada en él. En un marco más general, reponer esta tesis merleaupontyana permite colocar las reflexiones del fenomenólogo francés en diálogo con la tradición analítica sobre el tiempo (centrada en el debate entre las teorías “A” y “B”), y, en particular, en continuidad temática con el abordaje de la “paradoja de McTaggart” por parte de Michael Dummett

An optimal theory for an expansion of flow quantities to capture the flow structures

An optimal theory on how database analysis to capture the flow structures has been developed in this paper, which include the POD method as its special case. By means of the remainder minimization method in the Sobolev space, for more general optimal conditions the new theory has the potential to overcome an inherent limitation of the POD method, i.e., it cannot be used to the situations in which the optimal condition is other than the inner product global one. As an example, using the new theory, the database of a two-dimensional flow over a backward-facing step is analyzed in detail, with velocity and vorticity bases.

Evolution and propagation of density waves on galactic disk .1. General evolution equation of wavelet and discussion of its solution

This paper presents a general self-consistent theory of evolution and propagation of wavelets on the galactic disk. A simplified model for this theory, i. e. the thin transition-layer approximation is proposed.There are three types of solutions to the basic equation governing the evolution of wavelets on the disk: (ⅰ) normal propagating type; (ⅱ) swing type; (ⅲ) general evolving type. The results show that the first two types are applicable to a certain domain on the galactic disk and a certain region of the wave number of wavelets. The third is needed to join the other two types and to yield a coherent total picture of the wave motion. From the present theory, it can be seen that the well-known "swing theory" of the G-L sheet model holds only for a certain class of basic states of galaxies.

Microscopic theory of chemical-reaction rate

In this paper we deduce the formulae for rate-constant of microreaction with high resolving power of energy from the time-dependent Schrdinger equation for the general case when there is a depression on the reaetional potential surface (when the depression is zero in depth, the case is reduced to that of Eyring). Based on the assumption that Bolzmann distribution is appropriate to the description of reactants, the formula for the constant of macrorate in a form similar to Eyring's is deduced and the expression for the coefficient of transmission is given. When there is no depression on the reactional potential surface and the coefficient of transmission does not seriously depend upon temperature, it is reduced to Eyring's. Thus Eyring's is a special case of the present work.

On the non-linear stability theory of spinning solid bodies with liquid-filled cavities and its application to the columbus problem

In this paper, we first present a system of differential-integral equations for the largedisturbance to the general case that any arbitrarily shaped solid body with a cavity contain-ing viscous liquid rotates uniformly around the principal axis of inertia, and then develop aweakly non-linear stability theory by the Lyapunov direct approach. Applying this theoryto the Columbus problem, we have proved the consistency between the theory and Kelvin'sexperiments.

Visual impact assessment of small dock & piers: Theory and practice

From a manager’s perspective, oftentimes the publicly held concerns related to small docks and piers are not really related to the environment. They may be more related to visual impacts and aesthetic concerns, a sense of over-development of the shore, or simply change. While individuals may hold personal aesthetic values related to small docks in general or an individual structure in particular, techniques have evolved that appear to provide reproducible, predictive assessments of the visual impacts and aesthetic values of an area and how those might change with development, including an increase in numbers of small docks. These assessments may be used to develop regulatory or non-regulatory methods for the management of small docks based on state or community standards. Visual impact assessments are increasingly used in the regulatory review of proposed development—although this process is still in its infancy as regards small docks and piers. Some political jurisdictions have established visual impact or aesthetic standards as relate to docks and others are in the process of investigating how to go about such an effort. (PDF contains 42 pages)

Applying Habermas's critical theory to public administration and policy: A case study of Florida Everglades restoration program

The foundation of Habermas's argument, a leading critical theorist, lies in the unequal distribution of wealth across society. He states that in an advanced capitalist society, the possibility of a crisis has shifted from the economic and political spheres to the legitimation system. Legitimation crises increase the more government intervenes into the economy (market) and the "simultaneous political enfranchisement of almost the entire adult population" (Holub, 1991, p. 88). The reason for this increase is because policymakers in advanced capitalist democracies are caught between conflicting imperatives: they are expected to serve the interests of their nation as a whole, but they must prop up an economic system that benefits the wealthy at the expense of most workers and the environment. Habermas argues that the driving force in history is an expectation, built into the nature of language, that norms, laws, and institutions will serve the interests of the entire population and not just those of a special group. In his view, policy makers in capitalist societies are having to fend off this expectation by simultaneously correcting some of the inequities of the market, denying that they have control over people's economic circumstances, and defending the market as an equitable allocator of income. (deHaven-Smith, 1988, p. 14). Critical theory suggests that this contradiction will be reflected in Everglades policy by communicative narratives that suppress and conceal tensions between environmental and economic priorities. Habermas’ Legitimation Crisis states that political actors use various symbols, ideologies, narratives, and language to engage the public and avoid a legitimation crisis. These influences not only manipulate the general population into desiring what has been manufactured for them, but also leave them feeling unfulfilled and alienated. Also known as false reconciliation, the public's view of society as rational, and "conductive to human freedom and happiness" is altered to become deeply irrational and an obstacle to the desired freedom and happiness (Finlayson, 2005, p. 5). These obstacles and irrationalities give rise to potential crises in the society. Government's increasing involvement in Everglades under advanced capitalism leads to Habermas's four crises: economic/environmental, rationality, legitimation, and motivation. These crises are occurring simultaneously, work in conjunction with each other, and arise when a principle of organization is challenged by increased production needs (deHaven-Smith, 1988). Habermas states that governments use narratives in an attempt to rationalize, legitimize, obscure, and conceal its actions under advanced capitalism. Although there have been many narratives told throughout the history of the Everglades (such as the Everglades was a wilderness that was valued as a wasteland in its natural state), the most recent narrative, “Everglades Restoration”, is the focus of this paper.(PDF contains 4 pages)

Topics in black hole perturbation theory and the visualization of curved spacetime

This thesis presents recent research into analytic topics in the classical theory of General Relativity. It is a thesis in two parts. The first part features investigations into the spectrum of perturbed, rotating black holes. These include the study of near horizon perturbations, leading to a new generic frequency mode for black hole ringdown; an treatment of high frequency waves using WKB methods for Kerr black holes; and the discovery of a bifurcation of the quasinormal mode spectrum of rapidly rotating black holes. These results represent new discoveries in the field of black hole perturbation theory, and rely on additional approximations to the linearized field equations around the background black hole. The second part of this thesis presents a recently developed method for the visualization of curved spacetimes, using field lines called the tendex and vortex lines of the spacetime. The works presented here both introduce these visualization techniques, and explore them in simple situations. These include the visualization of asymptotic gravitational radiation; weak gravity situations with and without radiation; stationary black hole spacetimes; and some preliminary study into numerically simulated black hole mergers. The second part of thesis culminates in the investigation of perturbed black holes using these field line methods, which have uncovered new insights into the dynamics of curved spacetime around black holes.

Descriptive set theory and the ergodic theory of countable groups

The primary focus of this thesis is on the interplay of descriptive set theory and the ergodic theory of group actions. This incorporates the study of turbulence and Borel reducibility on the one hand, and the theory of orbit equivalence and weak equivalence on the other. Chapter 2 is joint work with Clinton Conley and Alexander Kechris; we study measurable graph combinatorial invariants of group actions and employ the ultraproduct construction as a way of constructing various measure preserving actions with desirable properties. Chapter 3 is joint work with Lewis Bowen; we study the property MD of residually finite groups, and we prove a conjecture of Kechris by showing that under general hypotheses property MD is inherited by a group from one of its co-amenable subgroups. Chapter 4 is a study of weak equivalence. One of the main results answers a question of Abért and Elek by showing that within any free weak equivalence class the isomorphism relation does not admit classification by countable structures. The proof relies on affirming a conjecture of Ioana by showing that the product of a free action with a Bernoulli shift is weakly equivalent to the original action. Chapter 5 studies the relationship between mixing and freeness properties of measure preserving actions. Chapter 6 studies how approximation properties of ergodic actions and unitary representations are reflected group theoretically and also operator algebraically via a group's reduced C^*-algebra. Chapter 7 is an appendix which includes various results on mixing via filters and on Gaussian actions.

Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Distributed optimization in power networks and general multi-agent systems

The dissertation studies the general area of complex networked systems that consist of interconnected and active heterogeneous components and usually operate in uncertain environments and with incomplete information. Problems associated with those systems are typically large-scale and computationally intractable, yet they are also very well-structured and have features that can be exploited by appropriate modeling and computational methods. The goal of this thesis is to develop foundational theories and tools to exploit those structures that can lead to computationally-efficient and distributed solutions, and apply them to improve systems operations and architecture.

Specifically, the thesis focuses on two concrete areas. The first one is to design distributed rules to manage distributed energy resources in the power network. The power network is undergoing a fundamental transformation. The future smart grid, especially on the distribution system, will be a large-scale network of distributed energy resources (DERs), each introducing random and rapid fluctuations in power supply, demand, voltage and frequency. These DERs provide a tremendous opportunity for sustainability, efficiency, and power reliability. However, there are daunting technical challenges in managing these DERs and optimizing their operation. The focus of this dissertation is to develop scalable, distributed, and real-time control and optimization to achieve system-wide efficiency, reliability, and robustness for the future power grid. In particular, we will present how to explore the power network structure to design efficient and distributed market and algorithms for the energy management. We will also show how to connect the algorithms with physical dynamics and existing control mechanisms for real-time control in power networks.

The second focus is to develop distributed optimization rules for general multi-agent engineering systems. A central goal in multiagent systems is to design local control laws for the individual agents to ensure that the emergent global behavior is desirable with respect to the given system level objective. Ideally, a system designer seeks to satisfy this goal while conditioning each agent’s control on the least amount of information possible. Our work focused on achieving this goal using the framework of game theory. In particular, we derived a systematic methodology for designing local agent objective functions that guarantees (i) an equivalence between the resulting game-theoretic equilibria and the system level design objective and (ii) that the resulting game possesses an inherent structure that can be exploited for distributed learning, e.g., potential games. The control design can then be completed by applying any distributed learning algorithm that guarantees convergence to the game-theoretic equilibrium. One main advantage of this game theoretic approach is that it provides a hierarchical decomposition between the decomposition of the systemic objective (game design) and the specific local decision rules (distributed learning algorithms). This decomposition provides the system designer with tremendous flexibility to meet the design objectives and constraints inherent in a broad class of multiagent systems. Furthermore, in many settings the resulting controllers will be inherently robust to a host of uncertainties including asynchronous clock rates, delays in information, and component failures.