Work and energy equations and the principle of generalized effective stress for unsaturated soils

The effective stress principle has been efficiently applied to saturated soils in the soil mechanics and geotechnical engineering practice; however, its applicability to unsaturated soils is still under debate. The appropriate selection of stress state variables is essential for the construction of constitutive models for unsaturated soils. Owing to the complexity of unsaturated soils, it is difficult to determine the deformation and strength behaviors of unsaturated soils uniquely with the previous single-effective-stress variable theory and two-effective-stress-variable theory in all the situations. In this paper, based on the porous media theory, the specific expression of work is proposed, and the effective stress of unsaturated soils conjugated with the displacement of the soil skeleton is further derived. In the derived work and energy balance equations, the energy dissipation in unsaturated soils is taken into account. According to the derived work and energy balance equations, all of the three generalized stresses and the conjugated strains have effects on the deformation of unsaturated soils. For considering these effects, a principle of generalized effective stress to describe the behaviors of unsaturated soils is proposed. The proposed principle of generalized effective stress may reduce to the previous effective stress theory of single-stress variable or the two-stress variables under certain conditions. This principle provides a helpful reference for the development of constitutive models for unsaturated soils.

Iso-specific Ziegler-Natta polymerization of α-olefins with a single-component organoyttrium catalyst

The synthesis of a sterically tailored ligand array (M)_2((C_5H_2-2-Si(CH_3)_3-4-C(CH_3)_3)S_2i(CH_3)_2]("M_2Bp") (M = Li, 16; K, 19) is described. Transmetallation of Li_2Bp with YCl_3(THF)_3 affords exclusively the C_2 symmetric product rac-[BpY(µ_2-Cl)_2Li(THF)_2], 20. A X-ray crystal structure of 20 has been determined; triclinic, P1, a= 13.110 (8), b = 17.163 (15), c = 20.623 (14) Å, α = 104.02 (7), β = 99.38 (5), γ = 100.24 (6)° , Z = 4, R = 0.056. Transmetallation of K_2Bp with YCl_3(THF)_3 affords the halide free complex rac-BpYCl, 23. The corresponding rac-BpLaCl, 28, is prepared in an anlogous manner. In all cases the achiral meso isomer is not obtained since only for the racemic isomers are the unfavorable steric interactions between the Si(CH3)_3 groups in the narrow portion of the [Cp-M'-Cp] wedge avoided. Alkylation of 20 or 23 with LiCH(Si(CH_3)_3)_2 affords rac-BpYCH(Si(CH_3)_3)_2, 26 in good yield. Alkylation of 28 with LiCH(Si(CH_3)_3)_2 affords rac-BpLaCH(Si(CH_3)_3)_2 29. Hydrogenation of 26 cleanly affords the bridging hydride species [BpY(µ_2-H)]_2, 27, as the homochiral (R,R) and (S,S) dimeric pairs. 26 is an efficient initiator for the polymerization of ethylene to high molecular weight linear polyethylene. 27 catalyzes the polymerization of propylene (25% v/v in methylcyclohexane) and neat samples of 1-butene, 1-pentene, 1-hexene to moderately high molecular weight polymers: polypropylene (M_n = 4,200, PDI 2.32, T_m 157 °C); poly-1-butene (M_n = 8,500, PDI 3.44, T_m 105 °C); poly-1-pentene (M_n = 20,000, PDI 1.99, T_m 73 °C); poly-1-hexene (M_n = 24,000, PDI 1.75, T_m < 25 °C). ^(13)C NMR spectra at the pentad analysis level indicates that the degree of isotacticity is 99% mmmm for all polymer samples. 27 is the first single component iso-specific α-olefin polymerization catalyst. The presumed origins of the high isospecificity are presented.

Coupled effects of mechanics, geometry, and chemistry on bio-membrane behavior

Lipid bilayer membranes are models for cell membranes--the structure that helps regulate cell function. Cell membranes are heterogeneous, and the coupling between composition and shape gives rise to complex behaviors that are important to regulation. This thesis seeks to systematically build and analyze complete models to understand the behavior of multi-component membranes.

We propose a model and use it to derive the equilibrium and stability conditions for a general class of closed multi-component biological membranes. Our analysis shows that the critical modes of these membranes have high frequencies, unlike single-component vesicles, and their stability depends on system size, unlike in systems undergoing spinodal decomposition in flat space. An important implication is that small perturbations may nucleate localized but very large deformations. We compare these results with experimental observations.

We also study open membranes to gain insight into long tubular membranes that arise for example in nerve cells. We derive a complete system of equations for open membranes by using the principle of virtual work. Our linear stability analysis predicts that the tubular membranes tend to have coiling shapes if the tension is small, cylindrical shapes if the tension is moderate, and beading shapes if the tension is large. This is consistent with experimental observations reported in the literature in nerve fibers. Further, we provide numerical solutions to the fully nonlinear equilibrium equations in some problems, and show that the observed mode shapes are consistent with those suggested by linear stability. Our work also proves that beadings of nerve fibers can appear purely as a mechanical response of the membrane.

The Equivalency Principle for Discounting the Value of Natural Assets: An Application to an Investment Project in the Basque Coast

25 p.

Macroscopically Dissipative Systems with Underlying Microscopic Dynamics : Properties and Limits of Measurement

While some of the deepest results in nature are those that give explicit bounds between important physical quantities, some of the most intriguing and celebrated of such bounds come from fields where there is still a great deal of disagreement and confusion regarding even the most fundamental aspects of the theories. For example, in quantum mechanics, there is still no complete consensus as to whether the limitations associated with Heisenberg's Uncertainty Principle derive from an inherent randomness in physics, or rather from limitations in the measurement process itself, resulting from phenomena like back action. Likewise, the second law of thermodynamics makes a statement regarding the increase in entropy of closed systems, yet the theory itself has neither a universally-accepted definition of equilibrium, nor an adequate explanation of how a system with underlying microscopically Hamiltonian dynamics (reversible) settles into a fixed distribution.

Motivated by these physical theories, and perhaps their inconsistencies, in this thesis we use dynamical systems theory to investigate how the very simplest of systems, even with no physical constraints, are characterized by bounds that give limits to the ability to make measurements on them. Using an existing interpretation, we start by examining how dissipative systems can be viewed as high-dimensional lossless systems, and how taking this view necessarily implies the existence of a noise process that results from the uncertainty in the initial system state. This fluctuation-dissipation result plays a central role in a measurement model that we examine, in particular describing how noise is inevitably injected into a system during a measurement, noise that can be viewed as originating either from the randomness of the many degrees of freedom of the measurement device, or of the environment. This noise constitutes one component of measurement back action, and ultimately imposes limits on measurement uncertainty. Depending on the assumptions we make about active devices, and their limitations, this back action can be offset to varying degrees via control. It turns out that using active devices to reduce measurement back action leads to estimation problems that have non-zero uncertainty lower bounds, the most interesting of which arise when the observed system is lossless. One such lower bound, a main contribution of this work, can be viewed as a classical version of a Heisenberg uncertainty relation between the system's position and momentum. We finally also revisit the murky question of how macroscopic dissipation appears from lossless dynamics, and propose alternative approaches for framing the question using existing systematic methods of model reduction.

Energy spectrum of two-component Bose-Einstein condensates in optical lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.

基于基频分量消光的1/4波片快轴标定方法

提出了一种基于基频分量消光的波片快轴标定方法,并利用琼斯矩阵对其标定原理进行了分析。激光器、起偏器、相位调制器、待标定1/4波片、检偏器和光电探测器构成标定光路,起偏器、检偏器的透光轴与相位调制器的振动轴分别成+45°和0°夹角。准直激光束依次经过起偏器、相位调制器、待标定1/4波片和检偏器,由光电探测器接收。理论分析表明该标定方法标定精度主要取决于检偏器的定位误差。实验验证了该标定方法的有效性,1/4波片快轴标定结果的最大偏差为0.043°,标准差为0.012°,标定精度为0.05°。

Optimisation of the first principle code Octopus for massive parallel architectures: application to light harvesting complexes

150 p.

Physiological modules for generating discrete and rhythmic movements: Component analysis of EMG signals

A central question in Neuroscience is that of how the nervous system generates the spatiotemporal commands needed to realize complex gestures, such as handwriting. A key postulate is that the central nervous system (CNS) builds up complex movements from a set of simpler motor primitives or control modules. In this study we examined the control modules underlying the generation of muscle activations when performing different types of movement: discrete, point-to-point movements in eight different directions and continuous figure-eight movements in both the normal, upright orientation and rotated 90 degrees. To test for the effects of biomechanical constraints, movements were performed in the frontal-parallel or sagittal planes, corresponding to two different nominal flexion/abduction postures of the shoulder. In all cases we measured limb kinematics and surface electromyographic activity (EMB) signals for seven different muscles acting around the shoulder. We first performed principal component analysis (PCA) of the EMG signals on a movement-by-movement basis. We found a surprisingly consistent pattern of muscle groupings across movement types and movement planes, although we could detect systematic differences between the PCs derived from movements performed in each sholder posture and between the principal components associated with the different orientations of the figure. Unexpectedly we found no systematic differences between the figute eights and the point-to-point movements. The first three principal components could be associated with a general co-contraction of all seven muscles plus two patterns of reciprocal activatoin. From these results, we surmise that both "discrete-rhythmic movements" such as the figure eight, and discrete point-to-point movement may be constructed from three different fundamental modules, one regulating the impedance of the limb over the time span of the movement and two others operating to generate movement, one aligned with the vertical and the other aligned with the horizontal.

Spin squeezing, macrorealism and the heisenberg uncertainty principle

169 p.